diff --git a/Archive/Examples/Eisenstein.lean b/Archive/Examples/Eisenstein.lean
index a12cf0f39819b9..5e8b4c00345d38 100644
--- a/Archive/Examples/Eisenstein.lean
+++ b/Archive/Examples/Eisenstein.lean
@@ -59,7 +59,7 @@ example : Irreducible (X ^ 4 - 10 * X ^ 2 + 1 : ℤ[X]) := by
       CharP.ker_intAlgebraMap_eq_span 3, span_singleton_pow, mem_span_singleton]
       norm_num
     rw [hfq, ← modByMonicHom_apply, map_add]
-    convert zero_add _
+    convert! zero_add _
     · rw [← LinearMap.mem_ker, mem_ker_modByMonic hq_monic]
       rw [pow_two, ← sub_mul]
       apply dvd_mul_left
diff --git a/Archive/Imo/Imo1959Q2.lean b/Archive/Imo/Imo1959Q2.lean
index f74b5be11fec59..d65fb89ea1cd0f 100644
--- a/Archive/Imo/Imo1959Q2.lean
+++ b/Archive/Imo/Imo1959Q2.lean
@@ -60,7 +60,7 @@ theorem sqrt_two_mul_sub_one_le_one : sqrt (2 * x - 1) ≤ 1 ↔ x ≤ 1 := by
 theorem isGood_iff_eq_sqrt_two (hx : x ∈ Icc (1 / 2) 1) : IsGood x A ↔ A = sqrt 2 := by
   have : sqrt (2 * x - 1) ≤ 1 := sqrt_two_mul_sub_one_le_one.2 hx.2
   simp only [isGood_iff, hx.1, abs_sub_comm _ (1 : ℝ), abs_of_nonneg (sub_nonneg.2 this), and_true]
-  suffices 2 = A * sqrt 2 ↔ A = sqrt 2 by convert this using 2; ring
+  suffices 2 = A * sqrt 2 ↔ A = sqrt 2 by convert! this using 2; ring
   rw [← div_eq_iff, div_sqrt, eq_comm]
   positivity
 
diff --git a/Archive/Imo/Imo1982Q3.lean b/Archive/Imo/Imo1982Q3.lean
index 98d2fbaf94cd09..ed2dee108f5b35 100644
--- a/Archive/Imo/Imo1982Q3.lean
+++ b/Archive/Imo/Imo1982Q3.lean
@@ -74,7 +74,7 @@ end Imo1982Q3
 theorem imo1982_q3a (hx : Antitone x) (h0 : x 0 = 1) (hp : ∀ k, 0 < x k) :
     ∃ n : ℕ, 3.999 ≤ ∑ k ∈ range n, (x k) ^ 2 / x (k + 1) := by
   use 4000
-  convert Imo1982Q3.ineq (Nat.succ_ne_zero 3998) hx h0 hp
+  convert! Imo1982Q3.ineq (Nat.succ_ne_zero 3998) hx h0 hp
   norm_num
 
 /-- Part b of the problem is solved by `x k = (1 / 2) ^ k`. -/
@@ -88,6 +88,6 @@ theorem imo1982_q3b : ∃ x : ℕ → ℝ, Antitone x ∧ x 0 = 1 ∧ (∀ k, 0
     simp_rw [← pow_mul, pow_succ, ← div_eq_mul_inv, div_div_eq_mul_div, mul_comm, mul_div_assoc,
       ← mul_sum, div_eq_mul_inv, this, ← two_add_two_eq_four, ← mul_two,
       mul_lt_mul_iff_of_pos_left two_pos]
-    convert NNReal.coe_lt_coe.2 <| geom_sum_lt (inv_ne_zero two_ne_zero) two_inv_lt_one n
+    convert! NNReal.coe_lt_coe.2 <| geom_sum_lt (inv_ne_zero two_ne_zero) two_inv_lt_one n
     · simp
     · norm_num
diff --git a/Archive/Imo/Imo1994Q1.lean b/Archive/Imo/Imo1994Q1.lean
index fc9895a0964e58..16409d17ebcc29 100644
--- a/Archive/Imo/Imo1994Q1.lean
+++ b/Archive/Imo/Imo1994Q1.lean
@@ -54,7 +54,7 @@ theorem imo1994_q1 (n : ℕ) (m : ℕ) (A : Finset ℕ) (hm : #A = m + 1)
   -- `i ↦ m-i`
   -- We reindex the sum by fin (m+1)
   have : ∑ x ∈ A, x = ∑ i : Fin (m + 1), a i := by
-    convert sum_image fun x _ y _ => a.eq_iff_eq.1
+    convert! sum_image fun x _ y _ => a.eq_iff_eq.1
     rw [← coe_inj]; simp [a]
   rw [this]; clear this
   -- The main proof is a simple calculation by rearranging one of the two sums
diff --git a/Archive/Imo/Imo1998Q2.lean b/Archive/Imo/Imo1998Q2.lean
index 10f87262bc1468..fe51caef4ee585 100644
--- a/Archive/Imo/Imo1998Q2.lean
+++ b/Archive/Imo/Imo1998Q2.lean
@@ -210,7 +210,7 @@ end
 theorem clear_denominators {a b k : ℕ} (ha : 0 < a) (hb : 0 < b) :
     (b - 1 : ℚ) / (2 * b) ≤ k / a ↔ ((b : ℕ) - 1) * a ≤ k * (2 * b) := by
   rw [div_le_div_iff₀]
-  on_goal 1 => convert Nat.cast_le (α := ℚ)
+  on_goal 1 => convert! Nat.cast_le (α := ℚ)
   all_goals simp [ha, hb]
 
 end
diff --git a/Archive/Imo/Imo2001Q5.lean b/Archive/Imo/Imo2001Q5.lean
index 00ea647e1aa560..8b8f45817bbd96 100644
--- a/Archive/Imo/Imo2001Q5.lean
+++ b/Archive/Imo/Imo2001Q5.lean
@@ -104,7 +104,7 @@ lemma x_pos : 0 < s.x := by
   have col := s.ABC_eq; rw [h, mul_zero] at col
   replace col : Collinear ℝ {s.A, s.B, s.C} := by
     apply collinear_of_sin_eq_zero; rw [col, Real.sin_zero]
-  apply s.not_collinear_BAC; convert col using 1; grind
+  apply s.not_collinear_BAC; convert! col using 1; grind
 
 lemma Q_ne_A : s.Q ≠ s.A := by
   by_contra h; have := s.ABQ_eq
@@ -127,7 +127,7 @@ lemma x_lt_pi_div_three : s.x < π / 3 := by
   have col : ∠ s.A s.C s.B = 0 := by linarith [s.ACB_eq, angle_nonneg s.A s.C s.B]
   replace col : Collinear ℝ {s.A, s.C, s.B} := by
     apply collinear_of_sin_eq_zero; rw [col, Real.sin_zero]
-  apply s.not_collinear_BAC; convert col using 1; grind
+  apply s.not_collinear_BAC; convert! col using 1; grind
 
 lemma APB_eq : ∠ s.A s.P s.B = 5 * π / 6 - 2 * s.x := by
   have := angle_add_angle_add_angle_eq_pi s.P s.A_ne_B
diff --git a/Archive/Imo/Imo2006Q3.lean b/Archive/Imo/Imo2006Q3.lean
index 22daf36f13ad66..9a60dba50d1b0b 100644
--- a/Archive/Imo/Imo2006Q3.lean
+++ b/Archive/Imo/Imo2006Q3.lean
@@ -79,8 +79,8 @@ theorem subst_proof₁ (x y z s : ℝ) (hxyz : x + y + z = 0) :
   · rw [div_mul_eq_mul_div, le_div_iff₀' zero_lt_32]
     exact subst_wlog h' hxyz
   rcases (mul_nonneg_of_three x y z).resolve_left h' with h | h
-  · convert this y z x _ h using 2 <;> linarith
-  · convert this z x y _ h using 2 <;> linarith
+  · convert! this y z x _ h using 2 <;> linarith
+  · convert! this z x y _ h using 2 <;> linarith
 
 theorem proof₁ {a b c : ℝ} :
     |a * b * (a ^ 2 - b ^ 2) + b * c * (b ^ 2 - c ^ 2) + c * a * (c ^ 2 - a ^ 2)| ≤
diff --git a/Archive/Imo/Imo2006Q5.lean b/Archive/Imo/Imo2006Q5.lean
index 802399e503790c..cb8ebeaf4d7784 100644
--- a/Archive/Imo/Imo2006Q5.lean
+++ b/Archive/Imo/Imo2006Q5.lean
@@ -72,7 +72,7 @@ theorem Polynomial.isPeriodicPt_eval_two {P : Polynomial ℤ} {t : ℤ}
   have Hdvd : C.Chain (· ∣ ·) := by
     rw [Cycle.chain_map, periodicOrbit_chain' _ ht]
     intro n
-    convert sub_dvd_eval_sub ((fun x => P.eval x)^[n + 1] t) ((fun x => P.eval x)^[n] t) P <;>
+    convert! sub_dvd_eval_sub ((fun x => P.eval x)^[n + 1] t) ((fun x => P.eval x)^[n] t) P <;>
       rw [Function.iterate_succ_apply']
   -- Any two entries in C have the same absolute value.
   have Habs :
@@ -112,7 +112,7 @@ theorem Polynomial.isPeriodicPt_eval_two {P : Polynomial ℤ} {t : ℤ}
     -- They must have opposite sign, so that P^{k + 1}(t) - P^k(t) = P^{k + 2}(t) - P^{k + 1}(t).
     rcases Int.natAbs_eq_natAbs_iff.1 (Habs n n.succ) with hn' | hn'
     · apply (hn _).elim
-      convert hn' <;> simp only [Function.iterate_succ_apply']
+      convert! hn' <;> simp only [Function.iterate_succ_apply']
     -- We deduce P^{k + 2}(t) = P^k(t) and hence P(P(t)) = t.
     · rw [neg_sub, sub_right_inj] at hn'
       simp only [Function.iterate_succ_apply'] at hn'
diff --git a/Archive/Imo/Imo2008Q2.lean b/Archive/Imo/Imo2008Q2.lean
index 4b42c50b06d645..485185b47bd7bf 100644
--- a/Archive/Imo/Imo2008Q2.lean
+++ b/Archive/Imo/Imo2008Q2.lean
@@ -51,7 +51,7 @@ theorem imo2008_q2a (x y z : ℝ) (h : x * y * z = 1) (hx : x ≠ 1) (hy : y ≠
   have hmn_ne_zero : m + n ≠ 0 := by contrapose hz; field_simp; linarith
   have hc_sub_sub : c - (c - m - n) = m + n := by abel
   rw [ge_iff_le, ← sub_nonneg]
-  convert sq_nonneg ((c * (m ^ 2 + n ^ 2 + m * n) - m * (m + n) ^ 2) / (m * n * (m + n)))
+  convert! sq_nonneg ((c * (m ^ 2 + n ^ 2 + m * n) - m * (m + n) ^ 2) / (m * n * (m + n)))
   simp [field, hc_sub_sub]; ring
 
 def rationalSolutions :=
diff --git a/Archive/Imo/Imo2010Q5.lean b/Archive/Imo/Imo2010Q5.lean
index 7e660b13f98668..31379441aa4ea8 100644
--- a/Archive/Imo/Imo2010Q5.lean
+++ b/Archive/Imo/Imo2010Q5.lean
@@ -79,7 +79,7 @@ lemma push {B : Fin 6 → ℕ} {i : Fin 6} (rB : Reachable B) (hi : i < 5) :
     Reachable (B - single i (B i) + single (i + 1) (2 * B i)) := by
   obtain hc | hc := (B i).eq_zero_or_pos
   · rwa [hc, mul_zero, single_zero, single_zero, add_zero, tsub_zero]
-  · convert (rB.move1 hi hc).push hi using 1
+  · convert! (rB.move1 hi hc).push hi using 1
     ext k; simp only [add_apply, sub_apply]
     rcases eq_or_ne k i with rfl | hk
     · simp_rw [single_eq_same, tsub_self, single_succ]
@@ -92,29 +92,29 @@ termination_by B i
 /-- `(0, 0, 5, 11, 0, 0)` is reachable. -/
 lemma five_eleven : Reachable (single 2 5 + single 3 11) := by
   have R : Reachable (single 1 3 + single 2 1 + single 3 1 + single 4 1 + single 5 1) := by
-    convert base.push (show 0 < 5 by decide) using 1; decide
+    convert! base.push (show 0 < 5 by decide) using 1; decide
   replace R : Reachable (single 2 7 + single 3 1 + single 4 1 + single 5 1) := by
-    convert R.push (show 1 < 5 by decide) using 1; decide
+    convert! R.push (show 1 < 5 by decide) using 1; decide
   replace R : Reachable (single 2 7 + single 4 3 + single 5 1) := by
-    convert R.push (show 3 < 5 by decide) using 1; decide
+    convert! R.push (show 3 < 5 by decide) using 1; decide
   replace R : Reachable (single 2 7 + single 5 7) := by
-    convert R.push (show 4 < 5 by decide) using 1; decide
+    convert! R.push (show 4 < 5 by decide) using 1; decide
   replace R : Reachable (single 2 6 + single 3 2 + single 5 7) := by
-    convert R.move1 (show 2 < 5 by decide) (by decide) using 1; decide
+    convert! R.move1 (show 2 < 5 by decide) (by decide) using 1; decide
   replace R : Reachable (single 2 6 + single 3 1 + single 4 2 + single 5 7) := by
-    convert R.move1 (show 3 < 5 by decide) (by decide) using 1; decide
+    convert! R.move1 (show 3 < 5 by decide) (by decide) using 1; decide
   replace R : Reachable (single 2 6 + single 3 1 + single 5 11) := by
-    convert R.push (show 4 < 5 by decide) using 1; decide
+    convert! R.push (show 4 < 5 by decide) using 1; decide
   replace R : Reachable (single 2 6 + single 4 11) := by
-    convert R.move2 (show 3 < 4 by decide) (by decide) using 1; decide
-  convert R.move2 (show 2 < 4 by decide) (by decide) using 1; decide
+    convert! R.move2 (show 3 < 4 by decide) (by decide) using 1; decide
+  convert! R.move2 (show 2 < 4 by decide) (by decide) using 1; decide
 
 /-- Decrement $B_i$ and double $B_{i+1}$, assuming $B_{i+2} = 0$, by doing `push, move2`. -/
 lemma double {B : Fin 6 → ℕ} {i : Fin 6}
     (rB : Reachable B) (hi : i < 4) (pB : 0 < B i) (zB : B (i + 2) = 0) :
     Reachable (B + single (i + 1) (B (i + 1)) - single i 1) := by
-  convert (rB.push (show i + 1 < 5 by grind)).move2 hi (by
-    rw [add_apply, sub_apply, single_succ]; grind)
+  convert!
+    (rB.push (show i + 1 < 5 by grind)).move2 hi (by rw [add_apply, sub_apply, single_succ]; grind)
   ext k; simp only [comp_apply, add_apply, sub_apply]
   have (j : Fin 6) : j + 1 + 1 = j + 2 := by grind
   rcases eq_or_ne k i with rfl | hk
@@ -132,7 +132,7 @@ lemma doubles {B : Fin 6 → ℕ} {i : Fin 6} (rB : Reachable B) (hi : i < 4) (z
     Reachable (update (B - single i (B i)) (i + 1) (B (i + 1) * 2 ^ B i)) := by
   obtain hc | hc := (B i).eq_zero_or_pos
   · rwa [hc, single_zero, tsub_zero, pow_zero, mul_one, update_eq_self]
-  · convert (rB.double hi hc zB).doubles hi (by
+  · convert! (rB.double hi hc zB).doubles hi (by
       rw [sub_apply, add_apply, single_eq_of_ne (by simp), zB, zero_add, zero_tsub]) using 1
     ext k
     simp_rw [sub_apply, add_apply, single_eq_same, single_succ, single_succ', add_zero, tsub_zero,
@@ -149,9 +149,9 @@ termination_by B i
 lemma exp {B : Fin 6 → ℕ} {i : Fin 6}
     (rB : Reachable B) (hi : i < 4) (pB : 0 < B i) (zB : B (i + 1) = 0) (zB' : B (i + 2) = 0) :
     Reachable (B - single i (B i) + single (i + 1) (2 ^ B i)) := by
-  convert (rB.move1 (show i < 5 by grind) pB).doubles hi (by
+  convert! (rB.move1 (show i < 5 by grind) pB).doubles hi (by
     rw [add_apply, sub_apply, zB', single_eq_of_ne (by simp), tsub_zero,
-      single_eq_of_ne (by simp), zero_add]) using 1
+        single_eq_of_ne (by simp), zero_add]) using 1
   simp_rw [add_apply, sub_apply, single_eq_same, single_succ, single_succ', zB, zero_tsub, zero_add,
     add_zero, ← pow_succ', Nat.sub_add_cancel pB]
   ext k; simp only [add_apply, sub_apply]
@@ -167,7 +167,7 @@ lemma exp_mid {k n : ℕ} (h : Reachable (single 2 (k + 1) + single 3 n)) (hn :
     Reachable (single 2 k + single 3 (2 ^ n)) := by
   have md := h.exp (show 3 < 4 by decide) (by simp [hn])
     (by simp [add_apply, single_eq_of_ne]) (by simp [add_apply, single_eq_of_ne])
-  convert md.move2 (show 2 < 4 by decide) (by
+  convert! md.move2 (show 2 < 4 by decide) (by
     simp only [add_apply, sub_apply, single_eq_same]
     iterate 3 rw [single_eq_of_ne (by decide)]
     simp) using 1
@@ -192,7 +192,7 @@ lemma reduce {m n : ℕ} (h : Reachable (single 3 n)) (hmn : m ≤ n) : Reachabl
   | base => exact h
   | succ k _ ih =>
     apply ih
-    convert h.move2 (show 3 < 4 by decide) k.succ_pos
+    convert! h.move2 (show 3 < 4 by decide) k.succ_pos
     ext i; simp only [sub_apply, comp_apply]
     rcases eq_or_ne i 3 with rfl | i3
     · rw [swap_apply_of_ne_of_ne (by decide) (by decide)]
@@ -231,7 +231,7 @@ theorem result : Reachable (single 5 (2010 ^ 2010 ^ 2010)) := by
   -- See https://github.com/leanprover/lean4/issues/11713
   set m : ℕ := 2010
   have hm : m = 2010 := by rfl
-  convert ((quarter_target hm).push (show 3 < 5 by decide)).push (show 4 < 5 by decide)
+  convert! ((quarter_target hm).push (show 3 < 5 by decide)).push (show 4 < 5 by decide)
   simp only [single_eq_same, tsub_self, Fin.reduceAdd, zero_add, single_inj]
   rw [← mul_assoc, show 2 * 2 = 4 by rfl, mul_comm, Nat.div_mul_cancel]
   trans 2010 ^ 2
diff --git a/Archive/Imo/Imo2015Q6.lean b/Archive/Imo/Imo2015Q6.lean
index 330154cb6f49a4..28cb4886f76cef 100644
--- a/Archive/Imo/Imo2015Q6.lean
+++ b/Archive/Imo/Imo2015Q6.lean
@@ -161,7 +161,7 @@ lemma sum_telescope {m n : ℕ} (hm : N ≤ m) (hn : m < n) :
 
 include ht in
 lemma le_sum_pool : ∑ i ∈ range b, (i : ℤ) ≤ ∑ x ∈ pool a t, x := by
-  convert sum_range_le_sum fun x mx ↦ (mem_Icc.mp ((pool_subset_Icc ha) mx)).1
+  convert! sum_range_le_sum fun x mx ↦ (mem_Icc.mp ((pool_subset_Icc ha) mx)).1
   · rw [hbN _ ht]
   · rw [zero_add]
 
@@ -169,7 +169,7 @@ include ht in
 lemma sum_pool_le : ∑ x ∈ pool a t, x ≤ ∑ i ∈ range (b - 1), (2014 - i : ℤ) := by
   have zmp := zero_mem_pool ha hbN ht
   rw [← insert_erase zmp, sum_insert (notMem_erase _ _), zero_add]
-  convert sum_le_sum_range fun x mx ↦ ?_
+  convert! sum_le_sum_range fun x mx ↦ ?_
   · rw [card_erase_of_mem zmp, hbN _ ht]
   · exact (mem_Icc.mp ((pool_subset_Icc ha) (mem_erase.mp mx).2)).2
 
diff --git a/Archive/Imo/Imo2019Q2.lean b/Archive/Imo/Imo2019Q2.lean
index 7d447ae03db0c8..9a8aafe704dd53 100644
--- a/Archive/Imo/Imo2019Q2.lean
+++ b/Archive/Imo/Imo2019Q2.lean
@@ -309,7 +309,7 @@ theorem sbtw_A_B₁_C : Sbtw ℝ cfg.A cfg.B₁ cfg.C :=
 
 theorem sbtw_A_A₁_A₂ : Sbtw ℝ cfg.A cfg.A₁ cfg.A₂ := by
   refine Sphere.sbtw_secondInter cfg.A_mem_circumsphere ?_
-  convert cfg.sbtw_B_A₁_C.dist_lt_max_dist _
+  convert! cfg.sbtw_B_A₁_C.dist_lt_max_dist _
   change _ = max (dist (cfg.triangleABC.points 1) _) (dist (cfg.triangleABC.points 2) _)
   simp_rw [circumsphere_center, circumsphere_radius, dist_circumcenter_eq_circumradius, max_self]
 
@@ -375,7 +375,7 @@ variable [Module.Oriented ℝ V (Fin 2)]
 theorem two_zsmul_oangle_QPA₂_eq_two_zsmul_oangle_BAA₂ :
     (2 : ℤ) • ∡ cfg.Q cfg.P cfg.A₂ = (2 : ℤ) • ∡ cfg.B cfg.A cfg.A₂ := by
   refine two_zsmul_oangle_of_parallel cfg.QP_parallel_BA ?_
-  convert AffineSubspace.Parallel.refl (k := ℝ) (P := Pt) _ using 1
+  convert! AffineSubspace.Parallel.refl (k := ℝ) (P := Pt) _ using 1
   rw [cfg.collinear_PAA₁A₂.affineSpan_eq_of_ne (Set.mem_insert_of_mem _
     (Set.mem_insert_of_mem _ (Set.mem_insert_of_mem _ (Set.mem_singleton _))))
     (Set.mem_insert_of_mem _ (Set.mem_insert _ _)) cfg.A₂_ne_A,
diff --git a/Archive/Imo/Imo2024Q1.lean b/Archive/Imo/Imo2024Q1.lean
index 41f351c433b42c..680dc4c3d6fc48 100644
--- a/Archive/Imo/Imo2024Q1.lean
+++ b/Archive/Imo/Imo2024Q1.lean
@@ -52,7 +52,7 @@ lemma condition_sub_two_mul_int_iff {α : ℝ} (m : ℤ) : Condition (α - 2 * m
   simp_rw [← Finset.sum_sub_distrib, mul_sub]
   norm_cast
   simp_rw [Int.floor_sub_intCast, sub_sub_cancel_left]
-  convert condition_two_mul_int (-m) n hn
+  convert! condition_two_mul_int (-m) n hn
   norm_cast
   rw [Int.floor_intCast]
   simp
@@ -76,9 +76,9 @@ lemma mem_Ico_one_of_mem_Ioo (h : α ∈ Set.Ioo 0 2) : α ∈ Set.Ico 1 2 := by
   apply hr.ne'
   suffices ⌈α⁻¹⌉₊ = (1 : ℤ) from mod_cast this
   apply Int.eq_one_of_dvd_one (Int.zero_le_ofNat _)
-  convert hc ⌈α⁻¹⌉₊ (zero_lt_one.trans hr)
+  convert! hc ⌈α⁻¹⌉₊ (zero_lt_one.trans hr)
   rw [← Finset.add_sum_Ico_eq_sum_Icc hr.le]
-  convert (add_zero _).symm
+  convert! (add_zero _).symm
   · rw [Int.floor_eq_iff]
     constructor
     · rw [Int.cast_one]
@@ -129,7 +129,7 @@ lemma mem_Ico_n_of_mem_Ioo (h : α ∈ Set.Ioo 0 2) {n : ℕ} (hn : 0 < n) :
       by_contra
       rw [show ⌊(k + 1 : ℕ) * α⌋ = 2 * k by lia] at hc
       have hc' : ((k + 1 : ℕ) : ℤ) ∣ ((k + 1 : ℕ) : ℤ) * ((k + 1 : ℕ) : ℤ) - 1 := by
-        convert hc using 1
+        convert! hc using 1
         push_cast
         ring
       rw [dvd_sub_right (dvd_mul_right _ _), ← isUnit_iff_dvd_one, Int.isUnit_iff] at hc'
@@ -140,7 +140,7 @@ lemma mem_Ico_n_of_mem_Ioo (h : α ∈ Set.Ioo 0 2) {n : ℕ} (hn : 0 < n) :
       ring
     · rw [Int.floor_eq_iff] at hk'
       rw [div_le_iff₀ (by norm_cast; lia), mul_comm α]
-      convert hk'.1
+      convert! hk'.1
       push_cast
       ring
 
@@ -153,7 +153,7 @@ lemma not_condition_of_mem_Ioo {α : ℝ} (h : α ∈ Set.Ioo 0 2) : ¬Condition
   have hna := (hc.mem_Ico_n_of_mem_Ioo h hn).1
   rcases h with ⟨-, h2⟩
   have hna' : 2 - (n : ℝ)⁻¹ ≤ α := by
-    convert hna using 1
+    convert! hna using 1
     field
   rw [sub_eq_add_neg, ← le_sub_iff_add_le', neg_le, neg_sub] at hna'
   rw [le_inv_comm₀ (by linarith) (mod_cast hn), ← not_lt] at hna'
@@ -167,7 +167,7 @@ lemma condition_iff_of_mem_Ico {α : ℝ} (h : α ∈ Set.Ico 0 2) : Condition 
     | inl h => exact h
     | inr ho => exact False.elim (not_condition_of_mem_Ioo ho hc)
   · rintro rfl
-    convert condition_two_mul_int 0
+    convert! condition_two_mul_int 0
     norm_num
 
 recall Imo2024Q1.Condition (α : ℝ) := (∀ n : ℕ, 0 < n → (n : ℤ) ∣ ∑ i ∈ Finset.Icc 1 n, ⌊i * α⌋)
diff --git a/Archive/Imo/Imo2024Q2.lean b/Archive/Imo/Imo2024Q2.lean
index b863dbed4e0a09..6334c708815153 100644
--- a/Archive/Imo/Imo2024Q2.lean
+++ b/Archive/Imo/Imo2024Q2.lean
@@ -32,12 +32,12 @@ lemma dvd_pow_iff_of_dvd_sub {a b d n : ℕ} {z : ℤ} (ha : a.Coprime d)
     d ∣ a ^ n + b ↔ (((ZMod.unitOfCoprime _ ha) ^ z : (ZMod d)ˣ) : ZMod d) + b = 0 := by
   rcases hd with ⟨k, hk⟩
   rw [← ZMod.natCast_eq_zero_iff]
-  convert Iff.rfl
+  convert! Iff.rfl
   push_cast
   congr
   suffices (((ZMod.unitOfCoprime _ ha) ^ z : (ZMod d)ˣ) : ZMod d) =
       (((ZMod.unitOfCoprime _ ha) ^ (n : ℤ) : (ZMod d)ˣ) : ZMod d) by
-    convert this
+    convert! this
   rw [sub_eq_iff_eq_add] at hk
   rw [hk, zpow_add, zpow_mul]
   norm_cast
@@ -139,11 +139,11 @@ lemma ab_add_one_dvd_a_pow_large_n_add_b : a * b + 1 ∣ a ^ h.large_n + b := by
   norm_cast
   simp only [mul_inv_cancel, Units.val_one, ZMod.coe_unitOfCoprime]
   norm_cast
-  convert ZMod.natCast_self (a * b + 1) using 2
+  convert! ZMod.natCast_self (a * b + 1) using 2
   exact add_comm _ _
 
 lemma ab_add_one_dvd_b_pow_large_n_add_a : a * b + 1 ∣ b ^ h.large_n + a := by
-  convert h.symm.ab_add_one_dvd_a_pow_large_n_add_b using 1
+  convert! h.symm.ab_add_one_dvd_a_pow_large_n_add_b using 1
   · rw [mul_comm]
   · rw [h.symm_large_n]
 
diff --git a/Archive/Imo/Imo2024Q3.lean b/Archive/Imo/Imo2024Q3.lean
index 0fd39443836125..0c740c9682efe2 100644
--- a/Archive/Imo/Imo2024Q3.lean
+++ b/Archive/Imo/Imo2024Q3.lean
@@ -113,7 +113,7 @@ lemma apply_add_one_eq_card {n : ℕ} (h : N ≤ n) :
   simp
 
 @[simp] lemma nth_apply_eq_zero (n : ℕ) : Nat.nth (a · = 0) n = 0 := by
-  convert Nat.nth_false _ with i
+  convert! Nat.nth_false _ with i
   simp only [(hc.pos i).ne']
 
 lemma nth_apply_add_one_eq {n : ℕ} (h : N ≤ n) : Nat.nth (a · = a n) (a (n + 1) - 1) = n := by
@@ -173,7 +173,7 @@ lemma exists_infinite_setOf_apply_eq : ∃ m, {i | a i = m}.Infinite := by
     rintro _ ⟨⟨_, rfl⟩, hi⟩ _ ⟨⟨_, rfl⟩, hj⟩ h
     simp only [Set.mem_Ico, zero_le, true_and, not_lt] at hi hj
     simp only [add_left_inj] at h
-    convert congr(a $h) using 1 <;> simp [apply_nth_zero]
+    convert! congr(a $h) using 1 <;> simp [apply_nth_zero]
   refine (Set.infinite_of_injOn_mapsTo hinj (fun i hi ↦ ?_) (hr.diff (Set.finite_Ico _ _))) (hi 1)
   simp only [Set.mem_diff, Set.mem_range, Set.mem_Ico, zero_le, true_and, not_lt] at hi
   rcases hi with ⟨⟨_, rfl⟩, hi⟩
@@ -244,7 +244,7 @@ lemma card_lt_M_of_M_le {n : ℕ} (h : M a N ≤ n) :
   have ha : M a N ≤ a (Nat.nth (a · = n) (M a N - 1)) := (Nat.nth_mem _ hin').symm ▸ h
   refine ⟨ha, ?_⟩
   suffices H : a (Nat.nth (fun x ↦ a x = n) (M a N - 1) + 1) = M a N from Nat.le_of_eq H.symm
-  convert hc.apply_nth_add_one_eq hin' (N_lt_of_M_le_apply ha).le using 1
+  convert! hc.apply_nth_add_one_eq hin' (N_lt_of_M_le_apply ha).le using 1
 
 lemma bddAbove_setOf_infinite_setOf_apply_eq : BddAbove {m | {i | a i = m}.Infinite} := by
   refine ⟨M a N, fun x hi ↦ ?_⟩
@@ -257,7 +257,7 @@ lemma infinite_setOf_apply_eq_anti {j k : ℕ} (hj : 0 < j) (hk : {i | a i = k}.
     have hinj : Set.InjOn (· + 1) {i | a (i + 1) = k} := (add_left_injective _).injOn
     rw [← Set.infinite_image_iff hinj]
     have hk0 : ({i | a i = k} \ {0}).Infinite := hk.diff (Set.finite_singleton _)
-    convert hk0 using 1
+    convert! hk0 using 1
     ext i
     simp only [Set.mem_image, Set.mem_setOf_eq, Set.mem_diff, Set.mem_singleton_iff]
     refine ⟨?_, ?_⟩
@@ -336,7 +336,7 @@ lemma bddAbove_setOf_k_lt_card : BddAbove {m | ∀ hf : {i | a i = m}.Finite, k
 lemma k_pos : 0 < k a := by
   by_contra! hn
   apply nonpos_iff_eq_zero.mp hn ▸ hc.infinite_setOf_apply_eq_k
-  convert Set.finite_empty
+  convert! Set.finite_empty
   ext i
   simp [(hc.pos i).ne']
 
@@ -542,8 +542,9 @@ lemma apply_sub_one_big_of_apply_small_of_N'_lt {i : ℕ} (h : Small a (a i)) (h
 
 lemma apply_sub_two_small_of_apply_small_of_N'_lt {i : ℕ} (h : Small a (a i)) (hN' : N' a N < i) :
     Small a (a (i - 2)) := by
-  convert hc.apply_sub_one_small_of_apply_big_of_N'_le
-    (hc.apply_sub_one_big_of_apply_small_of_N'_lt h hN') (by lia) using 1
+  convert!
+    hc.apply_sub_one_small_of_apply_big_of_N'_le
+      (hc.apply_sub_one_big_of_apply_small_of_N'_lt h hN') (by lia) using 1
 
 lemma N_add_one_lt_apply_of_apply_big_of_N'_le {i : ℕ} (h : Big a (a i)) (hN' : N' a N ≤ i) :
     N + 1 < a i := by
@@ -567,7 +568,7 @@ lemma setOf_apply_eq_of_apply_big_of_N'_le {i : ℕ} (h : Big a (a i)) (hN' : N'
   rw [← Set.Finite.toFinset_subset_toFinset (hs := hf') (ht := hf)] at hs
   refine (Finset.eq_of_subset_of_card_le hs (hck.trans ?_)).symm
   have hs : #((Finset.Icc 1 (k a)).image (fun t ↦ Nat.nth (a · = t) (a i - 1) + 1)) = k a := by
-    convert Finset.card_image_of_injOn fun t ht u hu htu ↦ ?_
+    convert! Finset.card_image_of_injOn fun t ht u hu htu ↦ ?_
     · simp only [Nat.card_Icc, add_tsub_cancel_right]
     · simp only [add_left_inj] at htu
       simp only [Finset.coe_Icc, Set.mem_Icc] at ht hu
@@ -608,7 +609,7 @@ lemma small_apply_sub_one_of_apply_eq_of_apply_big_of_N'_le {i j : ℕ} (hj : a
 lemma apply_add_one_eq_card_small_le_card_eq {i : ℕ} (hi : N' a N < i) (hib : Big a (a i)) :
     a (i + 1) = #{m ∈ Finset.range (k a + 1) | a i ≤ #{j ∈ Finset.range i | a j = m}} := by
   rw [hc.apply_add_one_eq_card (hc.N_lt_N'.trans hi).le]
-  convert Finset.card_image_of_injOn (f := fun j ↦ Nat.nth (a · = j) (a i - 1) + 1) ?_ using 1
+  convert! Finset.card_image_of_injOn (f := fun j ↦ Nat.nth (a · = j) (a i - 1) + 1) ?_ using 1
   · congr
     ext j
     simp only [Finset.mem_filter, Finset.mem_range, Finset.mem_image]
@@ -666,7 +667,7 @@ lemma apply_eq_card_small_le_card_eq_of_small {i : ℕ} (hi : N' a N + 1 < i)
   ext j
   simp only [Finset.mem_filter, Finset.mem_range, and_congr_right_iff]
   intro hj
-  convert Iff.rfl using 2
+  convert! Iff.rfl using 2
   congr 1
   ext t
   simp only [Finset.mem_filter, Finset.mem_range]
@@ -751,8 +752,8 @@ lemma exists_apply_sub_two_eq_of_apply_eq {i j : ℕ} (hi : N' a N + 2 < i) (hij
           congr 1
           ext t
           simp only [Finset.mem_filter, Finset.mem_range]
-          refine ⟨fun ⟨htj, htj'⟩ ↦ ⟨?_, by convert htj' using 1⟩,
-            fun ⟨htj, htj'⟩ ↦ ⟨by lia, by convert htj' using 1⟩⟩
+          refine ⟨fun ⟨htj, htj'⟩ ↦ ⟨?_, by convert! htj' using 1⟩,
+            fun ⟨htj, htj'⟩ ↦ ⟨by lia, by convert! htj' using 1⟩⟩
           by_contra htj''
           have ht1 : t = j - 1 := by lia
           subst ht1
@@ -866,7 +867,7 @@ lemma p_le_two_mul_k {n : ℕ} (hn : N' a N + 2 < n) (hs : Small a (a n)) : p a
   by_contra hlt
   obtain ⟨x, hx, y, hy, hxyne, hxy⟩ : ∃ x ∈ Finset.range (k a + 1), ∃ y ∈ Finset.range (k a + 1),
       x ≠ y ∧ a (n + 2 * x) = a (n + 2 * y) := by
-    convert Finset.exists_ne_map_eq_of_card_lt_of_maps_to (t := Finset.Icc 1 (k a)) ?_ ?_
+    convert! Finset.exists_ne_map_eq_of_card_lt_of_maps_to (t := Finset.Icc 1 (k a)) ?_ ?_
     · simp
     · rintro i -
       simp only [Finset.coe_Icc, Set.mem_Icc]
@@ -923,7 +924,7 @@ lemma exists_p_eq : ∃ b c, ∀ n, b < n → p a (N' a N + 2 * n) = c := by
       · have hs : Small a (a (N' a N + 2 * (2 + t + u))) := by
           rw [hc.small_apply_N'_add_iff_even]
           simp
-        convert hc.p_apply_le_p_apply_add_two (by lia) hs using 1
+        convert! hc.p_apply_le_p_apply_add_two (by lia) hs using 1
   refine ⟨1 + t, c, fun n hn ↦ ?_⟩
   rw [show n = 2 + t + (n - (2 + t)) by lia]
   exact heqc _
@@ -937,7 +938,7 @@ lemma exists_a_apply_add_eq : ∃ b c, 0 < c ∧ ∀ n, b < n →
     have := hc.p_pos (N' a N + 2 * (b + 2))
     rcases hc.even_p (by lia) (hs (b + 2)) with ⟨_, _⟩
     lia
-  · convert hc.apply_add_p_eq (by lia) (hs n) using 3
+  · convert! hc.apply_add_p_eq (by lia) (hs n) using 3
     rcases hc.even_p (by lia) (hs n) with ⟨_, ht⟩
     simp [ht, ← two_mul]
 
@@ -948,8 +949,8 @@ theorem result {a : ℕ → ℕ} {N : ℕ} (h : Condition a N) :
   obtain ⟨b, c, hc, hbc⟩ := h.exists_a_apply_add_eq a N
   obtain ⟨t, _⟩ | ⟨t, _⟩ := Nat.even_or_odd (Condition.N' a N)
   · refine .inl ⟨c, Condition.N' a N / 2 + b + 1, hc, fun m hm ↦ ?_⟩
-    convert hbc (m - t) (by lia) using 1 <;> dsimp only <;> congr <;> lia
+    convert! hbc (m - t) (by lia) using 1 <;> dsimp only <;> congr <;> lia
   · refine .inr ⟨c, Condition.N' a N / 2 + b + 1, hc, fun m hm ↦ ?_⟩
-    convert hbc (m - t) (by lia) using 1 <;> dsimp only <;> congr 1 <;> lia
+    convert! hbc (m - t) (by lia) using 1 <;> dsimp only <;> congr 1 <;> lia
 
 end Imo2024Q3
diff --git a/Archive/Imo/Imo2024Q5.lean b/Archive/Imo/Imo2024Q5.lean
index 54e33c55cab4e4..5d78aba0b3f028 100644
--- a/Archive/Imo/Imo2024Q5.lean
+++ b/Archive/Imo/Imo2024Q5.lean
@@ -184,7 +184,7 @@ lemma Path.exists_mem_fst_eq (p : Path N) (r : Fin (N + 2)) : ∃ c ∈ p.cells,
     rw [Fin.le_def]
     have h := r.isLt
     rw [Nat.lt_succ_iff] at h
-    convert h
+    convert! h
   have hig : r ≤ (p.cells[i]).1 := of_decide_eq_true (List.findIdx_getElem (w := hi))
   refine ⟨p.cells[i], List.getElem_mem _, ?_⟩
   refine (hig.lt_or_eq.resolve_left fun h => ?_).symm
@@ -194,7 +194,7 @@ lemma Path.exists_mem_fst_eq (p : Path N) (r : Fin (N + 2)) : ∃ c ∈ p.cells,
       have hi' : i - 1 < i := by lia
       exact of_decide_eq_false (List.not_of_lt_findIdx hi') this
     have ha : Adjacent p.cells[i - 1] p.cells[i] := by
-      convert List.isChain_iff_getElem.1 p.valid_move_seq (i - 1) ?_
+      convert! List.isChain_iff_getElem.1 p.valid_move_seq (i - 1) ?_
       · simp [Nat.sub_add_cancel hi]
       · lia
     exact ha.le_of_lt h
@@ -243,18 +243,18 @@ lemma Path.findFstEq_eq_find?_le (p : Path N) (r : Fin (N + 2)) : p.findFstEq r
     (p.cells.find? (fun c ↦ r ≤ c.1)).get
       (List.find?_isSome.2 (by simpa using p.exists_mem_le_fst r)) := by
   rw [findFstEq]
-  convert rfl using 2
+  convert! rfl using 2
   refine (find?_eq_eq_find?_le p.nonempty ?_ p.valid_move_seq).symm
   simp [p.head_first_row]
 
 lemma Path.firstMonster_isSome {p : Path N} {m : MonsterData N} :
     (p.firstMonster m).isSome = true ↔ ∃ x, x ∈ p.cells ∧ x ∈ m.monsterCells := by
-  convert List.find?_isSome
+  convert! List.find?_isSome
   simp
 
 lemma Path.firstMonster_eq_none {p : Path N} {m : MonsterData N} :
     (p.firstMonster m) = none ↔ ∀ x, x ∈ p.cells → x ∉ m.monsterCells := by
-  convert List.find?_eq_none
+  convert! List.find?_eq_none
   simp
 
 lemma Path.one_lt_length_cells (p : Path N) : 1 < p.cells.length := by
@@ -280,7 +280,7 @@ def Path.tail (p : Path N) : Path N where
     · exact p.nonempty
   head_first_row := by
     split_ifs with h
-    · convert h
+    · convert! h
       rw [List.head_tail]
     · exact p.head_first_row
   last_last_row := by
@@ -339,7 +339,7 @@ lemma Path.firstMonster_eq_of_findFstEq_mem {p : Path N} {m : MonsterData N}
       List.isChain_iff_getElem.1 p.valid_move_seq 0 (by lia)
     simp_rw [Adjacent, Nat.dist] at adj
     have hc0 : (p.cells[0].1 : ℕ) = 0 := by
-      convert Fin.ext_iff.1 p.head_first_row
+      convert! Fin.ext_iff.1 p.head_first_row
       exact List.getElem_zero _
     have hc1 : (p.cells[1].1 : ℕ) ≠ 0 := Fin.val_ne_iff.2 h0
     have h1 : (p.cells[1].1 : ℕ) = 1 := by lia
@@ -388,7 +388,7 @@ lemma Path.findFstEq_fst_sub_one_mem (p : Path N) {r : Fin (N + 2)} (hr : r ≠
     Option.some.injEq, forall_eq'] at ha
   nth_rw 1 [← cells.takeWhile_append_dropWhile (p := fun c ↦ !decide (r ≤ c.1))]
   refine List.mem_append_left _ ?_
-  convert List.getLast_mem ht using 1
+  convert! List.getLast_mem ht using 1
   have htr : ((List.takeWhile (fun c ↦ !decide (r ≤ c.1)) cells).getLast ht).1 < r := by
     simpa using List.mem_takeWhile_imp (List.getLast_mem ht)
   have hdr : r ≤ ((List.dropWhile (fun c ↦ !decide (r ≤ c.1)) cells).head hd').1 := by
@@ -452,7 +452,7 @@ def Path.reflect (p : Path N) : Path N where
 lemma Path.firstMonster_reflect (p : Path N) (m : MonsterData N) :
     p.reflect.firstMonster m.reflect = (p.firstMonster m).map Cell.reflect := by
   simp_rw [firstMonster, reflect, List.find?_map]
-  convert rfl
+  convert! rfl
   simp only [Function.comp_apply, decide_eq_decide, MonsterData.monsterCells]
   refine ⟨fun h ↦ ?_, fun h ↦ ?_⟩
   · rcases h with ⟨i, hi⟩
@@ -470,7 +470,7 @@ lemma Strategy.play_comp_castLE (s : Strategy N) (m : MonsterData N) {k₁ k₂
   case refl => rfl
   case step k' hk' hki =>
     rw [← hki, ← Fin.castLE_comp_castLE hk' (Nat.le_succ k'), ← Function.comp_assoc]
-    convert rfl
+    convert! rfl
     exact Fin.snoc_comp_castSucc.symm
 
 lemma Strategy.play_apply_of_le (s : Strategy N) (m : MonsterData N) {i k₁ k₂ : ℕ} (hi : i < k₁)
@@ -509,7 +509,7 @@ lemma Strategy.play_two (s : Strategy N) (m : MonsterData N) {k : ℕ} (hk : 2 <
   · have h : (1 : Fin 2) = Fin.last 1 := rfl
     simp only [Fin.snoc_zero, Nat.reduceAdd, Fin.mk_one, Fin.isValue, Matrix.cons_val]
     simp only [h, Fin.snoc_last]
-    convert rfl
+    convert! rfl
     simp_rw [Fin.fin_one_eq_zero, Matrix.cons_val]
 
 lemma Strategy.WinsIn.mono (s : Strategy N) (m : MonsterData N) {k₁ k₂ : ℕ} (h : s.WinsIn m k₁)
@@ -555,7 +555,7 @@ lemma row1_mem_monsterCells_monsterData12 (hN : 2 ≤ N) (c₁ c₂ : Fin (N + 1
 
 lemma row2_mem_monsterCells_monsterData12 (hN : 2 ≤ N) {c₁ c₂ : Fin (N + 1)} (h : c₁ ≠ c₂) :
     (⟨2, by lia⟩, c₂) ∈ (monsterData12 hN c₁ c₂).monsterCells := by
-  convert Set.mem_range_self (row2 hN)
+  convert! Set.mem_range_self (row2 hN)
   exact (monsterData12_apply_row2 hN h).symm
 
 lemma Strategy.not_forcesWinIn_two (s : Strategy N) (hN : 2 ≤ N) : ¬ s.ForcesWinIn 2 := by
@@ -568,7 +568,7 @@ lemma Strategy.not_forcesWinIn_two (s : Strategy N) (hN : 2 ≤ N) : ¬ s.Forces
   have h1r : m1.1 = 1 := Path.findFstEq_fst _ _
   have h2r : m2.1 = 2 := Path.findFstEq_fst _ _
   have h1 : m1 ∈ m.monsterCells := by
-    convert row1_mem_monsterCells_monsterData12 hN m1.2 m2.2
+    convert! row1_mem_monsterCells_monsterData12 hN m1.2 m2.2
   refine ⟨m, fun i ↦ ?_⟩
   fin_cases i
   · simp only [Strategy.play_zero, Path.firstMonster_eq_of_findFstEq_mem h1, Option.isSome_some]
@@ -585,7 +585,7 @@ lemma Strategy.not_forcesWinIn_two (s : Strategy N) (hN : 2 ≤ N) : ¬ s.Forces
       exact Path.findFstEq_fst_sub_one_mem _ two_ne_zero
     · rw [Path.firstMonster_isSome]
       refine ⟨m2, Path.findFstEq_mem_cells _ _, ?_⟩
-      convert row2_mem_monsterCells_monsterData12 hN h using 1
+      convert! row2_mem_monsterCells_monsterData12 hN h using 1
       simpa [Prod.ext_iff, h2r, Fin.ext_iff]
 
 lemma Strategy.ForcesWinIn.three_le {s : Strategy N} {k : ℕ} (hf : s.ForcesWinIn k)
@@ -986,7 +986,7 @@ lemma winningStrategy_play_two_of_edge_N (hN : 2 ≤ N) {m : MonsterData N}
   simp_rw [winningStrategy_play_two hN, path1, path1OfEdgeN, path2, path2OfEdgeNDef, if_neg hc₁0,
     dif_neg hc₁0, if_pos hc₁N, dif_pos hc₁N, if_pos hc₁r0, dif_pos hc₁r0,
     ← Path.firstMonster_reflect, MonsterData.reflect_reflect]
-  convert rfl using 4
+  convert! rfl using 4
   nth_rw 2 [← m.reflect_reflect]
   rw [Path.firstMonster_reflect]
   rcases ((path1OfEdge0 hN).firstMonster m.reflect).eq_none_or_eq_some with h | h
@@ -1021,10 +1021,10 @@ lemma winningStrategy_forcesWinIn_three (hN : 2 ≤ N) :
   intro m
   rcases winningStrategy_play_one_eq_none_or_play_two_eq_none hN m with h | h
   · rw [Strategy.WinsIn]
-    convert Set.mem_range_self (⟨1, by simp⟩ : Fin 3)
+    convert! Set.mem_range_self (⟨1, by simp⟩ : Fin 3)
     exact h.symm
   · rw [Strategy.WinsIn]
-    convert Set.mem_range_self (⟨2, by simp⟩ : Fin 3)
+    convert! Set.mem_range_self (⟨2, by simp⟩ : Fin 3)
     exact h.symm
 
 /-- This is to be determined by the solver of the original problem (and much of the difficulty
diff --git a/Archive/Imo/Imo2024Q6.lean b/Archive/Imo/Imo2024Q6.lean
index 8e26eb7b9494f6..31c71c33fe46ec 100644
--- a/Archive/Imo/Imo2024Q6.lean
+++ b/Archive/Imo/Imo2024Q6.lean
@@ -58,7 +58,7 @@ lemma Aquaesulian.injective : Function.Injective f := by
 @[simp]
 lemma Aquaesulian.apply_zero : f 0 = 0 := by
   refine h.injective ?_
-  convert h.apply_apply_add 0 using 1 <;> simp
+  convert! h.apply_apply_add 0 using 1 <;> simp
 
 @[simp]
 lemma Aquaesulian.apply_neg_apply_add (x : G) : f (-(f x)) + x = 0 := by
@@ -82,7 +82,7 @@ lemma Aquaesulian.apply_neg_of_apply_eq {x₁ x₂ : G} (hx : f x₁ = x₂) : f
 
 lemma Aquaesulian.apply_neg_eq_neg_iff {x₁ x₂ : G} : f (-x₂) = -x₁ ↔ f x₁ = x₂ := by
   refine ⟨fun hn ↦ ?_, h.apply_neg_of_apply_eq⟩
-  convert h.apply_neg_of_apply_eq hn <;> rw [neg_neg]
+  convert! h.apply_neg_of_apply_eq hn <;> rw [neg_neg]
 
 lemma Aquaesulian.pair_lemma {x u v : G} (huv : u ≠ v) (hx : f x = u ∨ f u = x)
     (hy : f x = v ∨ f v = x) : f x = v ∨ f x = u := by
@@ -97,14 +97,14 @@ lemma Aquaesulian.g_two {x y u v : G} (huv : u ≠ v) (hx : f x + f (-x) = u)
     f (x + y) = -(f (-x)) + -(f (-y)) + v ∨ f (x + y) = -(f (-x)) + -(f (-y)) + u := by
   refine h.pair_lemma ?_ ?_ ?_
   · simp [huv]
-  · convert h x (-(f (-y))) using 2
+  · convert! h x (-(f (-y))) using 2
     · rw [h.apply_neg_apply_neg, add_comm]
     · rw [← hx]
       abel
     · rw [← hx]
       abel_nf
     · rw [h.apply_neg_apply_neg, add_comm]
-  · convert h y (-(f (-x))) using 2
+  · convert! h y (-(f (-x))) using 2
     · rw [h.apply_neg_apply_neg]
     · rw [← hy]
       abel
diff --git a/Archive/Kuratowski.lean b/Archive/Kuratowski.lean
index 49059d8452860a..7f7f7d8d6b22a4 100644
--- a/Archive/Kuratowski.lean
+++ b/Archive/Kuratowski.lean
@@ -102,7 +102,7 @@ theorem mem_theFourteen_iff_isObtainable {s t : Set X} :
 complement operations from a single set `s` is at most 14. -/
 theorem ncard_isObtainable_le_fourteen (s : Set X) : {t | IsObtainable s t}.ncard ≤ 14 := by
   classical
-  convert Set.ncard_coe_finset _ ▸ (theFourteen s).toFinset_card_le
+  convert! Set.ncard_coe_finset _ ▸ (theFourteen s).toFinset_card_le
   simp [Set.ext_iff, mem_theFourteen_iff_isObtainable]
 
 end Topology.ClosureCompl
diff --git a/Archive/MinimalSheffer.lean b/Archive/MinimalSheffer.lean
index 5eb903463f1085..329aa377c84033 100644
--- a/Archive/MinimalSheffer.lean
+++ b/Archive/MinimalSheffer.lean
@@ -121,7 +121,7 @@ lemma sup_le (h₁ : a ≤ c) (h₂ : b ≤ c) : aᶜ | bᶜ ≤ c := by
   rw [h₂]
   have l1 := (abba (aᶜ | (b | c)) (b | c | c)).symm
   rw [comm _ (aᶜ | _), ← le_def] at l1
-  convert l1 using 1
+  convert! l1 using 1
   have l2 := veroff (b | c) c a
   rw [comm _ a, ← h₁, comm, comm _ aᶜ] at l2
   nth_rw 1 [l2, comm (b | c) c, comm b, veroff]
diff --git a/Archive/MiuLanguage/DecisionSuf.lean b/Archive/MiuLanguage/DecisionSuf.lean
index 39c987397c5418..e4b1c5f4d9f5fd 100644
--- a/Archive/MiuLanguage/DecisionSuf.lean
+++ b/Archive/MiuLanguage/DecisionSuf.lean
@@ -163,7 +163,7 @@ theorem le_pow2_and_pow2_eq_mod3 (a : ℕ) (h : a % 3 = 1 ∨ a % 3 = 2) :
   obtain ⟨m, hm⟩ := le_pow2_and_pow2_eq_mod3' (a % 3) (a / 3) h
   use m
   constructor
-  · convert hm.1; exact (mod_add_div a 3).symm
+  · convert! hm.1; exact (mod_add_div a 3).symm
   · rw [hm.2, mod_mod _ 3]
 
 end Arithmetic
@@ -194,7 +194,7 @@ theorem der_replicate_I_of_mod3 (c : ℕ) (h : c % 3 = 1 ∨ c % 3 = 2) :
       replicate ((2 ^ m - c) / 3) U ++ replicate ((2 ^ m - c) / 3 % 2) U) := by
     apply
       der_cons_replicate_I_replicate_U_append_of_der_cons_replicate_I_append c ((2 ^ m - c) / 3) h
-    convert hw₂ using 4
+    convert! hw₂ using 4
     -- now we must show `c + 3 * ((2 ^ m - c) / 3) = 2 ^ m`
     rw [Nat.mul_div_cancel']
     · exact add_tsub_cancel_of_le hm.1
@@ -220,7 +220,7 @@ example (c : ℕ) (h : c % 3 = 1 ∨ c % 3 = 2) : Derivable (M :: replicate c I)
       replicate ((2 ^ m - c) / 3) U ++ replicate ((2 ^ m - c) / 3 % 2) U) := by
     apply
       der_cons_replicate_I_replicate_U_append_of_der_cons_replicate_I_append c ((2 ^ m - c) / 3) h
-    convert hw₂ using 4
+    convert! hw₂ using 4
     -- now we must show `c + 3 * ((2 ^ m - c) / 3) = 2 ^ m`
     rw [Nat.mul_div_cancel']
     · exact add_tsub_cancel_of_le hm.1
diff --git a/Archive/Sensitivity.lean b/Archive/Sensitivity.lean
index b48847812ab9a1..228e4a2fb4edbb 100644
--- a/Archive/Sensitivity.lean
+++ b/Archive/Sensitivity.lean
@@ -90,7 +90,7 @@ theorem succ_n_eq (p q : Q n.succ) : p = q ↔ p 0 = q 0 ∧ π p = π q := by
     by_cases hx : x = 0
     · rwa [hx]
     · rw [← Fin.succ_pred x hx]
-      convert congr_fun h (Fin.pred x hx)
+      convert! congr_fun h (Fin.pred x hx)
 
 /-- The adjacency relation defining the graph structure on `Q n`:
 `p.adjacent q` if there is an edge from `p` to `q` in `Q n`. -/
@@ -383,21 +383,21 @@ theorem exists_eigenvalue (H : Set (Q m.succ)) (hH : Card H ≥ 2 ^ m + 1) :
   suffices 0 < dim (W ⊓ img) by
     exact mod_cast exists_mem_ne_zero_of_rank_pos this
   have dim_le : dim (W ⊔ img) ≤ 2 ^ (m + 1 : Cardinal) := by
-    convert ← Submodule.rank_le (W ⊔ img)
+    convert! ← Submodule.rank_le (W ⊔ img)
     rw [← Nat.cast_succ]
     apply dim_V
   have dim_add : dim (W ⊔ img) + dim (W ⊓ img) = dim W + 2 ^ m := by
-    convert ← Submodule.rank_sup_add_rank_inf_eq W img
+    convert! ← Submodule.rank_sup_add_rank_inf_eq W img
     rw [rank_range_of_injective (g m) g_injective]
     apply dim_V
   have dimW : dim W = card H := by
     have li : LinearIndependent ℝ (H.restrict e) := by
-      convert (dualBases_e_ε m.succ).basis.linearIndependent.comp _ Subtype.val_injective
+      convert! (dualBases_e_ε m.succ).basis.linearIndependent.comp _ Subtype.val_injective
       rw [(dualBases_e_ε _).coe_basis]
       rfl
     have hdW := rank_span li
     rw [Set.range_restrict] at hdW
-    convert hdW
+    convert! hdW
     rw [← (dualBases_e_ε _).coe_basis, Cardinal.mk_image_eq (dualBases_e_ε _).basis.injective,
       Cardinal.mk_fintype]
   rw [← finrank_eq_rank ℝ] at dim_le dim_add dimW ⊢
@@ -452,7 +452,7 @@ theorem huang_degree_theorem (H : Set (Q m.succ)) (hH : Card H ≥ 2 ^ m + 1) :
       norm_cast
       apply card_le_card
       rw [Set.toFinset_inter]
-      convert inter_subset_inter_right coeffs_support
+      convert! inter_subset_inter_right coeffs_support
 
 end
 
diff --git a/Archive/Wiedijk100Theorems/AbelRuffini.lean b/Archive/Wiedijk100Theorems/AbelRuffini.lean
index 9e686d91399255..b4e87d9ea25164 100644
--- a/Archive/Wiedijk100Theorems/AbelRuffini.lean
+++ b/Archive/Wiedijk100Theorems/AbelRuffini.lean
@@ -55,7 +55,7 @@ variable [Nontrivial R]
 theorem degree_Phi : (Φ R a b).degree = ((5 : ℕ) : WithBot ℕ) := by
   suffices degree (X ^ 5 - C (a : R) * X) = ((5 : ℕ) : WithBot ℕ) by
     rwa [Φ, degree_add_eq_left_of_degree_lt]
-    convert (degree_C_le (R := R)).trans_lt (WithBot.coe_lt_coe.mpr (show 0 < 5 by simp))
+    convert! (degree_C_le (R := R)).trans_lt (WithBot.coe_lt_coe.mpr (show 0 < 5 by simp))
   rw [degree_sub_eq_left_of_degree_lt] <;> rw [degree_X_pow]
   exact (degree_C_mul_X_le (a : R)).trans_lt (WithBot.coe_lt_coe.mpr (show 1 < 5 by simp))
 
@@ -134,7 +134,7 @@ theorem real_roots_Phi_ge (hab : b < a) : 2 ≤ Fintype.card ((Φ ℚ a b).rootS
   obtain ⟨x, y, hxy, hx, hy⟩ := real_roots_Phi_ge_aux a b hab
   have key : ↑({x, y} : Finset ℝ) ⊆ (Φ ℚ a b).rootSet ℝ := by
     simp [Set.insert_subset, mem_rootSet_of_ne q_ne_zero, hx, hy]
-  convert Fintype.card_le_of_embedding (Set.embeddingOfSubset _ _ key)
+  convert! Fintype.card_le_of_embedding (Set.embeddingOfSubset _ _ key)
   simp only [Finset.coe_sort_coe, Fintype.card_coe, Finset.card_singleton,
     Finset.card_insert_of_notMem (mt Finset.mem_singleton.mp hxy)]
 
diff --git a/Archive/Wiedijk100Theorems/AreaOfACircle.lean b/Archive/Wiedijk100Theorems/AreaOfACircle.lean
index dab12166f1f201..71aaa05c5d0099 100644
--- a/Archive/Wiedijk100Theorems/AreaOfACircle.lean
+++ b/Archive/Wiedijk100Theorems/AreaOfACircle.lean
@@ -98,12 +98,12 @@ theorem area_disc : volume (disc r) = NNReal.pi * r ^ 2 := by
   obtain heq | hlt := hle.eq_or_lt; · simp [← heq]
   have hderiv : ∀ x ∈ Ioo (-r : ℝ) r, HasDerivAt F (2 * f x) x := by
     rintro x ⟨hx1, hx2⟩
-    convert
+    convert!
       ((hasDerivAt_const x ((r : ℝ) ^ 2)).mul
-          ((hasDerivAt_arcsin _ _).comp x
-            ((hasDerivAt_const x (r : ℝ)⁻¹).mul (hasDerivAt_id' x)))).add
-        ((hasDerivAt_id' x).mul ((((hasDerivAt_id' x).fun_pow 2).const_sub ((r : ℝ) ^ 2)).sqrt _))
-      using 1
+            ((hasDerivAt_arcsin _ _).comp x
+              ((hasDerivAt_const x (r : ℝ)⁻¹).mul (hasDerivAt_id' x)))).add
+        ((hasDerivAt_id' x).mul
+          ((((hasDerivAt_id' x).fun_pow 2).const_sub ((r : ℝ) ^ 2)).sqrt _)) using 1
     · have h₁ : 0 < (r : ℝ) ^ 2 - x ^ 2 := sub_pos_of_lt (sq_lt_sq' hx1 hx2)
       have h : sqrt ((r : ℝ) ^ 2 - x ^ 2) ^ 3 =
           ((r : ℝ) ^ 2 - x ^ 2) * sqrt ((r : ℝ) ^ 2 - x ^ 2) := by
diff --git a/Archive/Wiedijk100Theorems/AscendingDescendingSequences.lean b/Archive/Wiedijk100Theorems/AscendingDescendingSequences.lean
index 213794df94ade2..ec92034f0ad98c 100644
--- a/Archive/Wiedijk100Theorems/AscendingDescendingSequences.lean
+++ b/Archive/Wiedijk100Theorems/AscendingDescendingSequences.lean
@@ -91,7 +91,7 @@ private lemma maxIncSequencesTo_lt {i j : α} (hij : i < j) (hfij : f i < f j) :
     exact (hti.2 hx).trans_lt hij
   refine ⟨insert j t, ?_, ?_, ?_⟩
   next =>
-    convert hti.insert j using 1
+    convert! hti.insert j using 1
     next => simp
     next => rw [max_eq_left hij.le]
   next =>
diff --git a/Archive/Wiedijk100Theorems/CubingACube.lean b/Archive/Wiedijk100Theorems/CubingACube.lean
index 31c9c0f26df100..b495afdf771008 100644
--- a/Archive/Wiedijk100Theorems/CubingACube.lean
+++ b/Archive/Wiedijk100Theorems/CubingACube.lean
@@ -137,7 +137,7 @@ variable (h : Correct cs)
 include h
 
 theorem toSet_subset_unitCube {i} : (cs i).toSet ⊆ unitCube.toSet := by
-  convert h.iUnion_eq ▸ subset_iUnion _ i
+  convert! h.iUnion_eq ▸ subset_iUnion _ i
 
 theorem side_subset {i j} : (cs i).side j ⊆ Ico 0 1 := by
   simpa only [side_unitCube] using toSet_subset.1 h.toSet_subset_unitCube j
@@ -154,7 +154,7 @@ theorem zero_le_b {i j} : 0 ≤ (cs i).b j :=
 theorem b_add_w_le_one {j} : (cs i).b j + (cs i).w ≤ 1 := by
   have : side (cs i) j ⊆ Ico 0 1 := side_subset h
   rw [side, Ico_subset_Ico_iff] at this
-  · convert this.2
+  · convert! this.2
   · simp [hw]
 
 theorem nontrivial_fin : Nontrivial (Fin n) :=
@@ -169,7 +169,7 @@ theorem w_ne_one [Nontrivial ι] (i : ι) : (cs i).w ≠ 1 := by
   have h2p : p ∈ (cs i).toSet := by
     intro j; constructor
     · trans (0 : ℝ)
-      · rw [← add_le_add_iff_right (1 : ℝ)]; convert b_add_w_le_one h
+      · rw [← add_le_add_iff_right (1 : ℝ)]; convert! b_add_w_le_one h
         · rw [hi]
         · rw [zero_add]
       · apply zero_le_b h
@@ -197,7 +197,7 @@ theorem shiftUp_bottom_subset_bottoms (hc : (cs i).xm ≠ 1) :
   rw [onFun, comp_apply, comp_apply, toSet_disjoint, exists_fin_succ] at this
   rcases this with (h0 | ⟨j, hj⟩)
   · rw [hp0]; symm; apply eq_of_Ico_disjoint h0 (by simp [hw]) _
-    convert hi' 0; rw [hp0]; rfl
+    convert! hi' 0; rw [hp0]; rfl
   · exfalso; apply not_disjoint_iff.mpr ⟨tail p j, hps j, hi' j.succ⟩ hj
 
 end Correct
@@ -237,7 +237,7 @@ theorem valley_unitCube [Nontrivial ι] (h : Correct cs) : Valley cs unitCube :=
       · rw [h0]; exact h.zero_le_b
       · exact (hi 0).1
     intro j; exact hi _
-  · intro i _ _; rw [toSet_subset]; intro j; convert h.side_subset using 1; simp [side_tail]
+  · intro i _ _; rw [toSet_subset]; intro j; convert! h.side_subset using 1; simp [side_tail]
   · intro i _; exact h.w_ne_one i
 
 /-- the cubes which lie in the valley `c` -/
@@ -252,7 +252,7 @@ theorem tail_sub (hi : i ∈ bcubes cs c) : ∀ j, (cs i).tail.side j ⊆ c.tail
   rw [← toSet_subset]; exact hi.2
 
 theorem bottom_mem_side (hi : i ∈ bcubes cs c) : c.b 0 ∈ (cs i).side 0 := by
-  convert b_mem_side (cs i) _ using 1; rw [hi.1]
+  convert! b_mem_side (cs i) _ using 1; rw [hi.1]
 
 theorem b_le_b (hi : i ∈ bcubes cs c) (j : Fin n) : c.b j.succ ≤ (cs i).b j.succ :=
   (tail_sub hi j <| b_mem_side _ _).1
@@ -422,13 +422,13 @@ theorem mi_not_onBoundary (j : Fin n) : ¬OnBoundary (mi_mem_bcubes : mi h v ∈
   intro j₂
   by_cases hj₂ : j₂ = j
   · cases hj₂; refine ⟨x, ?_, ?_⟩
-    · convert hi'.2 j using 1; simp [i, p]
-    apply h3x h2i'' i_i''.symm; convert hi''.2 j using 1; simp [i, p', hj'.symm]
+    · convert! hi'.2 j using 1; simp [i, p]
+    apply h3x h2i'' i_i''.symm; convert! hi''.2 j using 1; simp [i, p', hj'.symm]
   by_cases h2j₂ : j₂ = j'
-  · cases h2j₂; refine ⟨x', hx'.1, ?_⟩; convert hi''.2 j' using 1; simp [p']
+  · cases h2j₂; refine ⟨x', hx'.1, ?_⟩; convert! hi''.2 j' using 1; simp [p']
   refine ⟨(cs i).b j₂.succ, ?_, ?_⟩
-  · convert hi'.2 j₂ using 1; simp [p, hj₂]
-  · convert hi''.2 j₂ using 1; simp [p', h2j₂]
+  · convert! hi'.2 j₂ using 1; simp [p, hj₂]
+  · convert! hi''.2 j₂ using 1; simp [p', h2j₂]
 
 variable {h v}
 
@@ -466,7 +466,7 @@ theorem valley_mi : Valley cs (cs (mi h v)).shiftUp := by
       · intro j'; by_cases h : j' = j
         · simp only [if_pos h]; exact h ▸ h3w
         · simp only [if_neg h]; exact hp2 j'
-      · simp only [toSet, not_forall, mem_setOf_eq]; use j; rw [if_pos rfl]; convert h2w
+      · simp only [toSet, not_forall, mem_setOf_eq]; use j; rw [if_pos rfl]; convert! h2w
       · intro j'; by_cases h : j' = j
         · simp only [if_pos h, side_tail]; exact h ▸ hw
         · simp only [if_neg h]; apply hi.2; apply h2p2
@@ -480,7 +480,7 @@ theorem valley_mi : Valley cs (cs (mi h v)).shiftUp := by
       · exact hi''.2
       · rw [tail_cons]; exact h3p3
     have h3i'' : (cs i).w < (cs i'').w := by
-      apply mi_strict_minimal _ h2i''; rintro rfl; apply h2p3; convert hi''.2
+      apply mi_strict_minimal _ h2i''; rintro rfl; apply h2p3; convert! hi''.2
     let p' := @cons n (fun _ => ℝ) (cs i).xm p3
     have hp' : p' ∈ (cs i').toSet := by simpa [i, p', toSet, forall_iff_succ, hi'.symm] using h1p3
     have h2p' : p' ∈ (cs i'').toSet := by
diff --git a/Counterexamples/CliffordAlgebraNotInjective.lean b/Counterexamples/CliffordAlgebraNotInjective.lean
index ce016c182617a7..98e8270597431f 100644
--- a/Counterexamples/CliffordAlgebraNotInjective.lean
+++ b/Counterexamples/CliffordAlgebraNotInjective.lean
@@ -234,7 +234,7 @@ theorem quot_obv : α • x' - β • y' - γ • z' = 0 := by
   dsimp only [gen]
   simp_rw [← map_smul, ← map_sub, ← Submodule.Quotient.mk_smul _ (_ : K),
     ← Submodule.Quotient.mk_sub]
-  convert LinearMap.map_zero _ using 2
+  convert! LinearMap.map_zero _ using 2
   rw [Submodule.Quotient.mk_eq_zero]
   simp +decide [sub_zero]
 
diff --git a/Counterexamples/EulerSumOfPowers.lean b/Counterexamples/EulerSumOfPowers.lean
index 72e92f06908961..69b1fba2b18bcd 100644
--- a/Counterexamples/EulerSumOfPowers.lean
+++ b/Counterexamples/EulerSumOfPowers.lean
@@ -76,7 +76,7 @@ lemma sumOfPowersConjecture_of_ringHom {R S : Type*} [Semiring R] [Semiring S] {
     SumOfPowersConjectureWith R n := by
   intro a b ha ha₀ hb hsum
   have h : (· ^ n) ∘ f = f ∘ (· ^ n) := by ext; simp
-  convert conj (a.map f) (f b) ?_ ?_ ?_ (by simp [h, hsum, List.sum_map_hom]) <;> grind
+  convert! conj (a.map f) (f b) ?_ ?_ ?_ (by simp [h, hsum, List.sum_map_hom]) <;> grind
 
 /-- Given an injective ring homomorphism from `R` to `S`,
 the conjecture over `S` implies the conjecture over `R`. -/
diff --git a/Counterexamples/MapFloor.lean b/Counterexamples/MapFloor.lean
index 075e16714ac418..c45e5c9454e12d 100644
--- a/Counterexamples/MapFloor.lean
+++ b/Counterexamples/MapFloor.lean
@@ -65,7 +65,7 @@ theorem pos_iff {p : ℤ[ε]} : 0 < p ↔ 0 < p.trailingCoeff := by
     ⟨?_, fun h =>
       ⟨p.natTrailingDegree, fun m hm => (coeff_eq_zero_of_lt_natTrailingDegree hm).symm, h⟩⟩
   rintro ⟨n, hn⟩
-  convert hn.2
+  convert! hn.2
   exact (natTrailingDegree_le_of_ne_zero hn.2.ne').antisymm
     (le_natTrailingDegree (by rintro rfl; cases hn.2.false) fun m hm => (hn.1 _ hm).symm)
 
diff --git a/Counterexamples/NowhereDifferentiable.lean b/Counterexamples/NowhereDifferentiable.lean
index 2497df7520bf8f..998caa01d49e12 100644
--- a/Counterexamples/NowhereDifferentiable.lean
+++ b/Counterexamples/NowhereDifferentiable.lean
@@ -160,7 +160,7 @@ theorem weierstrass_remainder {a : ℝ} (ha : 0 < a) {b : ℕ} (hb : Odd b) {x :
   · -- Show that the first term (after simplification) satisfies the bound
     suffices a ^ m * (2 / 3 * b ^ m * |seq b x m - x|) ≤
         a ^ m * (1 + cos ((b ^ m * x - ⌊b ^ m * x + 2⁻¹⌋) * π)) by
-      convert this using 1
+      convert! this using 1
       ring
     refine mul_le_mul_of_nonneg_left ?_ (pow_nonneg ha.le _)
     trans 1
@@ -261,7 +261,7 @@ theorem not_differentiableAt_weierstrass
   obtain ⟨f', h⟩ := this
   have : Tendsto (fun m ↦ (seq b x m - x)⁻¹ * (weierstrass a b (seq b x m) - weierstrass a b x))
       atTop (𝓝 (f' 1)) := by
-    convert (h.lim_real 1).comp (tendsto_seq_sub_inv hb1 x)
+    convert! (h.lim_real 1).comp (tendsto_seq_sub_inv hb1 x)
     simp
   have h := (continuous_abs.tendsto _).comp this
   contrapose! h
@@ -274,7 +274,7 @@ theorem not_differentiableAt_weierstrass
     exact weierstrass_slope ha hb hab' x m
   have hpos : 0 < 2 / 3 - π / (a * b - 1) := by
     rw [sub_pos, div_lt_iff₀ (by simpa using hab'), ← div_lt_iff₀' (by norm_num), lt_sub_iff_add_lt]
-    convert hab using 1
+    convert! hab using 1
     grind
   exact (tendsto_const_nhds_iff.mpr rfl).pos_mul_atTop hpos (tendsto_pow_atTop_atTop_of_one_lt hab')
 
diff --git a/Counterexamples/Phillips.lean b/Counterexamples/Phillips.lean
index fc086f68755d25..efe03d538ec013 100644
--- a/Counterexamples/Phillips.lean
+++ b/Counterexamples/Phillips.lean
@@ -283,7 +283,7 @@ theorem exists_discrete_support_nonpos (f : BoundedAdditiveMeasure α) :
   have I1 : ∀ n, ε / 2 ≤ f (↑(s (n + 1)) \ ↑(s n)) := by
     intro n
     rw [div_le_iff₀' (show (0 : ℝ) < 2 by simp), hε]
-    convert hF (s n) u using 2
+    convert! hF (s n) u using 2
     · dsimp
       ext x
       simp only [u, not_exists, mem_iUnion, mem_diff]
@@ -361,7 +361,7 @@ theorem discretePart_apply (f : BoundedAdditiveMeasure α) (s : Set α) :
 theorem continuousPart_apply_eq_zero_of_countable (f : BoundedAdditiveMeasure α) (s : Set α)
     (hs : s.Countable) : f.continuousPart s = 0 := by
   simp only [continuousPart, restrict_apply]
-  convert f.apply_countable s hs using 2
+  convert! f.apply_countable s hs using 2
   ext x
   simp [and_comm]
 
diff --git a/Counterexamples/SorgenfreyLine.lean b/Counterexamples/SorgenfreyLine.lean
index 25b780bcb1b451..71a0c5b4d0edd3 100644
--- a/Counterexamples/SorgenfreyLine.lean
+++ b/Counterexamples/SorgenfreyLine.lean
@@ -221,7 +221,7 @@ theorem isClosed_of_subset_antidiagonal {s : Set (ℝₗ × ℝₗ)} {c : ℝₗ
     exact closure_minimal (hs : s ⊆ {x | x.1 + x.2 = c}) (isClosed_antidiagonal c) H
   rcases mem_closure_iff.1 H (Ici (x, y)) (isClopen_Ici_prod _).2 self_mem_Ici with
     ⟨⟨x', y'⟩, ⟨hx : x ≤ x', hy : y ≤ y'⟩, H⟩
-  convert H
+  convert! H
   · refine hx.antisymm ?_
     rwa [← add_le_add_iff_right, hs _ H, add_le_add_iff_left]
   · refine hy.antisymm ?_
diff --git a/Counterexamples/TopologistsSineCurve.lean b/Counterexamples/TopologistsSineCurve.lean
index e28ebfe1d74302..b2db6093cdeb70 100644
--- a/Counterexamples/TopologistsSineCurve.lean
+++ b/Counterexamples/TopologistsSineCurve.lean
@@ -82,7 +82,7 @@ lemma closure_S : closure S = T := by
       have : ContinuousAt (fun x ↦ sin x⁻¹) x :=
         continuous_sin.continuousAt.comp <| continuousAt_inv₀ h.ne'
       refine tendsto_nhds_unique ?_ hf_lim.2
-      convert this.tendsto.comp hf_lim.1 with n
+      convert! this.tendsto.comp hf_lim.1 with n
       obtain ⟨y, hy⟩ := hf_mem n
       simp [← hy.2]
   · -- Show that every `p ∈ T` is the limit of a sequence in `S`.
diff --git a/Counterexamples/ZeroDivisorsInAddMonoidAlgebras.lean b/Counterexamples/ZeroDivisorsInAddMonoidAlgebras.lean
index 78c59342600104..d3e6059c5ef7fc 100644
--- a/Counterexamples/ZeroDivisorsInAddMonoidAlgebras.lean
+++ b/Counterexamples/ZeroDivisorsInAddMonoidAlgebras.lean
@@ -97,7 +97,7 @@ theorem zero_divisors_of_torsion {R A} [Nontrivial R] [Ring R] [AddMonoid A] (a
           (nsmul_ne_zero_of_lt_addOrderOf one_ne_zero (Nat.succ_le_iff.mp o2))
       simp only [a0, single_eq_of_ne', Ne, not_false_iff]
     · simpa only [single_eq_same] using zero_ne_one
-  · convert Commute.geom_sum₂_mul (R := AddMonoidAlgebra R A) _ (addOrderOf a) using 3
+  · convert! Commute.geom_sum₂_mul (R := AddMonoidAlgebra R A) _ (addOrderOf a) using 3
     · rw [single_zero_one, one_pow, mul_one]
     · rw [single_pow, one_pow, addOrderOf_nsmul_eq_zero, single_zero_one, one_pow, sub_self]
     · simp only [single_zero_one, Commute.one_right]
diff --git a/Mathlib/Algebra/AffineMonoid/Irreducible.lean b/Mathlib/Algebra/AffineMonoid/Irreducible.lean
index 233b25ec015a41..25361838cedfaf 100644
--- a/Mathlib/Algebra/AffineMonoid/Irreducible.lean
+++ b/Mathlib/Algebra/AffineMonoid/Irreducible.lean
@@ -74,7 +74,7 @@ lemma Submonoid.closure_irreducible [Monoid.FG M] :
   -- Pick a minimal set `S` generating `M`.
   obtain ⟨S, hSgen, hSmax⟩ := Submonoid.exists_minimal_closure_eq_top M
   -- We claim that `S` is the set of irreducible elements of `M`.
-  convert hSgen
+  convert! hSgen
   -- We already know that `S` contains all irreducible elements...
   refine (irreducible_subset_of_submonoidClosure_eq_top hSgen).antisymm fun r hrS ↦ ?_
   -- So let us for contradiction assume that `r ∈ S` is reducible.
diff --git a/Mathlib/Algebra/Algebra/Operations.lean b/Mathlib/Algebra/Algebra/Operations.lean
index 6d78838e2478c4..54267e7ffb5618 100644
--- a/Mathlib/Algebra/Algebra/Operations.lean
+++ b/Mathlib/Algebra/Algebra/Operations.lean
@@ -902,7 +902,7 @@ protected theorem map_div {B : Type*} [CommSemiring B] [Algebra R B] (I J : Subm
   · rintro hx
     refine ⟨h.symm x, fun z hz => ?_, h.apply_symm_apply x⟩
     obtain ⟨xz, xz_mem, hxz⟩ := hx (h z) ⟨z, hz, rfl⟩
-    convert xz_mem
+    convert! xz_mem
     apply h.injective
     rw [map_mul, h.apply_symm_apply, hxz]
 
diff --git a/Mathlib/Algebra/Algebra/Spectrum/Quasispectrum.lean b/Mathlib/Algebra/Algebra/Spectrum/Quasispectrum.lean
index 72dab6b30b5fac..352921912f0081 100644
--- a/Mathlib/Algebra/Algebra/Spectrum/Quasispectrum.lean
+++ b/Mathlib/Algebra/Algebra/Spectrum/Quasispectrum.lean
@@ -156,13 +156,13 @@ def unitsFstOne_mulEquiv_quasiregular : unitsFstOne R A ≃* (PreQuasiregular A)
       { val := 1 + PreQuasiregular.equiv.symm x.val
         inv := 1 + PreQuasiregular.equiv.symm x⁻¹.val
         val_inv := by
-          convert congr((1 + $(inv_add_add_mul_eq_zero x) : Unitization R A)) using 1
+          convert! congr((1 + $(inv_add_add_mul_eq_zero x) : Unitization R A)) using 1
           · simp only [mul_one, PreQuasiregular.equiv_symm_apply, one_mul, mul_add,
               add_mul, inr_add, inr_mul]
             abel
           · simp only [inr_zero, add_zero]
         inv_val := by
-          convert congr((1 + $(add_inv_add_mul_eq_zero x) : Unitization R A)) using 1
+          convert! congr((1 + $(add_inv_add_mul_eq_zero x) : Unitization R A)) using 1
           · simp only [mul_one, PreQuasiregular.equiv_symm_apply, one_mul, mul_add,
               add_mul, inr_add, inr_mul]
             abel
@@ -216,8 +216,8 @@ lemma IsQuasiregular.isUnit_one_add {R : Type*} [Semiring R] {x : R} (hx : IsQua
     IsUnit (1 + x) := by
   obtain ⟨y, hy₁, hy₂⟩ := isQuasiregular_iff.mp hx
   refine ⟨⟨1 + x, 1 + y, ?_, ?_⟩, rfl⟩
-  · convert congr(1 + $(hy₁)) using 1 <;> [noncomm_ring; simp]
-  · convert congr(1 + $(hy₂)) using 1 <;> [noncomm_ring; simp]
+  · convert! congr(1 + $(hy₁)) using 1 <;> [noncomm_ring; simp]
+  · convert! congr(1 + $(hy₂)) using 1 <;> [noncomm_ring; simp]
 
 lemma isQuasiregular_iff_isUnit {R : Type*} [Ring R] {x : R} :
     IsQuasiregular x ↔ IsUnit (1 + x) := by
@@ -229,7 +229,7 @@ lemma isQuasiregular_iff_isUnit {R : Type*} [Ring R] {x : R} :
   case' h.right => have := congr($(hx.val_inv_mul) - 1)
   all_goals
     rw [← sub_add_cancel (↑hx.unit⁻¹ : R) 1, sub_self] at this
-    convert this using 1
+    convert! this using 1
     noncomm_ring
 
 -- interestingly, this holds even in the semiring case.
@@ -314,7 +314,7 @@ lemma spectrum_subset_quasispectrum (R : Type*) {A : Type*} [CommSemiring R] [Ri
 
 lemma quasispectrum_eq_spectrum_union_zero (R : Type*) {A : Type*} [Semifield R] [Ring A]
     [Algebra R A] (a : A) : quasispectrum R a = spectrum R a ∪ {0} := by
-  convert quasispectrum_eq_spectrum_union R a
+  convert! quasispectrum_eq_spectrum_union R a
   simp
 
 lemma mem_quasispectrum_iff {R A : Type*} [Semifield R] [Ring A]
@@ -518,10 +518,10 @@ protected lemma comp {R₁ R₂ R₃ A : Type*} [Semifield R₁] [Field R₂] [F
     (hf : QuasispectrumRestricts a f) (hg : QuasispectrumRestricts a g) :
     QuasispectrumRestricts a e where
   left_inv := by
-    convert hfge ▸ hf.left_inv.comp hg.left_inv
+    convert! hfge ▸ hf.left_inv.comp hg.left_inv
     congrm (⇑$(IsScalarTower.algebraMap_eq R₁ R₂ R₃))
   rightInvOn := by
-    convert hfge ▸ hg.rightInvOn.comp hf.rightInvOn fun _ ↦ hf.apply_mem
+    convert! hfge ▸ hg.rightInvOn.comp hf.rightInvOn fun _ ↦ hf.apply_mem
     congrm (⇑$(IsScalarTower.algebraMap_eq R₁ R₂ R₃))
 
 end NonUnital
diff --git a/Mathlib/Algebra/Algebra/Subalgebra/Basic.lean b/Mathlib/Algebra/Algebra/Subalgebra/Basic.lean
index 0929d4e5ac04d1..89b7e8ae8207bd 100644
--- a/Mathlib/Algebra/Algebra/Subalgebra/Basic.lean
+++ b/Mathlib/Algebra/Algebra/Subalgebra/Basic.lean
@@ -725,7 +725,7 @@ scoped instance faithfulSMul :
     letI := (inclusion h).toModule; FaithfulSMul S T :=
   letI := (inclusion h).toModule
   ⟨fun {x y} h ↦ Subtype.ext <| by
-    convert Subtype.ext_iff.mp (h 1) using 1 <;> exact (mul_one _).symm⟩
+    convert! Subtype.ext_iff.mp (h 1) using 1 <;> exact (mul_one _).symm⟩
 
 end inclusion
 
diff --git a/Mathlib/Algebra/Algebra/Subalgebra/Centralizer.lean b/Mathlib/Algebra/Algebra/Subalgebra/Centralizer.lean
index 34561e733bd8cf..50fffbc6381b3c 100644
--- a/Mathlib/Algebra/Algebra/Subalgebra/Centralizer.lean
+++ b/Mathlib/Algebra/Algebra/Subalgebra/Centralizer.lean
@@ -111,7 +111,7 @@ lemma centralizer_coe_image_includeRight_eq_center_tensorProduct
       (Subalgebra.centralizer R (S : Set B)).val).range := by
   have eq1 := centralizer_coe_image_includeLeft_eq_center_tensorProduct R B A S
   apply_fun Subalgebra.comap (Algebra.TensorProduct.comm R A B).toAlgHom at eq1
-  convert eq1
+  convert! eq1
   · ext x
     simpa [mem_centralizer_iff] using
       ⟨fun h b hb ↦ (Algebra.TensorProduct.comm R A B).symm.injective <| by aesop, fun h b hb ↦
diff --git a/Mathlib/Algebra/Algebra/Subalgebra/Lattice.lean b/Mathlib/Algebra/Algebra/Subalgebra/Lattice.lean
index 5e4698cedbf0b8..004c36e77fc6ae 100644
--- a/Mathlib/Algebra/Algebra/Subalgebra/Lattice.lean
+++ b/Mathlib/Algebra/Algebra/Subalgebra/Lattice.lean
@@ -713,7 +713,7 @@ theorem mem_adjoin_of_map_mul {s} {x : A} {f : A →ₗ[R] B} (hf : ∀ a₁ a
   | algebraMap r =>
     have : f 1 ∈ adjoin R (f '' (s ∪ {1})) :=
       subset_adjoin ⟨1, ⟨Set.subset_union_right <| Set.mem_singleton 1, rfl⟩⟩
-    convert Subalgebra.smul_mem (adjoin R (f '' (s ∪ {1}))) this r
+    convert! Subalgebra.smul_mem (adjoin R (f '' (s ∪ { 1 }))) this r
     rw [algebraMap_eq_smul_one]
     exact f.map_smul _ _
   | add y z _ _ hy hz => simpa [hy, hz] using Subalgebra.add_mem _ hy hz
@@ -860,8 +860,8 @@ theorem eqOn_adjoin_iff {φ ψ : A →ₐ[R] B} {s : Set A} :
 theorem adjoin_ext {s : Set A} ⦃φ₁ φ₂ : adjoin R s →ₐ[R] B⦄
     (h : ∀ x hx, φ₁ ⟨x, subset_adjoin hx⟩ = φ₂ ⟨x, subset_adjoin hx⟩) : φ₁ = φ₂ :=
   ext fun ⟨x, hx⟩ ↦ adjoin_induction h (fun _ ↦ φ₂.commutes _ ▸ φ₁.commutes _)
-    (fun _ _ _ _ h₁ h₂ ↦ by convert congr_arg₂ (· + ·) h₁ h₂ <;> rw [← map_add] <;> rfl)
-    (fun _ _ _ _ h₁ h₂ ↦ by convert congr_arg₂ (· * ·) h₁ h₂ <;> rw [← map_mul] <;> rfl) hx
+    (fun _ _ _ _ h₁ h₂ ↦ by convert! congr_arg₂ (· + ·) h₁ h₂ <;> rw [← map_add] <;> rfl)
+    (fun _ _ _ _ h₁ h₂ ↦ by convert! congr_arg₂ (· * ·) h₁ h₂ <;> rw [← map_mul] <;> rfl) hx
 
 theorem ext_of_eq_adjoin {S : Subalgebra R A} {s : Set A} (hS : S = adjoin R s) ⦃φ₁ φ₂ : S →ₐ[R] B⦄
     (h : ∀ x hx, φ₁ ⟨x, hS.ge (subset_adjoin hx)⟩ = φ₂ ⟨x, hS.ge (subset_adjoin hx)⟩) :
@@ -977,7 +977,7 @@ theorem comap_map_eq (f : A →ₐ[R] B) (S : Subalgebra R A) :
 
 theorem comap_map_eq_self {f : A →ₐ[R] B} {S : Subalgebra R A}
     (h : f ⁻¹' {0} ⊆ S) : (S.map f).comap f = S := by
-  convert comap_map_eq f S
+  convert! comap_map_eq f S
   rwa [left_eq_sup, Algebra.adjoin_le_iff]
 
 end Subalgebra
diff --git a/Mathlib/Algebra/BigOperators/Fin.lean b/Mathlib/Algebra/BigOperators/Fin.lean
index 73ac53464e1500..9e42dbf60f91fc 100644
--- a/Mathlib/Algebra/BigOperators/Fin.lean
+++ b/Mathlib/Algebra/BigOperators/Fin.lean
@@ -663,7 +663,7 @@ def finPiFinEquiv {m : ℕ} {n : Fin m → ℕ} : (∀ i : Fin m, Fin (n i)) ≃
         simp_rw [Fin.val_zero, Fintype.prod_empty, Nat.div_one, mul_one, Fin.cons_zero,
           Fin.prod_univ_succ, Fin.castLE_zero, Fin.cons_zero, ← Nat.div_div_eq_div_mul,
           mul_left_comm (_ % _ : ℕ), ← mul_sum]
-        convert Nat.mod_add_div _ _
+        convert! Nat.mod_add_div _ _
         exact ih (a / x) (Nat.div_lt_of_lt_mul <| a.is_lt.trans_eq (Fin.prod_univ_succ _)))
 
 theorem finPiFinEquiv_apply {m : ℕ} {n : Fin m → ℕ} (f : ∀ i : Fin m, Fin (n i)) :
diff --git a/Mathlib/Algebra/BigOperators/Finprod.lean b/Mathlib/Algebra/BigOperators/Finprod.lean
index 1de4d50576a677..ec2b992d915110 100644
--- a/Mathlib/Algebra/BigOperators/Finprod.lean
+++ b/Mathlib/Algebra/BigOperators/Finprod.lean
@@ -336,7 +336,7 @@ variable {α β ι G M N : Type*} [CommMonoid M] [CommMonoid N]
 @[to_additive]
 theorem finprod_eq_mulIndicator_apply (s : Set α) (f : α → M) (a : α) :
     ∏ᶠ _ : a ∈ s, f a = mulIndicator s f a := by
-  classical convert finprod_eq_if (M := M) (p := a ∈ s) (x := f a)
+  classical convert! finprod_eq_if (M := M) (p := a ∈ s) (x := f a)
 
 @[to_additive (attr := simp)]
 theorem finprod_apply_ne_one (f : α → M) (a : α) : ∏ᶠ _ : f a ≠ 1, f a = f a := by
@@ -1065,8 +1065,8 @@ theorem finprod_mem_sUnion {t : Set (Set α)} (h : t.PairwiseDisjoint id) (ht₀
 lemma finprod_option {f : Option α → M} (hf : HasFiniteMulSupport (f ∘ some)) :
     ∏ᶠ o, f o = f none * ∏ᶠ a, f (some a) := by
   replace hf : (mulSupport f).Finite := by simpa [finite_option]
-  convert finprod_mem_insert' f (show none ∉ Set.range Option.some by simp)
-    (hf.subset inter_subset_right)
+  convert!
+    finprod_mem_insert' f (show none ∉ Set.range Option.some by simp) (hf.subset inter_subset_right)
   · simp
   · rw [finprod_mem_range]
     exact Option.some_injective _
diff --git a/Mathlib/Algebra/BigOperators/Group/Finset/Basic.lean b/Mathlib/Algebra/BigOperators/Group/Finset/Basic.lean
index f0c05c6a1fa5f9..2d6a839ae18056 100644
--- a/Mathlib/Algebra/BigOperators/Group/Finset/Basic.lean
+++ b/Mathlib/Algebra/BigOperators/Group/Finset/Basic.lean
@@ -596,7 +596,7 @@ theorem prod_multiset_map_count [DecidableEq ι] (s : Multiset ι) {M : Type*} [
 @[to_additive]
 theorem prod_multiset_count [DecidableEq M] (s : Multiset M) :
     s.prod = ∏ m ∈ s.toFinset, m ^ s.count m := by
-  convert prod_multiset_map_count s id
+  convert! prod_multiset_map_count s id
   rw [Multiset.map_id]
 
 @[to_additive]
diff --git a/Mathlib/Algebra/BigOperators/Group/Finset/Defs.lean b/Mathlib/Algebra/BigOperators/Group/Finset/Defs.lean
index 8c0c7daef6d965..5581009ca29a22 100644
--- a/Mathlib/Algebra/BigOperators/Group/Finset/Defs.lean
+++ b/Mathlib/Algebra/BigOperators/Group/Finset/Defs.lean
@@ -400,13 +400,13 @@ end ToList
 @[to_additive]
 theorem _root_.Equiv.Perm.prod_comp (σ : Equiv.Perm ι) (s : Finset ι) (f : ι → M)
     (hs : { a | σ a ≠ a } ⊆ s) : (∏ x ∈ s, f (σ x)) = ∏ x ∈ s, f x := by
-  convert (prod_map s σ.toEmbedding f).symm
+  convert! (prod_map s σ.toEmbedding f).symm
   exact (map_perm hs).symm
 
 @[to_additive]
 theorem _root_.Equiv.Perm.prod_comp' (σ : Equiv.Perm ι) (s : Finset ι) (f : ι → ι → M)
     (hs : { a | σ a ≠ a } ⊆ s) : (∏ x ∈ s, f (σ x) x) = ∏ x ∈ s, f x (σ.symm x) := by
-  convert σ.prod_comp s (fun x => f x (σ.symm x)) hs
+  convert! σ.prod_comp s (fun x => f x (σ.symm x)) hs
   rw [Equiv.symm_apply_apply]
 
 end CommMonoid
@@ -782,7 +782,7 @@ theorem disjoint_sum_right {a : Multiset α} {i : Multiset (Multiset α)} :
 
 theorem disjoint_finsetSum_left {i : Finset ι} {f : ι → Multiset α} {a : Multiset α} :
     Disjoint (i.sum f) a ↔ ∀ b ∈ i, Disjoint (f b) a := by
-  convert @disjoint_sum_left _ a (map f i.val)
+  convert! @disjoint_sum_left _ a (map f i.val)
   simp
 
 @[deprecated (since := "2026-04-08")] alias disjoint_finset_sum_left := disjoint_finsetSum_left
diff --git a/Mathlib/Algebra/BigOperators/Group/Finset/Piecewise.lean b/Mathlib/Algebra/BigOperators/Group/Finset/Piecewise.lean
index 79ee76108083fb..ef8a3fbe8da4e4 100644
--- a/Mathlib/Algebra/BigOperators/Group/Finset/Piecewise.lean
+++ b/Mathlib/Algebra/BigOperators/Group/Finset/Piecewise.lean
@@ -184,14 +184,14 @@ theorem prod_piecewise [DecidableEq ι] (s t : Finset ι) (f g : ι → M) :
 @[to_additive]
 theorem prod_inter_mul_prod_diff [DecidableEq ι] (s t : Finset ι) (f : ι → M) :
     (∏ x ∈ s ∩ t, f x) * ∏ x ∈ s \ t, f x = ∏ x ∈ s, f x := by
-  convert (s.prod_piecewise t f f).symm
+  convert! (s.prod_piecewise t f f).symm
   simp +unfoldPartialApp [Finset.piecewise]
 
 @[to_additive]
 theorem prod_eq_mul_prod_diff_singleton [DecidableEq ι] {s : Finset ι} (i : ι) (f : ι → M)
     (h : i ∉ s → f i = 1) : ∏ x ∈ s, f x = f i * ∏ x ∈ s \ {i}, f x := by
   by_cases hs : i ∈ s
-  · convert (s.prod_inter_mul_prod_diff {i} f).symm
+  · convert! (s.prod_inter_mul_prod_diff { i } f).symm
     simp [hs]
   · simp_all only [not_false_eq_true, forall_const, one_mul]
     apply Finset.prod_congr <;> aesop
diff --git a/Mathlib/Algebra/BigOperators/Group/List/Basic.lean b/Mathlib/Algebra/BigOperators/Group/List/Basic.lean
index ab99b94bf57ebc..87538fdb3643ae 100644
--- a/Mathlib/Algebra/BigOperators/Group/List/Basic.lean
+++ b/Mathlib/Algebra/BigOperators/Group/List/Basic.lean
@@ -306,7 +306,7 @@ lemma eq_of_prod_take_eq [LeftCancelMonoid M] {L L' : List M} (h : L.length = L'
   refine ext_get h fun i h₁ h₂ => ?_
   have : (L.take (i + 1)).prod = (L'.take (i + 1)).prod := h' _ (Nat.succ_le_of_lt h₁)
   rw [prod_take_succ L i h₁, prod_take_succ L' i h₂, h' i (Nat.le_of_lt h₁)] at this
-  convert mul_left_cancel this
+  convert! mul_left_cancel this
 
 section Group
 
diff --git a/Mathlib/Algebra/BigOperators/Group/Multiset/Basic.lean b/Mathlib/Algebra/BigOperators/Group/Multiset/Basic.lean
index c90841397d546a..a4f7d95f92c9c3 100644
--- a/Mathlib/Algebra/BigOperators/Group/Multiset/Basic.lean
+++ b/Mathlib/Algebra/BigOperators/Group/Multiset/Basic.lean
@@ -93,7 +93,7 @@ theorem prod_hom (s : Multiset M) {F : Type*} [FunLike F M N]
 theorem prod_hom' (s : Multiset ι) {F : Type*} [FunLike F M N]
     [MonoidHomClass F M N] (f : F)
     (g : ι → M) : (s.map fun i => f <| g i).prod = f (s.map g).prod := by
-  convert (s.map g).prod_hom f
+  convert! (s.map g).prod_hom f
   exact (map_map _ _ _).symm
 
 @[to_additive]
@@ -197,7 +197,7 @@ theorem prod_map_div : (m.map fun i => f i / g i).prod = (m.map f).prod / (m.map
 
 @[to_additive]
 theorem prod_map_zpow {n : ℤ} : (m.map fun i => f i ^ n).prod = (m.map f).prod ^ n := by
-  convert (m.map f).prod_hom (zpowGroupHom n : G →* G)
+  convert! (m.map f).prod_hom (zpowGroupHom n : G →* G)
   simp only [map_map, Function.comp_apply, zpowGroupHom_apply]
 
 end DivisionCommMonoid
diff --git a/Mathlib/Algebra/BigOperators/Intervals.lean b/Mathlib/Algebra/BigOperators/Intervals.lean
index 936f8892405154..ca21305873a8e0 100644
--- a/Mathlib/Algebra/BigOperators/Intervals.lean
+++ b/Mathlib/Algebra/BigOperators/Intervals.lean
@@ -38,7 +38,7 @@ theorem prod_Ico_add' [AddCommMonoid α] [PartialOrder α] [IsOrderedCancelAddMo
 theorem prod_Ico_add [AddCommMonoid α] [PartialOrder α] [IsOrderedCancelAddMonoid α]
     [ExistsAddOfLE α] [LocallyFiniteOrder α]
     (f : α → M) (a b c : α) : (∏ x ∈ Ico a b, f (c + x)) = ∏ x ∈ Ico (a + c) (b + c), f x := by
-  convert prod_Ico_add' f a b c using 2
+  convert! prod_Ico_add' f a b c using 2
   rw [add_comm]
 
 @[to_additive (attr := simp)]
@@ -256,8 +256,8 @@ lemma Finset.prod_fin_Icc_eq_prod_nat_Icc [CommMonoid α] {n : ℕ} (a b : Fin n
 lemma Fin.prod_Iic_div [CommGroup M] {n : ℕ} (a : Fin n) (f : Fin (n + 1) → M) :
     ∏ i ∈ Iic a, (f i.succ / f i.castSucc) = f a.succ / f 0 := by
   rw [← prod_ite_mem_eq, prod_fin_eq_prod_range]
-  convert prod_range_div (fun i ↦ if hi : i < n + 1 then f ⟨i, hi⟩ else 1) (a + 1)
-    using 1 with k hk
+  convert! prod_range_div (fun i ↦ if hi : i < n + 1 then f ⟨i, hi⟩ else 1) (a + 1) using 1 with k
+    hk
   · exact prod_congr_of_eq_on_inter (by grind) (by grind) (by simp_all; grind)
   · grind
 
@@ -267,7 +267,7 @@ lemma Fin.prod_Icc_div [CommGroup M] {n : ℕ} {a b : Fin n} (hab : a ≤ b)
     (f : Fin (n + 1) → M) :
     ∏ i ∈ Icc a b, (f i.succ / f i.castSucc) = f b.succ / f a.castSucc := by
   rw [prod_fin_Icc_eq_prod_nat_Icc]
-  convert Finset.prod_Icc_div (Fin.le_def.1 hab) (fun i ↦ if hi : i < n + 1 then f ⟨i, hi⟩ else 1)
+  convert! Finset.prod_Icc_div (Fin.le_def.1 hab) (fun i ↦ if hi : i < n + 1 then f ⟨i, hi⟩ else 1)
   · simp_all
     grind
   · grind
diff --git a/Mathlib/Algebra/BigOperators/Pi.lean b/Mathlib/Algebra/BigOperators/Pi.lean
index 5e4db3a80f1724..ef5f7165e1941d 100644
--- a/Mathlib/Algebra/BigOperators/Pi.lean
+++ b/Mathlib/Algebra/BigOperators/Pi.lean
@@ -71,7 +71,7 @@ theorem pi_eq_sum_univ {ι : Type*} [Fintype ι] [DecidableEq ι] {R : Type*} [N
 /-- Decomposing `x : ι → R` as a sum along the canonical basis `Pi.single i 1` for `i : ι`. -/
 theorem pi_eq_sum_univ' {ι : Type*} [Fintype ι] [DecidableEq ι] {R : Type*} [NonAssocSemiring R]
     (x : ι → R) : x = ∑ i, (x i) • Pi.single (M := fun _ ↦ R) i 1 := by
-  convert pi_eq_sum_univ x
+  convert! pi_eq_sum_univ x
   aesop
 
 section CommSemiring
@@ -227,6 +227,6 @@ theorem eqOn_finsetProd {ι α β : Type*} [CommMonoid α]
 theorem eqOn_fun_finsetProd {ι α β : Type*} [CommMonoid α]
     {s : Set β} {f f' : ι → β → α} (h : ∀ (i : ι), Set.EqOn (f i) (f' i) s) (v : Finset ι) :
     Set.EqOn (fun b ↦ ∏ i ∈ v, f i b) (fun b ↦ ∏ i ∈ v, f' i b) s := by
-  convert eqOn_finsetProd h v <;> simp
+  convert! eqOn_finsetProd h v <;> simp
 
 end EqOn
diff --git a/Mathlib/Algebra/BigOperators/Ring/Finset.lean b/Mathlib/Algebra/BigOperators/Ring/Finset.lean
index 2ee8d72944e41c..321296c1a7d889 100644
--- a/Mathlib/Algebra/BigOperators/Ring/Finset.lean
+++ b/Mathlib/Algebra/BigOperators/Ring/Finset.lean
@@ -164,7 +164,7 @@ lemma sum_prod_piFinset [Fintype ι] (s : Finset κ) (g : ι → κ → R) :
 
 lemma sum_pow' (s : Finset κ) (f : κ → R) (n : ℕ) :
     (∑ a ∈ s, f a) ^ n = ∑ p ∈ piFinset fun _i : Fin n ↦ s, ∏ i, f (p i) := by
-  convert @prod_univ_sum (Fin n) _ _ _ _ _ (fun _i ↦ s) fun _i d ↦ f d; simp
+  convert! @prod_univ_sum (Fin n) _ _ _ _ _ (fun _i ↦ s) fun _i d ↦ f d; simp
 
 /-- The product of `f a + g a` over all of `s` is the sum over the powerset of `s` of the product of
 `f` over a subset `t` times the product of `g` over the complement of `t` -/
@@ -266,7 +266,7 @@ lemma prod_sub_ordered [LinearOrder ι] (s : Finset ι) (f g : ι → R) :
       (∏ i ∈ s, f i) -
         ∑ i ∈ s, g i * (∏ j ∈ s with j < i, (f j - g j)) * ∏ j ∈ s with i < j, f j := by
   simp only [sub_eq_add_neg]
-  convert prod_add_ordered s f fun i => -g i
+  convert! prod_add_ordered s f fun i => -g i
   simp
 
 /-- `∏ i, (1 - f i) = 1 - ∑ i, f i * (∏ j < i, 1 - f j)`. This formula is useful in construction of
diff --git a/Mathlib/Algebra/Category/Grp/EpiMono.lean b/Mathlib/Algebra/Category/Grp/EpiMono.lean
index b18633df0d6b3a..441946c54d9b03 100644
--- a/Mathlib/Algebra/Category/Grp/EpiMono.lean
+++ b/Mathlib/Algebra/Category/Grp/EpiMono.lean
@@ -245,7 +245,7 @@ theorem h_apply_fromCoset_nin_range (x : B) (hx : x ∈ f.hom.range) (b : B) (hb
       (fromCoset ⟨b • ↑f.hom.range, b, rfl⟩) (fromCoset_ne_of_nin_range _ hb) (by simp)]
   simp only [g_apply_fromCoset, leftCoset_assoc]
   refine Equiv.swap_apply_of_ne_of_ne (fromCoset_ne_of_nin_range _ fun r => hb ?_) (by simp)
-  convert Subgroup.mul_mem _ (Subgroup.inv_mem _ hx) r
+  convert! Subgroup.mul_mem _ (Subgroup.inv_mem _ hx) r
   rw [← mul_assoc, inv_mul_cancel, one_mul]
 
 theorem agree : f.hom.range = { x | h x = g x } := by
diff --git a/Mathlib/Algebra/Category/Grp/ZModuleEquivalence.lean b/Mathlib/Algebra/Category/Grp/ZModuleEquivalence.lean
index 9fee49a7fe3309..0bd7d8a74a67f4 100644
--- a/Mathlib/Algebra/Category/Grp/ZModuleEquivalence.lean
+++ b/Mathlib/Algebra/Category/Grp/ZModuleEquivalence.lean
@@ -35,7 +35,7 @@ instance forget₂_addCommGroup_full : (forget₂ (ModuleCat ℤ) AddCommGrpCat.
             { toFun := f,
               map_add' := map_add f.hom }
             (fun n x => by
-              convert AddMonoidHom.map_zsmul f.hom n x <;>
+              convert! AddMonoidHom.map_zsmul f.hom n x <;>
                 ext <;> apply int_smul_eq_zsmul), rfl⟩
 
 /-- The forgetful functor from `ℤ` modules to `AddCommGrpCat` is essentially surjective. -/
diff --git a/Mathlib/Algebra/Category/ModuleCat/Descent.lean b/Mathlib/Algebra/Category/ModuleCat/Descent.lean
index b63d64b4b6aeef..f5bb399eb354fd 100644
--- a/Mathlib/Algebra/Category/ModuleCat/Descent.lean
+++ b/Mathlib/Algebra/Category/ModuleCat/Descent.lean
@@ -60,7 +60,8 @@ def comonadicExtendScalars (hf : f.FaithfullyFlat) :
     ComonadicLeftAdjoint (extendScalars f) := by
   have := preservesFiniteLimits_extendScalars_of_flat hf.flat
   have := reflectsIsomorphisms_extendScalars_of_faithfullyFlat hf
-  convert Comonad.comonadicOfHasPreservesFSplitEqualizersOfReflectsIsomorphisms
+  convert!
+    Comonad.comonadicOfHasPreservesFSplitEqualizersOfReflectsIsomorphisms
       (extendRestrictScalarsAdj f)
   · exact ⟨inferInstance⟩
   · exact ⟨inferInstance⟩
diff --git a/Mathlib/Algebra/Category/ModuleCat/EpiMono.lean b/Mathlib/Algebra/Category/ModuleCat/EpiMono.lean
index aa4917794699a3..a9a88bee1e05ce 100644
--- a/Mathlib/Algebra/Category/ModuleCat/EpiMono.lean
+++ b/Mathlib/Algebra/Category/ModuleCat/EpiMono.lean
@@ -38,14 +38,14 @@ theorem range_eq_top_of_epi [Epi f] : LinearMap.range f.hom = ⊤ :=
 
 theorem mono_iff_ker_eq_bot : Mono f ↔ LinearMap.ker f.hom = ⊥ :=
   ⟨fun _ => ker_eq_bot_of_mono _, fun hf =>
-    ConcreteCategory.mono_of_injective _ <| by convert LinearMap.ker_eq_bot.1 hf⟩
+    ConcreteCategory.mono_of_injective _ <| by convert! LinearMap.ker_eq_bot.1 hf⟩
 
 theorem mono_iff_injective : Mono f ↔ Function.Injective f := by
   rw [mono_iff_ker_eq_bot, LinearMap.ker_eq_bot]
 
 theorem epi_iff_range_eq_top : Epi f ↔ LinearMap.range f.hom = ⊤ :=
   ⟨fun _ => range_eq_top_of_epi _, fun hf =>
-    ConcreteCategory.epi_of_surjective _ <| by convert LinearMap.range_eq_top.1 hf⟩
+    ConcreteCategory.epi_of_surjective _ <| by convert! LinearMap.range_eq_top.1 hf⟩
 
 theorem epi_iff_surjective : Epi f ↔ Function.Surjective f := by
   rw [epi_iff_range_eq_top, LinearMap.range_eq_top]
diff --git a/Mathlib/Algebra/Category/ModuleCat/Free.lean b/Mathlib/Algebra/Category/ModuleCat/Free.lean
index 8db2775319996f..7b4c01add2785e 100644
--- a/Mathlib/Algebra/Category/ModuleCat/Free.lean
+++ b/Mathlib/Algebra/Category/ModuleCat/Free.lean
@@ -84,7 +84,7 @@ theorem linearIndependent_shortExact {w : ι' → S.X₃} (hw : LinearIndependen
     LinearIndependent R (Sum.elim (S.f ∘ v) (S.g.hom.toFun.invFun ∘ w)) := by
   apply linearIndependent_leftExact hS'.exact hv _ hS'.mono_f rfl
   dsimp
-  convert hw
+  convert! hw
   ext
   apply Function.rightInverse_invFun ((epi_iff_surjective _).mp hS'.epi_g)
 
@@ -144,7 +144,7 @@ theorem span_rightExact {w : ι' → S.X₃} (hv : ⊤ ≤ span R (range v))
     ⊤ ≤ span R (range (Sum.elim (S.f ∘ v) (S.g.hom.toFun.invFun ∘ w))) := by
   refine span_exact hS ?_ hv ?_
   · simp only [AddHom.toFun_eq_coe, LinearMap.coe_toAddHom, Sum.elim_comp_inl]
-  · convert hw
+  · convert! hw
     simp only [AddHom.toFun_eq_coe, LinearMap.coe_toAddHom, Sum.elim_comp_inr]
     rw [ModuleCat.epi_iff_surjective] at hE
     rw [← Function.comp_assoc, Function.RightInverse.comp_eq_id (Function.rightInverse_invFun hE),
diff --git a/Mathlib/Algebra/Category/ModuleCat/Sheaf/PullbackFree.lean b/Mathlib/Algebra/Category/ModuleCat/Sheaf/PullbackFree.lean
index c4fecc4bd5cd51..8fb91292c0d3f0 100644
--- a/Mathlib/Algebra/Category/ModuleCat/Sheaf/PullbackFree.lean
+++ b/Mathlib/Algebra/Category/ModuleCat/Sheaf/PullbackFree.lean
@@ -107,7 +107,7 @@ instance [F.Final] : IsIso (pullbackObjUnitToUnit φ) := by
   intro M
   rw [← ((pullbackPushforwardAdjunction.{u} φ).homEquiv _ _).bijective.of_comp_iff',
     ← (unitHomEquiv _).bijective.of_comp_iff']
-  convert (bijective_pushforwardSections φ M).comp (unitHomEquiv _).bijective
+  convert! (bijective_pushforwardSections φ M).comp (unitHomEquiv _).bijective
   ext f : 1
   dsimp
   rw [pushforwardSections_unitHomEquiv, EmbeddingLike.apply_eq_iff_eq,
diff --git a/Mathlib/Algebra/Category/ModuleCat/Subobject.lean b/Mathlib/Algebra/Category/ModuleCat/Subobject.lean
index 81560275d7964c..01e1f412cfaecc 100644
--- a/Mathlib/Algebra/Category/ModuleCat/Subobject.lean
+++ b/Mathlib/Algebra/Category/ModuleCat/Subobject.lean
@@ -47,8 +47,9 @@ noncomputable def subobjectModule : Subobject M ≃o Submodule R M :=
         · ext x
           rfl)
       left_inv := fun N => by
-        convert congr_arg LinearMap.range (ModuleCat.hom_ext_iff.mp
-            (underlyingIso_arrow (ofHom N.subtype))) using 1
+        convert!
+          congr_arg LinearMap.range
+            (ModuleCat.hom_ext_iff.mp (underlyingIso_arrow (ofHom N.subtype))) using 1
         · have :
             (underlyingIso (ofHom N.subtype)).inv =
               ofHom (underlyingIso (ofHom N.subtype)).symm.toLinearEquiv.toLinearMap := by
@@ -58,7 +59,7 @@ noncomputable def subobjectModule : Subobject M ≃o Submodule R M :=
         · exact (Submodule.range_subtype _).symm
       map_rel_iff' := fun {S T} => by
         refine ⟨fun h => ?_, fun h => mk_le_mk_of_comm (↟(Submodule.inclusion h)) rfl⟩
-        convert LinearMap.range_comp_le_range (ofMkLEMk _ _ h).hom (ofHom T.subtype).hom
+        convert! LinearMap.range_comp_le_range (ofMkLEMk _ _ h).hom (ofHom T.subtype).hom
         · rw [← hom_comp, ofMkLEMk_comp]
           exact (Submodule.range_subtype _).symm
         · exact (Submodule.range_subtype _).symm }
diff --git a/Mathlib/Algebra/Category/ModuleCat/Topology/Basic.lean b/Mathlib/Algebra/Category/ModuleCat/Topology/Basic.lean
index b628050da40e5a..15fa2d48b8b7e6 100644
--- a/Mathlib/Algebra/Category/ModuleCat/Topology/Basic.lean
+++ b/Mathlib/Algebra/Category/ModuleCat/Topology/Basic.lean
@@ -52,7 +52,7 @@ attribute [instance] topologicalSpace isTopologicalAddGroup continuousSMul
 /-- Make an object in `TopModuleCat R` from an unbundled topological module. -/
 abbrev of (M : Type v) [AddCommGroup M] [Module R M] [TopologicalSpace M] [ContinuousAdd M]
     [ContinuousSMul R M] : TopModuleCat R :=
-  have : ContinuousNeg M := ⟨by convert continuous_const_smul (-1 : R) (T := M); ext; simp⟩
+  have : ContinuousNeg M := ⟨by convert! continuous_const_smul (-1 : R) (T := M); ext; simp⟩
   have : IsTopologicalAddGroup M := ⟨⟩
   ⟨.of R M⟩
 
@@ -447,7 +447,7 @@ def freeAdj : free.{max v u} R ⊣ forget₂ (TopModuleCat.{max v u} R) TopCat.{
       refine sInf_le ⟨continuousSMul_induced (Finsupp.lift _ R X id),
         continuousAdd_induced (Finsupp.lift _ R X id), ?_⟩
       rw [coinduced_le_iff_le_induced, induced_compose]
-      convert induced_id.symm.le
+      convert! induced_id.symm.le
       ext
       simp [coe_freeObj]⟩,
     naturality {X Y} f := by
diff --git a/Mathlib/Algebra/Category/Ring/Instances.lean b/Mathlib/Algebra/Category/Ring/Instances.lean
index c84965f0c2bddb..f7bab1f53e7db6 100644
--- a/Mathlib/Algebra/Category/Ring/Instances.lean
+++ b/Mathlib/Algebra/Category/Ring/Instances.lean
@@ -48,7 +48,7 @@ theorem CommRingCat.isLocalHom_comp {R S T : CommRingCat} (f : R ⟶ S) (g : S 
 
 theorem isLocalHom_of_iso {R S : CommRingCat} (f : R ≅ S) : IsLocalHom f.hom.hom :=
   { map_nonunit := fun a ha => by
-      convert f.inv.hom.isUnit_map ha
+      convert! f.inv.hom.isUnit_map ha
       simp }
 
 -- see Note [lower instance priority]
diff --git a/Mathlib/Algebra/Category/Ring/Topology.lean b/Mathlib/Algebra/Category/Ring/Topology.lean
index aa7885d7d76426..0091d90b2d3289 100644
--- a/Mathlib/Algebra/Category/Ring/Topology.lean
+++ b/Mathlib/Algebra/Category/Ring/Topology.lean
@@ -97,7 +97,7 @@ lemma isClosedEmbedding_precomp_of_surjective
   refine ⟨isEmbedding_precomp_of_surjective f hf, ?_⟩
   have : IsClosed (⋂ i : RingHom.ker f.hom, { f : A ⟶ R | f i = 0 }) :=
     isClosed_iInter fun x ↦ (isClosed_singleton (x := 0)).preimage (continuous_apply (R := R) x.1)
-  convert this
+  convert! this
   ext x
   simp only [Set.mem_range, Set.mem_iInter, Set.mem_setOf_eq, Subtype.forall, RingHom.mem_ker]
   constructor
@@ -130,9 +130,11 @@ lemma isClosedEmbedding_hom [IsTopologicalRing R] [T1Space R] :
   let f : CommRingCat.of (MvPolynomial A (⊥_ CommRingCat)) ⟶ A :=
     CommRingCat.ofHom (MvPolynomial.eval₂Hom (initial.to A).hom id)
   have : Function.Surjective f := Function.LeftInverse.surjective (g := .X) fun x ↦ by simp [f]
-  convert ((mvPolynomialHomeomorph A R (.of _)).trans
-    (.uniqueProd (⊥_ CommRingCat ⟶ R) _)).isClosedEmbedding.comp
-    (isClosedEmbedding_precomp_of_surjective f this) using 2 with g
+  convert!
+    ((mvPolynomialHomeomorph A R (.of _)).trans
+          (.uniqueProd (⊥_ CommRingCat ⟶ R) _)).isClosedEmbedding.comp
+      (isClosedEmbedding_precomp_of_surjective f this) using
+    2 with g
   ext x
   simp +instances [f]
 
@@ -177,8 +179,9 @@ lemma isEmbedding_pushout [IsTopologicalRing R] (φ : A ⟶ B) (ψ : A ⟶ C) :
     ((isEmbedding_graph continuous_id).prodMap Homeomorph.sumArrowHomeomorphProdArrow.isEmbedding)
   have H := (mvPolynomialHomeomorph B R A).symm.isEmbedding.prodMap
     (mvPolynomialHomeomorph C R A).symm.isEmbedding
-  convert ((H.comp hF).comp (mvPolynomialHomeomorph _ R A).isEmbedding).comp
-    (isEmbedding_precomp_of_surjective (R := R) fBC hfBC)
+  convert!
+    ((H.comp hF).comp (mvPolynomialHomeomorph _ R A).isEmbedding).comp
+      (isEmbedding_precomp_of_surjective (R := R) fBC hfBC)
   have (s : _) : (pushout.inr φ ψ).hom (ψ.hom s) = (pushout.inl φ ψ).hom (φ.hom s) :=
     congr($(pushout.condition (f := φ)).hom s).symm
   ext f s <;> simp [fB, fC, fBC, PB, PC, PBC, F, this]
diff --git a/Mathlib/Algebra/CharP/Basic.lean b/Mathlib/Algebra/CharP/Basic.lean
index 6cc0ef06bd00f9..41e04d7a60168d 100644
--- a/Mathlib/Algebra/CharP/Basic.lean
+++ b/Mathlib/Algebra/CharP/Basic.lean
@@ -145,7 +145,7 @@ instance Nat.lcm.charP [CharP S q] : CharP (R × S) (Nat.lcm p q) where
 /-- The characteristic of the product of two rings of the same characteristic
   is the same as the characteristic of the rings -/
 instance Prod.charP [CharP S p] : CharP (R × S) p := by
-  convert Nat.lcm.charP R S p p; simp
+  convert! Nat.lcm.charP R S p p; simp
 
 instance Prod.charZero_of_left [CharZero R] : CharZero (R × S) where
   cast_injective _ _ h := CharZero.cast_injective congr(Prod.fst $h)
diff --git a/Mathlib/Algebra/CharP/Invertible.lean b/Mathlib/Algebra/CharP/Invertible.lean
index 1ffa05c0ca238b..7b36b94527fc62 100644
--- a/Mathlib/Algebra/CharP/Invertible.lean
+++ b/Mathlib/Algebra/CharP/Invertible.lean
@@ -66,7 +66,7 @@ def invertibleOfCoprime {n : ℕ} (h : n.Coprime p) :
 theorem invOf_eq_of_coprime {n : ℕ} [Invertible (n : R)] (h : n.Coprime p) :
     ⅟(n : R) = n.gcdA p := by
   letI : Invertible (n : R) := invertibleOfCoprime h
-  convert (rfl : ⅟(n : R) = _)
+  convert! (rfl : ⅟(n : R) = _)
 
 theorem CharP.isUnit_natCast_iff {n : ℕ} (hp : p.Prime) : IsUnit (n : R) ↔ ¬p ∣ n where
   mp h := by
diff --git a/Mathlib/Algebra/CharP/MixedCharZero.lean b/Mathlib/Algebra/CharP/MixedCharZero.lean
index 9e2ea58e82ce6f..6d184970dc9fdb 100644
--- a/Mathlib/Algebra/CharP/MixedCharZero.lean
+++ b/Mathlib/Algebra/CharP/MixedCharZero.lean
@@ -126,10 +126,10 @@ lemma reduce_to_maximal_ideal {p : ℕ} (hp : Nat.Prime p) :
     · exact hM_max
     · cases CharP.exists (R ⧸ M) with
       | intro r hr =>
-        convert hr
+        convert! hr
         have r_dvd_p : r ∣ p := by
           rw [← CharP.cast_eq_zero_iff (R ⧸ M) r p]
-          convert congr_arg (Ideal.Quotient.factor hM_ge) (CharP.cast_eq_zero (R ⧸ I) p)
+          convert! congr_arg (Ideal.Quotient.factor hM_ge) (CharP.cast_eq_zero (R ⧸ I) p)
         symm
         apply (Nat.Prime.eq_one_or_self_of_dvd hp r r_dvd_p).resolve_left
         exact CharP.char_ne_one (R ⧸ M) r
diff --git a/Mathlib/Algebra/CharP/Reduced.lean b/Mathlib/Algebra/CharP/Reduced.lean
index d6155a4a33388f..73cbf0284089b8 100644
--- a/Mathlib/Algebra/CharP/Reduced.lean
+++ b/Mathlib/Algebra/CharP/Reduced.lean
@@ -45,5 +45,5 @@ variable {R : Type*} [CommRing R] [IsReduced R]
 theorem ExpChar.pow_prime_pow_mul_eq_one_iff (p k m : ℕ) [ExpChar R p] (x : R) :
     x ^ (p ^ k * m) = 1 ↔ x ^ m = 1 := by
   rw [pow_mul']
-  convert ← (iterateFrobenius_inj R p k).eq_iff
+  convert! ← (iterateFrobenius_inj R p k).eq_iff
   apply map_one
diff --git a/Mathlib/Algebra/Colimit/Module.lean b/Mathlib/Algebra/Colimit/Module.lean
index 2d4596841a34ad..55ff912d75383f 100644
--- a/Mathlib/Algebra/Colimit/Module.lean
+++ b/Mathlib/Algebra/Colimit/Module.lean
@@ -271,7 +271,7 @@ theorem exists_eq_of_of_eq {i x y} (h : of R ι G f i x = of R ι G f i y) :
 bigger module in the directed system. -/
 theorem of.zero_exact {i x} (H : of R ι G f i x = 0) :
     ∃ j hij, f i j hij x = (0 : G j) := by
-  convert exists_eq_of_of_eq (H.trans (map_zero <| _).symm)
+  convert! exists_eq_of_of_eq (H.trans (map_zero <| _).symm)
   rw [map_zero]
 
 end DirectLimit
diff --git a/Mathlib/Algebra/DirectSum/LinearMap.lean b/Mathlib/Algebra/DirectSum/LinearMap.lean
index 4cb9d438df2c70..23b8e8137f2fc3 100644
--- a/Mathlib/Algebra/DirectSum/LinearMap.lean
+++ b/Mathlib/Algebra/DirectSum/LinearMap.lean
@@ -92,7 +92,7 @@ lemma trace_eq_zero_of_mapsTo_ne (h : IsInternal N) [IsNoetherian R M]
   let κ := fun i ↦ Module.Free.ChooseBasisIndex R (N i)
   let b : (i : s) → Basis (κ i) R (N i) := fun i ↦ Module.Free.chooseBasis R (N i)
   replace h : IsInternal fun i : s ↦ N i := by
-    convert DirectSum.isInternal_ne_bot_iff.mpr h <;> simp [s]
+    convert! DirectSum.isInternal_ne_bot_iff.mpr h <;> simp [s]
   simp_rw [trace_eq_matrix_trace R (h.collectedBasis b), Matrix.trace,
     diag_toMatrix_directSum_collectedBasis_eq_zero_of_mapsTo_ne h b σ hσ hf (by simp [s]),
     Pi.zero_apply, Finset.sum_const_zero]
diff --git a/Mathlib/Algebra/DirectSum/Module.lean b/Mathlib/Algebra/DirectSum/Module.lean
index e10dff85371f95..3ccff212babf6b 100644
--- a/Mathlib/Algebra/DirectSum/Module.lean
+++ b/Mathlib/Algebra/DirectSum/Module.lean
@@ -348,7 +348,7 @@ variable [DecidableEq ι] [∀ i j, AddCommMonoid (δ i j)] [∀ i j, Module R (
 
 /-- `curry` as a linear map. -/
 def sigmaLcurry : (⨁ i : Σ _, _, δ i.1 i.2) →ₗ[R] ⨁ (i) (j), δ i j :=
-  { sigmaCurry with map_smul' := fun r ↦ by convert DFinsupp.sigmaCurry_smul (δ := δ) r }
+  { sigmaCurry with map_smul' := fun r ↦ by convert! DFinsupp.sigmaCurry_smul (δ := δ) r }
 
 @[simp]
 theorem sigmaLcurry_apply (f : ⨁ i : Σ _, _, δ i.1 i.2) (i : ι) (j : α i) :
diff --git a/Mathlib/Algebra/Field/IsField.lean b/Mathlib/Algebra/Field/IsField.lean
index 95650bb70874d0..69710a3312cc6f 100644
--- a/Mathlib/Algebra/Field/IsField.lean
+++ b/Mathlib/Algebra/Field/IsField.lean
@@ -77,7 +77,7 @@ noncomputable def IsField.toSemifield {R : Type u} [Semiring R] (h : IsField R)
   __ := h
   inv a := if ha : a = 0 then 0 else Classical.choose (h.mul_inv_cancel ha)
   inv_zero := dif_pos rfl
-  mul_inv_cancel a ha := by convert Classical.choose_spec (h.mul_inv_cancel ha); exact dif_neg ha
+  mul_inv_cancel a ha := by convert! Classical.choose_spec (h.mul_inv_cancel ha); exact dif_neg ha
   nnqsmul := _
   nnqsmul_def _ _ := rfl
 
diff --git a/Mathlib/Algebra/Field/Subfield/Basic.lean b/Mathlib/Algebra/Field/Subfield/Basic.lean
index 0f34ab90c7b2b1..8535be0b023ae4 100644
--- a/Mathlib/Algebra/Field/Subfield/Basic.lean
+++ b/Mathlib/Algebra/Field/Subfield/Basic.lean
@@ -275,7 +275,7 @@ theorem sInf_toSubring (s : Set (Subfield K)) :
 theorem isGLB_sInf (S : Set (Subfield K)) : IsGLB S (sInf S) := by
   have : ∀ {s t : Subfield K}, (s : Set K) ≤ t ↔ s ≤ t := by simp [SetLike.coe_subset_coe]
   refine IsGLB.of_image this ?_
-  convert isGLB_biInf (s := S) (f := SetLike.coe)
+  convert! isGLB_biInf (s := S) (f := SetLike.coe)
   exact coe_sInf _
 
 /-- Subfields of a ring form a complete lattice. -/
diff --git a/Mathlib/Algebra/GCDMonoid/Basic.lean b/Mathlib/Algebra/GCDMonoid/Basic.lean
index b269f4d38a43e6..5c5fb38a783f39 100644
--- a/Mathlib/Algebra/GCDMonoid/Basic.lean
+++ b/Mathlib/Algebra/GCDMonoid/Basic.lean
@@ -624,7 +624,7 @@ theorem isUnit_gcd_of_eq_mul_gcd {α : Type*} [CommMonoidWithZero α] [GCDMonoid
     IsUnit (gcd x' y') := by
   rw [← associated_one_iff_isUnit]
   refine Associated.of_mul_left ?_ (Associated.refl <| gcd x y) h
-  convert (gcd_mul_left' (gcd x y) x' y').symm using 1
+  convert! (gcd_mul_left' (gcd x y) x' y').symm using 1
   rw [← ex, ← ey, mul_one]
 
 theorem extract_gcd {α : Type*} [CommMonoidWithZero α] [GCDMonoid α] (x y : α) :
diff --git a/Mathlib/Algebra/GCDMonoid/IntegrallyClosed.lean b/Mathlib/Algebra/GCDMonoid/IntegrallyClosed.lean
index dc872600aad875..ecd0c87bd2578b 100644
--- a/Mathlib/Algebra/GCDMonoid/IntegrallyClosed.lean
+++ b/Mathlib/Algebra/GCDMonoid/IntegrallyClosed.lean
@@ -28,7 +28,7 @@ theorem IsLocalization.surj_of_gcd_domain [GCDMonoid R] (M : Submonoid R) [IsLoc
   obtain ⟨x', y', hx', hy', hu⟩ := extract_gcd x y
   use x', y', hu
   rw [mul_comm, IsLocalization.mul_mk'_eq_mk'_of_mul]
-  convert IsLocalization.mk'_mul_cancel_left (M := M) (S := A) _ _ using 2
+  convert! IsLocalization.mk'_mul_cancel_left (M := M) (S := A) _ _ using 2
   grind
 
 instance (priority := 100) GCDMonoid.toIsIntegrallyClosed
diff --git a/Mathlib/Algebra/Group/Action/Basic.lean b/Mathlib/Algebra/Group/Action/Basic.lean
index af1f28cd06a114..c414d3ab2fdfc8 100644
--- a/Mathlib/Algebra/Group/Action/Basic.lean
+++ b/Mathlib/Algebra/Group/Action/Basic.lean
@@ -150,7 +150,7 @@ variable (M α) in
 @[to_additive
 /-- Embedding of `α` into functions `M → α` induced by an additive action of `M` on `α`. -/]
 def toFun : α ↪ M → α :=
-  ⟨fun y x ↦ x • y, fun y₁ y₂ H ↦ one_smul M y₁ ▸ one_smul M y₂ ▸ by convert congr_fun H 1⟩
+  ⟨fun y x ↦ x • y, fun y₁ y₂ H ↦ one_smul M y₁ ▸ one_smul M y₂ ▸ by convert! congr_fun H 1⟩
 
 @[to_additive (attr := simp)]
 lemma toFun_apply (x : M) (y : α) : MulAction.toFun M α y x = x • y := rfl
diff --git a/Mathlib/Algebra/Group/Action/Equidecomp.lean b/Mathlib/Algebra/Group/Action/Equidecomp.lean
index 44183e8a430f6c..c84317733ea596 100644
--- a/Mathlib/Algebra/Group/Action/Equidecomp.lean
+++ b/Mathlib/Algebra/Group/Action/Equidecomp.lean
@@ -191,7 +191,7 @@ theorem IsDecompOn.of_leftInvOn {f g : X → X} {A : Set X} {S : Finset G}
 noncomputable def symm (f : Equidecomp X G) : Equidecomp X G where
   toPartialEquiv := f.toPartialEquiv.symm
   isDecompOn' := by classical exact ⟨f.witness⁻¹, by
-    convert f.isDecompOn.of_leftInvOn f.leftInvOn
+    convert! f.isDecompOn.of_leftInvOn f.leftInvOn
     rw [image_source_eq_target, symm_source]⟩
 
 theorem map_target {f : Equidecomp X G} {x : X} (h : x ∈ f.target) :
diff --git a/Mathlib/Algebra/Group/Fin/Tuple.lean b/Mathlib/Algebra/Group/Fin/Tuple.lean
index 42d22e374e40e8..7d566c015fa76d 100644
--- a/Mathlib/Algebra/Group/Fin/Tuple.lean
+++ b/Mathlib/Algebra/Group/Fin/Tuple.lean
@@ -111,7 +111,7 @@ variable [Zero α]
 @[simp] lemma tail_zero : vecTail (0 : Fin n.succ → α) = 0 := rfl
 
 @[simp] lemma cons_eq_zero_iff {v : Fin n → α} {x : α} : vecCons x v = 0 ↔ x = 0 ∧ v = 0 where
-  mp h := ⟨congr_fun h 0, by convert congr_arg vecTail h⟩
+  mp h := ⟨congr_fun h 0, by convert! congr_arg vecTail h⟩
   mpr := fun ⟨hx, hv⟩ ↦ by simp [hx, hv]
 
 lemma cons_nonzero_iff {v : Fin n → α} {x : α} : vecCons x v ≠ 0 ↔ x ≠ 0 ∨ v ≠ 0 where
diff --git a/Mathlib/Algebra/Group/Finsupp.lean b/Mathlib/Algebra/Group/Finsupp.lean
index 5c98fbc6d8651b..4f87ef389726c9 100644
--- a/Mathlib/Algebra/Group/Finsupp.lean
+++ b/Mathlib/Algebra/Group/Finsupp.lean
@@ -269,7 +269,7 @@ lemma induction₂ {motive : (ι →₀ M) → Prop} (f : ι →₀ M) (zero : m
       a ∉ f.support → b ≠ 0 → motive f → motive (f + single a b)) : motive f := by
   classical
   refine f.induction zero ?_
-  convert add_single using 7
+  convert! add_single using 7
   apply (addCommute_of_disjoint _).eq
   simp_all
 
@@ -315,7 +315,7 @@ lemma induction_on_max₂ (f : ι →₀ M) (zero : motive 0)
       motive f → motive (f + single a b)) : motive f := by
   classical
   refine f.induction_on_max zero ?_
-  convert add_single using 7 with _ _ _ H
+  convert! add_single using 7 with _ _ _ H
   have := fun c hc ↦ (H c hc).ne
   apply (addCommute_of_disjoint _).eq
   simp_all [not_imp_not]
diff --git a/Mathlib/Algebra/Group/ForwardDiff.lean b/Mathlib/Algebra/Group/ForwardDiff.lean
index 0628ecfede324c..2c95d310a551fa 100644
--- a/Mathlib/Algebra/Group/ForwardDiff.lean
+++ b/Mathlib/Algebra/Group/ForwardDiff.lean
@@ -151,7 +151,7 @@ theorem fwdDiff_iter_eq_sum_shift (f : M → G) (n : ℕ) (y : M) :
   rw [← coe_fwdDiffₗ, this, ← Module.End.pow_apply]
   -- use binomial theorem `Commute.add_pow` to expand this
   have : Commute (shiftₗ M G h) (-1) := (Commute.one_right _).neg_right
-  convert congr_fun (LinearMap.congr_fun (this.add_pow n) f) y using 3
+  convert! congr_fun (LinearMap.congr_fun (this.add_pow n) f) y using 3
   · simp only [sub_eq_add_neg]
   · rw [LinearMap.sum_apply, sum_apply]
     congr 1 with k
@@ -174,8 +174,8 @@ of `f` at `y`.
 -/
 theorem shift_eq_sum_fwdDiff_iter (f : M → G) (n : ℕ) (y : M) :
     f (y + n • h) = ∑ k ∈ range (n + 1), n.choose k • Δ_[h]^[k] f y := by
-  convert congr_fun (LinearMap.congr_fun
-      ((Commute.one_right (fwdDiffₗ M G h)).add_pow n) f) y using 1
+  convert!
+    congr_fun (LinearMap.congr_fun ((Commute.one_right (fwdDiffₗ M G h)).add_pow n) f) y using 1
   · rw [← shiftₗ_pow_apply h f, shiftₗ]
   · simp [Module.End.pow_apply, coe_fwdDiffₗ]
 
diff --git a/Mathlib/Algebra/Group/Pointwise/Set/Finite.lean b/Mathlib/Algebra/Group/Pointwise/Set/Finite.lean
index 36e300751f2dbe..835186f78f36a2 100644
--- a/Mathlib/Algebra/Group/Pointwise/Set/Finite.lean
+++ b/Mathlib/Algebra/Group/Pointwise/Set/Finite.lean
@@ -182,7 +182,7 @@ theorem card_pow_eq_card_pow_card_univ [∀ k : ℕ, DecidablePred (· ∈ S ^ k
       apply fintypeMul
     refine Set.eq_of_subset_of_card_le ?_ (le_trans (ge_of_eq h) ?_)
     · exact mul_subset_mul Set.Subset.rfl (Set.singleton_subset_iff.mpr ha)
-    · convert key a (S ^ n) (S ^ n * {a}) fun b hb ↦ Set.mul_mem_mul hb (Set.mem_singleton a)
+    · convert! key a (S ^ n) (S ^ n * { a }) fun b hb ↦ Set.mul_mem_mul hb (Set.mem_singleton a)
   rw [pow_succ', ← h₂, ← mul_assoc, ← pow_succ', h₂, mul_singleton, forall_mem_image]
   intro x hx
   rwa [mul_inv_cancel_right]
diff --git a/Mathlib/Algebra/Group/Subgroup/Defs.lean b/Mathlib/Algebra/Group/Subgroup/Defs.lean
index 097719ec5895a1..f1dd1dd3f60220 100644
--- a/Mathlib/Algebra/Group/Subgroup/Defs.lean
+++ b/Mathlib/Algebra/Group/Subgroup/Defs.lean
@@ -638,7 +638,7 @@ namespace Normal
 @[to_additive]
 theorem conj_mem' (nH : H.Normal) (n : G) (hn : n ∈ H) (g : G) :
     g⁻¹ * n * g ∈ H := by
-  convert nH.conj_mem n hn g⁻¹
+  convert! nH.conj_mem n hn g⁻¹
   rw [inv_inv]
 
 @[to_additive]
diff --git a/Mathlib/Algebra/Group/Subgroup/Ker.lean b/Mathlib/Algebra/Group/Subgroup/Ker.lean
index 6ce710f02a8be2..1aa93164bf554e 100644
--- a/Mathlib/Algebra/Group/Subgroup/Ker.lean
+++ b/Mathlib/Algebra/Group/Subgroup/Ker.lean
@@ -116,7 +116,7 @@ theorem rangeRestrict_surjective (f : G →* N) : Function.Surjective f.rangeRes
 
 @[to_additive (attr := simp)]
 lemma rangeRestrict_injective_iff {f : G →* N} : Injective f.rangeRestrict ↔ Injective f := by
-  convert Set.injective_codRestrict _
+  convert! Set.injective_codRestrict _
 
 @[to_additive]
 theorem map_range (g : N →* P) (f : G →* N) : f.range.map g = (g.comp f).range := by
diff --git a/Mathlib/Algebra/Group/Subgroup/Lattice.lean b/Mathlib/Algebra/Group/Subgroup/Lattice.lean
index d8cecbc566480e..d9e6e73cfe5255 100644
--- a/Mathlib/Algebra/Group/Subgroup/Lattice.lean
+++ b/Mathlib/Algebra/Group/Subgroup/Lattice.lean
@@ -210,7 +210,7 @@ theorem bot_or_nontrivial (H : Subgroup G) : H = ⊥ ∨ Nontrivial H := by
 /-- A subgroup is either the trivial subgroup or contains a non-identity element. -/
 @[to_additive /-- A subgroup is either the trivial subgroup or contains a nonzero element. -/]
 theorem bot_or_exists_ne_one (H : Subgroup G) : H = ⊥ ∨ ∃ x ∈ H, x ≠ (1 : G) := by
-  convert H.bot_or_nontrivial
+  convert! H.bot_or_nontrivial
   rw [nontrivial_iff_exists_ne_one]
 
 @[to_additive]
diff --git a/Mathlib/Algebra/Group/Submonoid/Saturation.lean b/Mathlib/Algebra/Group/Submonoid/Saturation.lean
index 2e6b8f41913b0e..5e1d41a9e8860b 100644
--- a/Mathlib/Algebra/Group/Submonoid/Saturation.lean
+++ b/Mathlib/Algebra/Group/Submonoid/Saturation.lean
@@ -158,7 +158,7 @@ instance : InfSet (SaturatedSubmonoid M) where
     mul_mem' hx hy := by rw [Set.mem_iInter₂] at *; exact fun s hs ↦ mul_mem (hx s hs) (hy s hs)
     one_mem' := Set.mem_iInter₂.mpr fun _ _ ↦ one_mem _
     mulSaturated := by
-      convert Submonoid.MulSaturated.sInf (f := toSubmonoid '' f) (by simp)
+      convert! Submonoid.MulSaturated.sInf (f := toSubmonoid '' f) (by simp)
       ext; simp [Submonoid.mem_sInf] }
 
 @[to_additive]
diff --git a/Mathlib/Algebra/GroupWithZero/Associated.lean b/Mathlib/Algebra/GroupWithZero/Associated.lean
index f954c4071a8ea3..5b82330beb0ace 100644
--- a/Mathlib/Algebra/GroupWithZero/Associated.lean
+++ b/Mathlib/Algebra/GroupWithZero/Associated.lean
@@ -173,7 +173,7 @@ theorem Associated.mul_mul [CommMonoid M] {a₁ a₂ b₁ b₂ : M}
 theorem Associated.pow_pow [CommMonoid M] {a b : M} {n : ℕ} (h : a ~ᵤ b) : a ^ n ~ᵤ b ^ n := by
   induction n with
   | zero => simp [Associated.refl]
-  | succ n ih => convert h.mul_mul ih <;> rw [pow_succ']
+  | succ n ih => convert! h.mul_mul ih <;> rw [pow_succ']
 
 protected theorem Associated.dvd [Monoid M] {a b : M} : a ~ᵤ b → a ∣ b := fun ⟨u, hu⟩ =>
   ⟨u, hu.symm⟩
diff --git a/Mathlib/Algebra/GroupWithZero/Units/Basic.lean b/Mathlib/Algebra/GroupWithZero/Units/Basic.lean
index 54f918a50061ce..9916a90765c529 100644
--- a/Mathlib/Algebra/GroupWithZero/Units/Basic.lean
+++ b/Mathlib/Algebra/GroupWithZero/Units/Basic.lean
@@ -152,7 +152,7 @@ theorem IsUnit.ringInverse {a : M₀} : IsUnit a → IsUnit a⁻¹ʳ
 theorem isUnit_ringInverse {a : M₀} : IsUnit a⁻¹ʳ ↔ IsUnit a :=
   ⟨fun h => by
     cases subsingleton_or_nontrivial M₀
-    · convert h
+    · convert! h
     · contrapose h
       rw [Ring.inverse_non_unit _ h]
       exact not_isUnit_zero,
diff --git a/Mathlib/Algebra/Homology/CommSq.lean b/Mathlib/Algebra/Homology/CommSq.lean
index 6ff1d59d50cb96..06a429e92f39f0 100644
--- a/Mathlib/Algebra/Homology/CommSq.lean
+++ b/Mathlib/Algebra/Homology/CommSq.lean
@@ -64,7 +64,7 @@ noncomputable def CommSq.isColimitEquivIsColimitCokernelCofork (sq : CommSq f g
       (fun s ↦ PushoutCocone.IsColimit.desc h
         (biprod.inl ≫ s.π) (biprod.inr ≫ s.π) (by
           rw [← sub_eq_zero, ← assoc, ← assoc, ← Preadditive.sub_comp]
-          convert s.condition <;> cat_disch))
+          convert! s.condition <;> cat_disch))
       (fun s ↦ by
         dsimp
         ext
@@ -98,8 +98,8 @@ noncomputable def CommSq.isColimitEquivIsColimitCokernelCofork (sq : CommSq f g
                   (by simp [s.condition])) .one)
       (fun s m hm₁ hm₂ ↦ by
         apply Cofork.IsColimit.hom_ext h
-        convert (h.fac (CokernelCofork.ofπ (biprod.desc s.inl s.inr)
-          (by simp [s.condition])) .one).symm
+        convert!
+          (h.fac (CokernelCofork.ofπ (biprod.desc s.inl s.inr) (by simp [s.condition])) .one).symm
         cat_disch)
   left_inv _ := Subsingleton.elim _ _
   right_inv _ := Subsingleton.elim _ _
@@ -144,7 +144,7 @@ noncomputable def CommSq.isLimitEquivIsLimitKernelFork (sq : CommSq fst snd f g)
       (fun s ↦ PullbackCone.IsLimit.lift h
         (s.ι ≫ biprod.fst) (s.ι ≫ biprod.snd) (by
           rw [← sub_eq_zero, assoc, assoc, ← Preadditive.comp_sub]
-          convert s.condition <;> cat_disch))
+          convert! s.condition <;> cat_disch))
       (fun s ↦ by
         dsimp
         ext
@@ -176,8 +176,8 @@ noncomputable def CommSq.isLimitEquivIsLimitKernelFork (sq : CommSq fst snd f g)
         (by simp [s.condition])) .zero =≫ biprod.snd)
       (fun s m hm₁ hm₂ ↦ by
         apply Fork.IsLimit.hom_ext h
-        convert (h.fac (KernelFork.ofι (biprod.lift s.fst s.snd)
-          (by simp [s.condition])) .zero).symm
+        convert!
+          (h.fac (KernelFork.ofι (biprod.lift s.fst s.snd) (by simp [s.condition])) .zero).symm
         cat_disch)
   left_inv _ := Subsingleton.elim _ _
   right_inv _ := Subsingleton.elim _ _
diff --git a/Mathlib/Algebra/Homology/DerivedCategory/KInjective.lean b/Mathlib/Algebra/Homology/DerivedCategory/KInjective.lean
index fc71341ebfa741..e69f08aafa28d6 100644
--- a/Mathlib/Algebra/Homology/DerivedCategory/KInjective.lean
+++ b/Mathlib/Algebra/Homology/DerivedCategory/KInjective.lean
@@ -74,7 +74,7 @@ lemma bijective_toSmallShiftedHom_of_isKInjective [L.IsKInjective] :
       (SmallShiftedHom.equiv _ DerivedCategory.Q).bijective,
     ← Function.Bijective.of_comp_iff' (Iso.homCongr ((quotientCompQhIso C).symm.app K)
       ((Q.commShiftIso n).symm.app L ≪≫ (quotientCompQhIso C).symm.app (L⟦n⟧))).bijective]
-  convert (CochainComplex.IsKInjective.Qh_map_bijective _ _).comp (toHom_bijective K L n)
+  convert! (CochainComplex.IsKInjective.Qh_map_bijective _ _).comp (toHom_bijective K L n)
   ext x
   obtain ⟨x, rfl⟩ := x.mk_surjective
   simp [toHom_mk, ShiftedHom.map]
diff --git a/Mathlib/Algebra/Homology/DerivedCategory/KProjective.lean b/Mathlib/Algebra/Homology/DerivedCategory/KProjective.lean
index 865f95d1c027d8..48bd3ef6a42769 100644
--- a/Mathlib/Algebra/Homology/DerivedCategory/KProjective.lean
+++ b/Mathlib/Algebra/Homology/DerivedCategory/KProjective.lean
@@ -75,7 +75,7 @@ lemma bijective_toSmallShiftedHom_of_isKProjective [K.IsKProjective] :
       (SmallShiftedHom.equiv _ DerivedCategory.Q).bijective,
     ← Function.Bijective.of_comp_iff' (Iso.homCongr ((quotientCompQhIso C).symm.app K)
       ((Q.commShiftIso n).symm.app L ≪≫ (quotientCompQhIso C).symm.app (L⟦n⟧))).bijective]
-  convert (CochainComplex.IsKProjective.Qh_map_bijective _ _).comp (toHom_bijective K L n)
+  convert! (CochainComplex.IsKProjective.Qh_map_bijective _ _).comp (toHom_bijective K L n)
   ext x
   obtain ⟨x, rfl⟩ := x.mk_surjective
   simp [toHom_mk, ShiftedHom.map]
diff --git a/Mathlib/Algebra/Homology/DifferentialObject.lean b/Mathlib/Algebra/Homology/DifferentialObject.lean
index 298660c786b1a0..c6b10e7c02e11d 100644
--- a/Mathlib/Algebra/Homology/DifferentialObject.lean
+++ b/Mathlib/Algebra/Homology/DifferentialObject.lean
@@ -86,7 +86,7 @@ def dgoToHomologicalComplex :
     { X := fun i => X.obj i
       d := fun i j =>
         if h : i + b = j then X.d i ≫ X.objEqToHom (show i + (1 : ℤ) • b = j by simp [h]) else 0
-      shape := fun i j w => by dsimp at w; convert dif_neg w
+      shape := fun i j w => by dsimp at w; convert! dif_neg w
       d_comp_d' := fun i j k hij hjk => by
         dsimp at hij hjk; substs hij hjk
         simp [objEqToHom_d_assoc] }
diff --git a/Mathlib/Algebra/Homology/LeftResolution/Basic.lean b/Mathlib/Algebra/Homology/LeftResolution/Basic.lean
index a4e5526bed1168..494125a9dc4d6e 100644
--- a/Mathlib/Algebra/Homology/LeftResolution/Basic.lean
+++ b/Mathlib/Algebra/Homology/LeftResolution/Basic.lean
@@ -103,7 +103,7 @@ lemma exactAt_map_chainComplex_succ (n : ℕ) :
   rw [HomologicalComplex.exactAt_iff' _ (n + 2) (n + 1) n
     (ComplexShape.prev_eq' _ (by dsimp; lia)) (by simp),
     ShortComplex.exact_iff_epi_kernel_lift]
-  convert epi_comp (ι.map (Λ.chainComplexXIso X n).hom) (Λ.π.app _)
+  convert! epi_comp (ι.map (Λ.chainComplexXIso X n).hom) (Λ.π.app _)
   rw [← cancel_mono (kernel.ι _), kernel.lift_ι]
   simp [map_chainComplex_d]
 
diff --git a/Mathlib/Algebra/Homology/Single.lean b/Mathlib/Algebra/Homology/Single.lean
index 4ab1e05842a022..c6a560579c4004 100644
--- a/Mathlib/Algebra/Homology/Single.lean
+++ b/Mathlib/Algebra/Homology/Single.lean
@@ -52,7 +52,7 @@ noncomputable def single (j : ι) : V ⥤ HomologicalComplex V c where
       previously was `rw [if_neg h]; simp`, but that fails with "motive not type correct"
       This is because dsimp does not simplify numerals;
       this note should be removable once https://github.com/leanprover/lean4/pull/8433 lands. -/
-      convert (id_zero (C := V)).symm
+      convert! (id_zero (C := V)).symm
       all_goals simp [if_neg h]
   map_comp f g := by
     ext
diff --git a/Mathlib/Algebra/Homology/SpectralObject/Basic.lean b/Mathlib/Algebra/Homology/SpectralObject/Basic.lean
index 96a0a4e46065e2..533d72f4923669 100644
--- a/Mathlib/Algebra/Homology/SpectralObject/Basic.lean
+++ b/Mathlib/Algebra/Homology/SpectralObject/Basic.lean
@@ -74,7 +74,7 @@ lemma δ_naturality {i j k : ι} (f : i ⟶ j) (g : j ⟶ k)
     (homMk₂ (α.app 0) (α.app 1) (β.app 1) (naturality' α 0 1)
       (by simpa only [hαβ] using naturality' β 0 1) : mk₂ f g ⟶ mk₂ f' g')
   dsimp at h
-  convert h <;> cat_disch
+  convert! h <;> cat_disch
 
 end
 
diff --git a/Mathlib/Algebra/Homology/SpectralObject/EpiMono.lean b/Mathlib/Algebra/Homology/SpectralObject/EpiMono.lean
index 89c2844ed467a9..fbfb0a96a8290d 100644
--- a/Mathlib/Algebra/Homology/SpectralObject/EpiMono.lean
+++ b/Mathlib/Algebra/Homology/SpectralObject/EpiMono.lean
@@ -86,10 +86,10 @@ lemma isIso_map_fourδ₄Toδ₃ (h : (X.H n₁).map (twoδ₁Toδ₀ f₃ f₄
   apply ShortComplex.isIso_homologyMap_of_epi_of_isIso_of_mono'
   · exact (X.exact₂ f₃ f₄ f₃₄ h₃₄ _).epi_f h
   · dsimp
-    convert (inferInstance : IsIso ((X.H n₂).map (𝟙 _)))
+    convert! (inferInstance : IsIso ((X.H n₂).map (𝟙 _)))
     cat_disch
   · dsimp
-    convert (inferInstance : Mono ((X.H n₃).map (𝟙 (mk₁ f₁))))
+    convert! (inferInstance : Mono ((X.H n₃).map (𝟙 (mk₁ f₁))))
     cat_disch
 
 lemma isIso_map_fourδ₄Toδ₃_of_isZero (h : IsZero ((X.H n₁).obj (mk₁ f₄)) := by cat_disch)
@@ -116,10 +116,10 @@ lemma isIso_map_fourδ₁Toδ₀ (h : (X.H n₂).map (twoδ₂Toδ₁ f₂ f₃
     IsIso (X.map f₂₃ f₄ f₅ f₃ f₄ f₅ (fourδ₁Toδ₀ f₂ f₃ f₄ f₅ f₂₃ h₂₃) n₀ n₁ n₂ hn₁ hn₂) := by
   apply ShortComplex.isIso_homologyMap_of_epi_of_isIso_of_mono'
   · dsimp
-    convert (inferInstance : Epi ((X.H n₀).map (𝟙 _)))
+    convert! (inferInstance : Epi ((X.H n₀).map (𝟙 _)))
     cat_disch
   · dsimp
-    convert (inferInstance : IsIso ((X.H n₁).map (𝟙 _)))
+    convert! (inferInstance : IsIso ((X.H n₁).map (𝟙 _)))
     cat_disch
   · exact (X.exact₂ f₂ f₃ f₂₃ h₂₃ n₂).mono_g h
 
diff --git a/Mathlib/Algebra/Homology/SpectralObject/Page.lean b/Mathlib/Algebra/Homology/SpectralObject/Page.lean
index 8f06e24911d776..d7f3d7201e6a46 100644
--- a/Mathlib/Algebra/Homology/SpectralObject/Page.lean
+++ b/Mathlib/Algebra/Homology/SpectralObject/Page.lean
@@ -99,7 +99,7 @@ def shortComplexMap (hn₁ : n₀ + 1 = n₁ := by lia) (hn₂ : n₁ + 1 = n₂
 lemma shortComplexMap_id (hn₁ : n₀ + 1 = n₁ := by lia) (hn₂ : n₁ + 1 = n₂ := by lia) :
     X.shortComplexMap f₁ f₂ f₃ f₁ f₂ f₃ (𝟙 _) n₀ n₁ n₂ hn₁ hn₂ = 𝟙 _ := by
   ext
-  all_goals dsimp; convert (X.H _).map_id _; cat_disch
+  all_goals dsimp; convert! (X.H _).map_id _; cat_disch
 
 @[reassoc, simp]
 lemma shortComplexMap_comp (hn₁ : n₀ + 1 = n₁ := by lia) (hn₂ : n₁ + 1 = n₂ := by lia) :
diff --git a/Mathlib/Algebra/Jordan/Basic.lean b/Mathlib/Algebra/Jordan/Basic.lean
index 28f792a102ec39..d395627577d3e3 100644
--- a/Mathlib/Algebra/Jordan/Basic.lean
+++ b/Mathlib/Algebra/Jordan/Basic.lean
@@ -163,7 +163,7 @@ theorem two_nsmul_lie_lmul_lmul_add_eq_lie_lmul_lmul_add [IsCommJordan A] (a b :
     2 • (⁅L a, L (a * b)⁆ + ⁅L b, L (b * a)⁆) = ⁅L (a * a), L b⁆ + ⁅L (b * b), L a⁆ := by
   suffices 2 • ⁅L a, L (a * b)⁆ + 2 • ⁅L b, L (b * a)⁆ + ⁅L b, L (a * a)⁆ + ⁅L a, L (b * b)⁆ = 0 by
     rwa [← sub_eq_zero, ← sub_sub, sub_eq_add_neg, sub_eq_add_neg, lie_skew, lie_skew, nsmul_add]
-  convert (commute_lmul_lmul_sq (a + b)).lie_eq using 1
+  convert! (commute_lmul_lmul_sq (a + b)).lie_eq using 1
   simp only [add_mul, mul_add, map_add, lie_add, add_lie, mul_comm b a,
     (commute_lmul_lmul_sq a).lie_eq, (commute_lmul_lmul_sq b).lie_eq, zero_add, add_zero, two_smul]
   abel
diff --git a/Mathlib/Algebra/Lie/Basic.lean b/Mathlib/Algebra/Lie/Basic.lean
index 88d0dfd8916718..f1a9094f84b662 100644
--- a/Mathlib/Algebra/Lie/Basic.lean
+++ b/Mathlib/Algebra/Lie/Basic.lean
@@ -121,7 +121,7 @@ lemma lie_swap_lie [Bracket L₂ L₁] [AddCommGroup M] [IsLieTower L₁ L₂ M]
     (x : L₁) (y : L₂) (m : M) : ⁅⁅x, y⁆, m⁆ = -⁅⁅y, x⁆, m⁆ := by
   have h1 := leibniz_lie x y m
   have h2 := leibniz_lie y x m
-  convert congr($h1.symm - $h2) using 1 <;> simp only [add_sub_cancel_right, sub_add_cancel_right]
+  convert! congr($h1.symm - $h2) using 1 <;> simp only [add_sub_cancel_right, sub_add_cancel_right]
 
 end IsLieTower
 
diff --git a/Mathlib/Algebra/Lie/Basis.lean b/Mathlib/Algebra/Lie/Basis.lean
index b18c3bce23cf19..a4d699e4ba0b6c 100644
--- a/Mathlib/Algebra/Lie/Basis.lean
+++ b/Mathlib/Algebra/Lie/Basis.lean
@@ -367,10 +367,10 @@ lemma borelUpper_le_biSup :
         ext i
         simpa using congr_fun χ.property.choose_spec.2.symm i
     replace hu : u ∈ ⨆ χ, ⨆ (_ : χ ∈ s), rootSpace b.cartan χ := by
-      convert hu; rw [iSup_subtype', iSup_subtype', ← e.iSup_comp]; rfl
+      convert! hu; rw [iSup_subtype', iSup_subtype', ← e.iSup_comp]; rfl
     replace hv : v ∈ ⨆ χ, ⨆ (_ : χ ∈ s), rootSpace b.cartan χ := by
-      convert hv; rw [iSup_subtype', iSup_subtype', ← e.iSup_comp]; rfl
-    convert mem_biSup_genWeightSpace_of hs hu hv
+      convert! hv; rw [iSup_subtype', iSup_subtype', ← e.iSup_comp]; rfl
+    convert! mem_biSup_genWeightSpace_of hs hu hv
     rw [iSup_subtype', iSup_subtype', ← e.iSup_comp]; rfl
 
 /-- Lemma 4.4 from [Geck](Geck2017). -/
@@ -450,13 +450,13 @@ lemma iSupIndep_rootSpace :
     simpa using this.2
   have key := LieModule.iSupIndep_genWeightSpace R b.cartan L
   have h₀ : Disjoint (rootSpace b.cartan 0) (U ⊔ V) := by
-    convert key.disjoint_biSup_biSup (hU0.union_right hV0)
+    convert! key.disjoint_biSup_biSup (hU0.union_right hV0)
     rw [iSup_union, hsU', hsV']
   have h₁ : Disjoint U (V ⊔ rootSpace b.cartan 0) := by
-    convert key.disjoint_biSup_biSup (hUV.union_right hU0.symm)
+    convert! key.disjoint_biSup_biSup (hUV.union_right hU0.symm)
     rw [iSup_union, hs0', hsV']
   have h₂ : Disjoint V (rootSpace b.cartan 0 ⊔ U) := by
-    convert key.disjoint_biSup_biSup (Disjoint.union_left hV0 hUV).symm
+    convert! key.disjoint_biSup_biSup (Disjoint.union_left hV0 hUV).symm
     rw [iSup_union, hs0', hsU']
   simp [iSupIndep_fin_three, h₀, h₁, h₂]
 
diff --git a/Mathlib/Algebra/Lie/Derivation/Killing.lean b/Mathlib/Algebra/Lie/Derivation/Killing.lean
index e57b295206a5a7..eceaee0ebeef75 100644
--- a/Mathlib/Algebra/Lie/Derivation/Killing.lean
+++ b/Mathlib/Algebra/Lie/Derivation/Killing.lean
@@ -91,7 +91,7 @@ instance instIsKilling_range_ad : LieAlgebra.IsKilling R 𝕀 :=
 the adjoint action is nondegenerate. -/
 lemma killingForm_restrict_range_ad_nondegenerate :
     ((killingForm R 𝔻).restrict 𝕀).Nondegenerate := by
-  convert LieAlgebra.IsKilling.killingForm_nondegenerate R 𝕀
+  convert! LieAlgebra.IsKilling.killingForm_nondegenerate R 𝕀
   exact killingForm_restrict_range_ad R L
 
 set_option backward.isDefEq.respectTransparency false in
diff --git a/Mathlib/Algebra/Lie/Nilpotent.lean b/Mathlib/Algebra/Lie/Nilpotent.lean
index 45dc61da8b14e4..c9b3a49592389d 100644
--- a/Mathlib/Algebra/Lie/Nilpotent.lean
+++ b/Mathlib/Algebra/Lie/Nilpotent.lean
@@ -573,7 +573,7 @@ theorem lcs_add_le_iff (l k : ℕ) : N₁.lcs (l + k) ≤ N₂ ↔ N₁.lcs l 
     rw [(by abel : l + (k + 1) = l + 1 + k), ih, ucs_succ, lcs_succ, top_lie_le_iff_le_normalizer]
 
 theorem lcs_le_iff (k : ℕ) : N₁.lcs k ≤ N₂ ↔ N₁ ≤ N₂.ucs k := by
-  convert lcs_add_le_iff (R := R) (L := L) (M := M) 0 k
+  convert! lcs_add_le_iff (R := R) (L := L) (M := M) 0 k
   rw [zero_add]
 
 theorem gc_lcs_ucs (k : ℕ) :
diff --git a/Mathlib/Algebra/Lie/Submodule.lean b/Mathlib/Algebra/Lie/Submodule.lean
index cd5c87eb5945c4..a5a978511e024c 100644
--- a/Mathlib/Algebra/Lie/Submodule.lean
+++ b/Mathlib/Algebra/Lie/Submodule.lean
@@ -974,7 +974,7 @@ lemma map_le_range {M' : Type*}
 @[simp]
 lemma map_incl_lt_iff_lt_top {N' : LieSubmodule R L N} :
     N'.map (LieSubmodule.incl N) < N ↔ N' < ⊤ := by
-  convert (LieSubmodule.mapOrderEmbedding (f := N.incl) Subtype.coe_injective).lt_iff_lt
+  convert! (LieSubmodule.mapOrderEmbedding (f := N.incl) Subtype.coe_injective).lt_iff_lt
   simp
 
 @[simp]
diff --git a/Mathlib/Algebra/Lie/Weights/Basic.lean b/Mathlib/Algebra/Lie/Weights/Basic.lean
index e201cd4b044862..153c3b7c19d15f 100644
--- a/Mathlib/Algebra/Lie/Weights/Basic.lean
+++ b/Mathlib/Algebra/Lie/Weights/Basic.lean
@@ -552,7 +552,7 @@ lemma map_posFittingComp_eq (e : M ≃ₗ⁅R,L⁆ M₂) :
     rw [this]
     exact LieSubmodule.map_mono (map_posFittingComp_le _)
   rw [← LieSubmodule.map_comp]
-  convert LieSubmodule.map_id
+  convert! LieSubmodule.map_id
   ext
   simp
 
diff --git a/Mathlib/Algebra/Lie/Weights/Cartan.lean b/Mathlib/Algebra/Lie/Weights/Cartan.lean
index 9712d99c452293..ac6795709a85ac 100644
--- a/Mathlib/Algebra/Lie/Weights/Cartan.lean
+++ b/Mathlib/Algebra/Lie/Weights/Cartan.lean
@@ -75,7 +75,7 @@ lemma toEnd_pow_apply_mem {χ₁ χ₂ : H → R} {x : L} {m : M}
   | zero => simpa using hm
   | succ n IH =>
     simp only [pow_succ', Module.End.mul_apply, toEnd_apply_apply]
-    convert lie_mem_genWeightSpace_of_mem_genWeightSpace hx IH using 2
+    convert! lie_mem_genWeightSpace_of_mem_genWeightSpace hx IH using 2
     rw [succ_nsmul, ← add_assoc, add_comm (n • _)]
 
 lemma mem_biSup_genWeightSpace_of {s : Set (H → R)} (hs : ∀ᵉ (χ₁ ∈ s) (χ₂ ∈ s), χ₁ + χ₂ ∈ s)
@@ -309,7 +309,7 @@ lemma mem_corootSpace' {x : H} :
     exists_and_right, exists_eq_right, mem_setOf_eq, s]
   refine ⟨fun ⟨_, y, hy, z, hz, hyz⟩ ↦ ⟨y, hy, z, hz, hyz⟩,
     fun ⟨y, hy, z, hz, hyz⟩ ↦ ⟨?_, y, hy, z, hz, hyz⟩⟩
-  convert
+  convert!
     (rootSpaceProduct R L H α (-α) 0 (add_neg_cancel α) (⟨y, hy⟩ ⊗ₜ[R] ⟨z, hz⟩)).property using 0
   simp [hyz]
 
diff --git a/Mathlib/Algebra/Lie/Weights/IsSimple.lean b/Mathlib/Algebra/Lie/Weights/IsSimple.lean
index 5b756b0f2647ab..46c7955c7d3236 100644
--- a/Mathlib/Algebra/Lie/Weights/IsSimple.lean
+++ b/Mathlib/Algebra/Lie/Weights/IsSimple.lean
@@ -259,7 +259,7 @@ private theorem chi_in_q_aux (h_chi_in_q : ↑χ ∈ q) :
     have h_zero_weight : H.toLieSubmodule.incl y ∈ genWeightSpace L (0 : H → K) := by
       apply toLieSubmodule_le_rootSpace_zero
       exact y.property
-    convert lie_mem_genWeightSpace_of_mem_genWeightSpace hx_χ h_zero_weight
+    convert! lie_mem_genWeightSpace_of_mem_genWeightSpace hx_χ h_zero_weight
     ext h; simp
   have h_bracket_decomp : ⁅x_χ, m_α⁆ ∈
       genWeightSpace L (χ.toLinear + α.toLinear) ⊔
@@ -324,7 +324,7 @@ private theorem chi_not_in_q_aux (h_chi_not_in_q : ↑χ ∉ q) :
     rw [hi] at h_equiv
     exact h_chi_not_in_q (h_equiv.mpr (by
       rw [hj, Weight.toLinear_neg]
-      convert q.smul_mem (-1) hαq using 1
+      convert! q.smul_mem (-1) hαq using 1
       rw [neg_smul, one_smul]))
   obtain ⟨i, hi⟩ := exists_root_index χ (Weight.coe_toLinear_ne_zero_iff.mp w_chi)
   obtain ⟨j, hj⟩ := exists_root_index α hα₀
@@ -413,7 +413,7 @@ private theorem invtSubmoduleToLieIdeal_aux (hm_α : m_α ∈ sl2SubmoduleOfRoot
   by_cases w_chi : χ.toLinear = 0
   · have hx_χ_in_H : x_χ ∈ H.toLieSubmodule := by
       rw [← rootSpace_zero_eq K L H]
-      convert hx_χ; ext h; simp only [Pi.zero_apply]
+      convert! hx_χ; ext h; simp only [Pi.zero_apply]
       have h_apply : (χ.toLinear : H → K) h = 0 := by rw [w_chi, LinearMap.zero_apply]
       exact h_apply.symm
     apply LieSubmodule.mem_iSup_of_mem ⟨α, hαq, hα₀⟩
diff --git a/Mathlib/Algebra/Lie/Weights/Killing.lean b/Mathlib/Algebra/Lie/Weights/Killing.lean
index 4c4a222cc7db18..5e7f645f6b0e01 100644
--- a/Mathlib/Algebra/Lie/Weights/Killing.lean
+++ b/Mathlib/Algebra/Lie/Weights/Killing.lean
@@ -160,7 +160,7 @@ variable [FiniteDimensional K L] [IsKilling K L]
 instance : InvolutiveNeg (Weight K H L) where
   neg α := ⟨-α, by
     by_cases hα : α.IsZero
-    · convert α.genWeightSpace_ne_bot; rw [hα, neg_zero]
+    · convert! α.genWeightSpace_ne_bot; rw [hα, neg_zero]
     · intro e
       obtain ⟨x, hx, x_ne0⟩ := α.exists_ne_zero
       have := mem_ker_killingForm_of_mem_rootSpace_of_forall_rootSpace_neg K L H hx
diff --git a/Mathlib/Algebra/Lie/Weights/RootSystem.lean b/Mathlib/Algebra/Lie/Weights/RootSystem.lean
index dcb388499ada96..80f11ac0d01b73 100644
--- a/Mathlib/Algebra/Lie/Weights/RootSystem.lean
+++ b/Mathlib/Algebra/Lie/Weights/RootSystem.lean
@@ -274,7 +274,7 @@ lemma chainTopCoeff_zero_right [Nontrivial L] (hα : α.IsNonZero) :
   obtain ⟨k, hk⟩ : ∃ k : K, k • f =
       (toEnd K L L f ^ (chainTopCoeff α (0 : Weight K H L) + 1)) x := by
     have : (toEnd K L L f ^ (chainTopCoeff α (0 : Weight K H L) + 1)) x ∈ rootSpace H (-α) := by
-      convert toEnd_pow_apply_mem hf hx (chainTopCoeff α (0 : Weight K H L) + 1) using 2
+      convert! toEnd_pow_apply_mem hf hx (chainTopCoeff α (0 : Weight K H L) + 1) using 2
       rw [coe_chainTop', Weight.coe_zero, add_zero, succ_nsmul',
         add_assoc, smul_neg, neg_add_cancel, add_zero]
     simpa using (finrank_eq_one_iff_of_nonzero' ⟨f, hf⟩ (by simpa using isSl2.f_ne_zero)).mp
@@ -398,7 +398,7 @@ def rootSystem :
       rintro ⟨α, hα⟩ - ⟨⟨β, hβ⟩, rfl⟩
       simpa using
         ⟨reflectRoot α β, by simpa using reflectRoot_isNonZero α β <| by simpa using hβ, rfl⟩)
-    (by convert span_weight_isNonZero_eq_top K L H; ext; simp)
+    (by convert! span_weight_isNonZero_eq_top K L H; ext; simp)
 
 instance : (rootSystem H).IsRootSystem :=
   RootPairing.isRootSystem_mk'' fun α β ↦
diff --git a/Mathlib/Algebra/Module/DedekindDomain.lean b/Mathlib/Algebra/Module/DedekindDomain.lean
index 6d4ed4a7c864f9..8185c795c70e12 100644
--- a/Mathlib/Algebra/Module/DedekindDomain.lean
+++ b/Mathlib/Algebra/Module/DedekindDomain.lean
@@ -42,7 +42,7 @@ theorem isInternal_prime_power_torsion_of_is_torsion_by_ideal
   have prime_of_mem := fun p (hp : p ∈ P.toFinset) =>
     prime_of_factor p (Multiset.mem_toFinset.mp hp)
   apply torsionBySet_isInternal (p := fun p => p ^ P.count p) _
-  · convert hM
+  · convert! hM
     rw [← Finset.inf_eq_iInf, IsDedekindDomain.inf_pow_eq_prod_of_prime,
       ← Finset.prod_multiset_count, ← associated_iff_eq]
     · exact factors_prod hI
diff --git a/Mathlib/Algebra/Module/Equiv/Basic.lean b/Mathlib/Algebra/Module/Equiv/Basic.lean
index 8495f58a40800d..d54d846e37e0eb 100644
--- a/Mathlib/Algebra/Module/Equiv/Basic.lean
+++ b/Mathlib/Algebra/Module/Equiv/Basic.lean
@@ -278,7 +278,7 @@ variable {modM : Module ℤ M} {modM₂ : Module ℤ M₂} {modM₃ : Module ℤ
 equivalence between ℤ-modules -/
 def toIntLinearEquiv : M ≃ₗ[ℤ] M₂ := by
   refine e.toLinearEquiv fun c a ↦ ?_
-  convert e.toAddMonoidHom.map_zsmul c a using 1
+  convert! e.toAddMonoidHom.map_zsmul c a using 1
   · exact congr(e $(int_smul_eq_zsmul ..))
   · exact int_smul_eq_zsmul ..
 
diff --git a/Mathlib/Algebra/Module/FinitePresentation.lean b/Mathlib/Algebra/Module/FinitePresentation.lean
index ba90a5cd241acd..71029470069912 100644
--- a/Mathlib/Algebra/Module/FinitePresentation.lean
+++ b/Mathlib/Algebra/Module/FinitePresentation.lean
@@ -137,7 +137,7 @@ lemma Module.finitePresentation_of_free_of_surjective [Module.Free R M] [Module.
     by simpa [Set.range_comp, LinearMap.range_eq_top], ?_⟩
   let f : M →ₗ[R] (Set.finite_range (l ∘ b)).toFinset →₀ R :=
     Finsupp.lmapDomain _ _ π ∘ₗ b.repr.toLinearMap
-  convert hl'.map f
+  convert! hl'.map f
   ext x; simp only [LinearMap.mem_ker, Submodule.mem_map]
   constructor
   · intro hx
@@ -384,7 +384,7 @@ lemma Module.FinitePresentation.exists_lift_of_isLocalizedModule
     · simp only [smul_zero]
     apply IsLocalizedModule.exists_of_eq (S := S) (f := f)
     rw [← LinearMap.comp_apply, map_zero, hi, LinearMap.comp_apply]
-    convert map_zero (s₀ • g)
+    convert! map_zero (s₀ • g)
     rw [← LinearMap.mem_ker, ← hτ]
     exact Submodule.subset_span x.prop
   choose s' hs' using this
@@ -395,7 +395,7 @@ lemma Module.FinitePresentation.exists_lift_of_isLocalizedModule
     simp only [s₁]
     rw [SetLike.mem_coe, LinearMap.mem_ker, LinearMap.smul_apply,
       ← Finset.prod_erase_mul _ _ (Finset.mem_univ ⟨x, hxσ⟩), mul_smul]
-    convert smul_zero _
+    convert! smul_zero _
     exact hs' ⟨x, hxσ⟩
   refine ⟨Submodule.liftQ _ _ this ∘ₗ
     (LinearMap.quotKerEquivOfSurjective _ hπ).symm.toLinearMap, s₁ * s₀, ?_⟩
@@ -586,7 +586,7 @@ lemma IsLocalizedModule.exists_isLocalizedModule_powers_of_finitePresentation
     ⟨IsLocalizedModule.map_units f, fun y ↦ ⟨⟨y, 1⟩, by simp⟩, by simpa using ⟨1, S.one_mem⟩⟩
   obtain ⟨r, hrp, H⟩ := exists_bijective_map_powers S
       f (.id (R := R) (M := M')) f <| by
-    convert show Function.Bijective LinearMap.id from Function.bijective_id
+    convert! show Function.Bijective LinearMap.id from Function.bijective_id
     apply IsLocalizedModule.ext S f
     · exact IsLocalizedModule.map_units f
     · simp [IsLocalizedModule.map_comp]
diff --git a/Mathlib/Algebra/Module/GradedModule.lean b/Mathlib/Algebra/Module/GradedModule.lean
index ef3b584f93367d..019d32ab4861e9 100644
--- a/Mathlib/Algebra/Module/GradedModule.lean
+++ b/Mathlib/Algebra/Module/GradedModule.lean
@@ -223,7 +223,7 @@ def linearEquiv [DecidableEq ιA] [DecidableEq ιM] [GradedRing 𝓐] [DirectSum
     DirectSum.Gmodule.smulAddMonoidHom _ _ (decompose 𝓐 ↑(decompose 𝓐 x i))
     (decomposeAddEquiv 𝓜 ↑(decompose 𝓜 y j)) from DirectSum.Gmodule.smul_def _ _ _ _]
   simp only [decomposeAddEquiv_apply, decompose_coe, Gmodule.smulAddMonoidHom_apply_of_of]
-  convert DirectSum.decompose_coe 𝓜 _
+  convert! DirectSum.decompose_coe 𝓜 _
   rfl
 
 end GradedModule
diff --git a/Mathlib/Algebra/Module/Injective.lean b/Mathlib/Algebra/Module/Injective.lean
index da35d3423cc89f..68b5c4debd2949 100644
--- a/Mathlib/Algebra/Module/Injective.lean
+++ b/Mathlib/Algebra/Module/Injective.lean
@@ -292,7 +292,7 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_wd (h : Module.Baer R Q) {y : N} (r r
     (eq1 : r • y = r' • y) : ExtensionOfMaxAdjoin.extendIdealTo i f h y r =
     ExtensionOfMaxAdjoin.extendIdealTo i f h y r' := by
   rw [← sub_eq_zero, ← map_sub]
-  convert ExtensionOfMaxAdjoin.extendIdealTo_wd' i f h (r - r') _
+  convert! ExtensionOfMaxAdjoin.extendIdealTo_wd' i f h (r - r') _
   rw [sub_smul, sub_eq_zero, eq1]
 
 theorem ExtensionOfMaxAdjoin.extendIdealTo_eq (h : Module.Baer R Q) {y : N} (r : R)
diff --git a/Mathlib/Algebra/Module/LocalizedModule/Basic.lean b/Mathlib/Algebra/Module/LocalizedModule/Basic.lean
index 07dd45e351c516..d4e732feb760fb 100644
--- a/Mathlib/Algebra/Module/LocalizedModule/Basic.lean
+++ b/Mathlib/Algebra/Module/LocalizedModule/Basic.lean
@@ -123,7 +123,7 @@ def liftOn {α : Type*} (x : LocalizedModule S M) (f : M × S → α)
   Quotient.liftOn x f (by simpa +instances only [r.setoid, ← oreEqv_eq_r S M] using wd)
 
 theorem liftOn_mk {α : Type*} {f : M × S → α} (wd : ∀ (p p' : M × S), p ≈ p' → f p = f p')
-    (m : M) (s : S) : liftOn (mk m s) f wd = f ⟨m, s⟩ := by convert Quotient.liftOn_mk f wd ⟨m, s⟩
+    (m : M) (s : S) : liftOn (mk m s) f wd = f ⟨m, s⟩ := by convert! Quotient.liftOn_mk f wd ⟨m, s⟩
 
 /-- If `f : M × S → M × S → α` respects the equivalence relation `LocalizedModule.r`, then
 `f` descents to a map `LocalizedModule M S → LocalizedModule M S → α`.
@@ -135,7 +135,7 @@ def liftOn₂ {α : Type*} (x y : LocalizedModule S M) (f : M × S → M × S 
 theorem liftOn₂_mk {α : Type*} (f : M × S → M × S → α)
     (wd : ∀ (p q p' q' : M × S), p ≈ p' → q ≈ q' → f p q = f p' q') (m m' : M)
     (s s' : S) : liftOn₂ (mk m s) (mk m' s') f wd = f ⟨m, s⟩ ⟨m', s'⟩ := by
-  convert Quotient.liftOn₂_mk f wd _ _
+  convert! Quotient.liftOn₂_mk f wd _ _
 
 /-- If `S` contains `0` then the localization at `S` is trivial. -/
 theorem subsingleton (h : 0 ∈ S) : Subsingleton (LocalizedModule S M) := by
diff --git a/Mathlib/Algebra/Module/LocalizedModule/Int.lean b/Mathlib/Algebra/Module/LocalizedModule/Int.lean
index cef950b6bfb040..e43294f55d06fe 100644
--- a/Mathlib/Algebra/Module/LocalizedModule/Int.lean
+++ b/Mathlib/Algebra/Module/LocalizedModule/Int.lean
@@ -134,10 +134,10 @@ theorem smul_mem_finsetIntegerMultiple_span [DecidableEq M] (x : M) (s : Finset
   obtain ⟨x', hx', hx''⟩ := hx
   obtain ⟨a, ha⟩ := (IsLocalizedModule.eq_iff_exists S f).mp hx''
   use a * y
-  convert (Submodule.span R
-    (IsLocalizedModule.finsetIntegerMultiple S f s : Set M)).smul_mem
-      a hx' using 1
-  convert ha.symm using 1
+  convert!
+    (Submodule.span R (IsLocalizedModule.finsetIntegerMultiple S f s : Set M)).smul_mem a hx'
+      using 1
+  convert! ha.symm using 1
   simp only [Submonoid.smul_def, ← smul_smul]
 
 end IsLocalizedModule
diff --git a/Mathlib/Algebra/Module/LocalizedModule/IsLocalization.lean b/Mathlib/Algebra/Module/LocalizedModule/IsLocalization.lean
index 15ff7aee7b8fb1..89f0714709261a 100644
--- a/Mathlib/Algebra/Module/LocalizedModule/IsLocalization.lean
+++ b/Mathlib/Algebra/Module/LocalizedModule/IsLocalization.lean
@@ -43,7 +43,7 @@ variable (A)
 the associated linear map `R →ₗ[R] A` is a localization of modules with respect to `S`. -/
 lemma isLocalizedModule_iff_isLocalization' :
     IsLocalizedModule S (Algebra.linearMap R A) ↔ IsLocalization S A := by
-  convert isLocalizedModule_iff_isLocalization (S := S) (A := R) (Aₛ := A)
+  convert! isLocalizedModule_iff_isLocalization (S := S) (A := R) (Aₛ := A)
   exact (Submonoid.map_id S).symm
 
 instance [IsLocalization S A] : IsLocalizedModule S (Algebra.linearMap R A) :=
diff --git a/Mathlib/Algebra/Module/NatInt.lean b/Mathlib/Algebra/Module/NatInt.lean
index 3ef0af81898905..9daa84aa1c71eb 100644
--- a/Mathlib/Algebra/Module/NatInt.lean
+++ b/Mathlib/Algebra/Module/NatInt.lean
@@ -134,7 +134,7 @@ should normally have exactly one `ℕ`-module structure by design. -/
 @[implicit_reducible]
 def AddCommMonoid.uniqueNatModule : Unique (Module ℕ M) where
   default := inferInstance
-  uniq P := (Module.ext' P _) fun n => by convert nat_smul_eq_nsmul P n
+  uniq P := (Module.ext' P _) fun n => by convert! nat_smul_eq_nsmul P n
 
 /-- All `ℕ`-module structures are equal. See also `AddCommMonoid.uniqueNatModule`. -/
 instance AddCommMonoid.subsingletonNatModule : Subsingleton (Module ℕ M) :=
@@ -186,7 +186,7 @@ should normally have exactly one `ℤ`-module structure by design. -/
 @[implicit_reducible]
 def AddCommGroup.uniqueIntModule : Unique (Module ℤ M) where
   default := inferInstance
-  uniq P := (Module.ext' P _) fun n => by convert int_smul_eq_zsmul P n
+  uniq P := (Module.ext' P _) fun n => by convert! int_smul_eq_zsmul P n
 
 end AddCommGroup
 
diff --git a/Mathlib/Algebra/Module/PID.lean b/Mathlib/Algebra/Module/PID.lean
index 3a0d5fd8cef26b..afc20225a1d2ba 100644
--- a/Mathlib/Algebra/Module/PID.lean
+++ b/Mathlib/Algebra/Module/PID.lean
@@ -80,7 +80,7 @@ theorem Submodule.isInternal_prime_power_torsion_of_pid [Module.Finite R M]
       torsionBy R M
         (IsPrincipal.generator (p : Ideal R) ^
           (factors (⊤ : Submodule R M).annihilator).count ↑p) := by
-  convert isInternal_prime_power_torsion hM
+  convert! isInternal_prime_power_torsion hM
   rw [← torsionBySet_span_singleton_eq, Ideal.submodule_span_eq, ← Ideal.span_singleton_pow,
     Ideal.span_singleton_generator]
 
@@ -120,8 +120,9 @@ theorem _root_.Ideal.torsionOf_eq_span_pow_pOrder (x : M) :
       (Associates.mk <| generator <| torsionOf R M x) ∣ Associates.mk p ^ n := by
     ext n; rw [← Associates.mk_pow, Associates.mk_dvd_mk, ← mem_iff_generator_dvd]; rfl
   have := (isTorsion'_powers_iff p).mp hM x; rw [prop] at this
-  convert Associates.eq_pow_find_of_dvd_irreducible_pow (Associates.irreducible_mk.mpr hp)
-    this.choose_spec
+  convert!
+    Associates.eq_pow_find_of_dvd_irreducible_pow (Associates.irreducible_mk.mpr hp)
+      this.choose_spec
 
 theorem p_pow_smul_lift {x y : M} {k : ℕ} (hM' : Module.IsTorsionBy R M (p ^ pOrder hM y))
     (h : p ^ k • x ∈ R ∙ y) : ∃ a : R, p ^ k • x = p ^ k • a • y := by
@@ -132,7 +133,7 @@ theorem p_pow_smul_lift {x y : M} {k : ℕ} (hM' : Module.IsTorsionBy R M (p ^ p
     · have : f.symm ⟨p ^ k • x, h⟩ ∈
           R ∙ Ideal.Quotient.mk (R ∙ p ^ (pOrder hM y - k) * p ^ k) (p ^ k) := by
         rw [← Quotient.torsionBy_eq_span_singleton, mem_torsionBy_iff, ← f.symm.map_smul]
-        · convert f.symm.map_zero; ext
+        · convert! f.symm.map_zero; ext
           rw [coe_smul_of_tower, coe_mk, coe_zero, smul_smul, ← pow_add, Nat.sub_add_cancel hk,
             @hM' x]
         · exact mem_nonZeroDivisors_of_ne_zero (pow_ne_zero _ hp.ne_zero)
@@ -141,7 +142,7 @@ theorem p_pow_smul_lift {x y : M} {k : ℕ} (hM' : Module.IsTorsionBy R M (p ^ p
       dsimp only [smul_eq_mul, LinearEquiv.trans_apply, Submodule.quotEquivOfEq_mk,
         quotTorsionOfEquivSpanSingleton_apply_mk] at ha
       rw [smul_smul, mul_comm]; exact congr_arg ((↑) : _ → M) ha.symm
-    · symm; convert Ideal.torsionOf_eq_span_pow_pOrder hp hM y
+    · symm; convert! Ideal.torsionOf_eq_span_pow_pOrder hp hM y
       rw [← pow_add, Nat.sub_add_cancel hk]
   · use 0
     rw [zero_smul, smul_zero, ← Nat.sub_add_cancel hk.le, pow_add, mul_smul, hM',
@@ -155,7 +156,7 @@ theorem exists_smul_eq_zero_and_mk_eq {z : M} (hz : Module.IsTorsionBy R M (p ^
   have f1 := mk_surjective (R ∙ z) (f 1)
   have : p ^ k • f1.choose ∈ R ∙ z := by
     rw [← Quotient.mk_eq_zero, mk_smul, f1.choose_spec, ← f.map_smul]
-    convert f.map_zero; change _ • Submodule.Quotient.mk _ = _
+    convert! f.map_zero; change _ • Submodule.Quotient.mk _ = _
     rw [← mk_smul, Quotient.mk_eq_zero, smul_eq_mul, mul_one]
     exact Submodule.mem_span_singleton_self _
   obtain ⟨a, ha⟩ := p_pow_smul_lift hp hM hz this
diff --git a/Mathlib/Algebra/Module/Presentation/Tensor.lean b/Mathlib/Algebra/Module/Presentation/Tensor.lean
index 6228317222b3af..113f78c9782890 100644
--- a/Mathlib/Algebra/Module/Presentation/Tensor.lean
+++ b/Mathlib/Algebra/Module/Presentation/Tensor.lean
@@ -82,7 +82,7 @@ noncomputable def isPresentationCoreTensor :
         erw [Finsupp.apply_linearCombination A (LinearMap.applyₗ (solution₂.var g₂))]
         have := s.linearCombination_var_relation (.inl ⟨r₁, g₂⟩)
         erw [Finsupp.linearCombination_embDomain] at this
-        convert this
+        convert! this
         ext g₁
         simp) })
   postcomp_desc _ := by aesop
diff --git a/Mathlib/Algebra/Module/SpanRank.lean b/Mathlib/Algebra/Module/SpanRank.lean
index 33f0758e90c49e..b987823c938eba 100644
--- a/Mathlib/Algebra/Module/SpanRank.lean
+++ b/Mathlib/Algebra/Module/SpanRank.lean
@@ -154,7 +154,7 @@ lemma spanRank_span_range_of_linearIndependent [RankCondition R] {ι : Type u} {
   rw [this]
   refine le_trans ?_ ((Module.Basis.span hs).le_span (R := R) (J := Subtype.val ⁻¹' x.1) ?_)
   · rw [mk_range_eq]
-    exact .of_comp (f := Subtype.val) (by convert hv; ext; simp [Module.Basis.span_apply])
+    exact .of_comp (f := Subtype.val) (by convert! hv; ext; simp [Module.Basis.span_apply])
   · apply map_injective_of_injective (f := (span R _).subtype) (injective_subtype _)
     simp [map_span, Set.image_preimage_eq_inter_range, Set.inter_eq_self_of_subset_left, ← x.2]
 
@@ -210,7 +210,7 @@ lemma lift_spanRank_le_iff_exists_span_set_card_le (p : Submodule R M) {a : Card
   if and only if there is a generating subset with cardinality less than or equal to `a`. -/
 lemma FG.spanRank_le_iff_exists_span_set_card_le (p : Submodule R M) {a : Cardinal} :
     p.spanRank ≤ a ↔ ∃ s : Set M, #s ≤ a ∧ span R s = p := by
-  convert lift_spanRank_le_iff_exists_span_set_card_le p (a := a) <;> simp
+  convert! lift_spanRank_le_iff_exists_span_set_card_le p (a := a) <;> simp
 
 @[simp]
 lemma spanRank_eq_zero_iff_eq_bot {I : Submodule R M} : I.spanRank = 0 ↔ I = ⊥ := by
diff --git a/Mathlib/Algebra/Module/SpanRankOperations.lean b/Mathlib/Algebra/Module/SpanRankOperations.lean
index d9e70da64c568f..1fbbd6c6ab8a0d 100644
--- a/Mathlib/Algebra/Module/SpanRankOperations.lean
+++ b/Mathlib/Algebra/Module/SpanRankOperations.lean
@@ -36,7 +36,7 @@ variable {R A : Type*} [CommRing R] [CommRing A] [Algebra R A]
 lemma Submodule.spanRank_baseChange_le : (N.baseChange A).spanRank ≤ N.spanRank.lift := by
   obtain ⟨s, hs₁, hs₂⟩ := N.exists_span_set_card_eq_spanRank
   grw [← hs₁, ← hs₂, baseChange_span, spanRank_span_le_card]
-  convert Cardinal.mk_image_le_lift (f := TensorProduct.mk R A M 1) (s := s)
+  convert! Cardinal.mk_image_le_lift (f := TensorProduct.mk R A M 1) (s := s)
   · exact (Cardinal.lift_id' _).symm
   · exact Cardinal.lift_umax.symm
 
diff --git a/Mathlib/Algebra/Module/Submodule/Union.lean b/Mathlib/Algebra/Module/Submodule/Union.lean
index 29dbb5e9fdb41e..d0d0cd335e64d3 100644
--- a/Mathlib/Algebra/Module/Submodule/Union.lean
+++ b/Mathlib/Algebra/Module/Submodule/Union.lean
@@ -79,10 +79,10 @@ lemma Submodule.iUnion_ssubset_of_forall_ne_top_of_card_lt (s : Finset ι) (p :
       obtain ⟨z₁, -, z₂, -, h⟩ := exists_ne_map_eq_of_encard_lt_of_maps_to (by simpa) hf'
       exact ⟨z₁, z₂, h⟩
     replace ht : y ∈ p k := by
-      have : (t₁ - t₂) • y ∈ p k := by convert sub_mem ht₁ ht₂ using 1; module
+      have : (t₁ - t₂) • y ∈ p k := by convert! sub_mem ht₁ ht₂ using 1; module
       refine ((p k).smul_mem_iff ?_).mp this
       rwa [sub_ne_zero]
-    replace ht : x ∈ p k := by convert sub_mem ht₁ ((p k).smul_mem t₁ ht); simp
+    replace ht : x ∈ p k := by convert! sub_mem ht₁ ((p k).smul_mem t₁ ht); simp
     simpa using ⟨k, hk, ht⟩
 
 variable [Finite ι] [Infinite K]
diff --git a/Mathlib/Algebra/Module/Torsion/Basic.lean b/Mathlib/Algebra/Module/Torsion/Basic.lean
index 234865b3c92a94..31b3af552ce7d4 100644
--- a/Mathlib/Algebra/Module/Torsion/Basic.lean
+++ b/Mathlib/Algebra/Module/Torsion/Basic.lean
@@ -134,7 +134,7 @@ theorem iSupIndep.linearIndependent' {ι R M : Type*} {v : ι → M} [Ring R]
   have : r • v i ∈ (⊥ : Submodule R M) := by
     rw [← hv, Submodule.mem_inf]
     refine ⟨Submodule.mem_span_singleton.mpr ⟨r, rfl⟩, ?_⟩
-    convert hi
+    convert! hi
     ext
     simp
   rw [← Submodule.mem_bot R, ← h_ne_zero i]
@@ -495,7 +495,8 @@ theorem iSup_torsionBy_eq_torsionBy_prod (hq : (S : Set ι).Pairwise <| (IsCopri
 
 theorem supIndep_torsionBy (hq : (S : Set ι).Pairwise <| (IsCoprime on q)) :
     S.SupIndep fun i => torsionBy R M <| q i := by
-  convert supIndep_torsionBySet_ideal (M := M) fun i hi j hj ij =>
+  convert!
+    supIndep_torsionBySet_ideal (M := M) fun i hi j hj ij =>
       (Ideal.sup_eq_top_iff_isCoprime (q i) _).mpr <| hq hi hj ij
   exact (torsionBySet_span_singleton_eq (R := R) (M := M) _).symm
 
@@ -534,7 +535,8 @@ theorem torsionBy_isInternal {q : ι → R} (hq : (S : Set ι).Pairwise <| (IsCo
     DirectSum.IsInternal fun i : S => torsionBy R M <| q i := by
   rw [← Module.isTorsionBySet_span_singleton_iff, Ideal.submodule_span_eq, ←
     Ideal.finset_inf_span_singleton _ _ hq, Finset.inf_eq_iInf] at hM
-  convert torsionBySet_isInternal
+  convert!
+    torsionBySet_isInternal
       (fun i hi j hj ij => (Ideal.sup_eq_top_iff_isCoprime (q i) _).mpr <| hq hi hj ij) hM
   exact (torsionBySet_span_singleton_eq _ (R := R) (M := M)).symm
 
diff --git a/Mathlib/Algebra/Module/ZLattice/Basic.lean b/Mathlib/Algebra/Module/ZLattice/Basic.lean
index 9587b73067d755..d64159380b87c0 100644
--- a/Mathlib/Algebra/Module/ZLattice/Basic.lean
+++ b/Mathlib/Algebra/Module/ZLattice/Basic.lean
@@ -220,7 +220,7 @@ theorem norm_fract_le [HasSolidNorm K] (m : E) : ‖fract b m‖ ≤ ∑ i, ‖b
     _ = ∑ i, ‖Int.fract (b.repr m i)‖ * ‖b i‖ := by simp_rw [norm_smul]
     _ ≤ ∑ i, ‖b i‖ := Finset.sum_le_sum fun i _ => ?_
   suffices ‖Int.fract ((b.repr m) i)‖ ≤ 1 by
-    convert mul_le_mul_of_nonneg_right this (norm_nonneg _ : 0 ≤ ‖b i‖)
+    convert! mul_le_mul_of_nonneg_right this (norm_nonneg _ : 0 ≤ ‖b i‖)
     exact (one_mul _).symm
   rw [(norm_one.symm : 1 = ‖(1 : K)‖)]
   apply norm_le_norm_of_abs_le_abs
@@ -321,7 +321,7 @@ instance [Finite ι] : DiscreteTopology (span ℤ (Set.range b)) := by
   have h : Set.MapsTo b.equivFun (span ℤ (Set.range b)) (span ℤ (Set.range (Pi.basisFun ℝ ι))) := by
     intro _ hx
     rwa [SetLike.mem_coe, Basis.mem_span_iff_repr_mem] at hx ⊢
-  convert DiscreteTopology.of_continuous_injective ((continuous_equivFun_basis b).restrict h) ?_
+  convert! DiscreteTopology.of_continuous_injective ((continuous_equivFun_basis b).restrict h) ?_
   · exact discreteTopology_pi_basisFun
   · refine Subtype.map_injective _ (Basis.equivFun b).injective
 
@@ -366,14 +366,14 @@ protected theorem isAddFundamentalDomain' [Finite ι] [MeasurableSpace E] [Opens
 theorem measure_fundamentalDomain_ne_zero [Finite ι] [MeasurableSpace E] [BorelSpace E]
     {μ : Measure E} [Measure.IsAddHaarMeasure μ] :
     μ (fundamentalDomain b) ≠ 0 := by
-  convert (ZSpan.isAddFundamentalDomain b μ).measure_ne_zero (NeZero.ne μ)
+  convert! (ZSpan.isAddFundamentalDomain b μ).measure_ne_zero (NeZero.ne μ)
   exact inferInstanceAs <| VAddInvariantMeasure (span ℤ (Set.range b)).toAddSubgroup E μ
 
 theorem measure_fundamentalDomain [Fintype ι] [DecidableEq ι] [MeasurableSpace E] (μ : Measure E)
     [BorelSpace E] [Measure.IsAddHaarMeasure μ] (b₀ : Basis ι ℝ E) :
     μ (fundamentalDomain b) = ENNReal.ofReal |b₀.det b| * μ (fundamentalDomain b₀) := by
   have : FiniteDimensional ℝ E := b.finiteDimensional_of_finite
-  convert μ.addHaar_preimage_linearEquiv (b.equiv b₀ (Equiv.refl ι)) (fundamentalDomain b₀)
+  convert! μ.addHaar_preimage_linearEquiv (b.equiv b₀ (Equiv.refl ι)) (fundamentalDomain b₀)
   · rw [Set.eq_preimage_iff_image_eq (LinearEquiv.bijective _), map_fundamentalDomain,
       Basis.map_equiv, Equiv.refl_symm, Basis.reindex_refl]
   · simp
@@ -500,7 +500,7 @@ instance instModuleFinite_of_discrete_submodule {E : Type*} [NormedAddCommGroup
   suffices Module.Finite ℤ L₀ by
     have : L₀.map (f.restrictScalars ℤ) = L :=
       SetLike.ext'_iff.mpr h_img
-    convert this ▸ Module.Finite.map L₀ (f.restrictScalars ℤ)
+    convert! this ▸ Module.Finite.map L₀ (f.restrictScalars ℤ)
   have : DiscreteTopology L₀ := by
     refine DiscreteTopology.preimage_of_continuous_injective (L : Set E) ?_ (injective_subtype _)
     exact LinearMap.continuous_of_finiteDimensional f
@@ -534,7 +534,7 @@ theorem ZLattice.rank [hs : IsZLattice K L] : finrank ℤ L = finrank K E := by
     LinearIndependent.map' b₀.linearIndependent (L.subtype) (ker_subtype _)
   -- We prove some assertions that will be useful later on
   have h_spanL : span ℤ (Set.range b) = L := by
-    convert congrArg (map (Submodule.subtype L)) b₀.span_eq
+    convert! congrArg (map (Submodule.subtype L)) b₀.span_eq
     · rw [map_span, Set.range_comp]
       rfl
     · exact (map_subtype_top _).symm
@@ -602,7 +602,7 @@ theorem ZLattice.rank [hs : IsZLattice K L] : finrank ℤ L = finrank K E := by
   · -- To prove that `finrank K E ≤ finrank ℤ L`, we use the fact `b` generates `E` over `K`
     -- and thus `finrank K E ≤ card b = finrank ℤ L`
     rw [← topEquiv.finrank_eq, ← h_spanE]
-    convert finrank_span_le_card (R := K) (Set.range b)
+    convert! finrank_span_le_card (R := K) (Set.range b)
 
 variable {ι : Type*} [hs : IsZLattice K L] (b : Basis ι ℤ L)
 
@@ -647,7 +647,7 @@ theorem ZLattice.isAddFundamentalDomain {E : Type*} [NormedAddCommGroup E] [Norm
     [FiniteDimensional ℝ E] {L : Submodule ℤ E} [DiscreteTopology L] [IsZLattice ℝ L] [Finite ι]
     (b : Basis ι ℤ L) [MeasurableSpace E] [OpensMeasurableSpace E] (μ : Measure E) :
     IsAddFundamentalDomain L (fundamentalDomain (b.ofZLatticeBasis ℝ)) μ := by
-  convert ZSpan.isAddFundamentalDomain (b.ofZLatticeBasis ℝ) μ
+  convert! ZSpan.isAddFundamentalDomain (b.ofZLatticeBasis ℝ) μ
   all_goals exact (b.ofZLatticeBasis_span ℝ).symm
 
 instance instCountable_of_discrete_submodule {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]
@@ -795,7 +795,7 @@ lemma IsZLattice.isCompact_range_of_periodic
     (hf' : ∀ z w, w ∈ L → f (z + w) = f z) : IsCompact (Set.range f) := by
   have := ZLattice.module_free ℝ L
   let b := Module.Free.chooseBasis ℤ L
-  convert (b.ofZLatticeBasis ℝ).parallelepiped.isCompact.image hf
+  convert! (b.ofZLatticeBasis ℝ).parallelepiped.isCompact.image hf
   refine le_antisymm ?_ (Set.image_subset_range _ _)
   rintro _ ⟨x, rfl⟩
   let x' : L := b.repr.symm (Finsupp.equivFunOnFinite.symm
diff --git a/Mathlib/Algebra/Module/ZLattice/Covolume.lean b/Mathlib/Algebra/Module/ZLattice/Covolume.lean
index f80dac1228c44b..05d7349d94a083 100644
--- a/Mathlib/Algebra/Module/ZLattice/Covolume.lean
+++ b/Mathlib/Algebra/Module/ZLattice/Covolume.lean
@@ -313,7 +313,7 @@ theorem tendsto_card_div_pow (b : Basis ι ℤ L) {s : Set (ι → ℝ)} (hs₁
     Tendsto (fun n : ℕ ↦ (Nat.card (s ∩ (n : ℝ)⁻¹ • L : Set (ι → ℝ)) : ℝ) / n ^ card ι)
       atTop (𝓝 (volume.real s / covolume L)) := by
   classical
-  convert tendsto_card_div_pow'' b hs₁ hs₂ ?_
+  convert! tendsto_card_div_pow'' b hs₁ hs₂ ?_
   · simp only [measureReal_def]
     rw [volume_image_eq_volume_div_covolume L b, ENNReal.toReal_div,
       ENNReal.toReal_ofReal (covolume_pos L volume).le]
@@ -331,7 +331,7 @@ theorem tendsto_card_le_div {X : Set (ι → ℝ)} (hX : ∀ ⦃x⦄ ⦃r : ℝ
     refine Fintype.equivOfCardEq ?_
     rw [← finrank_eq_card_chooseBasisIndex, ZLattice.rank ℝ, finrank_fintype_fun_eq_card]
   let b := (Module.Free.chooseBasis ℤ L).reindex e
-  convert tendsto_card_le_div'' b hX h₁ h₂ h₃ ?_
+  convert! tendsto_card_le_div'' b hX h₁ h₂ h₃ ?_
   · simp only [measureReal_def]
     rw [volume_image_eq_volume_div_covolume L b, ENNReal.toReal_div,
       ENNReal.toReal_ofReal (covolume_pos L volume).le]
@@ -354,7 +354,7 @@ theorem tendsto_card_div_pow' {s : Set E} (hs₁ : IsBounded s) (hs₂ : Measura
     Tendsto (fun n : ℕ ↦ (Nat.card (s ∩ (n : ℝ)⁻¹ • L : Set E) : ℝ) / n ^ finrank ℝ E)
       atTop (𝓝 (volume.real s / covolume L)) := by
   let b := Module.Free.chooseBasis ℤ L
-  convert tendsto_card_div_pow'' b hs₁ hs₂ ?_
+  convert! tendsto_card_div_pow'' b hs₁ hs₂ ?_
   · rw [← finrank_eq_card_chooseBasisIndex, ZLattice.rank ℝ L]
   · simp only [measureReal_def]
     rw [volume_image_eq_volume_div_covolume' L b hs₂.nullMeasurableSet, ENNReal.toReal_div,
@@ -373,7 +373,7 @@ theorem tendsto_card_le_div' [Nontrivial E] {X : Set E} {F : E → ℝ}
       Nat.card ({x ∈ X | F x ≤ c} ∩ L : Set E) / (c : ℝ))
         atTop (𝓝 (volume.real {x ∈ X | F x ≤ 1} / covolume L)) := by
   let b := Module.Free.chooseBasis ℤ L
-  convert tendsto_card_le_div'' b hX ?_ h₂ h₃ ?_
+  convert! tendsto_card_le_div'' b hX ?_ h₂ h₃ ?_
   · simp only [measureReal_def]
     rw [volume_image_eq_volume_div_covolume' L b h₃.nullMeasurableSet, ENNReal.toReal_div,
       ENNReal.toReal_ofReal (covolume_pos L volume).le]
diff --git a/Mathlib/Algebra/Module/ZLattice/Summable.lean b/Mathlib/Algebra/Module/ZLattice/Summable.lean
index f5153042db9894..6eebe7ce684f72 100644
--- a/Mathlib/Algebra/Module/ZLattice/Summable.lean
+++ b/Mathlib/Algebra/Module/ZLattice/Summable.lean
@@ -194,7 +194,7 @@ lemma exists_finsetSum_norm_rpow_le_tsum :
     refine (Finset.sum_le_sum_of_subset_of_nonneg hn (by intros; positivity)).trans ?_
     dsimp
     simp only [Submodule.norm_coe]
-    convert sum_piFinset_Icc_rpow_le b rfl n r hr with x
+    convert! sum_piFinset_Icc_rpow_le b rfl n r hr with x
     simp [e, Finsupp.linearCombination]
   by_cases hA' : A ≤ 1
   · refine ⟨B, hB, fun r hr s ↦ (H r hr s).trans ?_⟩
diff --git a/Mathlib/Algebra/MonoidAlgebra/Grading.lean b/Mathlib/Algebra/MonoidAlgebra/Grading.lean
index 4224d143ee24d4..618855dacd15c4 100644
--- a/Mathlib/Algebra/MonoidAlgebra/Grading.lean
+++ b/Mathlib/Algebra/MonoidAlgebra/Grading.lean
@@ -125,7 +125,7 @@ def decomposeAux : R[M] →ₐ[R] ⨁ i : ι, gradeBy R f i :=
         symm
         dsimp +instances only [toAdd_one, Eq.ndrec, Set.mem_setOf_eq, ne_eq, OneHom.toFun_eq_coe,
           OneHom.coe_mk, toAdd_mul]
-        convert DirectSum.of_mul_of (A := (fun i : ι => gradeBy R f i)) _ _
+        convert! DirectSum.of_mul_of (A := (fun i : ι => gradeBy R f i)) _ _
         repeat { rw [map_add] }
         simp only [SetLike.coe_gMul]
         exact Eq.trans (by rw [one_mul]) (single_mul_single ..).symm }
diff --git a/Mathlib/Algebra/MvPolynomial/Basic.lean b/Mathlib/Algebra/MvPolynomial/Basic.lean
index f3eb44382587c7..5864892d7b989a 100644
--- a/Mathlib/Algebra/MvPolynomial/Basic.lean
+++ b/Mathlib/Algebra/MvPolynomial/Basic.lean
@@ -1029,7 +1029,7 @@ lemma mem_coeffsIn_iff_coeffs_subset : p ∈ coeffsIn σ M ↔ (p.coeffs : Set S
   refine ⟨fun h x _ ↦ h x, fun h i ↦ ?_⟩
   by_cases hp : i ∈ p.support
   · exact h hp
-  · convert M.zero_mem
+  · convert! M.zero_mem
     simpa using hp
 
 end Module
diff --git a/Mathlib/Algebra/MvPolynomial/Comap.lean b/Mathlib/Algebra/MvPolynomial/Comap.lean
index 44f783485ab228..42d07387513d8b 100644
--- a/Mathlib/Algebra/MvPolynomial/Comap.lean
+++ b/Mathlib/Algebra/MvPolynomial/Comap.lean
@@ -78,7 +78,7 @@ theorem comap_comp (f : MvPolynomial σ R →ₐ[R] MvPolynomial τ R)
 
 theorem comap_eq_id_of_eq_id (f : MvPolynomial σ R →ₐ[R] MvPolynomial σ R) (hf : ∀ φ, f φ = φ)
     (x : σ → R) : comap f x = x := by
-  convert comap_id_apply x
+  convert! comap_id_apply x
   ext1 φ
   simp [hf, AlgHom.id_apply]
 
diff --git a/Mathlib/Algebra/MvPolynomial/CommRing.lean b/Mathlib/Algebra/MvPolynomial/CommRing.lean
index 179dbb992331bd..5c3e6834ebc6ba 100644
--- a/Mathlib/Algebra/MvPolynomial/CommRing.lean
+++ b/Mathlib/Algebra/MvPolynomial/CommRing.lean
@@ -112,13 +112,13 @@ section Vars
 theorem vars_neg : (-p).vars = p.vars := by simp [vars, degrees_neg]
 
 theorem vars_sub_subset [DecidableEq σ] : (p - q).vars ⊆ p.vars ∪ q.vars := by
-  convert vars_add_subset p (-q) using 2 <;> simp [sub_eq_add_neg]
+  convert! vars_add_subset p (-q) using 2 <;> simp [sub_eq_add_neg]
 
 @[simp]
 theorem vars_sub_of_disjoint [DecidableEq σ] (hpq : Disjoint p.vars q.vars) :
     (p - q).vars = p.vars ∪ q.vars := by
   rw [← vars_neg q] at hpq
-  convert vars_add_of_disjoint hpq using 2 <;> simp [sub_eq_add_neg]
+  convert! vars_add_of_disjoint hpq using 2 <;> simp [sub_eq_add_neg]
 
 end Vars
 
diff --git a/Mathlib/Algebra/MvPolynomial/Degrees.lean b/Mathlib/Algebra/MvPolynomial/Degrees.lean
index 0decdace651b86..7b595c7d04643f 100644
--- a/Mathlib/Algebra/MvPolynomial/Degrees.lean
+++ b/Mathlib/Algebra/MvPolynomial/Degrees.lean
@@ -82,7 +82,8 @@ def degrees (p : MvPolynomial σ R) : Multiset σ :=
   p.support.sup fun s : σ →₀ ℕ => toMultiset s
 
 theorem degrees_def [DecidableEq σ] (p : MvPolynomial σ R) :
-    p.degrees = p.support.sup fun s : σ →₀ ℕ => Finsupp.toMultiset s := by rw [degrees]; convert rfl
+    p.degrees = p.support.sup fun s : σ →₀ ℕ => Finsupp.toMultiset s := by rw [degrees]; convert!
+      rfl
 
 theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) ≤ toMultiset s := by
   classical
@@ -217,7 +218,7 @@ def degreeOf (n : σ) (p : MvPolynomial σ R) : ℕ :=
   p.degrees.count n
 
 theorem degreeOf_def [DecidableEq σ] (n : σ) (p : MvPolynomial σ R) :
-    p.degreeOf n = p.degrees.count n := by rw [degreeOf]; convert rfl
+    p.degreeOf n = p.degrees.count n := by rw [degreeOf]; convert! rfl
 
 theorem degreeOf_eq_sup (n : σ) (f : MvPolynomial σ R) :
     degreeOf n f = f.support.sup fun m => m n := by
@@ -297,7 +298,7 @@ theorem degreeOf_mul_le (i : σ) (f g : MvPolynomial σ R) :
     degreeOf i (f * g) ≤ degreeOf i f + degreeOf i g := by
   classical
   simp only [degreeOf]
-  convert Multiset.count_le_of_le i degrees_mul_le
+  convert! Multiset.count_le_of_le i degrees_mul_le
   rw [Multiset.count_add]
 
 theorem degreeOf_sum_le {ι : Type*} (i : σ) (s : Finset ι) (f : ι → MvPolynomial σ R) :
@@ -335,7 +336,7 @@ theorem degreeOf_mul_X_self (j : σ) (f : MvPolynomial σ R) :
   simp only [degreeOf]
   apply (Multiset.count_le_of_le j degrees_mul_le).trans
   simp only [Multiset.count_add, add_le_add_iff_left]
-  convert Multiset.count_le_of_le j <| degrees_X' j
+  convert! Multiset.count_le_of_le j <| degrees_X' j
   rw [Multiset.count_singleton_self]
 
 theorem degreeOf_X_pow_of_ne {i j : σ} (k : ℕ) (h : i ≠ j) :
@@ -407,13 +408,13 @@ theorem degreeOf_eq_of_degreeOf_add_lt {i : σ} (h : (p + q).degreeOf i < p.degr
 theorem degreeOf_C_mul_le (p : MvPolynomial σ R) (i : σ) (c : R) :
     (C c * p).degreeOf i ≤ p.degreeOf i := by
   unfold degreeOf
-  convert Multiset.count_le_of_le i degrees_mul_le
+  convert! Multiset.count_le_of_le i degrees_mul_le
   simp only [degrees_C, zero_add]
 
 theorem degreeOf_mul_C_le (p : MvPolynomial σ R) (i : σ) (c : R) :
     (p * C c).degreeOf i ≤ p.degreeOf i := by
   unfold degreeOf
-  convert Multiset.count_le_of_le i degrees_mul_le
+  convert! Multiset.count_le_of_le i degrees_mul_le
   simp only [degrees_C, add_zero]
 
 theorem degreeOf_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f)
diff --git a/Mathlib/Algebra/MvPolynomial/Equiv.lean b/Mathlib/Algebra/MvPolynomial/Equiv.lean
index 7f75f77ee60549..f2c178f30e62ec 100644
--- a/Mathlib/Algebra/MvPolynomial/Equiv.lean
+++ b/Mathlib/Algebra/MvPolynomial/Equiv.lean
@@ -499,7 +499,7 @@ theorem optionEquivLeft_elim_eval (s : S₁ → R) (y : R) (f : MvPolynomial (Op
   let φ : (MvPolynomial S₁ R)[X] →ₐ[R] R[X] :=
     { Polynomial.mapRingHom (eval s) with
       commutes' := fun r => by
-        convert Polynomial.map_C (eval s)
+        convert! Polynomial.map_C (eval s)
         exact (eval_C _).symm }
   change
     aeval (fun x ↦ Option.elim x y s) f =
@@ -681,7 +681,7 @@ theorem eval_eq_eval_mv_eval' (s : Fin n → R) (y : R) (f : MvPolynomial (Fin (
   let φ : (MvPolynomial (Fin n) R)[X] →ₐ[R] R[X] :=
     { Polynomial.mapRingHom (eval s) with
       commutes' := fun r => by
-        convert Polynomial.map_C (eval s)
+        convert! Polynomial.map_C (eval s)
         exact (eval_C _).symm }
   change
     aeval (Fin.cons y s : Fin (n + 1) → R) f =
@@ -725,7 +725,7 @@ lemma totalDegree_coeff_finSuccEquiv_add_le (f : MvPolynomial (Fin (n + 1)) R) (
                           (fun s => Finsupp.sum s fun _ e => e)
   -- Then cons i σ is a monomial index of p with total degree equal to the desired bound
   let σ' : Fin (n + 1) →₀ ℕ := cons i σ
-  convert le_totalDegree (s := σ') _
+  convert! le_totalDegree (s := σ') _
   · rw [totalDegree, hσ2, sum_cons, add_comm]
   · rw [← mem_support_coeff_finSuccEquiv]
     exact hσ1
@@ -802,7 +802,7 @@ lemma degreeOf_eq_natDegree [DecidableEq σ] (a : σ) (p : MvPolynomial σ R) :
     degreeOf a p =
       (optionEquivLeft R {b // b ≠ a} (rename (Equiv.optionSubtypeNe a).symm p)).natDegree := by
   rw [natDegree_optionEquivLeft, eq_comm]
-  convert degreeOf_rename_of_injective (Equiv.injective (Equiv.optionSubtypeNe a).symm) a
+  convert! degreeOf_rename_of_injective (Equiv.injective (Equiv.optionSubtypeNe a).symm) a
   rw [Equiv.optionSubtypeNe_symm_apply, dif_pos rfl]
 
 theorem degreeOf_coeff_finSuccEquiv (p : MvPolynomial (Fin (n + 1)) R) (j : Fin n) (i : ℕ) :
diff --git a/Mathlib/Algebra/MvPolynomial/Funext.lean b/Mathlib/Algebra/MvPolynomial/Funext.lean
index e4bc0a79200a5e..571af32ac4a8d0 100644
--- a/Mathlib/Algebra/MvPolynomial/Funext.lean
+++ b/Mathlib/Algebra/MvPolynomial/Funext.lean
@@ -37,7 +37,7 @@ private theorem funext_fin {n : ℕ} {p : MvPolynomial (Fin n) R}
   | zero =>
     apply (MvPolynomial.isEmptyRingEquiv R (Fin 0)).injective
     rw [map_zero]
-    convert h _ finZeroElim
+    convert! h _ finZeroElim
   | succ n ih =>
     apply (finSuccEquiv R n).injective
     rw [map_zero]
@@ -66,7 +66,7 @@ theorem funext_set (h : ∀ x ∈ Set.pi .univ s, eval x p = eval x q) :
   suffices p = 0 by rw [this, map_zero]
   refine funext_fin (s ∘ f) (fun _ ↦ hs _) fun x hx ↦ ?_
   choose g hg using fun i ↦ (hs i).nonempty
-  convert h (Function.extend f x g) fun i _ ↦ ?_
+  convert! h (Function.extend f x g) fun i _ ↦ ?_
   · simp only [eval, eval₂Hom_rename, Function.extend_comp hf]
   obtain ⟨i, rfl⟩ | nex := em (∃ x, f x = i)
   · rw [hf.extend_apply]; exact hx _ ⟨⟩
diff --git a/Mathlib/Algebra/MvPolynomial/Nilpotent.lean b/Mathlib/Algebra/MvPolynomial/Nilpotent.lean
index 4c3e1149197c78..817993a0c2ab17 100644
--- a/Mathlib/Algebra/MvPolynomial/Nilpotent.lean
+++ b/Mathlib/Algebra/MvPolynomial/Nilpotent.lean
@@ -63,7 +63,7 @@ theorem isUnit_iff : IsUnit P ↔ IsUnit (P.coeff 0) ∧ ∀ i ≠ 0, IsNilpoten
     let e := (optionEquivLeft _ _).symm.trans (renameEquiv R (Equiv.optionSubtypeNe i))
     have H := (Polynomial.coeff_isUnit_isNilpotent_of_isUnit (H.map e.symm)).2 (n i) hi
     simp only [ne_eq, isNilpotent_iff] at H
-    convert ← H (n.equivMapDomain (Equiv.optionSubtypeNe i).symm).some
+    convert! ← H (n.equivMapDomain (Equiv.optionSubtypeNe i).symm).some
     refine (optionEquivLeft_coeff_some_coeff_none _ _ _ _).trans ?_
     simp [Finsupp.equivMapDomain_eq_mapDomain,
       coeff_rename_mapDomain _ (Equiv.optionSubtypeNe i).symm.injective]
@@ -79,7 +79,7 @@ instance : IsLocalHom (algebraMap R (MvPolynomial σ R)) :=
 
 theorem isUnit_iff_totalDegree_of_isReduced [IsReduced R] :
     IsUnit P ↔ IsUnit (P.coeff 0) ∧ P.totalDegree = 0 := by
-  convert isUnit_iff (P := P)
+  convert! isUnit_iff (P := P)
   rw [totalDegree_eq_zero_iff]
   simp [not_imp_comm (a := _ = (0 : R)), Finsupp.ext_iff]
 
diff --git a/Mathlib/Algebra/MvPolynomial/Variables.lean b/Mathlib/Algebra/MvPolynomial/Variables.lean
index 7e19c42a224604..a832754446ea5a 100644
--- a/Mathlib/Algebra/MvPolynomial/Variables.lean
+++ b/Mathlib/Algebra/MvPolynomial/Variables.lean
@@ -72,7 +72,7 @@ def vars (p : MvPolynomial σ R) : Finset σ :=
 
 theorem vars_def [DecidableEq σ] (p : MvPolynomial σ R) : p.vars = p.degrees.toFinset := by
   rw [vars]
-  convert rfl
+  convert! rfl
 
 @[simp]
 theorem vars_0 : (0 : MvPolynomial σ R).vars = ∅ := by
diff --git a/Mathlib/Algebra/Notation/Indicator.lean b/Mathlib/Algebra/Notation/Indicator.lean
index 4bd45854615a3f..0e659ac8b3a3c5 100644
--- a/Mathlib/Algebra/Notation/Indicator.lean
+++ b/Mathlib/Algebra/Notation/Indicator.lean
@@ -204,7 +204,7 @@ lemma mulIndicator_inter_mulSupport (s : Set α) (f : α → M) :
 lemma comp_mulIndicator (h : M → β) (f : α → M) {s : Set α} {x : α} [DecidablePred (· ∈ s)] :
     h (s.mulIndicator f x) = s.piecewise (h ∘ f) (const α (h 1)) x := by
   letI := Classical.decPred (· ∈ s)
-  convert s.apply_piecewise f (const α 1) (fun _ => h) (x := x) using 2
+  convert! s.apply_piecewise f (const α 1) (fun _ => h) (x := x) using 2
 
 @[to_additive]
 lemma mulIndicator_comp_right {s : Set α} (f : β → α) {g : α → M} {x : β} :
diff --git a/Mathlib/Algebra/Order/Antidiag/Finsupp.lean b/Mathlib/Algebra/Order/Antidiag/Finsupp.lean
index 5f98bc13254b64..7d7efc43d009cf 100644
--- a/Mathlib/Algebra/Order/Antidiag/Finsupp.lean
+++ b/Mathlib/Algebra/Order/Antidiag/Finsupp.lean
@@ -141,9 +141,9 @@ lemma mapRange_finsuppAntidiag_eq {e : μ ≃+ μ'} {s : Finset ι} {n : μ} :
     rw [mem_map_equiv, this]
     apply mapRange_finsuppAntidiag_subset
     rw [← mem_map_equiv]
-    convert hf
+    convert! hf
     rw [map_map, hh]
-    convert map_refl
+    convert! map_refl
     apply Function.Embedding.equiv_symm_toEmbedding_trans_toEmbedding
 
 end AddCommMonoid
diff --git a/Mathlib/Algebra/Order/Antidiag/Nat.lean b/Mathlib/Algebra/Order/Antidiag/Nat.lean
index 1da55e696c5940..0aa55fa23256da 100644
--- a/Mathlib/Algebra/Order/Antidiag/Nat.lean
+++ b/Mathlib/Algebra/Order/Antidiag/Nat.lean
@@ -192,7 +192,7 @@ private theorem primeFactorsPiBij_inj (d n : ℕ)
   dsimp only [Nat.primeFactorsPiBij]
   apply ne_of_mem_of_not_mem (s := {x | p ∣ x}) <;> simp_rw [Set.mem_setOf_eq]
   · rw [Finset.prod_filter]
-    convert Finset.dvd_prod_of_mem _ (mem_attach (n.primeFactors) ⟨p, hp⟩)
+    convert! Finset.dvd_prod_of_mem _ (mem_attach (n.primeFactors) ⟨p, hp⟩)
     rw [if_pos rfl]
   · rw [mem_primeFactors] at hp
     rw [Prime.dvd_finsetProd_iff hp.1.prime]
diff --git a/Mathlib/Algebra/Order/Archimedean/Class.lean b/Mathlib/Algebra/Order/Archimedean/Class.lean
index 6ce4fd44749f45..0d946dc1124554 100644
--- a/Mathlib/Algebra/Order/Archimedean/Class.lean
+++ b/Mathlib/Algebra/Order/Archimedean/Class.lean
@@ -678,7 +678,7 @@ theorem mem_closedBallSubgroup_iff {a : M} {c : MulArchimedeanClass M} :
 variable (M) in
 @[to_additive (attr := simp)]
 theorem ballSubgroup_top : ballSubgroup (M := M) ⊤ = ⊥ := by
-  convert subgroup_eq_bot M
+  convert! subgroup_eq_bot M
   simp
 
 variable (M) in
diff --git a/Mathlib/Algebra/Order/BigOperators/Group/Finset.lean b/Mathlib/Algebra/Order/BigOperators/Group/Finset.lean
index dbca76f00bf72b..1da58707e8c8cc 100644
--- a/Mathlib/Algebra/Order/BigOperators/Group/Finset.lean
+++ b/Mathlib/Algebra/Order/BigOperators/Group/Finset.lean
@@ -677,7 +677,7 @@ alias finset_sum_eq_sup_iff_disjoint := finsetSum_eq_sup_iff_disjoint
 
 theorem sup_powerset_len [DecidableEq α] (x : Multiset α) :
     (Finset.sup (Finset.range (card x + 1)) fun k => x.powersetCard k) = x.powerset := by
-  convert bind_powerset_len x using 1
+  convert! bind_powerset_len x using 1
   rw [Multiset.bind, Multiset.join, ← Finset.range_val, ← Finset.sum_eq_multiset_sum]
   exact
     Eq.symm (finsetSum_eq_sup_iff_disjoint.mpr fun _ _ _ _ h => pairwise_disjoint_powersetCard x h)
diff --git a/Mathlib/Algebra/Order/BigOperators/GroupWithZero/Finset.lean b/Mathlib/Algebra/Order/BigOperators/GroupWithZero/Finset.lean
index bdfe4ca17dd65e..f94bbb07939676 100644
--- a/Mathlib/Algebra/Order/BigOperators/GroupWithZero/Finset.lean
+++ b/Mathlib/Algebra/Order/BigOperators/GroupWithZero/Finset.lean
@@ -48,7 +48,7 @@ lemma prod_le_prod (h0 : ∀ i ∈ s, 0 ≤ f i) (h1 : ∀ i ∈ s, f i ≤ g i)
 /-- If each `f i`, `i ∈ s` belongs to `[0, 1]`, then their product is less than or equal to one.
 See also `Finset.prod_le_one'` for the case of an ordered commutative multiplicative monoid. -/
 lemma prod_le_one (h0 : ∀ i ∈ s, 0 ≤ f i) (h1 : ∀ i ∈ s, f i ≤ 1) : ∏ i ∈ s, f i ≤ 1 := by
-  convert ← prod_le_prod h0 h1
+  convert! ← prod_le_prod h0 h1
   exact Finset.prod_const_one
 
 /-- A version of `Finset.one_le_prod'` for `PosMulMono` in place of `MulLeftMono`. -/
diff --git a/Mathlib/Algebra/Order/BigOperators/GroupWithZero/List.lean b/Mathlib/Algebra/Order/BigOperators/GroupWithZero/List.lean
index 1c670ac4fb37e8..db81bed9305aa6 100644
--- a/Mathlib/Algebra/Order/BigOperators/GroupWithZero/List.lean
+++ b/Mathlib/Algebra/Order/BigOperators/GroupWithZero/List.lean
@@ -56,7 +56,7 @@ theorem prod_map_le_prod_map₀ {ι : Type*} {s : List ι} (f : ι → R) (g : 
 theorem prod_map_le_pow_length₀ {F L : Type*} [FunLike F L R] {f : F} {r : R} {t : List L}
     (hf0 : ∀ x ∈ t, 0 ≤ f x) (hf : ∀ x ∈ t, f x ≤ r) :
     (map f t).prod ≤ r ^ length t := by
-  convert prod_map_le_prod_map₀ f (Function.const L r) hf0 hf
+  convert! prod_map_le_prod_map₀ f (Function.const L r) hf0 hf
   simp [map_const, prod_replicate]
 
 omit [PosMulMono R]
diff --git a/Mathlib/Algebra/Order/CauSeq/Basic.lean b/Mathlib/Algebra/Order/CauSeq/Basic.lean
index dcacc72c459780..68952d25c4f114 100644
--- a/Mathlib/Algebra/Order/CauSeq/Basic.lean
+++ b/Mathlib/Algebra/Order/CauSeq/Basic.lean
@@ -631,7 +631,7 @@ instance : LE (CauSeq α abs) :=
 
 theorem lt_of_lt_of_eq {f g h : CauSeq α abs} (fg : f < g) (gh : g ≈ h) : f < h :=
   show Pos (h - f) by
-    convert pos_add_limZero fg (neg_limZero gh) using 1
+    convert! pos_add_limZero fg (neg_limZero gh) using 1
     simp
 
 theorem lt_of_eq_of_lt {f g h : CauSeq α abs} (fg : f ≈ g) (gh : g < h) : f < h := by
@@ -640,7 +640,7 @@ theorem lt_of_eq_of_lt {f g h : CauSeq α abs} (fg : f ≈ g) (gh : g < h) : f <
 
 theorem lt_trans {f g h : CauSeq α abs} (fg : f < g) (gh : g < h) : f < h :=
   show Pos (h - f) by
-    convert add_pos fg gh using 1
+    convert! add_pos fg gh using 1
     simp
 
 theorem lt_irrefl {f : CauSeq α abs} : ¬f < f
diff --git a/Mathlib/Algebra/Order/CompleteField.lean b/Mathlib/Algebra/Order/CompleteField.lean
index b27461635cb892..368aabd6624c2a 100644
--- a/Mathlib/Algebra/Order/CompleteField.lean
+++ b/Mathlib/Algebra/Order/CompleteField.lean
@@ -266,7 +266,7 @@ def inducedOrderRingHom : α →+*o β :=
       suffices ∀ x, 0 < x → inducedAddHom α β (x * x) = inducedAddHom α β x * inducedAddHom α β x by
         intro x
         obtain h | rfl | h := lt_trichotomy x 0
-        · convert this (-x) (neg_pos.2 h) using 1
+        · convert! this (-x) (neg_pos.2 h) using 1
           · rw [neg_mul, mul_neg, neg_neg]
           · simp_rw [map_neg, neg_mul, mul_neg, neg_neg]
         · simp only [mul_zero, map_zero]
@@ -288,7 +288,7 @@ def inducedOrderRingIso : β ≃+*o γ :=
     map_le_map_iff' := by
       dsimp
       refine ⟨fun h => ?_, fun h => inducedMap_mono _ _ h⟩
-      convert inducedMap_mono γ β h <;>
+      convert! inducedMap_mono γ β h <;>
       · rw [inducedOrderRingHom, AddMonoidHom.coe_fn_mkRingHomOfMulSelfOfTwoNeZero, inducedAddHom]
         dsimp
         rw [inducedMap_inv_self β γ _] }
diff --git a/Mathlib/Algebra/Order/Field/Basic.lean b/Mathlib/Algebra/Order/Field/Basic.lean
index 25b0ac4f017443..d3df4f72f66b0c 100644
--- a/Mathlib/Algebra/Order/Field/Basic.lean
+++ b/Mathlib/Algebra/Order/Field/Basic.lean
@@ -217,10 +217,10 @@ theorem inv_strictAntiOn : StrictAntiOn (fun x : α => x⁻¹) (Set.Ioi 0) := fu
   (inv_lt_inv₀ hy hx).2 xy
 
 theorem inv_pow_le_inv_pow_of_le (a1 : 1 ≤ a) {m n : ℕ} (mn : m ≤ n) : (a ^ n)⁻¹ ≤ (a ^ m)⁻¹ := by
-  convert one_div_pow_le_one_div_pow_of_le a1 mn using 1 <;> simp
+  convert! one_div_pow_le_one_div_pow_of_le a1 mn using 1 <;> simp
 
 theorem inv_pow_lt_inv_pow_of_lt (a1 : 1 < a) {m n : ℕ} (mn : m < n) : (a ^ n)⁻¹ < (a ^ m)⁻¹ := by
-  convert one_div_pow_lt_one_div_pow_of_lt a1 mn using 1 <;> simp
+  convert! one_div_pow_lt_one_div_pow_of_lt a1 mn using 1 <;> simp
 
 theorem inv_pow_anti (a1 : 1 ≤ a) : Antitone fun n : ℕ => (a ^ n)⁻¹ := fun _ _ =>
   inv_pow_le_inv_pow_of_le a1
@@ -236,7 +236,7 @@ theorem le_iff_forall_one_lt_le_mul₀ {α : Type*}
   · simp_rw [zero_mul] at h
     exact h 2 one_lt_two
   refine le_of_forall_gt_imp_ge_of_dense fun x hbx => ?_
-  convert h (x / b) ((one_lt_div hb).mpr hbx)
+  convert! h (x / b) ((one_lt_div hb).mpr hbx)
   rw [mul_div_cancel₀ _ hb.ne']
 
 theorem div_nat_le_self_of_nonnneg (ha : 0 ≤ a) (n : ℕ) : a / n ≤ a :=
@@ -425,22 +425,22 @@ theorem sub_inv_antitoneOn_Icc_left (ha : b < c) :
 
 theorem inv_antitoneOn_Ioi :
     AntitoneOn (fun x : α ↦ x⁻¹) (Set.Ioi 0) := by
-  convert sub_inv_antitoneOn_Ioi (α := α)
+  convert! sub_inv_antitoneOn_Ioi (α := α)
   exact (sub_zero _).symm
 
 theorem inv_antitoneOn_Iio :
     AntitoneOn (fun x : α ↦ x⁻¹) (Set.Iio 0) := by
-  convert sub_inv_antitoneOn_Iio (α := α)
+  convert! sub_inv_antitoneOn_Iio (α := α)
   exact (sub_zero _).symm
 
 theorem inv_antitoneOn_Icc_right (ha : 0 < a) :
     AntitoneOn (fun x : α ↦ x⁻¹) (Set.Icc a b) := by
-  convert sub_inv_antitoneOn_Icc_right ha
+  convert! sub_inv_antitoneOn_Icc_right ha
   exact (sub_zero _).symm
 
 theorem inv_antitoneOn_Icc_left (hb : b < 0) :
     AntitoneOn (fun x : α ↦ x⁻¹) (Set.Icc a b) := by
-  convert sub_inv_antitoneOn_Icc_left hb
+  convert! sub_inv_antitoneOn_Icc_left hb
   exact (sub_zero _).symm
 
 /-! ### Relating two divisions -/
@@ -538,7 +538,9 @@ theorem sub_one_div_inv_le_two (a2 : 2 ≤ a) : (1 - 1 / a)⁻¹ ≤ 2 := by
   -- move `1 / a` to the left and `2⁻¹` to the right.
   rw [le_sub_iff_add_le, add_comm, ← le_sub_iff_add_le]
   -- take inverses on both sides and use the assumption `2 ≤ a`.
-  convert (one_div a).le.trans (inv_anti₀ zero_lt_two a2) using 1
+  convert! (one_div a).le.trans (inv_anti₀ zero_lt_two a2) using 1
+    -- show `1 - 1 / 2 = 1 / 2`.
+
   -- show `1 - 1 / 2 = 1 / 2`.
   rw [sub_eq_iff_eq_add, ← two_mul, mul_inv_cancel₀ two_ne_zero]
 
diff --git a/Mathlib/Algebra/Order/Floor/Ring.lean b/Mathlib/Algebra/Order/Floor/Ring.lean
index 51a93b92512cf2..b6a38d85ba6a37 100644
--- a/Mathlib/Algebra/Order/Floor/Ring.lean
+++ b/Mathlib/Algebra/Order/Floor/Ring.lean
@@ -271,7 +271,7 @@ theorem mul_fract_eq_one_iff_exists_int {x : R} {k : R} (hk : 1 < k) :
   rw [fract, mul_sub, sub_eq_iff_eq_add']
   refine ⟨fun hx ↦ ⟨⌊x⌋, hx⟩, ?_⟩
   rintro ⟨n, hn⟩
-  convert hn
+  convert! hn
   have hk0 : 0 < (k : R) := zero_le_one.trans_lt hk
   rw [floor_eq_iff, ← mul_le_mul_iff_right₀ hk0, ← mul_lt_mul_iff_right₀ hk0, hn]
   simp [mul_add, hk]
@@ -674,7 +674,7 @@ theorem ceil_sub_intCast (a : R) (z : ℤ) : ⌈a - z⌉ = ⌈a⌉ - z :=
 
 @[simp]
 theorem ceil_sub_natCast (a : R) (n : ℕ) : ⌈a - n⌉ = ⌈a⌉ - n := by
-  convert ceil_sub_intCast a n using 1
+  convert! ceil_sub_intCast a n using 1
   simp
 
 @[simp]
@@ -772,7 +772,7 @@ lemma ceil_div_ceil_inv_sub_one (ha : 1 ≤ a) : ⌈⌈(a - 1)⁻¹⌉ / a⌉ =
   refine le_antisymm (ceil_le.2 <| div_le_self (by positivity) ha.le) <| ?_
   rw [le_ceil_iff, sub_lt_comm, div_eq_mul_inv, ← mul_one_sub,
     ← lt_div_iff₀ (sub_pos.2 <| inv_lt_one_of_one_lt₀ ha)]
-  convert ceil_lt_add_one (R := k) _ using 1
+  convert! ceil_lt_add_one (R := k) _ using 1
   field
 
 lemma ceil_lt_mul (hb : 1 < b) (hba : ⌈(b - 1)⁻¹⌉ / b < a) : ⌈a⌉ < b * a := by
diff --git a/Mathlib/Algebra/Order/Floor/Semifield.lean b/Mathlib/Algebra/Order/Floor/Semifield.lean
index e3bdf9a4329851..49670521edd546 100644
--- a/Mathlib/Algebra/Order/Floor/Semifield.lean
+++ b/Mathlib/Algebra/Order/Floor/Semifield.lean
@@ -45,7 +45,7 @@ theorem floor_div_ofNat (a : K) (n : ℕ) [n.AtLeastTwo] :
 
 /-- Natural division is the floor of field division. -/
 theorem floor_div_eq_div (m n : ℕ) : ⌊(m : K) / n⌋₊ = m / n := by
-  convert floor_div_natCast (m : K) n
+  convert! floor_div_natCast (m : K) n
   rw [m.floor_natCast]
 
 end LinearOrderedSemifield
diff --git a/Mathlib/Algebra/Order/Group/Int/Sum.lean b/Mathlib/Algebra/Order/Group/Int/Sum.lean
index b325c6fd59c347..ed9a90f4a2ba7f 100644
--- a/Mathlib/Algebra/Order/Group/Int/Sum.lean
+++ b/Mathlib/Algebra/Order/Group/Int/Sum.lean
@@ -45,7 +45,7 @@ lemma sum_le_sum_Ioc {s : Finset ℤ} {c : ℤ} (hs : ∀ x ∈ s, x ≤ c) :
 /-- Sharp upper bound for the sum of a finset of integers that is bounded above, `range` version. -/
 lemma sum_le_sum_range {s : Finset ℤ} {c : ℤ} (hs : ∀ x ∈ s, x ≤ c) :
     ∑ x ∈ s, x ≤ ∑ n ∈ range #s, (c - n) := by
-  convert sum_le_sum_Ioc hs
+  convert! sum_le_sum_Ioc hs
   refine sum_nbij (c - ·) ?_ ?_ ?_ (fun _ _ ↦ rfl)
   · intro x mx; rw [mem_Ioc]; dsimp only; rw [mem_range] at mx; lia
   · intro x mx y my (h : c - x = c - y); lia
@@ -71,7 +71,7 @@ lemma sum_Ico_le_sum {s : Finset ℤ} {c : ℤ} (hs : ∀ x ∈ s, c ≤ x) :
 /-- Sharp lower bound for the sum of a finset of integers that is bounded below, `range` version. -/
 lemma sum_range_le_sum {s : Finset ℤ} {c : ℤ} (hs : ∀ x ∈ s, c ≤ x) :
     ∑ n ∈ range #s, (c + n) ≤ ∑ x ∈ s, x := by
-  convert sum_Ico_le_sum hs
+  convert! sum_Ico_le_sum hs
   refine sum_nbij (c + ·) ?_ ?_ ?_ (fun _ _ ↦ rfl)
   · intro x mx; rw [mem_Ico]; dsimp only; rw [mem_range] at mx; lia
   · intro x mx y my (h : c + x = c + y); lia
diff --git a/Mathlib/Algebra/Order/Group/Unbundled/Abs.lean b/Mathlib/Algebra/Order/Group/Unbundled/Abs.lean
index 307d844fe2d132..4bfefb2a0f32e8 100644
--- a/Mathlib/Algebra/Order/Group/Unbundled/Abs.lean
+++ b/Mathlib/Algebra/Order/Group/Unbundled/Abs.lean
@@ -133,10 +133,10 @@ lemma mabs_mabs_div_mabs_le (a b : α) : |(|a|ₘ / |b|ₘ)|ₘ ≤ |a / b|ₘ :
   rw [mabs, sup_le_iff]
   constructor
   · apply div_le_iff_le_mul.2
-    convert mabs_mul_le (a / b) b
+    convert! mabs_mul_le (a / b) b
     rw [div_mul_cancel]
   · rw [div_eq_mul_inv, mul_inv_rev, inv_inv, mul_inv_le_iff_le_mul, mabs_div_comm]
-    convert mabs_mul_le (b / a) a
+    convert! mabs_mul_le (b / a) a
     · rw [div_mul_cancel]
 
 @[to_additive] lemma sup_div_inf_eq_mabs_div (a b : α) : (a ⊔ b) / (a ⊓ b) = |b / a|ₘ := by
diff --git a/Mathlib/Algebra/Order/Hom/Monoid.lean b/Mathlib/Algebra/Order/Hom/Monoid.lean
index 61b4fa4b088fe8..64b8eb756a69a8 100644
--- a/Mathlib/Algebra/Order/Hom/Monoid.lean
+++ b/Mathlib/Algebra/Order/Hom/Monoid.lean
@@ -320,11 +320,11 @@ theorem coe_orderHom (f : α →*o β) : ((f : α →o β) : α → β) = f :=
 
 @[to_additive]
 theorem toMonoidHom_injective : Injective (toMonoidHom : _ → α →* β) := fun f g h =>
-  ext <| by convert DFunLike.ext_iff.1 h using 0
+  ext <| by convert! DFunLike.ext_iff.1 h using 0
 
 @[to_additive]
 theorem toOrderHom_injective : Injective (toOrderHom : _ → α →o β) := fun f g h =>
-  ext <| by convert DFunLike.ext_iff.1 h using 0
+  ext <| by convert! DFunLike.ext_iff.1 h using 0
 
 /-- Copy of an `OrderMonoidHom` with a new `toFun` equal to the old one. Useful to fix
 definitional equalities. -/
@@ -548,11 +548,11 @@ theorem coe_orderIso (f : α ≃*o β) : ((f : α →o β) : α → β) = f :=
 
 @[to_additive]
 theorem toMulEquiv_injective : Injective (toMulEquiv : _ → α ≃* β) := fun f g h =>
-  ext <| by convert DFunLike.ext_iff.1 h using 0
+  ext <| by convert! DFunLike.ext_iff.1 h using 0
 
 @[to_additive]
 theorem toOrderIso_injective : Injective (toOrderIso : _ → α ≃o β) := fun f g h =>
-  ext <| by convert DFunLike.ext_iff.1 h using 0
+  ext <| by convert! DFunLike.ext_iff.1 h using 0
 
 variable (α)
 
@@ -736,7 +736,7 @@ protected lemma strictMono : StrictMono f :=
 protected lemma strictMono_symm : StrictMono f.symm :=
   strictMono_of_le_iff_le <| fun a b ↦ by
     rw [← map_le_map_iff f]
-    convert Iff.rfl <;>
+    convert! Iff.rfl <;>
     exact f.toEquiv.apply_symm_apply _
 
 end Preorder
diff --git a/Mathlib/Algebra/Order/Hom/MonoidWithZero.lean b/Mathlib/Algebra/Order/Hom/MonoidWithZero.lean
index 82a46fa3173df0..75788dbd1d66da 100644
--- a/Mathlib/Algebra/Order/Hom/MonoidWithZero.lean
+++ b/Mathlib/Algebra/Order/Hom/MonoidWithZero.lean
@@ -131,10 +131,10 @@ theorem coe_orderMonoidHom (f : α →*₀o β) : ⇑(f : α →*o β) = f :=
   rfl
 
 theorem toOrderMonoidHom_injective : Injective (toOrderMonoidHom : _ → α →*o β) := fun f g h =>
-  ext <| by convert DFunLike.ext_iff.1 h using 0
+  ext <| by convert! DFunLike.ext_iff.1 h using 0
 
 theorem toMonoidWithZeroHom_injective : Injective (toMonoidWithZeroHom : _ → α →*₀ β) :=
-  fun f g h => ext <| by convert DFunLike.ext_iff.1 h using 0
+  fun f g h => ext <| by convert! DFunLike.ext_iff.1 h using 0
 
 /-- Copy of an `OrderMonoidWithZeroHom` with a new `toFun` equal to the old one. Useful to fix
 definitional equalities. -/
diff --git a/Mathlib/Algebra/Order/Hom/Ring.lean b/Mathlib/Algebra/Order/Hom/Ring.lean
index a3feecbe0a6ee6..d78055b1526ca8 100644
--- a/Mathlib/Algebra/Order/Hom/Ring.lean
+++ b/Mathlib/Algebra/Order/Hom/Ring.lean
@@ -463,7 +463,7 @@ theorem coe_toOrderRingHom_refl : (OrderRingIso.refl α : α →+*o α) = OrderR
   rfl
 
 theorem toOrderRingHom_injective : Injective (toOrderRingHom : α ≃+*o β → α →+*o β) :=
-  fun f g h => DFunLike.coe_injective <| by convert DFunLike.ext'_iff.1 h using 0
+  fun f g h => DFunLike.coe_injective <| by convert! DFunLike.ext'_iff.1 h using 0
 
 end NonAssocSemiring
 
diff --git a/Mathlib/Algebra/Order/Module/HahnEmbedding.lean b/Mathlib/Algebra/Order/Module/HahnEmbedding.lean
index f62941aabb2aa1..26f472ff8b55b4 100644
--- a/Mathlib/Algebra/Order/Module/HahnEmbedding.lean
+++ b/Mathlib/Algebra/Order/Module/HahnEmbedding.lean
@@ -158,7 +158,7 @@ abbrev stratum' (c : FiniteArchimedeanClass M) : Submodule K (baseDomain u) :=
 theorem iSupIndep_stratum' : iSupIndep u.stratum' := by
   apply (iSupIndep_map_orderIso_iff (Submodule.mapIic u.baseDomain)).mp
   apply iSupIndep.of_coe_Iic_comp
-  convert u.iSupIndep_stratum
+  convert! u.iSupIndep_stratum
   ext1 c
   simpa using le_iSup _ _
 
@@ -366,7 +366,7 @@ theorem truncLT_mem_range_baseEmbedding (x : seed.baseEmbedding.domain)
   · rw [HahnSeries.coe_truncLTLinearMap, HahnSeries.coeff_truncLT_of_le hdc]
     have hcd : c.val ≤ d.val := hdc
     simp only [DFinsupp.mk_apply, hcd, ↓reduceIte]
-    convert LinearMap.map_zero _
+    convert! LinearMap.map_zero _
     simp
 
 /-- `HahnEmbedding.Seed.baseEmbedding` is a partial Hahn embedding. -/
@@ -569,7 +569,7 @@ theorem isWF_support_evalCoeff [IsOrderedAddMonoid R] [Archimedean R] (x : M) :
   have hmem' (n : ℕ) : seq n ∈ (ofLex (f.val y)).coeff.support := by
     specialize hmem n
     rw [Function.mem_support] at ⊢ hmem
-    convert hmem using 1
+    convert! hmem using 1
     refine (f.evalCoeff_eq ((ball_strictAnti K).antitone ?_ hy)).symm
     simpa using hanti.antitone (show 0 ≤ n by simp)
   obtain hwf := (ofLex (f.val y)).isWF_support
@@ -587,7 +587,7 @@ def eval [IsOrderedAddMonoid R] [Archimedean R] (x : M) :
 @[simp]
 theorem eval_zero [IsOrderedAddMonoid R] [Archimedean R] : f.eval 0 = 0 := by
   unfold eval
-  convert toLex_zero
+  convert! toLex_zero
   ext c
   rw [f.evalCoeff_eq (y := 0) (by simp)]
   simp
diff --git a/Mathlib/Algebra/Order/Monoid/LocallyFiniteOrder.lean b/Mathlib/Algebra/Order/Monoid/LocallyFiniteOrder.lean
index 44942b4a803d64..0fda32118f060b 100644
--- a/Mathlib/Algebra/Order/Monoid/LocallyFiniteOrder.lean
+++ b/Mathlib/Algebra/Order/Monoid/LocallyFiniteOrder.lean
@@ -78,7 +78,7 @@ def LocallyFiniteOrder.addMonoidHom :
   map_zero' := by simp
   map_add' a b := by
     wlog hab : a ≤ b generalizing a b
-    · convert this b a (le_of_not_ge hab) using 1 <;> simp only [add_comm]
+    · convert! this b a (le_of_not_ge hab) using 1 <;> simp only [add_comm]
     obtain ha | ha := le_total 0 a <;> obtain hb | hb := le_total 0 b
     · have : -b ≤ a := by trans 0 <;> simp [ha, hb]
       simp [ha, hb, card_Ico_zero_add, this]
diff --git a/Mathlib/Algebra/Order/Rearrangement.lean b/Mathlib/Algebra/Order/Rearrangement.lean
index e212f91a232c05..44b20c6d3cf59b 100644
--- a/Mathlib/Algebra/Order/Rearrangement.lean
+++ b/Mathlib/Algebra/Order/Rearrangement.lean
@@ -121,8 +121,9 @@ theorem AntivaryOn.sum_smul_le_sum_smul_comp_perm (hfg : AntivaryOn f g s)
 `f` and `g` monovary together on `s`. Stated by permuting the entries of `f`. -/
 theorem MonovaryOn.sum_comp_perm_smul_le_sum_smul (hfg : MonovaryOn f g s)
     (hσ : {x | σ x ≠ x} ⊆ s) : ∑ i ∈ s, f (σ i) • g i ≤ ∑ i ∈ s, f i • g i := by
-  convert hfg.sum_smul_comp_perm_le_sum_smul
-    (show { x | σ⁻¹ x ≠ x } ⊆ s by simp [set_support_symm_eq, hσ]) using 1
+  convert!
+    hfg.sum_smul_comp_perm_le_sum_smul
+      (show {x | σ⁻¹ x ≠ x} ⊆ s by simp [set_support_symm_eq, hσ]) using 1
   exact σ.sum_comp' s (fun i j ↦ f i • g j) hσ
 
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
@@ -211,10 +212,10 @@ theorem MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff (hfg : MonovaryOn f g s)
   · apply eq_iff_eq_cancel_right.2
     rw [σ.sum_comp' s (fun i j ↦ f i • g j) hσ]
     congr
-  · convert h.comp_right σ
+  · convert! h.comp_right σ
     · rw [comp_assoc, inv_def, symm_comp_self, comp_id]
     · rw [σ.eq_preimage_iff_image_eq, Set.image_perm hσ]
-  · convert h.comp_right σ.symm
+  · convert! h.comp_right σ.symm
     · rw [comp_assoc, self_comp_symm, comp_id]
     · rw [σ.symm.eq_preimage_iff_image_eq]
       exact Set.image_perm hσinv
diff --git a/Mathlib/Algebra/Order/Ring/Abs.lean b/Mathlib/Algebra/Order/Ring/Abs.lean
index 55b6b50ea5fdc0..b2438fbcd6f484 100644
--- a/Mathlib/Algebra/Order/Ring/Abs.lean
+++ b/Mathlib/Algebra/Order/Ring/Abs.lean
@@ -89,7 +89,7 @@ section LinearStrictOrderedRing
 variable [Ring α] [LinearOrder α] [IsStrictOrderedRing α] {n : ℕ} {a b : α}
 
 lemma abs_pow_eq_one (a : α) (h : n ≠ 0) : |a ^ n| = 1 ↔ |a| = 1 := by
-  convert pow_left_inj₀ (abs_nonneg a) zero_le_one h
+  convert! pow_left_inj₀ (abs_nonneg a) zero_le_one h
   exacts [(pow_abs _ _).symm, (one_pow _).symm]
 
 lemma abs_eq_iff_mul_self_eq : |a| = |b| ↔ a * a = b * b := by
diff --git a/Mathlib/Algebra/Order/Ring/Archimedean.lean b/Mathlib/Algebra/Order/Ring/Archimedean.lean
index f85be72d328284..6bc0565a98cf90 100644
--- a/Mathlib/Algebra/Order/Ring/Archimedean.lean
+++ b/Mathlib/Algebra/Order/Ring/Archimedean.lean
@@ -62,7 +62,7 @@ private theorem mk_mul_le_of_le {x₁ y₁ x₂ y₂ : R} (hx : mk x₁ ≤ mk x
   obtain ⟨m, hm⟩ := hx
   obtain ⟨n, hn⟩ := hy
   use m * n
-  convert mul_le_mul hm hn (abs_nonneg _) (nsmul_nonneg (abs_nonneg _) _) using 1 <;>
+  convert! mul_le_mul hm hn (abs_nonneg _) (nsmul_nonneg (abs_nonneg _) _) using 1 <;>
     simp_rw [ArchimedeanOrder.val_of, abs_mul]
   ring
 
diff --git a/Mathlib/Algebra/Order/Ring/StandardPart.lean b/Mathlib/Algebra/Order/Ring/StandardPart.lean
index 809309e70f1788..7335e3be07016c 100644
--- a/Mathlib/Algebra/Order/Ring/StandardPart.lean
+++ b/Mathlib/Algebra/Order/Ring/StandardPart.lean
@@ -216,7 +216,7 @@ instance : Archimedean (FiniteResidueField K) where
     · obtain ⟨n, hn⟩ := ((mk_ne_zero.1 hy.ne').trans (mk_ne_zero.1 hx.ne').symm).le
       refine ⟨n, mk.monotone' ?_⟩
       change x.1 ≤ n • y.1
-      convert ← hn
+      convert! ← hn
       · exact abs_of_pos <| lt_of_mk_lt_mk hx
       · exact abs_of_pos <| lt_of_mk_lt_mk hy
 
@@ -461,10 +461,10 @@ theorem stdPart_eq_sInf (f : ℝ →+*o K) (x : K) : stdPart x = sInf {r | x < f
   · rw [stdPart_of_mk_ne_zero hx.ne]
     have hr {r} := hx.trans_le (mk_map_nonneg_of_archimedean f r)
     obtain h | h := le_or_gt 0 x
-    · convert Real.sInf_empty.symm
+    · convert! Real.sInf_empty.symm
       rw [Set.eq_empty_iff_forall_notMem]
       exact fun r ↦ (lt_of_mk_lt_mk_of_nonneg hr h).not_gt
-    · convert Real.sInf_univ.symm
+    · convert! Real.sInf_univ.symm
       rw [Set.eq_univ_iff_forall]
       exact fun r ↦ lt_of_mk_lt_mk_of_nonpos hr h.le
 
diff --git a/Mathlib/Algebra/Order/Ring/Unbundled/Basic.lean b/Mathlib/Algebra/Order/Ring/Unbundled/Basic.lean
index cd50c663197a9e..8beb12c95faf3f 100644
--- a/Mathlib/Algebra/Order/Ring/Unbundled/Basic.lean
+++ b/Mathlib/Algebra/Order/Ring/Unbundled/Basic.lean
@@ -441,7 +441,7 @@ theorem nonpos_of_mul_nonpos_right [PosMulStrictMono R]
 @[simp]
 theorem mul_nonneg_iff_of_pos_left [PosMulStrictMono R]
     (h : 0 < c) : 0 ≤ c * b ↔ 0 ≤ b := by
-  convert mul_le_mul_iff_right₀ h
+  convert! mul_le_mul_iff_right₀ h
   simp
 
 @[simp]
diff --git a/Mathlib/Algebra/Order/Star/Basic.lean b/Mathlib/Algebra/Order/Star/Basic.lean
index f9505185526ebb..a08f2154d10610 100644
--- a/Mathlib/Algebra/Order/Star/Basic.lean
+++ b/Mathlib/Algebra/Order/Star/Basic.lean
@@ -213,7 +213,7 @@ theorem star_left_conjugate_nonneg {a : R} (ha : 0 ≤ a) (c : R) : 0 ≤ star c
   refine AddSubmonoid.closure_induction (fun x hx => ?_)
     (by rw [mul_zero, zero_mul]) (fun x y _ _ hx hy => ?_) ha
   · obtain ⟨x, rfl⟩ := hx
-    convert star_mul_self_nonneg (x * c) using 1
+    convert! star_mul_self_nonneg (x * c) using 1
     rw [star_mul, ← mul_assoc, mul_assoc _ _ c]
   · calc
       0 ≤ star c * x * c + 0 := by rw [add_zero]; exact hx
diff --git a/Mathlib/Algebra/Order/Sub/Unbundled/Basic.lean b/Mathlib/Algebra/Order/Sub/Unbundled/Basic.lean
index 674f09d7ba6863..5d0cf4b2868b44 100644
--- a/Mathlib/Algebra/Order/Sub/Unbundled/Basic.lean
+++ b/Mathlib/Algebra/Order/Sub/Unbundled/Basic.lean
@@ -56,7 +56,7 @@ theorem lt_of_tsub_lt_tsub_right_of_le (h : c ≤ b) (h2 : a - c < b - c) : a <
   exact h2.false
 
 theorem tsub_add_tsub_cancel (hab : b ≤ a) (hcb : c ≤ b) : a - b + (b - c) = a - c := by
-  convert tsub_add_cancel_of_le (tsub_le_tsub_right hab c) using 2
+  convert! tsub_add_cancel_of_le (tsub_le_tsub_right hab c) using 2
   rw [tsub_tsub, add_tsub_cancel_of_le hcb]
 
 theorem tsub_tsub_tsub_cancel_right (h : c ≤ b) : a - c - (b - c) = a - b := by
diff --git a/Mathlib/Algebra/Order/ToIntervalMod.lean b/Mathlib/Algebra/Order/ToIntervalMod.lean
index 20794291bfb051..0ac987cb2d166d 100644
--- a/Mathlib/Algebra/Order/ToIntervalMod.lean
+++ b/Mathlib/Algebra/Order/ToIntervalMod.lean
@@ -83,7 +83,7 @@ theorem toIcoMod_mem_Ico (a b : α) : toIcoMod hp a b ∈ Set.Ico a (a + p) :=
   sub_toIcoDiv_zsmul_mem_Ico hp a b
 
 theorem toIcoMod_mem_Ico' (b : α) : toIcoMod hp 0 b ∈ Set.Ico 0 p := by
-  convert toIcoMod_mem_Ico hp 0 b
+  convert! toIcoMod_mem_Ico hp 0 b
   exact (zero_add p).symm
 
 theorem toIocMod_mem_Ioc (a b : α) : toIocMod hp a b ∈ Set.Ioc a (a + p) :=
@@ -1407,14 +1407,14 @@ theorem iUnion_Ioc_add_zsmul : ⋃ n : ℤ, Ioc (a + n • p) (a + (n + 1) • p
   rcases sub_toIocDiv_zsmul_mem_Ioc hp a b with ⟨hl, hr⟩
   refine ⟨toIocDiv hp a b, ⟨lt_sub_iff_add_lt.mp hl, ?_⟩⟩
   rw [add_smul, one_smul, ← add_assoc]
-  convert sub_le_iff_le_add.mp hr using 1; abel
+  convert! sub_le_iff_le_add.mp hr using 1; abel
 
 theorem iUnion_Ico_add_zsmul : ⋃ n : ℤ, Ico (a + n • p) (a + (n + 1) • p) = univ := by
   refine eq_univ_iff_forall.mpr fun b => mem_iUnion.mpr ?_
   rcases sub_toIcoDiv_zsmul_mem_Ico hp a b with ⟨hl, hr⟩
   refine ⟨toIcoDiv hp a b, ⟨le_sub_iff_add_le.mp hl, ?_⟩⟩
   rw [add_smul, one_smul, ← add_assoc]
-  convert sub_lt_iff_lt_add.mp hr using 1; abel
+  convert! sub_lt_iff_lt_add.mp hr using 1; abel
 
 theorem iUnion_Icc_add_zsmul : ⋃ n : ℤ, Icc (a + n • p) (a + (n + 1) • p) = univ := by
   simpa only [iUnion_Ioc_add_zsmul hp a, univ_subset_iff] using
diff --git a/Mathlib/Algebra/Polynomial/AlgebraMap.lean b/Mathlib/Algebra/Polynomial/AlgebraMap.lean
index e513752ccb8e9e..31ab4a5df5786d 100644
--- a/Mathlib/Algebra/Polynomial/AlgebraMap.lean
+++ b/Mathlib/Algebra/Polynomial/AlgebraMap.lean
@@ -62,7 +62,7 @@ instance algebraOfAlgebra : Algebra R A[X] where
     toFinsupp_injective <| by
       dsimp only [RingHom.toFun_eq_coe, RingHom.comp_apply]
       simp_rw [toFinsupp_mul, toFinsupp_C]
-      convert Algebra.commutes' r p.toFinsupp
+      convert! Algebra.commutes' r p.toFinsupp
   algebraMap := C.comp (algebraMap R A)
 
 @[simp]
@@ -613,7 +613,7 @@ theorem dvd_term_of_dvd_eval_of_dvd_terms {z p : S} {f : S[X]} (i : ℕ) (dvd_ev
     apply Finset.dvd_sum
     intro j hj
     exact dvd_terms j (Finset.ne_of_mem_erase hj)
-  · convert dvd_zero p
+  · convert! dvd_zero p
     rw [notMem_support_iff] at hi
     simp [hi]
 
@@ -659,7 +659,7 @@ theorem aeval_endomorphism {M : Type*} [AddCommGroup M] [Module R M] (f : M →
   exact map_sum (LinearMap.applyₗ v) _ _
 
 lemma X_sub_C_pow_dvd_iff {n : ℕ} : (X - C t) ^ n ∣ p ↔ X ^ n ∣ p.comp (X + C t) := by
-  convert (map_dvd_iff <| algEquivAevalXAddC t).symm using 2
+  convert! (map_dvd_iff <| algEquivAevalXAddC t).symm using 2
   simp [C_eq_algebraMap]
 
 lemma comp_X_add_C_eq_zero_iff : p.comp (X + C t) = 0 ↔ p = 0 :=
@@ -669,7 +669,7 @@ lemma comp_X_add_C_ne_zero_iff : p.comp (X + C t) ≠ 0 ↔ p ≠ 0 := comp_X_ad
 
 lemma dvd_comp_C_mul_X_add_C_iff (p q : R[X]) (a b : R) [Invertible a] :
     p ∣ q.comp (C a * X + C b) ↔ p.comp (C ⅟a * (X - C b)) ∣ q := by
-  convert map_dvd_iff <| algEquivCMulXAddC a b using 2
+  convert! map_dvd_iff <| algEquivCMulXAddC a b using 2
   simp [← comp_eq_aeval, comp_assoc, ← mul_assoc, ← C_mul]
 
 lemma dvd_comp_X_sub_C_iff (p q : R[X]) (a : R) :
diff --git a/Mathlib/Algebra/Polynomial/Basic.lean b/Mathlib/Algebra/Polynomial/Basic.lean
index db5c596a13dd02..d106502236c636 100644
--- a/Mathlib/Algebra/Polynomial/Basic.lean
+++ b/Mathlib/Algebra/Polynomial/Basic.lean
@@ -633,7 +633,7 @@ theorem notMem_support_iff : n ∉ p.support ↔ p.coeff n = 0 := by simp
 
 @[aesop simp]
 theorem coeff_C : coeff (C a) n = ite (n = 0) a 0 := by
-  convert coeff_monomial (a := a) (m := n) (n := 0) using 2
+  convert! coeff_monomial (a := a) (m := n) (n := 0) using 2
   simp [eq_comm]
 
 @[simp]
@@ -806,7 +806,7 @@ theorem smul_X_eq_monomial {n} : a • X ^ n = monomial n (a : R) := by
   rw [X_pow_eq_monomial, smul_monomial, smul_eq_mul, mul_one]
 
 theorem support_X_pow (H : ¬(1 : R) = 0) (n : ℕ) : (X ^ n : R[X]).support = singleton n := by
-  convert support_monomial n H
+  convert! support_monomial n H
   exact X_pow_eq_monomial n
 
 theorem support_X_empty (H : (1 : R) = 0) : (X : R[X]).support = ∅ := by
@@ -913,7 +913,7 @@ protected theorem induction_on {motive : R[X] → Prop} (p : R[X]) (C : ∀ a, m
     | succ n ih => exact monomial _ _ ih
   have B : ∀ s : Finset ℕ, motive (s.sum fun n : ℕ => Polynomial.C (p.coeff n) * X ^ n) := by
     apply Finset.induction
-    · convert C 0
+    · convert! C 0
       exact C_0.symm
     · intro n s ns ih
       rw [sum_insert ns]
diff --git a/Mathlib/Algebra/Polynomial/BigOperators.lean b/Mathlib/Algebra/Polynomial/BigOperators.lean
index 0274236ff2ffb2..3886e38da6077a 100644
--- a/Mathlib/Algebra/Polynomial/BigOperators.lean
+++ b/Mathlib/Algebra/Polynomial/BigOperators.lean
@@ -229,7 +229,7 @@ theorem coeff_multiset_prod_of_natDegree_le (n : ℕ) (hl : ∀ p ∈ t, natDegr
 theorem coeff_prod_of_natDegree_le (f : ι → R[X]) (n : ℕ) (h : ∀ p ∈ s, natDegree (f p) ≤ n) :
     coeff (∏ i ∈ s, f i) (#s * n) = ∏ i ∈ s, coeff (f i) n := by
   obtain ⟨l, hl⟩ := s
-  convert coeff_multiset_prod_of_natDegree_le (l.map f) n ?_
+  convert! coeff_multiset_prod_of_natDegree_le (l.map f) n ?_
   · simp
   · simp
   · simpa using h
@@ -266,7 +266,7 @@ theorem prod_X_sub_C_nextCoeff {s : Finset ι} (f : ι → R) :
 theorem multiset_prod_X_sub_C_coeff_card_pred (t : Multiset R) (ht : 0 < Multiset.card t) :
     (t.map fun x => X - C x).prod.coeff ((Multiset.card t) - 1) = -t.sum := by
   nontriviality R
-  convert multiset_prod_X_sub_C_nextCoeff (by assumption)
+  convert! multiset_prod_X_sub_C_nextCoeff (by assumption)
   rw [nextCoeff, if_neg]
   swap
   · rw [natDegree_multiset_prod_of_monic]
diff --git a/Mathlib/Algebra/Polynomial/CancelLeads.lean b/Mathlib/Algebra/Polynomial/CancelLeads.lean
index 963350a3567d4e..bb61c6a76fc056 100644
--- a/Mathlib/Algebra/Polynomial/CancelLeads.lean
+++ b/Mathlib/Algebra/Polynomial/CancelLeads.lean
@@ -53,7 +53,7 @@ theorem natDegree_cancelLeads_lt_of_natDegree_le_natDegree_of_comm
     (h : p.natDegree ≤ q.natDegree) (hq : 0 < q.natDegree) :
     (p.cancelLeads q).natDegree < q.natDegree := by
   by_cases hp : p = 0
-  · convert hq
+  · convert! hq
     simp [hp, cancelLeads]
   rw [cancelLeads, sub_eq_add_neg, tsub_eq_zero_iff_le.mpr h, pow_zero, mul_one]
   by_cases h0 :
diff --git a/Mathlib/Algebra/Polynomial/Degree/IsMonicOfDegree.lean b/Mathlib/Algebra/Polynomial/Degree/IsMonicOfDegree.lean
index 415f893a9dc8d2..0acdfb7850f3fb 100644
--- a/Mathlib/Algebra/Polynomial/Degree/IsMonicOfDegree.lean
+++ b/Mathlib/Algebra/Polynomial/Degree/IsMonicOfDegree.lean
@@ -267,7 +267,7 @@ lemma IsMonicOfDegree.of_dvd_add {a b r : R[X]} {m n : ℕ} (hmn : n ≤ m) (ha
 lemma IsMonicOfDegree.of_dvd_sub {a b r : R[X]} {m n : ℕ} (hmn : n ≤ m) (ha : IsMonicOfDegree a m)
     (hb : IsMonicOfDegree b n) (hr : r.natDegree < m) (h : b ∣ a - r) :
     ∃ q : R[X], IsMonicOfDegree q (m - n) ∧ a = q * b + r := by
-  convert ha.of_dvd_add hmn hb ?_ h using 4 with q
+  convert! ha.of_dvd_add hmn hb ?_ h using 4 with q
   · rw [sub_neg_eq_add]
   · rwa [natDegree_neg]
 
diff --git a/Mathlib/Algebra/Polynomial/Degree/Lemmas.lean b/Mathlib/Algebra/Polynomial/Degree/Lemmas.lean
index 7d783b482f6dec..42f608a6073af3 100644
--- a/Mathlib/Algebra/Polynomial/Degree/Lemmas.lean
+++ b/Mathlib/Algebra/Polynomial/Degree/Lemmas.lean
@@ -82,7 +82,7 @@ theorem natDegree_add_le_iff_left {n : ℕ} (p q : R[X]) (qn : q.natDegree ≤ n
     (p + q).natDegree ≤ n ↔ p.natDegree ≤ n := by
   refine ⟨fun h => ?_, fun h => natDegree_add_le_of_degree_le h qn⟩
   refine natDegree_le_iff_coeff_eq_zero.mpr fun m hm => ?_
-  convert natDegree_le_iff_coeff_eq_zero.mp h m hm using 1
+  convert! natDegree_le_iff_coeff_eq_zero.mp h m hm using 1
   rw [coeff_add, natDegree_le_iff_coeff_eq_zero.mp qn _ hm, add_zero]
 
 theorem natDegree_add_le_iff_right {n : ℕ} (p q : R[X]) (pn : p.natDegree ≤ n) :
diff --git a/Mathlib/Algebra/Polynomial/Derivative.lean b/Mathlib/Algebra/Polynomial/Derivative.lean
index 8e5b18bf65ce4b..09c1861101d102 100644
--- a/Mathlib/Algebra/Polynomial/Derivative.lean
+++ b/Mathlib/Algebra/Polynomial/Derivative.lean
@@ -97,7 +97,7 @@ theorem derivative_C_mul_X_sq (a : R) : derivative (C a * X ^ 2) = C (a * 2) * X
   rw [derivative_C_mul_X_pow, Nat.cast_two, pow_one]
 
 theorem derivative_X_pow (n : ℕ) : derivative (X ^ n : R[X]) = C (n : R) * X ^ (n - 1) := by
-  convert derivative_C_mul_X_pow (1 : R) n <;> simp
+  convert! derivative_C_mul_X_pow (1 : R) n <;> simp
 
 @[simp]
 theorem derivative_X_pow_succ (n : ℕ) :
@@ -539,19 +539,19 @@ theorem iterate_derivative_mul_X_pow (n m : ℕ) (p : R[X]) :
 
 theorem iterate_derivative_mul_X {n : ℕ} (p : R[X]) :
     derivative^[n] (p * X) = (derivative^[n] p) * X + n • derivative^[n - 1] p := by
-  convert p.iterate_derivative_mul_X_pow n 1; · simp
+  convert! p.iterate_derivative_mul_X_pow n 1; · simp
   rcases n with rfl | n <;> simp [sum_range_succ]
 
 theorem iterate_derivative_derivative_mul_X {n : ℕ} (p : R[X]) :
     derivative^[n] (derivative p * X) = (derivative^[n + 1] p) * X + n • derivative^[n] p := by
-  convert (derivative p).iterate_derivative_mul_X_pow n 1; · simp
+  convert! (derivative p).iterate_derivative_mul_X_pow n 1; · simp
   rcases n with rfl | n <;> simp [sum_range_succ]
 
 theorem iterate_derivative_derivative_mul_X_sq {n : ℕ} (p : R[X]) :
     derivative^[n] (derivative^[2] p * X ^ 2) =
       (derivative^[n + 2] p) * X ^ 2 + (2 * n) • (derivative^[n + 1] p) * X +
         (n * (n - 1)) • derivative^[n] p := by
-  convert (derivative^[2] p).iterate_derivative_mul_X_pow n 2
+  convert! (derivative^[2] p).iterate_derivative_mul_X_pow n 2
   rcases n with rfl | n; · simp
   rcases n with rfl | n; · simp [sum_range_succ, ← mul_assoc]
   suffices ((n + 1 + 1) * (n + 1) / 2) * 2 = (n + 1 + 1) * (n + 1) by
diff --git a/Mathlib/Algebra/Polynomial/Div.lean b/Mathlib/Algebra/Polynomial/Div.lean
index 29a02efd5c24d1..47a937313aff9c 100644
--- a/Mathlib/Algebra/Polynomial/Div.lean
+++ b/Mathlib/Algebra/Polynomial/Div.lean
@@ -422,7 +422,7 @@ theorem map_dvd_map [Ring S] (f : R →+* S) (hf : Function.Injective f) {x y :
 
 @[simp]
 theorem modByMonic_one (p : R[X]) : p %ₘ 1 = 0 :=
-  (modByMonic_eq_zero_iff_dvd (by convert monic_one (R := R))).2 (one_dvd _)
+  (modByMonic_eq_zero_iff_dvd (by convert! monic_one (R := R))).2 (one_dvd _)
 
 @[simp]
 theorem divByMonic_one (p : R[X]) : p /ₘ 1 = p := by
diff --git a/Mathlib/Algebra/Polynomial/EraseLead.lean b/Mathlib/Algebra/Polynomial/EraseLead.lean
index 2e3cc9c33cdc25..d6c8a91e6136ed 100644
--- a/Mathlib/Algebra/Polynomial/EraseLead.lean
+++ b/Mathlib/Algebra/Polynomial/EraseLead.lean
@@ -322,13 +322,13 @@ theorem induction_with_natDegree_le (motive : R[X] → Prop) (N : ℕ) (zero : m
       motive f → motive g → motive (f + g)) (f : R[X]) (df : f.natDegree ≤ N) : motive f := by
   induction hf : #f.support generalizing f with
   | zero =>
-    convert zero
+    convert! zero
     simpa [support_eq_empty, card_eq_zero] using hf
   | succ c hc =>
     rw [← eraseLead_add_C_mul_X_pow f]
     cases c
-    · convert C_mul_pow f.natDegree f.leadingCoeff ?_ df using 1
-      · convert zero_add (C (leadingCoeff f) * X ^ f.natDegree)
+    · convert! C_mul_pow f.natDegree f.leadingCoeff ?_ df using 1
+      · convert! zero_add (C (leadingCoeff f) * X ^ f.natDegree)
         rw [← card_support_eq_zero, card_support_eraseLead' hf]
       · rw [leadingCoeff_ne_zero, Ne, ← card_support_eq_zero, hf]
         exact zero_ne_one.symm
diff --git a/Mathlib/Algebra/Polynomial/Eval/Defs.lean b/Mathlib/Algebra/Polynomial/Eval/Defs.lean
index c4479910af3a9a..6cfdf3fe6d567d 100644
--- a/Mathlib/Algebra/Polynomial/Eval/Defs.lean
+++ b/Mathlib/Algebra/Polynomial/Eval/Defs.lean
@@ -80,7 +80,7 @@ theorem eval₂_monomial {n : ℕ} {r : R} : (monomial n r).eval₂ f x = f r *
 @[simp]
 theorem eval₂_X_pow {n : ℕ} : (X ^ n).eval₂ f x = x ^ n := by
   rw [X_pow_eq_monomial]
-  convert eval₂_monomial f x (n := n) (r := 1)
+  convert! eval₂_monomial f x (n := n) (r := 1)
   simp
 
 @[simp]
@@ -260,13 +260,13 @@ theorem eval₂_at_apply {S : Type*} [Semiring S] (f : R →+* S) (r : R) :
 
 @[simp]
 theorem eval₂_at_one {S : Type*} [Semiring S] (f : R →+* S) : p.eval₂ f 1 = f (p.eval 1) := by
-  convert eval₂_at_apply (p := p) f 1
+  convert! eval₂_at_apply (p := p) f 1
   simp
 
 @[simp]
 theorem eval₂_at_natCast {S : Type*} [Semiring S] (f : R →+* S) (n : ℕ) :
     p.eval₂ f n = f (p.eval n) := by
-  convert eval₂_at_apply (p := p) f n
+  convert! eval₂_at_apply (p := p) f n
   simp
 
 @[simp]
@@ -778,7 +778,7 @@ theorem intCast_comp (i : ℤ) : comp (i : R[X]) p = i := by cases i <;> simp
 @[simp]
 theorem eval₂_at_intCast {S : Type*} [Ring S] (f : R →+* S) (n : ℤ) :
     p.eval₂ f n = f (p.eval n) := by
-  convert eval₂_at_apply (p := p) f n
+  convert! eval₂_at_apply (p := p) f n
   simp
 
 theorem mul_X_sub_intCast_comp {n : ℕ} :
diff --git a/Mathlib/Algebra/Polynomial/Eval/Degree.lean b/Mathlib/Algebra/Polynomial/Eval/Degree.lean
index 0ea93154dbfed2..2040f65da66435 100644
--- a/Mathlib/Algebra/Polynomial/Eval/Degree.lean
+++ b/Mathlib/Algebra/Polynomial/Eval/Degree.lean
@@ -238,7 +238,7 @@ lemma isUnit_of_isUnit_leadingCoeff_of_isUnit_map (hf : IsUnit f.leadingCoeff)
   rw [degree_map_eq_of_leadingCoeff_ne_zero] at dz
   · rw [eq_C_of_degree_eq_zero dz]
     refine IsUnit.map C ?_
-    convert hf
+    convert! hf
     change coeff f 0 = coeff f (natDegree f)
     rw [(degree_eq_iff_natDegree_eq _).1 dz]
     · rfl
diff --git a/Mathlib/Algebra/Polynomial/Laurent.lean b/Mathlib/Algebra/Polynomial/Laurent.lean
index 4006a861e9f960..e3b674a50ed46d 100644
--- a/Mathlib/Algebra/Polynomial/Laurent.lean
+++ b/Mathlib/Algebra/Polynomial/Laurent.lean
@@ -189,7 +189,7 @@ theorem _root_.Polynomial.toLaurent_C_mul_T (n : ℕ) (r : R) :
 
 @[simp]
 theorem _root_.Polynomial.toLaurent_C (r : R) : toLaurent (Polynomial.C r) = C r := by
-  convert Polynomial.toLaurent_C_mul_T 0 r
+  convert! Polynomial.toLaurent_C_mul_T 0 r
   simp only [Int.ofNat_zero, T_zero, mul_one]
 
 @[simp]
@@ -244,12 +244,12 @@ protected theorem induction_on {M : R[T;T⁻¹] → Prop} (p : R[T;T⁻¹]) (h_C
     · exact fun m => h_C_mul_T_Z m a
   have B : ∀ s : Finset ℤ, M (s.sum fun n : ℤ => C (p n) * T n) := by
     apply Finset.induction
-    · convert h_C 0
+    · convert! h_C 0
       simp only [Finset.sum_empty, map_zero]
     · intro n s ns ih
       rw [Finset.sum_insert ns]
       exact h_add A ih
-  convert B p.support
+  convert! B p.support
   ext a
   simp_rw [← single_eq_C_mul_T]
   rw [Finset.sum_apply', Finset.sum_eq_single a, single_eq_same]
@@ -268,7 +268,7 @@ protected theorem induction_on' {motive : R[T;T⁻¹] → Prop} (p : R[T;T⁻¹]
     (C_mul_T : ∀ (n : ℤ) (a : R), motive (C a * T n)) : motive p := by
   refine p.induction_on (fun a => ?_) (fun {p q} => add p q) ?_ ?_ <;>
       try exact fun n f _ => C_mul_T _ f
-  convert C_mul_T 0 a
+  convert! C_mul_T 0 a
   exact (mul_one _).symm
 
 theorem commute_T (n : ℤ) (f : R[T;T⁻¹]) : Commute (T n) f :=
@@ -375,7 +375,7 @@ theorem reduce_to_polynomial_of_mul_T (f : R[T;T⁻¹]) {Q : R[T;T⁻¹] → Pro
   induction f using LaurentPolynomial.induction_on_mul_T with | _ f n
   induction n with
   | zero => simpa only [Nat.cast_zero, neg_zero, T_zero, mul_one] using Qf _
-  | succ n hn => convert QT _ _; simpa using hn
+  | succ n hn => convert! QT _ _; simpa using hn
 
 section Support
 
@@ -542,7 +542,7 @@ theorem mk'_one_X_pow (n : ℕ) :
 @[simp]
 theorem mk'_one_X :
     IsLocalization.mk' R[T;T⁻¹] 1 (⟨X, 1, pow_one X⟩ : Submonoid.powers (X : R[X])) = T (-1) := by
-  convert mk'_one_X_pow 1
+  convert! mk'_one_X_pow 1
   exact (pow_one X).symm
 
 /-- Given a ring homomorphism `f : R →+* S` and a unit `x` in `S`, the induced homomorphism
diff --git a/Mathlib/Algebra/Polynomial/Monic.lean b/Mathlib/Algebra/Polynomial/Monic.lean
index 6b06c2d8c9f6ca..0d7f0841a6c6b6 100644
--- a/Mathlib/Algebra/Polynomial/Monic.lean
+++ b/Mathlib/Algebra/Polynomial/Monic.lean
@@ -192,7 +192,7 @@ theorem eq_one_of_map_eq_one {S : Type*} [Semiring S] [Nontrivial S] (f : R →+
       exact one_ne_zero
   have hndeg : p.natDegree = 0 :=
     WithBot.coe_eq_coe.mp ((degree_eq_natDegree hp.ne_zero).symm.trans hdeg)
-  convert eq_C_of_degree_eq_zero hdeg
+  convert! eq_C_of_degree_eq_zero hdeg
   rw [← hndeg, ← Polynomial.leadingCoeff, hp.leadingCoeff, C.map_one]
 
 theorem natDegree_pow (hp : p.Monic) (n : ℕ) : (p ^ n).natDegree = n * p.natDegree := by
diff --git a/Mathlib/Algebra/Polynomial/RingDivision.lean b/Mathlib/Algebra/Polynomial/RingDivision.lean
index bb683214c01175..387133c4b134b1 100644
--- a/Mathlib/Algebra/Polynomial/RingDivision.lean
+++ b/Mathlib/Algebra/Polynomial/RingDivision.lean
@@ -111,7 +111,7 @@ theorem rootMultiplicity_eq_rootMultiplicity {p : R[X]} {t : R} :
   simp_rw [rootMultiplicity_eq_multiplicity, comp_X_add_C_eq_zero_iff]
   congr 1
   rw [C_0, sub_zero]
-  convert (multiplicity_map_eq <| algEquivAevalXAddC t).symm using 2
+  convert! (multiplicity_map_eq <| algEquivAevalXAddC t).symm using 2
   simp [C_eq_algebraMap]
 
 /-- See `Polynomial.rootMultiplicity_eq_natTrailingDegree'` for the special case of `t = 0`. -/
@@ -205,7 +205,7 @@ theorem prime_X_sub_C (r : R) : Prime (X - C r) :=
     exact id⟩
 
 theorem prime_X : Prime (X : R[X]) := by
-  convert prime_X_sub_C (0 : R)
+  convert! prime_X_sub_C (0 : R)
   simp
 
 theorem Monic.prime_of_degree_eq_one (hp1 : degree p = 1) (hm : Monic p) : Prime p :=
diff --git a/Mathlib/Algebra/Polynomial/Roots.lean b/Mathlib/Algebra/Polynomial/Roots.lean
index 3602e5faa42aa9..41cffb24152941 100644
--- a/Mathlib/Algebra/Polynomial/Roots.lean
+++ b/Mathlib/Algebra/Polynomial/Roots.lean
@@ -364,7 +364,7 @@ def nthRootsFinset (n : ℕ) {R : Type*} (a : R) [CommRing R] [IsDomain R] : Fin
 lemma nthRootsFinset_def (n : ℕ) {R : Type*} (a : R) [CommRing R] [IsDomain R] [DecidableEq R] :
     nthRootsFinset n a = Multiset.toFinset (nthRoots n a) := by
   unfold nthRootsFinset
-  convert rfl
+  convert! rfl
 
 @[simp]
 theorem mem_nthRootsFinset {n : ℕ} (h : 0 < n) (a : R) {x : R} :
@@ -540,7 +540,7 @@ def rootSet (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] : Set S :=
 theorem rootSet_def (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] [DecidableEq S] :
     p.rootSet S = (p.aroots S).toFinset := by
   rw [rootSet]
-  convert rfl
+  convert! rfl
 
 @[simp]
 theorem rootSet_C [CommRing S] [IsDomain S] [Algebra T S] (a : T) : (C a).rootSet S = ∅ := by
@@ -816,7 +816,7 @@ theorem C_leadingCoeff_mul_prod_multiset_X_sub_C (hroots : Multiset.card p.roots
 can be written `p = ∏(X - a)`, for `a` in `p.roots`. -/
 theorem prod_multiset_X_sub_C_of_monic_of_roots_card_eq (hp : p.Monic)
     (hroots : Multiset.card p.roots = p.natDegree) : (p.roots.map fun a => X - C a).prod = p := by
-  convert C_leadingCoeff_mul_prod_multiset_X_sub_C hroots
+  convert! C_leadingCoeff_mul_prod_multiset_X_sub_C hroots
   rw [hp.leadingCoeff, C_1, one_mul]
 
 theorem Monic.isUnit_leadingCoeff_of_dvd {a p : R[X]} (hp : Monic p) (hap : a ∣ p) :
@@ -826,7 +826,7 @@ theorem Monic.isUnit_leadingCoeff_of_dvd {a p : R[X]} (hp : Monic p) (hap : a 
 theorem card_roots_le_one_of_irreducible (hirr : Irreducible p) : p.roots.card ≤ 1 := by
   obtain hp | ⟨x, hx⟩ := p.roots.empty_or_exists_mem
   · simp [hp]
-  convert p.card_roots'
+  convert! p.card_roots'
   exact (natDegree_eq_of_degree_eq_some <| degree_eq_one_of_irreducible_of_root hirr <|
     isRoot_of_mem_roots hx).symm
 
@@ -886,7 +886,7 @@ theorem count_map_roots [IsDomain A] [DecidableEq B] {p : A[X]} {f : A →+* B}
   rw [← Multiset.filter_eq]
   refine
     (Multiset.prod_dvd_prod_of_le <| Multiset.map_le_map <| Multiset.filter_le (Eq b) _).trans ?_
-  convert Polynomial.map_dvd f p.prod_multiset_X_sub_C_dvd
+  convert! Polynomial.map_dvd f p.prod_multiset_X_sub_C_dvd
   simp only [Polynomial.map_multiset_prod, Multiset.map_map, Function.comp_apply,
     Polynomial.map_sub, map_X, map_C]
 
diff --git a/Mathlib/Algebra/Polynomial/RuleOfSigns.lean b/Mathlib/Algebra/Polynomial/RuleOfSigns.lean
index d0335ff0694f79..754ca2bf825c69 100644
--- a/Mathlib/Algebra/Polynomial/RuleOfSigns.lean
+++ b/Mathlib/Algebra/Polynomial/RuleOfSigns.lean
@@ -209,7 +209,7 @@ lemma signVariations_eraseLead_mul_X_sub_C (hη : 0 < η) (hP₀ : 0 < leadingCo
 lemma succ_signVariations_X_sub_C_mul_monomial {d c} (hc : c ≠ 0) (hη : 0 < η) :
     (monomial d c).signVariations + 1 ≤ ((X - C η) * monomial d c).signVariations := by
   have h₁ : nextCoeff ((X - C η) * monomial d c) = -(η * c) := by
-    convert coeff_mul_monomial (X - C η) d 0 c using 1
+    convert! coeff_mul_monomial (X - C η) d 0 c using 1
     · simp [hc, nextCoeff, natDegree_mul (X_sub_C_ne_zero η)]
     · simp
   have h₂ : eraseLead ((X - C η) * monomial d c) ≠ 0 := by
diff --git a/Mathlib/Algebra/Polynomial/SumIteratedDerivative.lean b/Mathlib/Algebra/Polynomial/SumIteratedDerivative.lean
index 397f0f9e441105..3dfbf95ffe2ba2 100644
--- a/Mathlib/Algebra/Polynomial/SumIteratedDerivative.lean
+++ b/Mathlib/Algebra/Polynomial/SumIteratedDerivative.lean
@@ -143,7 +143,7 @@ theorem aeval_iterate_derivative_self (p : R[X]) (q : ℕ) (r : A) {p' : A[X]}
   simp_rw [hp, iterate_derivative_mul, iterate_derivative_X_sub_pow, ← smul_mul_assoc, smul_smul]
   rw [sum_range_succ', Nat.choose_zero_right, one_mul, tsub_zero, Nat.descFactorial_self, tsub_self,
     pow_zero, smul_mul_assoc, one_mul, Function.iterate_zero_apply, eval_add, eval_smul]
-  convert zero_add _
+  convert! zero_add _
   rw [eval_finsetSum]
   apply sum_eq_zero
   intro x hx
diff --git a/Mathlib/Algebra/Prime/Lemmas.lean b/Mathlib/Algebra/Prime/Lemmas.lean
index 600e11ba5d41a3..704735cad894a0 100644
--- a/Mathlib/Algebra/Prime/Lemmas.lean
+++ b/Mathlib/Algebra/Prime/Lemmas.lean
@@ -48,11 +48,11 @@ theorem comap_prime (hinv : ∀ a, g (f a : N) = a) (hp : Prime (f p)) : Prime p
   ⟨fun h => hp.1 <| by simp [h], fun h => hp.2.1 <| h.map f, fun a b h => by
     refine
         (hp.2.2 (f a) (f b) <| by
-              convert map_dvd f h
+              convert! map_dvd f h
               simp).imp
           ?_ ?_ <;>
       · intro h
-        convert ← map_dvd g h <;> apply hinv⟩
+        convert! ← map_dvd g h <;> apply hinv⟩
 
 theorem MulEquiv.prime_iff {E : Type*} [EquivLike E M N] [MulEquivClass E M N] (e : E) :
     Prime (e p) ↔ Prime p := by
diff --git a/Mathlib/Algebra/QuadraticAlgebra/NormDeterminant.lean b/Mathlib/Algebra/QuadraticAlgebra/NormDeterminant.lean
index c8959dc459100d..efa45141de504c 100644
--- a/Mathlib/Algebra/QuadraticAlgebra/NormDeterminant.lean
+++ b/Mathlib/Algebra/QuadraticAlgebra/NormDeterminant.lean
@@ -30,7 +30,7 @@ theorem det_toLinearMap_eq_norm (z : QuadraticAlgebra R a b) :
   have : !![z.re, a * z.im; z.im, z.re + b * z.im].det = z.norm := by
     simp [norm]
     ring
-  convert this
+  convert! this
   apply LinearEquiv.eq_symm_apply _ |>.mp
   ext1 w
   apply basis .. |>.repr.injective
diff --git a/Mathlib/Algebra/QuadraticDiscriminant.lean b/Mathlib/Algebra/QuadraticDiscriminant.lean
index 0b8720a5988fe0..d468d87f32ef32 100644
--- a/Mathlib/Algebra/QuadraticDiscriminant.lean
+++ b/Mathlib/Algebra/QuadraticDiscriminant.lean
@@ -139,7 +139,7 @@ theorem discrim_le_zero (h : ∀ x : K, 0 ≤ a * (x * x) + b * x + c) : discrim
       linarith
   -- if a > 0
   · have ha' : 0 ≤ 4 * a := mul_nonneg zero_le_four ha.le
-    convert neg_nonpos.2 (mul_nonneg ha' (h (-b / (2 * a)))) using 1
+    convert! neg_nonpos.2 (mul_nonneg ha' (h (-b / (2 * a)))) using 1
     field
 
 lemma discrim_le_zero_of_nonpos (h : ∀ x : K, a * (x * x) + b * x + c ≤ 0) : discrim a b c ≤ 0 :=
diff --git a/Mathlib/Algebra/Regular/SMul.lean b/Mathlib/Algebra/Regular/SMul.lean
index d504d483816eff..3d343ced450708 100644
--- a/Mathlib/Algebra/Regular/SMul.lean
+++ b/Mathlib/Algebra/Regular/SMul.lean
@@ -224,7 +224,7 @@ variable {G : Type*} [Group G]
 of the inverse given by groups, since there is no `LeftCancelSMul` typeclass. -/
 theorem isSMulRegular_of_group [MulAction G R] (g : G) : IsSMulRegular R g := by
   intro x y h
-  convert congr_arg (g⁻¹ • ·) h using 1 <;> simp [← smul_assoc]
+  convert! congr_arg (g⁻¹ • ·) h using 1 <;> simp [← smul_assoc]
 
 end Group
 
diff --git a/Mathlib/Algebra/Ring/Divisibility/Basic.lean b/Mathlib/Algebra/Ring/Divisibility/Basic.lean
index d00b8e581f8fe5..1dbced56baea73 100644
--- a/Mathlib/Algebra/Ring/Divisibility/Basic.lean
+++ b/Mathlib/Algebra/Ring/Divisibility/Basic.lean
@@ -182,7 +182,7 @@ variable [NonUnitalCommRing α]
 
 theorem dvd_mul_sub_mul {k a b x y : α} (hab : k ∣ a - b) (hxy : k ∣ x - y) :
     k ∣ a * x - b * y := by
-  convert dvd_add (hxy.mul_left a) (hab.mul_right y) using 1
+  convert! dvd_add (hxy.mul_left a) (hab.mul_right y) using 1
   rw [mul_sub_left_distrib, mul_sub_right_distrib]
   simp only [sub_eq_add_neg, add_assoc, neg_add_cancel_left]
 
diff --git a/Mathlib/Algebra/Ring/GeomSum.lean b/Mathlib/Algebra/Ring/GeomSum.lean
index 4a08fe78ade23e..ebe98646620e31 100644
--- a/Mathlib/Algebra/Ring/GeomSum.lean
+++ b/Mathlib/Algebra/Ring/GeomSum.lean
@@ -152,7 +152,7 @@ lemma geom_sum₂_mul_of_ge (hxy : y ≤ x) (n : ℕ) :
 lemma geom_sum₂_mul_of_le (hxy : x ≤ y) (n : ℕ) :
     (∑ i ∈ range n, x ^ i * y ^ (n - 1 - i)) * (y - x) = y ^ n - x ^ n := by
   rw [← Finset.sum_range_reflect]
-  convert geom_sum₂_mul_of_ge hxy n using 3
+  convert! geom_sum₂_mul_of_ge hxy n using 3
   simp_all only [Finset.mem_range]
   rw [mul_comm]
   congr
@@ -284,7 +284,7 @@ protected lemma Commute.geom_sum₂_Ico_mul (h : Commute x y) {m n : ℕ}
     have hp := Commute.pow_pow (Commute.op h.symm) (n - 1 - k) k
     simpa [Commute, SemiconjBy] using hp
   simp only [this]
-  convert (Commute.op h).mul_geom_sum₂_Ico hmn
+  convert! (Commute.op h).mul_geom_sum₂_Ico hmn
 
 lemma geom_sum_Ico_mul (x : R) {m n : ℕ} (hmn : m ≤ n) :
     (∑ i ∈ Finset.Ico m n, x ^ i) * (x - 1) = x ^ n - x ^ m := by
diff --git a/Mathlib/Algebra/Ring/Idempotent.lean b/Mathlib/Algebra/Ring/Idempotent.lean
index 83c8270ccafcb9..5e11e9f0f17344 100644
--- a/Mathlib/Algebra/Ring/Idempotent.lean
+++ b/Mathlib/Algebra/Ring/Idempotent.lean
@@ -143,7 +143,7 @@ theorem sub_iff [NonUnitalRing R] [IsAddTorsionFree R] {p q : R}
     simp_rw [sub_mul, add_mul, mul_assoc, hq.eq, add_sub_cancel_left, ← mul_assoc] at h2
     exact h2.symm.trans h1
   rw [hpq.eq, and_self, ← nsmul_right_inj (by simp : 2 ≠ 0), ← zero_add (2 • p)]
-  convert congrArg (· + 2 • p) h using 1
+  convert! congrArg (· + 2 • p) h using 1
   simp [sub_mul, mul_sub, hp.eq, hpq.eq, two_nsmul, sub_add, sub_sub]
 
 end IsIdempotentElem
diff --git a/Mathlib/Algebra/Ring/Parity.lean b/Mathlib/Algebra/Ring/Parity.lean
index 44d5c39bcaf2e4..8672c229f5f79c 100644
--- a/Mathlib/Algebra/Ring/Parity.lean
+++ b/Mathlib/Algebra/Ring/Parity.lean
@@ -220,27 +220,27 @@ lemma Odd.sub_odd (ha : Odd a) (hb : Odd b) : Even (a - b) := by
 
 @[simp]
 lemma even_add_one : Even (a + 1) ↔ Odd a :=
-  ⟨(by convert ·.sub_odd odd_one; rw [eq_sub_iff_add_eq]), (·.add_one)⟩
+  ⟨(by convert! ·.sub_odd odd_one; rw [eq_sub_iff_add_eq]), (·.add_one)⟩
 
 @[simp]
 lemma even_sub_one : Even (a - 1) ↔ Odd a :=
-  ⟨(by convert ·.add_odd odd_one; rw [sub_add_cancel]), (·.sub_odd odd_one)⟩
+  ⟨(by convert! ·.add_odd odd_one; rw [sub_add_cancel]), (·.sub_odd odd_one)⟩
 
 @[simp]
 lemma even_add_two : Even (a + 2) ↔ Even a :=
-  ⟨(by convert ·.sub even_two; rw [eq_sub_iff_add_eq]), (·.add even_two)⟩
+  ⟨(by convert! ·.sub even_two; rw [eq_sub_iff_add_eq]), (·.add even_two)⟩
 
 @[simp]
 lemma even_sub_two : Even (a - 2) ↔ Even a :=
-  ⟨(by convert ·.add even_two; rw [sub_add_cancel]), (·.sub even_two)⟩
+  ⟨(by convert! ·.add even_two; rw [sub_add_cancel]), (·.sub even_two)⟩
 
 @[simp]
 lemma odd_add_one : Odd (a + 1) ↔ Even a :=
-  ⟨(by convert ·.sub_odd odd_one; rw [eq_sub_iff_add_eq]), (·.add_one)⟩
+  ⟨(by convert! ·.sub_odd odd_one; rw [eq_sub_iff_add_eq]), (·.add_one)⟩
 
 @[simp]
 lemma odd_sub_one : Odd (a - 1) ↔ Even a :=
-  ⟨(by convert ·.add_odd odd_one; rw [sub_add_cancel]), (·.sub_odd odd_one)⟩
+  ⟨(by convert! ·.add_odd odd_one; rw [sub_add_cancel]), (·.sub_odd odd_one)⟩
 
 @[simp]
 lemma odd_add_two : Odd (a + 2) ↔ Odd a := by
diff --git a/Mathlib/Algebra/Ring/Subring/Basic.lean b/Mathlib/Algebra/Ring/Subring/Basic.lean
index c87b165c881707..4916cd9a6d7a6a 100644
--- a/Mathlib/Algebra/Ring/Subring/Basic.lean
+++ b/Mathlib/Algebra/Ring/Subring/Basic.lean
@@ -1152,7 +1152,7 @@ theorem comap_map_eq (f : R →+* S) (s : Subring R) :
 
 theorem comap_map_eq_self {f : R →+* S} {s : Subring R}
     (h : f ⁻¹' {0} ⊆ s) : (s.map f).comap f = s := by
-  convert comap_map_eq f s
+  convert! comap_map_eq f s
   rwa [left_eq_sup, closure_le]
 
 theorem comap_map_eq_self_of_injective
@@ -1163,5 +1163,5 @@ end Subring
 
 theorem AddSubgroup.int_mul_mem {G : AddSubgroup R} (k : ℤ) {g : R} (h : g ∈ G) :
     (k : R) * g ∈ G := by
-  convert AddSubgroup.zsmul_mem G h k using 1
+  convert! AddSubgroup.zsmul_mem G h k using 1
   rw [zsmul_eq_mul]
diff --git a/Mathlib/Algebra/Ring/Subsemiring/Basic.lean b/Mathlib/Algebra/Ring/Subsemiring/Basic.lean
index e49a70e64d89b9..d3a7ab89c659ad 100644
--- a/Mathlib/Algebra/Ring/Subsemiring/Basic.lean
+++ b/Mathlib/Algebra/Ring/Subsemiring/Basic.lean
@@ -390,7 +390,7 @@ theorem closure_eq_of_le {s : Set R} {t : Subsemiring R} (h₁ : s ⊆ t) (h₂
 
 theorem mem_map_equiv {f : R ≃+* S} {K : Subsemiring R} {x : S} :
     x ∈ K.map (f : R →+* S) ↔ f.symm x ∈ K := by
-  convert @Set.mem_image_equiv _ _ (↑K) f.toEquiv x using 1
+  convert! @Set.mem_image_equiv _ _ (↑K) f.toEquiv x using 1
 
 theorem map_equiv_eq_comap_symm (f : R ≃+* S) (K : Subsemiring R) :
     K.map (f : R →+* S) = K.comap f.symm :=
diff --git a/Mathlib/Algebra/SkewMonoidAlgebra/Basic.lean b/Mathlib/Algebra/SkewMonoidAlgebra/Basic.lean
index 8199498397b672..ee81cf588c266b 100644
--- a/Mathlib/Algebra/SkewMonoidAlgebra/Basic.lean
+++ b/Mathlib/Algebra/SkewMonoidAlgebra/Basic.lean
@@ -1078,7 +1078,7 @@ theorem mapDomain_mul [MulSemiringAction α β] [MulSemiringAction α₂ β]
     ext a b c
     rw [sum_mapDomain_index (by simp) (by simp [smul_add, mul_add, single_add])]
     simp_rw [hf]
-  convert this using 4
+  convert! this using 4
   rw [map_sum]
 
 /-- If f : G → H is a multiplicative homomorphism between two monoids and
diff --git a/Mathlib/Algebra/Star/NonUnitalSubalgebra.lean b/Mathlib/Algebra/Star/NonUnitalSubalgebra.lean
index 57667d66965a5a..74e8b6544b458d 100644
--- a/Mathlib/Algebra/Star/NonUnitalSubalgebra.lean
+++ b/Mathlib/Algebra/Star/NonUnitalSubalgebra.lean
@@ -1224,7 +1224,7 @@ lemma adjoin_le_centralizer_centralizer (s : Set A) :
     adjoin R s ≤ centralizer R (centralizer R s) := by
   rw [← toNonUnitalSubalgebra_le_iff, centralizer_toNonUnitalSubalgebra,
     adjoin_toNonUnitalSubalgebra]
-  convert NonUnitalAlgebra.adjoin_le_centralizer_centralizer R (s ∪ star s)
+  convert! NonUnitalAlgebra.adjoin_le_centralizer_centralizer R (s ∪ star s)
   rw [StarMemClass.star_coe_eq]
   simp
 
diff --git a/Mathlib/Algebra/Star/Subalgebra.lean b/Mathlib/Algebra/Star/Subalgebra.lean
index 5c70c3f315a805..973298bd7d4871 100644
--- a/Mathlib/Algebra/Star/Subalgebra.lean
+++ b/Mathlib/Algebra/Star/Subalgebra.lean
@@ -579,7 +579,7 @@ variable (R)
 lemma adjoin_le_centralizer_centralizer (s : Set A) :
     adjoin R s ≤ centralizer R (centralizer R s) := by
   rw [← toSubalgebra_le_iff, centralizer_toSubalgebra, adjoin_toSubalgebra]
-  convert Algebra.adjoin_le_centralizer_centralizer R (s ∪ star s)
+  convert! Algebra.adjoin_le_centralizer_centralizer R (s ∪ star s)
   rw [StarMemClass.star_coe_eq]
   simp
 
diff --git a/Mathlib/Algebra/Star/TensorProduct.lean b/Mathlib/Algebra/Star/TensorProduct.lean
index e4b70bb63681dd..2ba906bc061389 100644
--- a/Mathlib/Algebra/Star/TensorProduct.lean
+++ b/Mathlib/Algebra/Star/TensorProduct.lean
@@ -35,7 +35,7 @@ noncomputable instance : InvolutiveStar (A ⊗[R] B) where
   star_involutive x := by
     simp_rw [star]
     rw [congr_congr]
-    convert congr($congr_refl_refl x) <;> ext <;> simp
+    convert! congr($congr_refl_refl x) <;> ext <;> simp
 
 noncomputable instance : StarAddMonoid (A ⊗[R] B) where
   star_add := map_add _
diff --git a/Mathlib/Algebra/Symmetrized.lean b/Mathlib/Algebra/Symmetrized.lean
index 9a6ac8283f9827..87503423a78036 100644
--- a/Mathlib/Algebra/Symmetrized.lean
+++ b/Mathlib/Algebra/Symmetrized.lean
@@ -318,7 +318,7 @@ instance [Ring α] [Invertible (2 : α)] : IsCommJordan αˢʸᵐ where
       rw [add_mul, ← add_assoc, ← mul_assoc, ← mul_assoc]
       rw [unsym_mul_self]
       rw [← mul_assoc, ← mul_assoc, ← mul_assoc, ← mul_assoc, ← sub_eq_zero, ← mul_sub]
-      convert mul_zero (⅟(2 : α) * ⅟(2 : α))
+      convert! mul_zero (⅟(2 : α) * ⅟(2 : α))
       rw [add_sub_add_right_eq_sub, add_assoc, add_assoc, add_sub_add_left_eq_sub, add_comm,
         add_sub_add_right_eq_sub, sub_eq_zero]
     -- Rearrange RHS
diff --git a/Mathlib/Algebra/TrivSqZeroExt/Basic.lean b/Mathlib/Algebra/TrivSqZeroExt/Basic.lean
index 780d60faf98b42..6eafdd9b83c3dc 100644
--- a/Mathlib/Algebra/TrivSqZeroExt/Basic.lean
+++ b/Mathlib/Algebra/TrivSqZeroExt/Basic.lean
@@ -707,7 +707,7 @@ abbrev invertibleFstOfInvertible (x : tsze R M) [Invertible x] : Invertible x.fs
 
 theorem fst_invOf (x : tsze R M) [Invertible x] [Invertible x.fst] : (⅟x).fst = ⅟(x.fst) := by
   letI := invertibleFstOfInvertible x
-  convert (rfl : _ = ⅟x.fst)
+  convert! (rfl : _ = ⅟x.fst)
 
 theorem mul_left_eq_one (r : R) (x : tsze R M) (h : r * x.fst = 1) :
     (inl r + inr (-((r •> x.snd) <• r))) * x = 1 := by
@@ -728,17 +728,17 @@ variable [SMulCommClass R Rᵐᵒᵖ M]
 abbrev invertibleOfInvertibleFst (x : tsze R M) [Invertible x.fst] : Invertible x where
   invOf := (⅟x.fst, -(⅟x.fst •> x.snd <• ⅟x.fst))
   invOf_mul_self := by
-    convert mul_left_eq_one _ _ (invOf_mul_self x.fst)
+    convert! mul_left_eq_one _ _ (invOf_mul_self x.fst)
     ext <;> simp
   mul_invOf_self := by
-    convert mul_right_eq_one _ _ (mul_invOf_self x.fst)
+    convert! mul_right_eq_one _ _ (mul_invOf_self x.fst)
     ext <;> simp [smul_comm]
 
 theorem snd_invOf (x : tsze R M) [Invertible x] [Invertible x.fst] :
     (⅟x).snd = -(⅟x.fst •> x.snd <• ⅟x.fst) := by
   letI := invertibleOfInvertibleFst x
-  convert congr_arg (TrivSqZeroExt.snd (R := R) (M := M)) (_ : _ = ⅟x)
-  convert rfl
+  convert! congr_arg (TrivSqZeroExt.snd (R := R) (M := M)) (_ : _ = ⅟x)
+  convert! rfl
 
 /-- Together `TrivSqZeroExt.detInvertibleOfInvertible` and `TrivSqZeroExt.invertibleOfDetInvertible`
 form an equivalence, although both sides of the equiv are subsingleton anyway. -/
@@ -788,7 +788,7 @@ protected theorem inv_one : (1 : tsze R M)⁻¹ = (1 : tsze R M) := by
   rw [← inl_one, TrivSqZeroExt.inv_inl, inv_one]
 
 protected theorem inv_mul_cancel {x : tsze R M} (hx : fst x ≠ 0) : x⁻¹ * x = 1 := by
-  convert mul_left_eq_one _ _ (_root_.inv_mul_cancel₀ hx) using 2
+  convert! mul_left_eq_one _ _ (_root_.inv_mul_cancel₀ hx) using 2
   ext <;> simp
 
 variable [SMulCommClass R Rᵐᵒᵖ M]
diff --git a/Mathlib/Algebra/Tropical/BigOperators.lean b/Mathlib/Algebra/Tropical/BigOperators.lean
index 44cc67224797c5..c9dd058dada748 100644
--- a/Mathlib/Algebra/Tropical/BigOperators.lean
+++ b/Mathlib/Algebra/Tropical/BigOperators.lean
@@ -50,7 +50,7 @@ theorem Multiset.trop_sum [AddCommMonoid R] (s : Multiset R) :
 
 theorem trop_sum [AddCommMonoid R] (s : Finset S) (f : S → R) :
     trop (∑ i ∈ s, f i) = ∏ i ∈ s, trop (f i) := by
-  convert Multiset.trop_sum (s.val.map f)
+  convert! Multiset.trop_sum (s.val.map f)
   simp only [Multiset.map_map, Function.comp_apply]
   rfl
 
@@ -66,7 +66,7 @@ theorem Multiset.untrop_prod [AddCommMonoid R] (s : Multiset (Tropical R)) :
 
 theorem untrop_prod [AddCommMonoid R] (s : Finset S) (f : S → Tropical R) :
     untrop (∏ i ∈ s, f i) = ∑ i ∈ s, untrop (f i) := by
-  convert Multiset.untrop_prod (s.val.map f)
+  convert! Multiset.untrop_prod (s.val.map f)
   simp only [Multiset.map_map, Function.comp_apply]
   rfl
 
@@ -84,7 +84,7 @@ theorem Multiset.trop_inf [LinearOrder R] [OrderTop R] (s : Multiset R) :
 
 theorem Finset.trop_inf [LinearOrder R] [OrderTop R] (s : Finset S) (f : S → R) :
     trop (s.inf f) = ∑ i ∈ s, trop (f i) := by
-  convert Multiset.trop_inf (s.val.map f)
+  convert! Multiset.trop_inf (s.val.map f)
   simp only [Multiset.map_map, Function.comp_apply]
   rfl
 
@@ -106,7 +106,7 @@ theorem Multiset.untrop_sum [LinearOrder R] [OrderTop R] (s : Multiset (Tropical
 
 theorem Finset.untrop_sum' [LinearOrder R] [OrderTop R] (s : Finset S) (f : S → Tropical R) :
     untrop (∑ i ∈ s, f i) = s.inf (untrop ∘ f) := by
-  convert Multiset.untrop_sum (s.val.map f)
+  convert! Multiset.untrop_sum (s.val.map f)
   simp only [Multiset.map_map, Function.comp_apply, inf_def]
 
 theorem untrop_sum_eq_sInf_image [ConditionallyCompleteLinearOrder R] (s : Finset S)
diff --git a/Mathlib/AlgebraicGeometry/AffineScheme.lean b/Mathlib/AlgebraicGeometry/AffineScheme.lean
index 6d88881da5d29d..bbf0e4b5ae7347 100644
--- a/Mathlib/AlgebraicGeometry/AffineScheme.lean
+++ b/Mathlib/AlgebraicGeometry/AffineScheme.lean
@@ -264,7 +264,7 @@ theorem isAffineOpen_opensRange {X Y : Scheme} [IsAffine X] (f : X ⟶ Y)
   exact Subtype.range_val.symm
 
 theorem isAffineOpen_top (X : Scheme) [IsAffine X] : IsAffineOpen (⊤ : X.Opens) := by
-  convert isAffineOpen_opensRange (𝟙 X)
+  convert! isAffineOpen_opensRange (𝟙 X)
   ext1
   exact Set.range_id.symm
 
@@ -321,8 +321,9 @@ theorem Scheme.map_PrimeSpectrum_basicOpen_of_affine
 
 theorem isBasis_basicOpen (X : Scheme) [IsAffine X] :
     Opens.IsBasis (Set.range (X.basicOpen : Γ(X, ⊤) → X.Opens)) := by
-  convert PrimeSpectrum.isBasis_basic_opens.of_isInducing
-    (TopCat.homeoOfIso (Scheme.forgetToTop.mapIso X.isoSpec)).isInducing using 1
+  convert!
+    PrimeSpectrum.isBasis_basic_opens.of_isInducing
+      (TopCat.homeoOfIso (Scheme.forgetToTop.mapIso X.isoSpec)).isInducing using 1
   ext V
   simp only [Set.mem_range, exists_exists_eq_and, Set.mem_setOf,
     ← Opens.coe_inj (V := V), ← Scheme.toSpecΓ_preimage_basicOpen]
@@ -496,9 +497,8 @@ lemma fromSpec_app_of_le (V : X.Opens) (h : U ≤ V) :
 include hU in
 protected theorem isCompact :
     IsCompact (U : Set X) := by
-  convert @IsCompact.image _ _ _ _ Set.univ hU.fromSpec PrimeSpectrum.compactSpace.1
-    (by fun_prop)
-  convert hU.range_fromSpec.symm
+  convert! @IsCompact.image _ _ _ _ Set.univ hU.fromSpec PrimeSpectrum.compactSpace.1 (by fun_prop)
+  convert! hU.range_fromSpec.symm
   exact Set.image_univ
 
 theorem _root_.AlgebraicGeometry.Scheme.Hom.isAffineOpen_iff_of_isOpenImmersion
@@ -594,8 +594,9 @@ include hU in
 theorem basicOpen :
     IsAffineOpen (X.basicOpen f) := by
   rw [← hU.fromSpec_image_basicOpen, Scheme.Hom.isAffineOpen_iff_of_isOpenImmersion]
-  convert isAffineOpen_opensRange
-    (Spec.map (CommRingCat.ofHom <| algebraMap Γ(X, U) (Localization.Away f)))
+  convert!
+    isAffineOpen_opensRange
+      (Spec.map (CommRingCat.ofHom <| algebraMap Γ(X, U) (Localization.Away f)))
   exact Opens.ext (PrimeSpectrum.localization_away_comap_range (Localization.Away f) f).symm
 
 lemma Spec_basicOpen {R : CommRingCat} (f : R) :
@@ -657,7 +658,7 @@ theorem isLocalization_basicOpen :
   apply
     (IsLocalization.isLocalization_iff_of_ringEquiv (Submonoid.powers f)
       (asIso <| basicOpenSectionsToAffine hU f).commRingCatIsoToRingEquiv).mpr
-  convert StructureSheaf.IsLocalization.to_basicOpen _ f using 1
+  convert! StructureSheaf.IsLocalization.to_basicOpen _ f using 1
   apply Algebra.algebra_ext
   intro _
   congr 1
@@ -802,7 +803,7 @@ theorem isLocalization_stalk' (y : PrimeSpectrum Γ(X, U)) (hy : hU.fromSpec y 
       (S := X.presheaf.stalk (hU.fromSpec y)) _ y.asIdeal.primeCompl _
       (TopCat.Presheaf.algebra_section_stalk X.presheaf ⟨hU.fromSpec y, hy⟩) _ _
       (asIso <| hU.fromSpec.stalkMap y).commRingCatIsoToRingEquiv).mpr
-  convert StructureSheaf.IsLocalization.to_stalk Γ(X, U) y using 1
+  convert! StructureSheaf.IsLocalization.to_stalk Γ(X, U) y using 1
   delta IsLocalization.AtPrime StructureSheaf.stalkAlgebra
   congr!
   simp [RingHom.algebraMap_toAlgebra, ← CommRingCat.hom_comp, IsAffineOpen.fromSpec_app_self]
@@ -1032,7 +1033,7 @@ theorem of_affine_open_cover {X : Scheme} {P : X.affineOpens → Prop}
     obtain ⟨i, hi⟩ := Opens.mem_iSup.mp (iSup_U.ge (Set.mem_univ x))
     obtain ⟨f, g, e, hf⟩ := exists_basicOpen_le_affine_inter V.prop (U i).prop x ⟨x.prop, hi⟩
     refine ⟨f, hf, ?_⟩
-    convert basicOpen _ g (hU i) using 1
+    convert! basicOpen _ g (hU i) using 1
     ext1
     exact e
   choose f hf₁ hf₂ using this
diff --git a/Mathlib/AlgebraicGeometry/AffineSpace.lean b/Mathlib/AlgebraicGeometry/AffineSpace.lean
index b892058edf577c..15a4630cd7fdba 100644
--- a/Mathlib/AlgebraicGeometry/AffineSpace.lean
+++ b/Mathlib/AlgebraicGeometry/AffineSpace.lean
@@ -318,7 +318,7 @@ lemma isPullback_map {S T : Scheme.{max u v}} (f : S ⟶ T) :
     IsPullback (map n f) (𝔸(n; S) ↘ S) (𝔸(n; T) ↘ T) f := by
   refine (IsPullback.paste_horiz_iff (.flip <| .of_hasPullback _ _) (map_over f)).mp ?_
   simp only [terminal.comp_from, ]
-  convert (IsPullback.of_hasPullback _ _).flip
+  convert! (IsPullback.of_hasPullback _ _).flip
   rw [← toSpecMvPoly, ← toSpecMvPoly, map_toSpecMvPoly]
 
 /-- `𝔸(n; S)` is functorial w.r.t. `n`. -/
@@ -374,7 +374,7 @@ instance [Finite n] : LocallyOfFinitePresentation (𝔸(n; S) ↘ S) :=
   rw [← terminal.comp_from (Spec.map (CommRingCat.ofHom C)),
     MorphismProperty.cancel_right_of_respectsIso (P := @LocallyOfFinitePresentation),
     HasRingHomProperty.Spec_iff (P := @LocallyOfFinitePresentation), RingHom.FinitePresentation]
-  convert (inferInstance : Algebra.FinitePresentation (ULift ℤ) ℤ[n])
+  convert! (inferInstance : Algebra.FinitePresentation (ULift ℤ) ℤ[n])
   exact Algebra.algebra_ext _ _ fun _ ↦ rfl
 
 lemma isOpenMap_over : IsOpenMap (𝔸(n; S) ↘ S) := by
diff --git a/Mathlib/AlgebraicGeometry/AffineTransitionLimit.lean b/Mathlib/AlgebraicGeometry/AffineTransitionLimit.lean
index 08b1ad50d9a1fe..ddcd6db5faee5d 100644
--- a/Mathlib/AlgebraicGeometry/AffineTransitionLimit.lean
+++ b/Mathlib/AlgebraicGeometry/AffineTransitionLimit.lean
@@ -237,18 +237,20 @@ instance [∀ {i j} (f : i ⟶ j), IsAffineHom (D.map f)] {i : I}
     (U : (D.obj i).Opens) {j k : Over i} (f : j ⟶ k) :
     IsAffineHom ((opensDiagram D i U).map f) := by
   refine ⟨fun V hV ↦ ?_⟩
-  convert ((hV.image_of_isOpenImmersion (D.map k.hom ⁻¹ᵁ U).ι).preimage
-    (D.map f.left)).preimage_of_isOpenImmersion (D.map j.hom ⁻¹ᵁ U).ι ?_
+  convert!
+    ((hV.image_of_isOpenImmersion (D.map k.hom ⁻¹ᵁ U).ι).preimage
+          (D.map f.left)).preimage_of_isOpenImmersion
+      (D.map j.hom ⁻¹ᵁ U).ι ?_
   · ext x
     change _ ∈ V ↔ _
     refine ⟨fun h ↦ ⟨⟨(D.map f.left).base x.1, ?_⟩, ?_, rfl⟩, ?_⟩
     · change (D.map f.left ≫ D.map k.hom).base x.1 ∈ U
       rw [← D.map_comp, Over.w f]
       exact x.2
-    · convert h
+    · convert! h
       exact Subtype.ext (by simp)
     · rintro ⟨⟨_, hU⟩, hV, rfl⟩
-      convert hV
+      convert! hV
       exact Subtype.ext (by simp)
   · simp only [opensDiagram_obj, Scheme.Opens.opensRange_ι]
     rintro x ⟨⟨y, h₁ : (D.map k.hom).base y ∈ U⟩, h₂, e⟩
@@ -314,8 +316,9 @@ lemma isBasis_preimage_isAffineOpen [IsCofiltered I] [∀ {i j} (f : i ⟶ j), I
   obtain ⟨s, rfl⟩ := (D.map j.hom ⁻¹ᵁ V).topIso.symm.commRingCatIsoToRingEquiv.surjective s
   have h : c.π.app j.left ⁻¹ᵁ D.map j.hom ⁻¹ᵁ V = c.π.app i ⁻¹ᵁ V := congr($(c.w j.hom) ⁻¹ᵁ V)
   have : r = (c.π.app j.left).appLE (D.map j.hom ⁻¹ᵁ V) (c.π.app i ⁻¹ᵁ V) h.ge s := by
-    convert show r = ((topIso _).inv ≫ ((opensCone D c i V).π.app j).appTop ≫ (topIso _).hom) s
-      from (c.π.app i ⁻¹ᵁ V).topIso.commRingCatIsoToRingEquiv.symm_apply_eq.mp hs.symm using 3
+    convert!
+      show r = ((topIso _).inv ≫ ((opensCone D c i V).π.app j).appTop ≫ (topIso _).hom) s from
+        (c.π.app i ⁻¹ᵁ V).topIso.commRingCatIsoToRingEquiv.symm_apply_eq.mp hs.symm using 3
     simp [Scheme.Hom.app_eq_appLE, Scheme.Hom.resLE_appLE]
   refine ⟨_, ⟨j.left, _, (hV.preimage _).basicOpen s, rfl⟩, ?_⟩
   simp only [Functor.const_obj_obj, Scheme.preimage_basicOpen] at this ⊢
@@ -731,14 +734,14 @@ lemma exists_appTop_map_eq_zero_of_isLimit [∀ {i j} (f : i ⟶ j), IsAffineHom
     have (j : Over i) : IsAffine ((opensDiagram D i U).obj j) := hU.preimage (D.map _)
     obtain ⟨j, f, hj⟩ := exists_appTop_map_eq_zero_of_isAffine_of_isLimit _ _
       (isLimitOpensCone D c hc i U) (.mk (𝟙 i)) (((opensDiagramι D i U).app _).appTop s) (by
-        convert congr((c.pt.presheaf.map (homOfLE le_top).op).hom $hs) using 1
+        convert! congr((c.pt.presheaf.map (homOfLE le_top).op).hom $hs) using 1
         · simp [Scheme.Hom.app_eq_appLE, Scheme.Hom.resLE_appLE, ← ConcreteCategory.comp_apply]; rfl
         · simp)
     refine ⟨U, hU, hxU, j.left, j.hom, ?_⟩
     have hf : f.left = j.hom := by simpa using Over.w f
     let t' : Γ(D.map j.hom ⁻¹ᵁ U, ⊤) ⟶ Γ(D.obj j.left, D.map j.hom ⁻¹ᵁ U) :=
       (D.obj _).presheaf.map (eqToHom ((D.map j.hom ⁻¹ᵁ U).ι_image_top.symm)).op
-    convert congr(t' $hj)
+    convert! congr(t' $hj)
     · dsimp [TopCat.Presheaf.restrictOpen, TopCat.Presheaf.restrict]
       simp only [Scheme.Hom.app_eq_appLE, homOfLE_leOfHom, ← ConcreteCategory.comp_apply, hf,
         Scheme.Hom.map_appLE, TopologicalSpace.Opens.map_top, Scheme.Hom.resLE_appLE]
@@ -761,7 +764,7 @@ lemma exists_appTop_map_eq_zero_of_isLimit [∀ {i j} (f : i ⟶ j), IsAffineHom
   have h₂ : D.map (fk (Finset.mem_insert_self _ _)) ⁻¹ᵁ U l ≤ D.map (fk (Finset.mem_insert_of_mem
       (Finset.mem_image_of_mem _ hl))) ⁻¹ᵁ D.map (f l) ⁻¹ᵁ U l := by
     rw [← Scheme.Hom.comp_preimage, ← D.map_comp, h₁]
-  convert congr((D.map (fk _)).appLE _ _ h₂ $(H l))
+  convert! congr((D.map (fk _)).appLE _ _ h₂ $(H l))
   · dsimp [TopCat.Presheaf.restrictOpen, TopCat.Presheaf.restrict]
     simp [Scheme.Hom.app_eq_appLE, ← ConcreteCategory.comp_apply, -CommRingCat.hom_comp,
       Scheme.Hom.appLE_comp_appLE, ← Functor.map_comp, h₁]
@@ -788,8 +791,9 @@ lemma exists_app_map_eq_zero_of_isLimit [∀ {i j} (f : i ⟶ j), IsAffineHom (D
   dsimp at hf
   refine ⟨j.left, f.left, ?_⟩
   have hf' : f.left = j.hom := by simpa using Over.w f
-  convert congr((D.obj j.left).presheaf.map (homOfLE
-    (show D.map f.left ⁻¹ᵁ U ≤ (D.map j.hom ⁻¹ᵁ U).ι ''ᵁ ⊤ by simp [hf'])).op $hf)
+  convert!
+    congr((D.obj j.left).presheaf.map
+      (homOfLE (show D.map f.left ⁻¹ᵁ U ≤ (D.map j.hom ⁻¹ᵁ U).ι ''ᵁ ⊤ by simp [hf'])).op $hf)
   · dsimp [Scheme.Opens.toScheme_presheaf_obj]
     rw [← ConcreteCategory.comp_apply, ← ConcreteCategory.comp_apply]
     congr! 2
@@ -834,8 +838,8 @@ lemma exists_appTop_π_eq_of_isLimit [∀ {i j} (f : i ⟶ j), IsAffineHom (D.ma
       rwa [Cone.w]
     · have H : c.π.app j.left ⁻¹ᵁ (D.map j.hom ⁻¹ᵁ U).ι ''ᵁ ⊤ ≤ (c.π.app i ⁻¹ᵁ U).ι ''ᵁ ⊤ := by
         simp [← Scheme.Hom.comp_preimage]
-      convert congr(c.pt.presheaf.map (homOfLE H).op $hj)
-      · convert ConcreteCategory.comp_apply _ _ _
+      convert! congr(c.pt.presheaf.map (homOfLE H).op $hj)
+      · convert! ConcreteCategory.comp_apply _ _ _
         congr
         simp [Scheme.Hom.app_eq_appLE, Scheme.Hom.resLE_appLE]
       · dsimp [TopCat.Presheaf.restrictOpen, TopCat.Presheaf.restrict]
@@ -903,8 +907,9 @@ lemma exists_appTop_π_eq_of_isLimit [∀ {i j} (f : i ⟶ j), IsAffineHom (D.ma
       rw [← Functor.map_comp, ← Functor.map_comp, Category.assoc, Category.assoc,
         hk₁ x.2 y.2, hk₂ x.2 y.2, le_inf_iff]
       exact ⟨fVx.le, fVy.le⟩
-    convert congr(((D.map (fk'k ≫ fk (hjS x.2 y.2))).app _ ≫
-      (D.obj k').presheaf.map (homOfLE H).op) $(hj x y)) using 1
+    convert!
+      congr(((D.map (fk'k ≫ fk (hjS x.2 y.2))).app _ ≫ (D.obj k').presheaf.map (homOfLE H).op)
+        $(hj x y)) using 1
     · dsimp [TopCat.Presheaf.restrictOpen, TopCat.Presheaf.restrict]
       simp only [← ConcreteCategory.comp_apply]
       congr 2
@@ -920,7 +925,7 @@ lemma exists_appTop_π_eq_of_isLimit [∀ {i j} (f : i ⟶ j), IsAffineHom (D.ma
   have H : c.π.app (i (σi y)) ⁻¹ᵁ U (σi y) ≤
       c.π.app k' ⁻¹ᵁ D.map (fk'k ≫ fk (hiS (hσiσ _))) ⁻¹ᵁ U (σi y) := by
     rw [← Scheme.Hom.comp_preimage, Cone.w]
-  convert congr(c.pt.presheaf.map (homOfLE H).op ((c.π.app k').app _ $(ht₀ ⟨_, hσiσ y⟩))).symm
+  convert! congr(c.pt.presheaf.map (homOfLE H).op ((c.π.app k').app _ $(ht₀ ⟨_, hσiσ y⟩))).symm
   · refine (ht (σi y)).symm.trans ?_
     dsimp [Scheme.Opens.toScheme_presheaf_obj]
     rw [← ConcreteCategory.comp_apply, ← ConcreteCategory.comp_apply]
@@ -979,7 +984,8 @@ lemma Scheme.exists_isQuasiAffine_of_isLimit [IsCofiltered I]
         rwa [← preimage_basicOpen_top, ← Hom.comp_preimage, ← Hom.comp_preimage,
           c.w, c.w, preimage_basicOpen_top])
     refine ⟨l, (D.map (flk ≫ fkj)).appTop r, ?_, ?_⟩
-    · convert (hU.preimage (D.map (flk ≫ fki))).basicOpen
+    · convert!
+      (hU.preimage (D.map (flk ≫ fki))).basicOpen
         ((D.obj _).presheaf.map (homOfLE le_top).op ((D.map (flk ≫ fkj)).appTop r)) using 1
       rwa [Scheme.basicOpen_res, eq_comm, inf_eq_right, Functor.map_comp,
         elementwise_of% Scheme.Hom.comp_appTop, ← Scheme.preimage_basicOpen_top, Functor.map_comp,
diff --git a/Mathlib/AlgebraicGeometry/Birational/RationalMap.lean b/Mathlib/AlgebraicGeometry/Birational/RationalMap.lean
index bd67cca3b9d31e..45bdac11a8d6f5 100644
--- a/Mathlib/AlgebraicGeometry/Birational/RationalMap.lean
+++ b/Mathlib/AlgebraicGeometry/Birational/RationalMap.lean
@@ -254,7 +254,7 @@ lemma equiv_of_fromSpecStalkOfMem_eq [IrreducibleSpace X]
       ((Set.image_subset_range _ _).trans_eq (Subtype.range_val)).trans inf_le_right, ?_⟩
     rw [← cancel_epi (Scheme.Hom.isoImage _ _).hom]
     simp only [restrict_hom, ← Category.assoc] at e ⊢
-    convert e using 2 <;> rw [← cancel_mono (Scheme.Opens.ι _)] <;> simp
+    convert! e using 2 <;> rw [← cancel_mono (Scheme.Opens.ι _)] <;> simp
   · rw [← f.fromSpecStalkOfMem_restrict hdense inf_le_left ⟨hxf, hxg⟩,
       ← g.fromSpecStalkOfMem_restrict hdense inf_le_right ⟨hxf, hxg⟩] at H
     simpa only [fromSpecStalkOfMem, restrict_domain, Opens.fromSpecStalkOfMem, Spec.map_inv,
@@ -516,7 +516,7 @@ def RationalMap.toPartialMap [IsReduced X] [Y.IsSeparated] (f : X ⤏ Y) : X.Par
     IsPullback.isoPullback_hom_snd_assoc]
   change _ ≫ _ ≫ (g x).hom = _ ≫ _ ≫ (g y).hom
   simp_rw [← cancel_epi (X.isoOfEq congr($(hg₂ x) ⊓ $(hg₂ y))).hom, ← Category.assoc]
-  convert (PartialMap.equiv_iff_of_isSeparated (S := ⊤_ _) (f := g x) (g := g y)).mp ?_ using 1
+  convert! (PartialMap.equiv_iff_of_isSeparated (S := ⊤_ _) (f := g x) (g := g y)).mp ?_ using 1
   · dsimp; congr 1; simp [g, ← cancel_mono (Opens.ι _)]
   · dsimp; congr 1; simp [g, ← cancel_mono (Opens.ι _)]
   · rw [← PartialMap.toRationalMap_eq_iff, hg₁, hg₁]
diff --git a/Mathlib/AlgebraicGeometry/Cover/Directed.lean b/Mathlib/AlgebraicGeometry/Cover/Directed.lean
index 66524d329a8402..d72b37063ec79d 100644
--- a/Mathlib/AlgebraicGeometry/Cover/Directed.lean
+++ b/Mathlib/AlgebraicGeometry/Cover/Directed.lean
@@ -186,7 +186,7 @@ instance locallyDirectedPullbackCover : Cover.LocallyDirected (𝒰.pullback₁
     simp only [Precoverage.ZeroHypercover.pullback₁_toPreZeroHypercover,
       PreZeroHypercover.pullback₁_X, Iso.trans_inv, Iso.symm_inv, pullback.congrHom_inv,
       Category.assoc, iso]
-    convert P.pullback_fst (pullback.snd f (𝒰.f j)) _ (𝒰.property_trans hij)
+    convert! P.pullback_fst (pullback.snd f (𝒰.f j)) _ (𝒰.property_trans hij)
     apply pullback.hom_ext <;> simp [pullback.condition]
 
 end BaseChange
@@ -315,7 +315,7 @@ instance : Preorder X.directedAffineCover.I₀ := inferInstanceAs <| Preorder X.
 
 instance : Scheme.Cover.LocallyDirected X.directedAffineCover :=
   .ofIsBasisOpensRange (by intros; simp; rfl) <| by
-    convert X.isBasis_affineOpens
+    convert! X.isBasis_affineOpens
     simp
 
 @[simp]
diff --git a/Mathlib/AlgebraicGeometry/Cover/Open.lean b/Mathlib/AlgebraicGeometry/Cover/Open.lean
index b6dec005a93fb7..920ff977a9ab90 100644
--- a/Mathlib/AlgebraicGeometry/Cover/Open.lean
+++ b/Mathlib/AlgebraicGeometry/Cover/Open.lean
@@ -178,8 +178,8 @@ lemma OpenCover.pullbackCoverAffineRefinementObjIso_inv_map (f : X ⟶ Y) (𝒰
     PreZeroHypercover.pullback₁_f, pullbackSymmetry_inv_comp_fst, IsIso.inv_comp_eq,
     limit.lift_π_assoc, PullbackCone.mk_pt, cospan_left, PullbackCone.mk_π_app,
     pullbackSymmetry_hom_comp_fst]
-  convert pullbackSymmetry_inv_comp_snd_assoc
-    ((𝒰.X i.1).affineCover.f i.2) (pullback.fst _ _) _ using 2
+  convert!
+    pullbackSymmetry_inv_comp_snd_assoc ((𝒰.X i.1).affineCover.f i.2) (pullback.fst _ _) _ using 2
   exact pullbackRightPullbackFstIso_hom_snd _ _ _
 
 set_option backward.isDefEq.respectTransparency false in
@@ -194,7 +194,7 @@ lemma OpenCover.pullbackCoverAffineRefinementObjIso_inv_pullbackHom
     AffineOpenCover.openCover_f, pullbackCoverAffineRefinementObjIso, Iso.trans_inv, asIso_inv,
     Iso.symm_inv, Category.assoc, pullbackSymmetry_inv_comp_snd, IsIso.inv_comp_eq, limit.lift_π,
     PullbackCone.mk_pt, PullbackCone.mk_π_app, Category.comp_id]
-  convert pullbackSymmetry_inv_comp_fst ((𝒰.X i.1).affineCover.f i.2) (pullback.fst _ _)
+  convert! pullbackSymmetry_inv_comp_fst ((𝒰.X i.1).affineCover.f i.2) (pullback.fst _ _)
   exact pullbackRightPullbackFstIso_hom_fst _ _ _
 
 /-- A family of elements spanning the unit ideal of `R` gives an affine open cover of `Spec R`. -/
diff --git a/Mathlib/AlgebraicGeometry/Cover/QuasiCompact.lean b/Mathlib/AlgebraicGeometry/Cover/QuasiCompact.lean
index fb4b3e4e81c93a..efc7522e29d69a 100644
--- a/Mathlib/AlgebraicGeometry/Cover/QuasiCompact.lean
+++ b/Mathlib/AlgebraicGeometry/Cover/QuasiCompact.lean
@@ -150,7 +150,7 @@ instance [IsAffine S] {P : MorphismProperty Scheme.{u}} (𝒰 : S.AffineCover P)
 
 instance [IsEmpty S] : QuasiCompactCover 𝒰 where
   isCompactOpenCovered_of_isAffineOpen {U} hU := by
-    convert IsCompactOpenCovered.empty
+    convert! IsCompactOpenCovered.empty
     simp [eq_bot_iff]
 
 variable {P : MorphismProperty Scheme.{u}}
diff --git a/Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Basic.lean b/Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Basic.lean
index c0973851c4a65a..f19ccad7c1d53a 100644
--- a/Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Basic.lean
+++ b/Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Basic.lean
@@ -306,7 +306,7 @@ lemma baseChange_polynomial : (W⁄B).polynomial = (W⁄A).polynomial.map (mapRi
 
 variable {W} in
 lemma Equation.baseChange {x y : A} (h : (W⁄A).Equation x y) : (W⁄B).Equation (f x) (f y) := by
-  convert Equation.map f.toRingHom h using 1
+  convert! Equation.map f.toRingHom h using 1
   rw [AlgHom.toRingHom_eq_coe, map_baseChange]
 
 variable {f} in
diff --git a/Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Formula.lean b/Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Formula.lean
index febcdf799a0bd0..e9ccf5e5ae66bc 100644
--- a/Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Formula.lean
+++ b/Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Formula.lean
@@ -272,7 +272,7 @@ lemma addPolynomial_slope {x₁ x₂ y₁ y₂ : F} (h₁ : W.Equation x₁ y₁
     rw [equation_iff] at h₁ h₂
     rw [slope_of_Y_ne rfl hy]
     rw [negY, ← sub_ne_zero] at hy
-    replace hy : y₁ - (-y₁ - x₁ * W.a₁ - W.a₃) ≠ 0 := by convert hy using 1; ring
+    replace hy : y₁ - (-y₁ - x₁ * W.a₁ - W.a₃) ≠ 0 := by convert! hy using 1; ring
     ext
     · rfl
     · simp only [addX]
diff --git a/Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Point.lean b/Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Point.lean
index 7c3be2d89611b2..4c615b5efafb90 100644
--- a/Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Point.lean
+++ b/Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Point.lean
@@ -301,10 +301,10 @@ lemma XYIdeal_neg_mul {x y : F} (h : W.Nonsingular x y) :
   simp_rw [XYIdeal, XClass, YClass, span_pair_mul_span_pair, mul_comm, ← map_mul,
     AdjoinRoot.mk_eq_mk.mpr ⟨1, Y_rw⟩, map_mul, span_insert, ← span_singleton_mul_span_singleton,
     ← Ideal.mul_sup, ← span_insert]
-  convert mul_top (_ : Ideal W.CoordinateRing) using 2
+  convert! mul_top (_ : Ideal W.CoordinateRing) using 2
   on_goal 2 => infer_instance
   simp_rw [← Set.image_singleton (f := mk W), ← Set.image_insert_eq, ← map_span]
-  convert map_top (R := F[X][Y]) (mk W) using 1
+  convert! map_top (R := F[X][Y]) (mk W) using 1
   apply congr_arg
   simp_rw [eq_top_iff_one, mem_span_insert', mem_span_singleton']
   rcases ((nonsingular_iff' ..).mp h).right with hx | hy
@@ -341,7 +341,7 @@ lemma XYIdeal_mul_XYIdeal [DecidableEq F] {x₁ x₂ y₁ y₂ : F}
     ← sub_eq_add_neg, ← sub_mul, ← map_sub <| mk W, sub_sub_sub_cancel_right, span_insert,
     ← span_singleton_mul_span_singleton, ← sup_rw, ← Ideal.sup_mul, ← Ideal.sup_mul]
   apply congr_arg (_ ∘ _)
-  convert top_mul (_ : Ideal W.CoordinateRing)
+  convert! top_mul (_ : Ideal W.CoordinateRing)
   simp_rw [XClass, ← Set.image_singleton (f := mk W), ← map_span, ← Ideal.map_sup, eq_top_iff_one,
     mem_map_iff_of_surjective _ AdjoinRoot.mk_surjective, ← span_insert, mem_span_insert',
     mem_span_singleton']
@@ -432,14 +432,18 @@ lemma degree_norm_smul_basis [IsDomain R] (p q : R[X]) :
         · exact (hq hq').elim -- `hq'` should be `rfl`
         · rw [hq'] at hdpq hdq -- line should be redundant
           rcases le_or_gt dp (dq + 1) with hpq | hpq
-          · convert (degree_sub_eq_right_of_degree_lt <| (degree_sub_le _ _).trans_lt <|
-                      max_lt_iff.mpr ⟨hdp.trans_lt _, hdpq.trans_lt _⟩).trans
+          · convert!
+            (degree_sub_eq_right_of_degree_lt <|
+                  (degree_sub_le _ _).trans_lt <|
+                    max_lt_iff.mpr ⟨hdp.trans_lt _, hdpq.trans_lt _⟩).trans
               (max_eq_right_of_lt _).symm <;> rw [hdq] <;>
                 exact WithBot.coe_lt_coe.mpr <| by dsimp; linarith only [hpq]
           · rw [sub_sub]
-            convert (degree_sub_eq_left_of_degree_lt <| (degree_add_le _ _).trans_lt <|
+            convert!
+              (degree_sub_eq_left_of_degree_lt <|
+                    (degree_add_le _ _).trans_lt <|
                       max_lt_iff.mpr ⟨hdpq.trans_lt _, hdq.trans_lt _⟩).trans
-              (max_eq_left_of_lt _).symm <;> rw [hdp] <;>
+                (max_eq_left_of_lt _).symm <;> rw [hdp] <;>
                 exact WithBot.coe_lt_coe.mpr <| by dsimp; linarith only [hpq]
 
 lemma degree_norm_ne_one [IsDomain R] (x : W'.CoordinateRing) :
@@ -823,7 +827,7 @@ noncomputable abbrev baseChange [Algebra F K] [IsScalarTower R F K] :
 lemma map_baseChange [Algebra F K] [IsScalarTower R F K] [Algebra F L] [IsScalarTower R F L]
     (f : K →ₐ[F] L) (P : (W'⁄F).Point) : map f (baseChange F K P) = baseChange F L P := by
   have : Subsingleton (F →ₐ[F] L) := inferInstance
-  convert map_map (Algebra.ofId F K) f P
+  convert! map_map (Algebra.ofId F K) f P
 
 end Point
 
diff --git a/Mathlib/AlgebraicGeometry/EllipticCurve/DivisionPolynomial/Degree.lean b/Mathlib/AlgebraicGeometry/EllipticCurve/DivisionPolynomial/Degree.lean
index 6e6525ccbfe8cf..13c51f156243ec 100644
--- a/Mathlib/AlgebraicGeometry/EllipticCurve/DivisionPolynomial/Degree.lean
+++ b/Mathlib/AlgebraicGeometry/EllipticCurve/DivisionPolynomial/Degree.lean
@@ -236,7 +236,7 @@ lemma natDegree_preΨ'_le (n : ℕ) : (W.preΨ' n).natDegree ≤ (n ^ 2 - if Eve
 @[simp]
 lemma coeff_preΨ' (n : ℕ) : (W.preΨ' n).coeff ((n ^ 2 - if Even n then 4 else 1) / 2) =
     if Even n then n / 2 else n := by
-  convert (W.natDegree_coeff_preΨ' n).right using 1
+  convert! (W.natDegree_coeff_preΨ' n).right using 1
   rcases n.even_or_odd' with ⟨n, rfl | rfl⟩ <;> simp [expCoeff, n.not_even_two_mul_add_one]
 
 lemma coeff_preΨ'_ne_zero {n : ℕ} (h : (n : R) ≠ 0) :
diff --git a/Mathlib/AlgebraicGeometry/EllipticCurve/Jacobian/Basic.lean b/Mathlib/AlgebraicGeometry/EllipticCurve/Jacobian/Basic.lean
index 2ba34bec61ea71..3dbd6ab76983f1 100644
--- a/Mathlib/AlgebraicGeometry/EllipticCurve/Jacobian/Basic.lean
+++ b/Mathlib/AlgebraicGeometry/EllipticCurve/Jacobian/Basic.lean
@@ -273,7 +273,7 @@ lemma equation_smul (P : Fin 3 → R) {u : R} (hu : IsUnit u) : W'.Equation (u 
   have hP (u : R) {P : Fin 3 → R} (hP : W'.Equation P) : W'.Equation <| u • P := by
     rw [equation_iff] at hP ⊢
     linear_combination (norm := (simp only [smul_fin3_ext]; ring1)) u ^ 6 * hP
-  ⟨fun h => by convert hP ↑hu.unit⁻¹ h; rw [smul_smul, hu.val_inv_mul, one_smul], hP u⟩
+  ⟨fun h => by convert! hP (↑hu.unit⁻¹) h; rw [smul_smul, hu.val_inv_mul, one_smul], hP u⟩
 
 lemma equation_of_equiv {P Q : Fin 3 → R} (h : P ≈ Q) : W'.Equation P ↔ W'.Equation Q := by
   rcases h with ⟨u, rfl⟩
@@ -565,7 +565,7 @@ lemma baseChange_polynomial : (W'⁄B).polynomial = .map f (W'⁄A).polynomial :
 
 variable {W'} in
 lemma Equation.baseChange {P : Fin 3 → A} (h : (W'⁄A).Equation P) : (W'⁄B).Equation (f ∘ P) := by
-  convert Equation.map f.toRingHom h using 1
+  convert! Equation.map f.toRingHom h using 1
   rw [AlgHom.toRingHom_eq_coe, map_baseChange]
 
 variable {f} in
diff --git a/Mathlib/AlgebraicGeometry/EllipticCurve/Jacobian/Point.lean b/Mathlib/AlgebraicGeometry/EllipticCurve/Jacobian/Point.lean
index 03b6d1e22afe5e..982090c35d0dd6 100644
--- a/Mathlib/AlgebraicGeometry/EllipticCurve/Jacobian/Point.lean
+++ b/Mathlib/AlgebraicGeometry/EllipticCurve/Jacobian/Point.lean
@@ -217,8 +217,8 @@ lemma add_smul_of_not_equiv {P Q : Fin 3 → R} (h : ¬P ≈ Q) {u v : R} (hu :
 lemma add_smul_equiv (P Q : Fin 3 → R) {u v : R} (hu : IsUnit u) (hv : IsUnit v) :
     W'.add (u • P) (v • Q) ≈ W'.add P Q := by
   by_cases h : P ≈ Q
-  · exact ⟨hu.unit ^ 4, by convert (add_smul_of_equiv h hu hv).symm⟩
-  · exact ⟨(hu.unit * hv.unit) ^ 2, by convert (add_smul_of_not_equiv h hu hv).symm⟩
+  · exact ⟨hu.unit ^ 4, by convert! (add_smul_of_equiv h hu hv).symm⟩
+  · exact ⟨(hu.unit * hv.unit) ^ 2, by convert! (add_smul_of_not_equiv h hu hv).symm⟩
 
 lemma add_equiv {P P' Q Q' : Fin 3 → R} (hP : P ≈ P') (hQ : Q ≈ Q') :
     W'.add P Q ≈ W'.add P' Q' := by
diff --git a/Mathlib/AlgebraicGeometry/EllipticCurve/ModelsWithJ.lean b/Mathlib/AlgebraicGeometry/EllipticCurve/ModelsWithJ.lean
index 7179657b09d9e6..2853054fa8f308 100644
--- a/Mathlib/AlgebraicGeometry/EllipticCurve/ModelsWithJ.lean
+++ b/Mathlib/AlgebraicGeometry/EllipticCurve/ModelsWithJ.lean
@@ -87,7 +87,7 @@ variable (R) [W.IsElliptic]
 It is of j-invariant 0 (see `WeierstrassCurve.ofJ0_j`). -/
 instance [hu : Fact (IsUnit (3 : R))] : (ofJ0 R).IsElliptic := by
   rw [isElliptic_iff, ofJ0_Δ]
-  convert (hu.out.pow 3).neg
+  convert! (hu.out.pow 3).neg
   norm_num1
 
 -- TODO: change to `[IsUnit ...]` once https://github.com/leanprover-community/mathlib4/issues/17458 is merged
@@ -100,7 +100,7 @@ lemma ofJ0_j [Fact (IsUnit (3 : R))] : (ofJ0 R).j = 0 := by
 It is of j-invariant 1728 (see `WeierstrassCurve.ofJ1728_j`). -/
 instance [hu : Fact (IsUnit (2 : R))] : (ofJ1728 R).IsElliptic := by
   rw [isElliptic_iff, ofJ1728_Δ]
-  convert (hu.out.pow 6).neg
+  convert! (hu.out.pow 6).neg
   norm_num1
 
 -- TODO: change to `[IsUnit ...]` once https://github.com/leanprover-community/mathlib4/issues/17458 is merged
diff --git a/Mathlib/AlgebraicGeometry/EllipticCurve/Projective/Basic.lean b/Mathlib/AlgebraicGeometry/EllipticCurve/Projective/Basic.lean
index de570bf3c88465..4081c153035379 100644
--- a/Mathlib/AlgebraicGeometry/EllipticCurve/Projective/Basic.lean
+++ b/Mathlib/AlgebraicGeometry/EllipticCurve/Projective/Basic.lean
@@ -263,7 +263,7 @@ lemma equation_smul (P : Fin 3 → R) {u : R} (hu : IsUnit u) : W'.Equation (u 
   have hP (u : R) {P : Fin 3 → R} (hP : W'.Equation P) : W'.Equation <| u • P := by
     rw [equation_iff] at hP ⊢
     linear_combination (norm := (simp only [smul_fin3_ext]; ring1)) u ^ 3 * hP
-  ⟨fun h => by convert hP ↑hu.unit⁻¹ h; rw [smul_smul, hu.val_inv_mul, one_smul], hP u⟩
+  ⟨fun h => by convert! hP (↑hu.unit⁻¹) h; rw [smul_smul, hu.val_inv_mul, one_smul], hP u⟩
 
 lemma equation_of_equiv {P Q : Fin 3 → R} (h : P ≈ Q) : W'.Equation P ↔ W'.Equation Q := by
   rcases h with ⟨u, rfl⟩
@@ -540,7 +540,7 @@ lemma baseChange_polynomial : (W'⁄B).polynomial = .map f (W'⁄A).polynomial :
 
 variable {W'} in
 lemma Equation.baseChange {P : Fin 3 → A} (h : (W'⁄A).Equation P) : (W'⁄B).Equation (f ∘ P) := by
-  convert Equation.map f.toRingHom h using 1
+  convert! Equation.map f.toRingHom h using 1
   rw [AlgHom.toRingHom_eq_coe, map_baseChange]
 
 variable {f} in
diff --git a/Mathlib/AlgebraicGeometry/EllipticCurve/Projective/Point.lean b/Mathlib/AlgebraicGeometry/EllipticCurve/Projective/Point.lean
index b3cca1497603be..7ab6f1ad571321 100644
--- a/Mathlib/AlgebraicGeometry/EllipticCurve/Projective/Point.lean
+++ b/Mathlib/AlgebraicGeometry/EllipticCurve/Projective/Point.lean
@@ -205,8 +205,8 @@ lemma add_smul_of_not_equiv {P Q : Fin 3 → R} (h : ¬P ≈ Q) {u v : R} (hu :
 lemma add_smul_equiv (P Q : Fin 3 → R) {u v : R} (hu : IsUnit u) (hv : IsUnit v) :
     W'.add (u • P) (v • Q) ≈ W'.add P Q := by
   by_cases h : P ≈ Q
-  · exact ⟨hu.unit ^ 4, by convert (add_smul_of_equiv h hu hv).symm⟩
-  · exact ⟨(hu.unit * hv.unit) ^ 2, by convert (add_smul_of_not_equiv h hu hv).symm⟩
+  · exact ⟨hu.unit ^ 4, by convert! (add_smul_of_equiv h hu hv).symm⟩
+  · exact ⟨(hu.unit * hv.unit) ^ 2, by convert! (add_smul_of_not_equiv h hu hv).symm⟩
 
 lemma add_equiv {P P' Q Q' : Fin 3 → R} (hP : P ≈ P') (hQ : Q ≈ Q') :
     W'.add P Q ≈ W'.add P' Q' := by
diff --git a/Mathlib/AlgebraicGeometry/FunctionField.lean b/Mathlib/AlgebraicGeometry/FunctionField.lean
index 52ee1d92e86f0b..04b8ec01e7439f 100644
--- a/Mathlib/AlgebraicGeometry/FunctionField.lean
+++ b/Mathlib/AlgebraicGeometry/FunctionField.lean
@@ -70,10 +70,10 @@ theorem genericPoint_eq_of_isOpenImmersion {X Y : Scheme} (f : X ⟶ Y) [IsOpenI
     [hX : IrreducibleSpace X] [IrreducibleSpace Y] :
     f (genericPoint X) = genericPoint Y := by
   apply ((genericPoint_spec Y).eq _).symm
-  convert (genericPoint_spec X).image f.continuous
+  convert! (genericPoint_spec X).image f.continuous
   symm
   rw [← Set.univ_subset_iff]
-  convert subset_closure_inter_of_isPreirreducible_of_isOpen _ f.isOpenEmbedding.isOpen_range _
+  convert! subset_closure_inter_of_isPreirreducible_of_isOpen _ f.isOpenEmbedding.isOpen_range _
   · rw [Set.univ_inter, Set.image_univ]
   · apply PreirreducibleSpace.isPreirreducible_univ (X := Y)
   · exact ⟨_, trivial, Set.mem_range_self hX.2.some⟩
@@ -108,7 +108,7 @@ theorem genericPoint_eq_bot_of_affine (R : CommRingCat) [IsDomain R] :
 
 instance functionField_isFractionRing_of_affine (R : CommRingCat.{u}) [IsDomain R] :
     IsFractionRing R (Spec R).functionField := by
-  convert StructureSheaf.IsLocalization.to_stalk R (genericPoint (Spec R))
+  convert! StructureSheaf.IsLocalization.to_stalk R (genericPoint (Spec R))
   delta IsFractionRing IsLocalization.AtPrime
   -- Porting note: `congr` does not work for `Iff`
   apply Eq.to_iff
@@ -129,9 +129,11 @@ theorem IsAffineOpen.primeIdealOf_genericPoint {X : Scheme} [IsIntegral X] {U :
           ((genericPoint_spec X).mem_open_set_iff U.isOpen).mpr (by simpa using h)⟩ =
       genericPoint (Spec Γ(X, U)) := by
   delta IsAffineOpen.primeIdealOf
-  convert
+  convert!
     genericPoint_eq_of_isOpenImmersion
       (U.toScheme.isoSpec.hom ≫ Spec.map (X.presheaf.map (eqToHom U.isOpenEmbedding_obj_top).op))
+        -- Porting note: this was `ext1`
+
   -- Porting note: this was `ext1`
   apply Subtype.ext
   exact (genericPoint_eq_of_isOpenImmersion U.ι).symm
@@ -140,8 +142,11 @@ theorem functionField_isFractionRing_of_isAffineOpen [IsIntegral X] (U : X.Opens
     (hU : IsAffineOpen U) [Nonempty U] :
     IsFractionRing Γ(X, U) X.functionField := by
   delta IsFractionRing Scheme.functionField
-  convert hU.isLocalization_stalk ⟨genericPoint X,
-    (((genericPoint_spec X).mem_open_set_iff U.isOpen).mpr (by simpa using ‹Nonempty U›))⟩ using 1
+  convert!
+    hU.isLocalization_stalk
+      ⟨genericPoint X,
+        (((genericPoint_spec X).mem_open_set_iff U.isOpen).mpr (by simpa using ‹Nonempty U›))⟩
+    using 1
   rw [hU.primeIdealOf_genericPoint, genericPoint_eq_bot_of_affine]
   ext; exact mem_nonZeroDivisors_iff_ne_zero
 
diff --git a/Mathlib/AlgebraicGeometry/GammaSpecAdjunction.lean b/Mathlib/AlgebraicGeometry/GammaSpecAdjunction.lean
index 72f057cee51587..6eba84730ee53b 100644
--- a/Mathlib/AlgebraicGeometry/GammaSpecAdjunction.lean
+++ b/Mathlib/AlgebraicGeometry/GammaSpecAdjunction.lean
@@ -119,7 +119,7 @@ abbrev toToΓSpecMapBasicOpen :
 set_option backward.isDefEq.respectTransparency false in
 /-- `r` is a unit as a section on the basic open defined by `r`. -/
 theorem isUnit_res_toΓSpecMapBasicOpen : IsUnit (X.toToΓSpecMapBasicOpen r r) := by
-  convert
+  convert!
     (X.presheaf.map <| (eqToHom <| X.toΓSpecMapBasicOpen_eq r).op).hom.isUnit_map
       (X.toRingedSpace.isUnit_res_basicOpen r)
   rw [← CommRingCat.comp_apply, ← Functor.map_comp]
@@ -174,7 +174,7 @@ def toΓSpecCBasicOpens :
     rw [show algebraMap (Γ.obj (op X)) ((structureSheaf (Γ.obj (op X))).obj.obj _) = algebraMap _
       ((structureSheafInType (Γ.obj (op X)) (Γ.obj (op X))).obj.obj _) from rfl,
       X.toΓSpecCApp_spec r.unop]
-    convert X.toΓSpecCApp_spec s.unop
+    convert! X.toΓSpecCApp_spec s.unop
     symm
     apply X.presheaf.map_comp
 
@@ -275,7 +275,7 @@ theorem Γ_Spec_left_triangle : toSpecΓ (Γ.obj (op X)) ≫ X.toΓSpec.c.app (o
   have := X.toΓSpecSheafedSpace_app_spec 1
   unfold toToΓSpecMapBasicOpen toΓSpecMapBasicOpen at this
   rw! [basicOpen_one] at this
-  convert this
+  convert! this
   exact (X.presheaf.map_id ..).symm
 
 end LocallyRingedSpace
diff --git a/Mathlib/AlgebraicGeometry/Geometrically/Basic.lean b/Mathlib/AlgebraicGeometry/Geometrically/Basic.lean
index d3eb8af73b44f4..b6c245a2f37e03 100644
--- a/Mathlib/AlgebraicGeometry/Geometrically/Basic.lean
+++ b/Mathlib/AlgebraicGeometry/Geometrically/Basic.lean
@@ -112,7 +112,7 @@ lemma geometrically_iff_forall_fiberToSpecResidueField :
   apply H y (Spec.map φ) p snd
   simp only [Scheme.SpecToEquivOfField, Equiv.coe_fn_symm_mk] at h
   refine .flip (.of_bot (.flip ?_) ?_ (IsPullback.of_hasPullback f (Y.fromSpecResidueField y)).flip)
-  · convert h
+  · convert! h
     simp [p]
   · simp [p, Scheme.Hom.fiberToSpecResidueField]
 
diff --git a/Mathlib/AlgebraicGeometry/Gluing.lean b/Mathlib/AlgebraicGeometry/Gluing.lean
index f489cb2080de5b..83735f1e939ffd 100644
--- a/Mathlib/AlgebraicGeometry/Gluing.lean
+++ b/Mathlib/AlgebraicGeometry/Gluing.lean
@@ -397,7 +397,7 @@ theorem isOpenMap_fromGlued : IsOpenMap 𝒰.fromGlued := by
   constructor
   · rw [← Set.image_preimage_eq_inter_range]
     apply (𝒰.f (𝒰.idx x)).isOpenEmbedding.isOpenMap
-    convert hU (𝒰.idx x) using 1
+    convert! hU (𝒰.idx x) using 1
     simp only [← ι_fromGlued, gluedCover_U, Hom.comp_base, TopCat.hom_comp, ContinuousMap.coe_comp,
       Set.preimage_comp]
     congr! 1
@@ -706,7 +706,7 @@ lemma glueDataι_naturality {i j : Shrink.{u} J} (f : ↓i ⟶ ↓j) :
   rw [← cancel_epi (V F ↓i ↓j).ι, ← this, ← Category.assoc,
     ← (Iso.eq_inv_comp _).mp (homOfLE_tAux F ↓i ↓j (𝟙 _) f),
     ← Category.assoc, ← Category.assoc, Category.assoc]
-  convert Category.id_comp _
+  convert! Category.id_comp _
   simp [← cancel_mono (Opens.ι _), V]
 
 /-- (Implementation detail)
diff --git a/Mathlib/AlgebraicGeometry/Group/Abelian.lean b/Mathlib/AlgebraicGeometry/Group/Abelian.lean
index da915447a92aa0..fbe78d4ba2d6ff 100644
--- a/Mathlib/AlgebraicGeometry/Group/Abelian.lean
+++ b/Mathlib/AlgebraicGeometry/Group/Abelian.lean
@@ -111,8 +111,9 @@ theorem isCommMonObj_of_isProper_of_isIntegral_tensorObj_of_isAlgClosed [IsAlgCl
         γ.left.isClosedMap ((H ⟨_, hyU⟩).subset (Set.image_subset_iff.mpr fun _ ↦ by
           simp [← Scheme.Hom.comp_apply, -Scheme.Hom.comp_base, γ])) ?_ ?_
       · let α : G ⊗ G ⟶ G ⊗ G := toUnit _ ≫ x ⊗ₘ 𝟙 _
-        convert ((IrreducibleSpace.isIrreducible_univ _).image α.left
-          α.left.continuous.continuousOn).isPreirreducible
+        convert!
+          ((IrreducibleSpace.isIrreducible_univ _).image α.left
+              α.left.continuous.continuousOn).isPreirreducible
         rw [Over.tensorHom_left]
         simp [Set.range_comp, Scheme.Pullback.range_map, x]
       · exact ⟨y, subset_closure (by simp), rfl⟩
@@ -120,7 +121,7 @@ theorem isCommMonObj_of_isProper_of_isIntegral_tensorObj_of_isAlgClosed [IsAlgCl
         · simp [xe, ← Scheme.Hom.comp_apply, -Scheme.Hom.comp_base]
         · simp only [xe, γ, ← Scheme.Hom.comp_apply, ← Over.comp_left]
           congr 6; ext <;> simp
-    convert congr((snd G G).left $this) using 1
+    convert! congr((snd G G).left $this) using 1
     · simp [γ, ← Scheme.Hom.comp_apply]
     · simp [xe, ← Scheme.Hom.comp_apply, -Scheme.Hom.comp_base]
   · simp
diff --git a/Mathlib/AlgebraicGeometry/IdealSheaf/Subscheme.lean b/Mathlib/AlgebraicGeometry/IdealSheaf/Subscheme.lean
index 339afd4cfd4147..5a1987b459cd30 100644
--- a/Mathlib/AlgebraicGeometry/IdealSheaf/Subscheme.lean
+++ b/Mathlib/AlgebraicGeometry/IdealSheaf/Subscheme.lean
@@ -174,7 +174,7 @@ lemma ideal_le_ker_glueDataObjι (U V : X.affineOpens) :
   simp only [Scheme.Hom.comp_app, Scheme.Opens.ι_app, Scheme.homOfLE_app, ← Functor.map_comp_assoc,
     Scheme.Hom.app_eq _ H, Scheme.Opens.toScheme_presheaf_map, ← Functor.map_comp, Category.assoc]
   simp only [CommRingCat.hom_comp, RingHom.comp_apply]
-  convert RingHom.map_zero _ using 2
+  convert! RingHom.map_zero _ using 2
   rw [← RingHom.mem_ker, ker_glueDataObjι_appTop, ← Ideal.mem_comap, Ideal.comap_comap,
     ← CommRingCat.hom_comp]
   simp only [Scheme.affineBasicOpen_coe, homOfLE_leOfHom, Scheme.Hom.comp_base,
@@ -538,7 +538,7 @@ lemma subschemeι_app (U : X.affineOpens) : I.subschemeι.app U =
     Functor.op_obj, Functor.op_map, unop_comp, unop_inv, Quiver.Hom.unop_op,
     Hom.app_appIso_inv_assoc, TopologicalSpace.Opens.carrier_eq_coe, TopologicalSpace.Opens.map_coe,
     homOfLE_leOfHom]
-  convert (Category.comp_id _).symm
+  convert! (Category.comp_id _).symm
   exact CategoryTheory.Functor.map_id _ _
 
 lemma subschemeι_app_surjective (U : X.affineOpens) :
@@ -693,7 +693,7 @@ def Hom.toImage : X ⟶ f.image :=
 @[reassoc (attr := simp)]
 lemma Hom.toImage_imageι :
     f.toImage ≫ f.imageι = f := by
-  convert f.toImageAux_spec using 2
+  convert! f.toImageAux_spec using 2
   exact Scheme.Hom.copyBase_eq _ _ _
 
 instance [QuasiCompact f] : IsDominant f.toImage where
diff --git a/Mathlib/AlgebraicGeometry/Limits.lean b/Mathlib/AlgebraicGeometry/Limits.lean
index 2a63763f30703c..3425814d02ad2f 100644
--- a/Mathlib/AlgebraicGeometry/Limits.lean
+++ b/Mathlib/AlgebraicGeometry/Limits.lean
@@ -266,7 +266,7 @@ private lemma isOpenImmersion_sigmaDesc_aux
   rw [IsOpenImmersion.iff_isIso_stalkMap]
   constructor
   · suffices Topology.IsOpenEmbedding (Sigma.desc α ∘ sigmaMk f) by
-      convert this.comp (sigmaMk f).symm.isOpenEmbedding; ext; simp
+      convert! this.comp (sigmaMk f).symm.isOpenEmbedding; ext; simp
     refine .of_continuous_injective_isOpenMap ?_ ?_ ?_
     · fun_prop
     · rintro ⟨ix, x⟩ ⟨iy, y⟩ e
@@ -295,7 +295,7 @@ lemma isOpenImmersion_sigmaDesc [Small.{u} σ]
     (hα : Pairwise (Disjoint on (Set.range <| α ·))) :
     IsOpenImmersion (Sigma.desc α) := by
   obtain ⟨ι, ⟨e⟩⟩ := Small.equiv_small (α := σ)
-  convert IsOpenImmersion.comp ((Sigma.reindex e.symm g).inv) (Sigma.desc fun i ↦ α _)
+  convert! IsOpenImmersion.comp ((Sigma.reindex e.symm g).inv) (Sigma.desc fun i ↦ α _)
   · refine Sigma.hom_ext _ _ fun i ↦ ?_
     obtain ⟨i, rfl⟩ := e.symm.surjective i
     simp
@@ -352,7 +352,7 @@ lemma isCompl_range_inl_inr :
 
 lemma isCompl_opensRange_inl_inr :
     IsCompl (coprod.inl : X ⟶ X ⨿ Y).opensRange (coprod.inr : Y ⟶ X ⨿ Y).opensRange := by
-  convert isCompl_range_inl_inr X Y
+  convert! isCompl_range_inl_inr X Y
   simp only [isCompl_iff, disjoint_iff, codisjoint_iff, ← TopologicalSpace.Opens.coe_inj]
   rfl
 
@@ -421,7 +421,7 @@ lemma nonempty_isColimit_binaryCofanMk_of_isCompl {X Y S : Scheme.{u}}
   let i : BinaryCofan.mk f g ≅ c' := Cofan.ext (Iso.refl _) (by rintro (b | b) <;> rfl)
   refine ⟨IsColimit.ofIsoColimit (Nonempty.some ?_) i.symm⟩
   let fi (j : WalkingPair) : WalkingPair.casesOn j X Y ⟶ S := WalkingPair.casesOn j f g
-  convert nonempty_isColimit_cofanMk_of fi _ _
+  convert! nonempty_isColimit_cofanMk_of fi _ _
   · intro i
     cases i <;> (simp [fi]; infer_instance)
   · simpa [← WalkingPair.equivBool.symm.iSup_comp, iSup_bool_eq, ← codisjoint_iff] using hf.2
@@ -466,7 +466,7 @@ instance : FinitaryExtensive Scheme where
     · dsimp
       refine fun {Z} f ↦ (nonempty_isColimit_binaryCofanMk_of_isCompl _ _ ?_).some
       rw [Scheme.Hom.opensRange_pullbackFst, Scheme.Hom.opensRange_pullbackFst]
-      convert (isCompl_range_inl_inr X Y).map (CompleteLatticeHom.setPreimage f)
+      convert! (isCompl_range_inl_inr X Y).map (CompleteLatticeHom.setPreimage f)
       simp [isCompl_iff, disjoint_iff, codisjoint_iff, ← TopologicalSpace.Opens.coe_inj]
 
 variable {X Y}
@@ -659,8 +659,8 @@ private lemma IsAffineOpen.iSup_of_disjoint_aux [Finite ι] {U : ι → X.Opens}
     (hU : ∀ i, IsAffineOpen (U i)) (hU' : Pairwise (Disjoint on U)) :
     IsAffineOpen (iSup U) := by
   have := isOpenImmersion_sigmaDesc _ (fun i ↦ (U i).ι)
-    (fun i j e ↦ by convert hU' e using 0; simp [← Opens.coe_disjoint])
-  convert isAffineOpen_opensRange (Sigma.desc fun i ↦ (U i).ι)
+    (fun i j e ↦ by convert! hU' e using 0; simp [← Opens.coe_disjoint])
+  convert! isAffineOpen_opensRange (Sigma.desc fun i ↦ (U i).ι)
   · ext
     simp [(sigmaMk _).symm.exists_congr_left, ← Scheme.Hom.comp_apply, Scheme.Opens.exists_toScheme]
   · have (i : _) : IsAffine _ := hU i
@@ -686,15 +686,16 @@ lemma IsAffineOpen.biSup_of_disjoint {s : Set σ} (hs : s.Finite)
 lemma IsAffineOpen.sup_of_disjoint {U V : X.Opens} (hU : IsAffineOpen U) (hV : IsAffineOpen V)
     (H : Disjoint U V) :
     IsAffineOpen (U ⊔ V) := by
-  convert iSup_of_disjoint (U := fun i : Unit ⊕ Unit ↦ i.elim (fun _ ↦ U) (fun _ ↦ V)) (by simp_all)
-    (by simp_all [_root_.Pairwise, Unique.forall_iff, ← Opens.coe_disjoint, disjoint_comm])
+  convert!
+    iSup_of_disjoint (U := fun i : Unit ⊕ Unit ↦ i.elim (fun _ ↦ U) (fun _ ↦ V)) (by simp_all)
+      (by simp_all [_root_.Pairwise, Unique.forall_iff, ← Opens.coe_disjoint, disjoint_comm])
   aesop
 
 instance (priority := low) [Finite X] [DiscreteTopology X] : IsAffine X :=
   have : IsAffineOpen (⨆ (x : X), (⟨{x}, isOpen_discrete _⟩ : X.Opens)) :=
     .iSup_of_disjoint (fun i ↦ .of_subsingleton Set.subsingleton_singleton)
       fun i j e ↦ by simpa [← TopologicalSpace.Opens.coe_disjoint]
-  have : IsAffine (⊤ : X.Opens).toScheme := show IsAffineOpen _ by convert this; ext; simp
+  have : IsAffine (⊤ : X.Opens).toScheme := show IsAffineOpen _ by convert! this; ext; simp
   .of_isIso X.topIso.inv
 
 end Coproduct
diff --git a/Mathlib/AlgebraicGeometry/Modules/Tilde.lean b/Mathlib/AlgebraicGeometry/Modules/Tilde.lean
index b5d687ac24567b..d968c7b6dc9a2b 100644
--- a/Mathlib/AlgebraicGeometry/Modules/Tilde.lean
+++ b/Mathlib/AlgebraicGeometry/Modules/Tilde.lean
@@ -384,7 +384,7 @@ def presentationTilde (s : Set M) (hs : Submodule.span R s = ⊤)
           tilde.map (ModuleCat.ofHom (Finsupp.linearCombination R (↑)))) (by
     simp only [Category.assoc, Iso.hom_inv_id_assoc, Preadditive.IsIso.comp_left_eq_zero]
     rw [← tilde.map_comp, ← ModuleCat.ofHom_comp]
-    convert tilde.map_zero
+    convert! tilde.map_zero
     exact congr(ModuleCat.ofHom $(H₁.linearMap_comp_eq_zero))) ?_
   letI h₁ := ModuleCat.isColimitCokernelCofork _ _ H₁
     (by simp [← LinearMap.range_eq_top, Finsupp.range_linearCombination, hs])
diff --git a/Mathlib/AlgebraicGeometry/Morphisms/Affine.lean b/Mathlib/AlgebraicGeometry/Morphisms/Affine.lean
index 648670f27fc4a1..9d36185a73b8d5 100644
--- a/Mathlib/AlgebraicGeometry/Morphisms/Affine.lean
+++ b/Mathlib/AlgebraicGeometry/Morphisms/Affine.lean
@@ -75,7 +75,7 @@ instance {X : Scheme} (r : Γ(X, ⊤)) :
   constructor
   intro U hU
   fapply (Scheme.Hom.isAffineOpen_iff_of_isOpenImmersion (X.basicOpen r).ι).mp
-  convert hU.basicOpen (X.presheaf.map (homOfLE le_top).op r)
+  convert! hU.basicOpen (X.presheaf.map (homOfLE le_top).op r)
   rw [X.basicOpen_res]
   ext1
   refine Set.image_preimage_eq_inter_range.trans ?_
@@ -126,7 +126,7 @@ lemma isAffine_of_isAffineOpen_basicOpen (s : Set Γ(X, ⊤))
     exact hs₂ _ i.2
   · simp only [Opens.map_top, morphismRestrict_app]
     refine IsIso.comp_isIso' ?_ inferInstance
-    convert isIso_ΓSpec_adjunction_unit_app_basicOpen i.1 using 0
+    convert! isIso_ΓSpec_adjunction_unit_app_basicOpen i.1 using 0
     exact congr(IsIso ((ΓSpec.adjunction.unit.app X).app $(by simp)))
 
 set_option backward.isDefEq.respectTransparency false in
@@ -221,7 +221,7 @@ instance {U V X : Scheme.{u}} (f : U ⟶ X) (g : V ⟶ X) [IsAffineHom f] [IsAff
   have : IsAffine (f ⁻¹ᵁ W).toScheme := hW.preimage f
   have : IsAffine (g ⁻¹ᵁ W).toScheme := hW.preimage g
   let i : (f ⁻¹ᵁ W).toScheme ⨿ (g ⁻¹ᵁ W).toScheme ⟶ U ⨿ V := coprod.map (f ⁻¹ᵁ W).ι (g ⁻¹ᵁ W).ι
-  convert isAffineOpen_opensRange i
+  convert! isAffineOpen_opensRange i
   apply le_antisymm
   · intro x hx
     obtain ⟨(x | x), rfl⟩ := (coprodMk U V).surjective x
@@ -253,14 +253,14 @@ lemma isAffineHom_of_isInducing
       exact ⟨⟨U', hU'⟩ ⊓ U, inf_le_right, Opens.ext (by simpa [e] using hVU)⟩
     obtain ⟨r, hrU', hxr⟩ := hU.exists_basicOpen_le ⟨f x, hxV⟩ hxU
     refine ⟨_, hxr, hU.basicOpen r, ?_⟩
-    convert hV.basicOpen (f.app _ (Y.presheaf.map (homOfLE hU'U).op r)) using 1
+    convert! hV.basicOpen (f.app _ (Y.presheaf.map (homOfLE hU'U).op r)) using 1
     simp only [Scheme.preimage_basicOpen, ← CommRingCat.comp_apply, f.naturality]
     simpa using ((Opens.map f.base).map (homOfLE hrU')).le
   · obtain ⟨_, ⟨U, hU, rfl⟩, hyU, hU'⟩ :=
       Y.isBasis_affineOpens.exists_subset_of_mem_open hy hf₂.isOpen_compl
     rw [Set.subset_compl_iff_disjoint_right, ← Set.preimage_eq_empty_iff] at hU'
     refine ⟨U, hyU, hU, ?_⟩
-    convert isAffineOpen_bot _
+    convert! isAffineOpen_bot _
     exact Opens.ext hU'
 
 lemma IsAffineOpen.isCompact_pullback_inf {X Y Z : Scheme.{u}} {f : X ⟶ Z} {g : Y ⟶ Z}
@@ -275,7 +275,7 @@ lemma IsAffineOpen.isCompact_pullback_inf {X Y Z : Scheme.{u}} {f : X ⟶ Z} {g
     IsOpenImmersion.lift W.ι (Scheme.Opens.ι _ ≫ g) <| by simpa [Set.range_comp]
   let p : pullback f' q ⟶ pullback f g :=
     pullback.map _ _ _ _ U.ι (Scheme.Opens.ι _) W.ι (by simp [f']) (by simp [q])
-  convert isCompact_range p.continuous
+  convert! isCompact_range p.continuous
   simp [p, Scheme.Pullback.range_map]
 
 set_option backward.isDefEq.respectTransparency false in
@@ -303,7 +303,7 @@ theorem diagonal_isAffine_iff_forall_isAffineOpen_inf [IsAffine Y] (f : X ⟶ Y)
     exact .of_isIso this.isoPullback.hom
   · introv H h₁ h₂
     have : IsAffineOpen (pullback.fst f₁ f₂ ≫ f₁).opensRange := by
-      convert H _ _ (isAffineOpen_opensRange f₁) (isAffineOpen_opensRange f₂) using 1
+      convert! H _ _ (isAffineOpen_opensRange f₁) (isAffineOpen_opensRange f₂) using 1
       exact Opens.ext (IsOpenImmersion.range_pullback_to_base_of_left _ _)
     change IsAffine _ at this
     exact .of_isIso (pullback.fst f₁ f₂ ≫ f₁).isoOpensRange.hom
diff --git a/Mathlib/AlgebraicGeometry/Morphisms/AffineAnd.lean b/Mathlib/AlgebraicGeometry/Morphisms/AffineAnd.lean
index 06424f0fb4b481..795563aef108b4 100644
--- a/Mathlib/AlgebraicGeometry/Morphisms/AffineAnd.lean
+++ b/Mathlib/AlgebraicGeometry/Morphisms/AffineAnd.lean
@@ -304,11 +304,11 @@ lemma HasAffineProperty.coprodDesc_affineAnd {P : MorphismProperty Scheme.{u}}
   refine this _ ?_ ?_
   · have : (Limits.coprod.desc f g).app W ≫ e.hom ≫ Limits.prod.fst = f.app W := by
       simp [e, Scheme.Hom.app_eq_appLE, Scheme.Hom.appLE_comp_appLE]
-    convert (hf W hW).2
+    convert! (hf W hW).2
     exact congr(($this).1)
   · have : (Limits.coprod.desc f g).app W ≫ e.hom ≫ Limits.prod.snd = g.app W := by
       simp [e, Scheme.Hom.app_eq_appLE, Scheme.Hom.appLE_comp_appLE]
-    convert (hg W hW).2
+    convert! (hg W hW).2
     exact congr(($this).1)
 
 end
diff --git a/Mathlib/AlgebraicGeometry/Morphisms/Basic.lean b/Mathlib/AlgebraicGeometry/Morphisms/Basic.lean
index f0dde4f5e73528..b81c411ae442f6 100644
--- a/Mathlib/AlgebraicGeometry/Morphisms/Basic.lean
+++ b/Mathlib/AlgebraicGeometry/Morphisms/Basic.lean
@@ -207,11 +207,11 @@ lemma coprodMap {X Y X' Y' : Scheme.{u}} (f : X ⟶ X') (g : Y ⟶ Y') (hf : P f
   rintro (⟨⟨⟩⟩ | ⟨⟨⟩⟩)
   · rw [← MorphismProperty.cancel_left_of_respectsIso P
       (isPullback_inl_inl_coprodMap f g).flip.isoPullback.hom]
-    convert hf
+    convert! hf
     simp [Scheme.Cover.pullbackHom, coprodOpenCover]
   · rw [← MorphismProperty.cancel_left_of_respectsIso P
       (isPullback_inr_inr_coprodMap f g).flip.isoPullback.hom]
-    convert hg
+    convert! hg
     simp [Scheme.Cover.pullbackHom, coprodOpenCover]
 
 end IsZariskiLocalAtTarget
diff --git a/Mathlib/AlgebraicGeometry/Morphisms/ClosedImmersion.lean b/Mathlib/AlgebraicGeometry/Morphisms/ClosedImmersion.lean
index 11b2dd219c4a67..103ec5cd8db757 100644
--- a/Mathlib/AlgebraicGeometry/Morphisms/ClosedImmersion.lean
+++ b/Mathlib/AlgebraicGeometry/Morphisms/ClosedImmersion.lean
@@ -351,7 +351,7 @@ instance IsClosedImmersion.isZariskiLocalAtTarget : IsZariskiLocalAtTarget @IsCl
 and being surjective on global sections. -/
 instance IsClosedImmersion.hasAffineProperty : HasAffineProperty @IsClosedImmersion
     (fun X _ f ↦ IsAffine X ∧ Function.Surjective (f.appTop)) := by
-  convert HasAffineProperty.of_isZariskiLocalAtTarget @IsClosedImmersion
+  convert! HasAffineProperty.of_isZariskiLocalAtTarget @IsClosedImmersion
   refine ⟨fun ⟨h₁, h₂⟩ ↦ of_surjective_of_isAffine _ h₂, by apply isAffine_surjective_of_isAffine⟩
 
 lemma isClosedImmersion_iff_isAffineHom {f : X ⟶ Y} :
diff --git a/Mathlib/AlgebraicGeometry/Morphisms/Constructors.lean b/Mathlib/AlgebraicGeometry/Morphisms/Constructors.lean
index 174ce320905f19..5d6f69b2002583 100644
--- a/Mathlib/AlgebraicGeometry/Morphisms/Constructors.lean
+++ b/Mathlib/AlgebraicGeometry/Morphisms/Constructors.lean
@@ -78,14 +78,18 @@ theorem HasAffineProperty.diagonal_of_openCover (P) {Q} [HasAffineProperty P Q]
   apply of_openCover 𝒱
   rintro ⟨i, j, k⟩
   dsimp [𝒱]
-  convert (Q.cancel_left_of_respectsIso
-    ((pullbackDiagonalMapIso _ _ ((𝒰' i).f j) ((𝒰' i).f k)).inv ≫
-      pullback.map _ _ _ _ (𝟙 _) (𝟙 _) (𝟙 _) _ _) (pullback.snd _ _)).mp _ using 1
+  convert!
+    (Q.cancel_left_of_respectsIso
+          ((pullbackDiagonalMapIso _ _ ((𝒰' i).f j) ((𝒰' i).f k)).inv ≫
+            pullback.map _ _ _ _ (𝟙 _) (𝟙 _) (𝟙 _) _ _)
+          (pullback.snd _ _)).mp
+      _
+      using 1
   · simp
   · ext1 <;> simp
   · simp only [Category.assoc, limit.lift_π, PullbackCone.mk_pt, PullbackCone.mk_π_app,
       Category.comp_id]
-    convert h𝒰' i j k
+    convert! h𝒰' i j k
     ext1 <;> simp [Scheme.Cover.pullbackHom]
 
 theorem HasAffineProperty.diagonal_of_openCover_diagonal
@@ -108,7 +112,7 @@ theorem HasAffineProperty.diagonal_of_diagonal_of_isPullback
     h.isoPullback_inv_snd]
   rintro U V f₁ f₂ hU hV hf₁ hf₂
   rw [← Q.cancel_left_of_respectsIso (pullbackDiagonalMapIso f _ f₁ f₂).hom]
-  convert HasAffineProperty.of_isPullback (P := P) (.of_hasPullback _ _) H
+  convert! HasAffineProperty.of_isPullback (P := P) (.of_hasPullback _ _) H
   · apply pullback.hom_ext <;> simp
   · infer_instance
   · infer_instance
diff --git a/Mathlib/AlgebraicGeometry/Morphisms/Descent.lean b/Mathlib/AlgebraicGeometry/Morphisms/Descent.lean
index 8784a110c853ba..e66b740b2661f0 100644
--- a/Mathlib/AlgebraicGeometry/Morphisms/Descent.lean
+++ b/Mathlib/AlgebraicGeometry/Morphisms/Descent.lean
@@ -196,7 +196,7 @@ nonrec lemma HasAffineProperty.descendsAlong_of_affineAnd
   apply IsZariskiLocalAtTarget.descendsAlong_inf_quasiCompact _ _ H₁
   introv h hf
   have : IsAffine Y := by
-    convert isAffine_of_isAffineHom g
+    convert! isAffine_of_isAffineHom g
     exact MorphismProperty.of_pullback_fst_of_descendsAlong h <|
       AlgebraicGeometry.HasAffineProperty.affineAnd_le_isAffineHom P inferInstance _ hf
   wlog hY : ∃ S, Y = Spec S generalizing Y
diff --git a/Mathlib/AlgebraicGeometry/Morphisms/FinitePresentation.lean b/Mathlib/AlgebraicGeometry/Morphisms/FinitePresentation.lean
index 20b222fa620488..1a1a4b0ca4664e 100644
--- a/Mathlib/AlgebraicGeometry/Morphisms/FinitePresentation.lean
+++ b/Mathlib/AlgebraicGeometry/Morphisms/FinitePresentation.lean
@@ -124,9 +124,11 @@ nonrec lemma Scheme.Hom.isLocallyConstructible_image (f : X ⟶ Y)
       MorphismProperty.pullback_snd _ _ inferInstance
     have inst : QuasiCompact (Y.affineCover.pullbackHom f i) :=
       MorphismProperty.pullback_snd _ _ inferInstance
-    convert (this (Y.affineCover.pullbackHom f i) (hs.preimage_of_isOpenEmbedding
-      ((Y.affineCover.pullback₁ f).f i).isOpenEmbedding)
-      ⟨_, rfl⟩).preimage_of_isOpenEmbedding (Y.affineCover.f i).isoOpensRange.inv.isOpenEmbedding
+    convert!
+      (this (Y.affineCover.pullbackHom f i)
+            (hs.preimage_of_isOpenEmbedding ((Y.affineCover.pullback₁ f).f i).isOpenEmbedding)
+            ⟨_, rfl⟩).preimage_of_isOpenEmbedding
+        (Y.affineCover.f i).isoOpensRange.inv.isOpenEmbedding
     refine .trans ?_
       ((Scheme.homeoOfIso (Y.affineCover.f i).isoOpensRange).image_eq_preimage_symm _)
     apply Set.image_injective.mpr Subtype.val_injective
@@ -145,8 +147,7 @@ nonrec lemma Scheme.Hom.isLocallyConstructible_image (f : X ⟶ Y)
     refine .iUnion fun i ↦ ?_
     have inst : QuasiCompact (𝒰.f i ≫ f) :=
       HasAffineProperty.iff_of_isAffine.mpr (inferInstanceAs (CompactSpace (Spec _)))
-    convert this (hs.preimage_of_isOpenEmbedding (𝒰.f i).isOpenEmbedding) _
-      (𝒰.f i ≫ f) ⟨_, rfl⟩
+    convert! this (hs.preimage_of_isOpenEmbedding (𝒰.f i).isOpenEmbedding) _ (𝒰.f i ≫ f) ⟨_, rfl⟩
     rw [Scheme.Hom.comp_base, ← TopCat.Hom.hom, ← TopCat.Hom.hom, TopCat.hom_comp,
       ContinuousMap.coe_comp, Set.image_comp, Set.image_preimage_eq_inter_range, coe_opensRange]
   obtain ⟨S, rfl⟩ := hX
diff --git a/Mathlib/AlgebraicGeometry/Morphisms/Flat.lean b/Mathlib/AlgebraicGeometry/Morphisms/Flat.lean
index ea2689ea7b4b83..8aaf2ed315f40a 100644
--- a/Mathlib/AlgebraicGeometry/Morphisms/Flat.lean
+++ b/Mathlib/AlgebraicGeometry/Morphisms/Flat.lean
@@ -304,7 +304,7 @@ lemma mono_pushoutSection_of_iSup_eq {ι : Type*} [Finite ι] (VX : ι → X.Ope
   suffices (ψY.comp (pushoutSection H hUST hUSX hUY).hom).comp e.inv.hom = φ.comp
       (Algebra.TensorProduct.map (AlgHom.id Γ(T, UT) Γ(T, UT)) ψ).toRingHom by
     refine .of_comp (f := ψY) ?_
-    convert (hφ.comp hψ').comp e.commRingCatIsoToRingEquiv.injective
+    convert! (hφ.comp hψ').comp e.commRingCatIsoToRingEquiv.injective
     ext1 x; simpa using congr($this (e.hom x))
   ext1
   · have H₁ : e.inv.hom.comp Algebra.TensorProduct.includeLeftRingHom =
@@ -421,7 +421,7 @@ lemma isIso_pushoutSection_of_iSup_eq
     · rintro ⟨i | ⟨i, j⟩⟩
       · simp [f₁, f₂]
       · simpa [f₁, f₂] using c'.w (Quiver.Hom.op <| Pairwise.Hom.left i j)
-  convert e.isIso_hom using 1
+  convert! e.isIso_hom using 1
   · refine hc'.hom_ext fun i ↦ ?_
     rw [hc'.fac]
     ext1
@@ -443,7 +443,7 @@ lemma mono_pushoutSection_of_isCompact_of_flat_left [Flat iX]
     (hUS : IsAffineOpen US) (hUX : IsAffineOpen UX) (hUT : IsCompact (X := T) UT) :
     Mono (pushoutSection H hUST hUSX hUY) := by
   suffices Mono (pushoutSection H.flip hUSX hUST (hUY.trans (inf_comm _ _))) by
-    rw [← mono_comp_iff_of_isIso (pushoutSymmetry _ _).hom]; convert this; cat_disch
+    rw [← mono_comp_iff_of_isIso (pushoutSymmetry _ _).hom]; convert! this; cat_disch
   exact mono_pushoutSection_of_isCompact_of_flat_right _ _ _ _ hUS hUX hUT
 
 lemma isIso_pushoutSection_of_isQuasiSeparated_of_flat_right [Flat f]
@@ -466,7 +466,7 @@ lemma isIso_pushoutSection_of_isQuasiSeparated_of_flat_left [Flat iX]
     (hUT : IsCompact (X := T) UT) (hUT' : IsQuasiSeparated (α := T) UT) :
     IsIso (pushoutSection H hUST hUSX hUY) := by
   suffices IsIso (pushoutSection H.flip hUSX hUST (hUY.trans (inf_comm _ _))) by
-    rw [← isIso_comp_left_iff (pushoutSymmetry _ _).hom]; convert this; cat_disch
+    rw [← isIso_comp_left_iff (pushoutSymmetry _ _).hom]; convert! this; cat_disch
   exact isIso_pushoutSection_of_isQuasiSeparated_of_flat_right _ _ _ _ hUS hUX hUT hUT'
 
 lemma mono_pushoutSection_of_isCompact_of_flat_left_of_ringHomFlat [Flat iX]
@@ -484,7 +484,7 @@ lemma mono_pushoutSection_of_isCompact_of_flat_right_of_ringHomFlat [Flat f]
     (hUX : IsCompact (X := X) UX) (hiX : (iX.appLE US UX hUSX).hom.Flat) :
     Mono (pushoutSection H hUST hUSX hUY) := by
   suffices Mono (pushoutSection H.flip hUSX hUST (hUY.trans (inf_comm _ _))) by
-    rw [← mono_comp_iff_of_isIso (pushoutSymmetry _ _).hom]; convert this; cat_disch
+    rw [← mono_comp_iff_of_isIso (pushoutSymmetry _ _).hom]; convert! this; cat_disch
   exact mono_pushoutSection_of_isCompact_of_flat_left_of_ringHomFlat _ _ _ _ hUS hUX hUT hiX
 
 set_option backward.isDefEq.respectTransparency false in
@@ -495,7 +495,7 @@ lemma isIso_pushoutSection_of_isCompact_of_flat_right_of_ringHomFlat [Flat f]
     (hiX : (iX.appLE US UX hUSX).hom.Flat) :
     IsIso (pushoutSection H hUST hUSX hUY) := by
   suffices IsIso (pushoutSection H.flip hUSX hUST (hUY.trans (inf_comm _ _))) by
-    rw [← isIso_comp_left_iff (pushoutSymmetry _ _).hom]; convert this; cat_disch
+    rw [← isIso_comp_left_iff (pushoutSymmetry _ _).hom]; convert! this; cat_disch
   obtain ⟨I, hI, e⟩ := isCompact_iff_finite_and_eq_biUnion_affineOpens.mp hUT
   have hIUT (i : I) : i.1 ≤ UT := by rw [e]; intro i; aesop
   have := hI.to_subtype
diff --git a/Mathlib/AlgebraicGeometry/Morphisms/FormallyUnramified.lean b/Mathlib/AlgebraicGeometry/Morphisms/FormallyUnramified.lean
index d4a60f4ee35d62..897283b0a8f0f7 100644
--- a/Mathlib/AlgebraicGeometry/Morphisms/FormallyUnramified.lean
+++ b/Mathlib/AlgebraicGeometry/Morphisms/FormallyUnramified.lean
@@ -163,7 +163,7 @@ instance [FormallyUnramified f] [LocallyOfFiniteType f] (x : X) :
   suffices h : Algebra.IsSeparable
       (IsLocalRing.ResidueField <| Y.presheaf.stalk (f x))
       (IsLocalRing.ResidueField <| X.presheaf.stalk x) by
-    convert h
+    convert! h
     refine Algebra.algebra_ext _ _ fun x ↦ ?_
     obtain ⟨x, rfl⟩ := IsLocalRing.residue_surjective x
     rfl
diff --git a/Mathlib/AlgebraicGeometry/Morphisms/Immersion.lean b/Mathlib/AlgebraicGeometry/Morphisms/Immersion.lean
index c586ee106540ff..2ca18c67c4095c 100644
--- a/Mathlib/AlgebraicGeometry/Morphisms/Immersion.lean
+++ b/Mathlib/AlgebraicGeometry/Morphisms/Immersion.lean
@@ -92,7 +92,7 @@ instance [IsImmersion f] : IsClosedImmersion f.liftCoborder := by
     simp only [Scheme.Hom.liftCoborder_ι]; infer_instance
   have : IsPreimmersion f.liftCoborder := .of_comp f.liftCoborder f.coborderRange.ι
   refine .of_isPreimmersion _ ?_
-  convert isClosed_preimage_val_coborder
+  convert! isClosed_preimage_val_coborder
   apply Set.image_injective.mpr f.coborderRange.ι.isEmbedding.injective
   rw [← Set.range_comp, ← TopCat.coe_comp, ← Scheme.Hom.comp_base, f.liftCoborder_ι]
   exact (Set.image_preimage_eq_of_subset (by simpa using subset_coborder)).symm
@@ -221,7 +221,7 @@ theorem comp_iff {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z) [IsImmersion g] :
 set_option backward.isDefEq.respectTransparency false in
 instance : IsImmersion (prod.lift (𝟙 X) (𝟙 X)) := by
   rw [← MorphismProperty.cancel_right_of_respectsIso @IsImmersion _ (prodIsoPullback X X).hom]
-  convert (inferInstance : IsImmersion (pullback.diagonal (terminal.from X)))
+  convert! (inferInstance : IsImmersion (pullback.diagonal (terminal.from X)))
   ext : 1 <;> simp
 
 instance (f g : X ⟶ Y) : IsImmersion (equalizer.ι f g) :=
diff --git a/Mathlib/AlgebraicGeometry/Morphisms/IsIso.lean b/Mathlib/AlgebraicGeometry/Morphisms/IsIso.lean
index 71ddd0de646a6f..45624f1d13c12d 100644
--- a/Mathlib/AlgebraicGeometry/Morphisms/IsIso.lean
+++ b/Mathlib/AlgebraicGeometry/Morphisms/IsIso.lean
@@ -46,7 +46,7 @@ example : IsZariskiLocalAtTarget (isomorphisms Scheme) := inferInstance
 
 set_option backward.isDefEq.respectTransparency false in
 instance : HasAffineProperty (isomorphisms Scheme) fun X _ f _ ↦ IsAffine X ∧ IsIso (f.appTop) := by
-  convert HasAffineProperty.of_isZariskiLocalAtTarget (isomorphisms Scheme) with X Y f hY
+  convert! HasAffineProperty.of_isZariskiLocalAtTarget (isomorphisms Scheme) with X Y f hY
   exact ⟨fun ⟨_, _⟩ ↦ (arrow_mk_iso_iff (isomorphisms _) (arrowIsoSpecΓOfIsAffine f)).mpr
     (inferInstanceAs (IsIso (Spec.map (f.appTop)))),
     fun (_ : IsIso f) ↦ ⟨.of_isIso f, inferInstance⟩⟩
diff --git a/Mathlib/AlgebraicGeometry/Morphisms/OpenImmersion.lean b/Mathlib/AlgebraicGeometry/Morphisms/OpenImmersion.lean
index e278345099f6b1..c2bf27541b780d 100644
--- a/Mathlib/AlgebraicGeometry/Morphisms/OpenImmersion.lean
+++ b/Mathlib/AlgebraicGeometry/Morphisms/OpenImmersion.lean
@@ -76,7 +76,7 @@ theorem IsOpenImmersion.of_openCover_source (f : X ⟶ Y)
   refine IsOpenImmersion.iff_isIso_stalkMap.mpr
     ⟨.of_continuous_injective_isOpenMap f.continuous hf ?_, ?_⟩
   · intro U hU
-    convert (⨆ i, ((𝒰.f i ≫ f) ''ᵁ (𝒰.f i ⁻¹ᵁ ⟨U, hU⟩))).2
+    convert! (⨆ i, ((𝒰.f i ≫ f) ''ᵁ (𝒰.f i ⁻¹ᵁ ⟨U, hU⟩))).2
     ext x
     exact ⟨fun ⟨x, _, _⟩ ↦ by have := 𝒰.exists_eq x; simp; grind, by simp; grind⟩
   · intro x
@@ -103,7 +103,7 @@ theorem isOpenImmersion_eq_inf :
 instance : IsZariskiLocalAtTarget (stalkwise (Function.Bijective ·)) := by
   apply stalkwiseIsZariskiLocalAtTarget_of_respectsIso
   rw [RingHom.toMorphismProperty_respectsIso_iff]
-  convert (inferInstance : (MorphismProperty.isomorphisms CommRingCat).RespectsIso)
+  convert! (inferInstance : (MorphismProperty.isomorphisms CommRingCat).RespectsIso)
   ext
   exact (ConcreteCategory.isIso_iff_bijective _).symm
 
diff --git a/Mathlib/AlgebraicGeometry/Morphisms/QuasiCompact.lean b/Mathlib/AlgebraicGeometry/Morphisms/QuasiCompact.lean
index 4440bf8c46f313..949d58eebb95fe 100644
--- a/Mathlib/AlgebraicGeometry/Morphisms/QuasiCompact.lean
+++ b/Mathlib/AlgebraicGeometry/Morphisms/QuasiCompact.lean
@@ -60,7 +60,7 @@ instance (priority := 900) quasiCompact_of_isIso {X Y : Scheme} (f : X ⟶ Y) [I
     QuasiCompact f := by
   constructor
   intro U _ hU'
-  convert hU'.image (inv f.base).hom.continuous_toFun using 1
+  convert! hU'.image (inv f.base).hom.continuous_toFun using 1
   rw [Set.image_eq_preimage_of_inverse]
   · delta Function.LeftInverse
     exact IsIso.inv_hom_id_apply f.base
@@ -84,9 +84,9 @@ theorem isCompact_and_isOpen_iff_finite_and_eq_biUnion_affineOpens {U : Set X} :
 
 theorem isCompact_iff_finite_and_eq_biUnion_affineOpens {U : X.Opens} :
     IsCompact (X := X) U ↔ ∃ s : Set X.affineOpens, s.Finite ∧ U = ⨆ i ∈ s, (i : X.Opens) := by
-  convert isCompact_and_isOpen_iff_finite_and_eq_biUnion_affineOpens (U := U.1) using 4 with s
+  convert! isCompact_and_isOpen_iff_finite_and_eq_biUnion_affineOpens (U := U.1) using 4 with s
   · simp [U.isOpen]
-  · convert SetLike.coe_injective.eq_iff.symm; simp
+  · convert! SetLike.coe_injective.eq_iff.symm; simp
 
 theorem isCompact_and_isOpen_iff_finite_and_eq_biUnion_basicOpen [IsAffine X] {U : Set X} :
     IsCompact U ∧ IsOpen U ↔ ∃ s : Set Γ(X, ⊤), s.Finite ∧ U = ⋃ i ∈ s, X.basicOpen i :=
@@ -267,7 +267,7 @@ theorem exists_pow_mul_eq_zero_of_res_basicOpen_eq_zero_of_isCompact (X : Scheme
   swap
   · change (X.presheaf.map (homOfLE _).op) ((X.presheaf.map (homOfLE _).op).hom x) = 0
     have H : (X.presheaf.map (homOfLE _).op) x = 0 := H
-    convert congr_arg (X.presheaf.map (homOfLE _).op).hom H
+    convert! congr_arg (X.presheaf.map (homOfLE _).op).hom H
     · simp only [← CommRingCat.comp_apply, ← Functor.map_comp]
       · rfl
     · rw [map_zero]
diff --git a/Mathlib/AlgebraicGeometry/Morphisms/QuasiFinite.lean b/Mathlib/AlgebraicGeometry/Morphisms/QuasiFinite.lean
index afbdcc7b2ade4d..bf8b7375fbea2a 100644
--- a/Mathlib/AlgebraicGeometry/Morphisms/QuasiFinite.lean
+++ b/Mathlib/AlgebraicGeometry/Morphisms/QuasiFinite.lean
@@ -221,7 +221,7 @@ nonrec lemma LocallyQuasiFinite.of_fiberToSpecResidueField
       pullback.map _ _ _ _ (pullback.fst _ _) (Spec.map ((Y.affineCover.f i).residueFieldMap _))
         (Y.affineCover.f i) (by simp [pullback.condition]) (by simp)
     have : IsClosedImmersion g := .of_isPreimmersion _ (isClosed_discrete _)
-    convert (inferInstance : LocallyQuasiFinite <| g ≫ f.fiberToSpecResidueField _) using 1
+    convert! (inferInstance : LocallyQuasiFinite <| g ≫ f.fiberToSpecResidueField _) using 1
     simp [g, Hom.fiberToSpecResidueField]
   obtain ⟨R, rfl⟩ := hY
   wlog hX : ∃ S, X = Spec S
@@ -232,7 +232,7 @@ nonrec lemma LocallyQuasiFinite.of_fiberToSpecResidueField
     let g : (X.affineCover.f i ≫ f).fiber x ⟶ f.fiber x :=
       pullback.map _ _ _ _ (X.affineCover.f i) (𝟙 _) (𝟙 _) (by simp) (by simp)
     have : IsClosedImmersion g := .of_isPreimmersion _ (isClosed_discrete _)
-    convert (inferInstance : LocallyQuasiFinite <| g ≫ f.fiberToSpecResidueField _) using 1
+    convert! (inferInstance : LocallyQuasiFinite <| g ≫ f.fiberToSpecResidueField _) using 1
     simp [g, Hom.fiberToSpecResidueField]
   obtain ⟨S, rfl⟩ := hX
   obtain ⟨φ, rfl⟩ := Spec.map_surjective f
@@ -275,8 +275,9 @@ nonrec lemma locallyQuasiFinite_iff_isDiscrete_preimage_singleton
   wlog hY : ∃ R, Y = Spec R
   · refine (IsZariskiLocalAtTarget.iff_of_openCover Y.affineCover).mpr fun i ↦
       this (f := pullback.snd _ _) (fun x ↦ ?_) ⟨_, rfl⟩
-    convert (H (Y.affineCover.f i x)).preimage ((pullback.fst f _).continuous.continuousOn)
-      (pullback.fst f (Y.affineCover.f i)).isOpenEmbedding.injective
+    convert!
+      (H (Y.affineCover.f i x)).preimage ((pullback.fst f _).continuous.continuousOn)
+        (pullback.fst f (Y.affineCover.f i)).isOpenEmbedding.injective
     ext
     simp [← (Y.affineCover.f i).isOpenEmbedding.injective.eq_iff, ← Scheme.Hom.comp_apply,
       -Hom.comp_base, pullback.condition]
@@ -298,8 +299,9 @@ nonrec lemma LocallyQuasiFinite.of_finite_preimage_singleton
   wlog hY : ∃ R, Y = Spec R
   · refine (IsZariskiLocalAtTarget.iff_of_openCover Y.affineCover).mpr fun i ↦
       this (f := pullback.snd _ _) (fun x ↦ ?_) ⟨_, rfl⟩
-    convert (hf (Y.affineCover.f i x)).preimage
-      (pullback.fst f (Y.affineCover.f i)).isOpenEmbedding.injective.injOn
+    convert!
+      (hf (Y.affineCover.f i x)).preimage
+        (pullback.fst f (Y.affineCover.f i)).isOpenEmbedding.injective.injOn
     ext
     simp [← (Y.affineCover.f i).isOpenEmbedding.injective.eq_iff, ← Scheme.Hom.comp_apply,
       -Hom.comp_base, pullback.condition]
@@ -346,7 +348,7 @@ lemma Scheme.Hom.QuasiFiniteAt.quasiFiniteAt
   let e := IsLocalization.algEquiv (hV.primeIdealOf ⟨x, hxV⟩).asIdeal.primeCompl
     (X.presheaf.stalk (⟨x, hxV⟩ : V.1)) (Localization.AtPrime (hV.primeIdealOf ⟨x, hxV⟩).asIdeal)
   rw [RingHom.QuasiFiniteAt, Algebra.QuasiFiniteAt, ← RingHom.quasiFinite_algebraMap]
-  convert (RingHom.QuasiFinite.of_finite e.finite).comp (hx.comp H)
+  convert! (RingHom.QuasiFinite.of_finite e.finite).comp (hx.comp H)
   rw [← CommRingCat.hom_comp, f.germ_stalkMap, ← X.presheaf.germ_res (homOfLE hVU) _ hxV,
     Scheme.Hom.app_eq_appLE, Scheme.Hom.appLE_map_assoc, CommRingCat.hom_comp, ← RingHom.comp_assoc,
     IsScalarTower.algebraMap_eq Γ(Y, U) Γ(X, V), e.toAlgHom.comp_algebraMap.symm]
@@ -358,8 +360,9 @@ lemma Scheme.Hom.quasiFiniteAt [LocallyQuasiFinite f] (x : X) :
   introv hf
   algebraize [f]
   refine .of_comp (g := algebraMap R _) ?_
-  convert RingHom.quasiFinite_algebraMap.mpr (inferInstance :
-    Algebra.QuasiFinite R (Localization.AtPrime J))
+  convert!
+    RingHom.quasiFinite_algebraMap.mpr
+      (inferInstance : Algebra.QuasiFinite R (Localization.AtPrime J))
   ext; simp; rfl
 
 set_option backward.isDefEq.respectTransparency false in
@@ -390,7 +393,7 @@ nonrec lemma Scheme.Hom.quasiFiniteAt_iff_isOpen_singleton_asFiber
   · obtain ⟨i, y, hy⟩ := Y.affineCover.exists_eq (f x)
     obtain ⟨x, rfl, rfl⟩ := Scheme.Pullback.exists_preimage_pullback _ _ hy.symm
     let ι := Y.affineCover.f i
-    convert this (f := pullback.snd f ι) (x := x) ⟨_, rfl⟩ using 1
+    convert! this (f := pullback.snd f ι) (x := x) ⟨_, rfl⟩ using 1
     · exact (RingHom.QuasiFinite.respectsIso.arrow_mk_iso_iff
         (Scheme.stalkMapIsoOfIsPullback (.of_hasPullback f ι) x))
     have H : pullback.snd f ι ⁻¹' {pullback.snd f ι x} =
@@ -401,8 +404,9 @@ nonrec lemma Scheme.Hom.quasiFiniteAt_iff_isOpen_singleton_asFiber
     let f' : pullback.snd f ι ⁻¹' {pullback.snd f ι x} → f ⁻¹' {f (pullback.fst f ι x)} :=
       Set.MapsTo.restrict (pullback.fst f ι) _ _ fun a ha ↦ H.le ha
     have : Topology.IsOpenEmbedding f' := by
-      convert (f ⁻¹' {f (pullback.fst f ι x)}).restrictPreimage_isOpenEmbedding
-        (pullback.fst f ι).isOpenEmbedding using 0
+      convert!
+        (f ⁻¹' {f (pullback.fst f ι x)}).restrictPreimage_isOpenEmbedding
+          (pullback.fst f ι).isOpenEmbedding using 0
       dsimp [f', Set.restrictPreimage]
       congr!
     rw [this.isOpen_iff_image_isOpen, Set.image_singleton]; rfl
@@ -410,7 +414,7 @@ nonrec lemma Scheme.Hom.quasiFiniteAt_iff_isOpen_singleton_asFiber
   wlog hX : ∃ S, X = Spec S
   · obtain ⟨i, x, rfl⟩ := X.affineCover.exists_eq x
     let ι := X.affineCover.f i
-    convert this (x := x) _ (f := ι ≫ f) ⟨_, rfl⟩ using 1
+    convert! this (x := x) _ (f := ι ≫ f) ⟨_, rfl⟩ using 1
     · exact quasiFiniteAt_comp_iff_of_isOpenImmersion.symm
     rw [((f ⁻¹' {f (ι x)}).restrictPreimage_isOpenEmbedding
       ι.isOpenEmbedding).isOpen_iff_image_isOpen, Set.image_singleton]; rfl
diff --git a/Mathlib/AlgebraicGeometry/Morphisms/RingHomProperties.lean b/Mathlib/AlgebraicGeometry/Morphisms/RingHomProperties.lean
index 826d4095dee4af..53e5f2bf79d156 100644
--- a/Mathlib/AlgebraicGeometry/Morphisms/RingHomProperties.lean
+++ b/Mathlib/AlgebraicGeometry/Morphisms/RingHomProperties.lean
@@ -468,8 +468,9 @@ lemma stalkwise {P} (hP : RingHom.RespectsIso P) :
       ∀ (p : Ideal S) (_ : p.IsPrime), P (Localization.localRingHom _ p φ rfl) := by
   have := stalkwiseIsZariskiLocalAtTarget_of_respectsIso hP
   have := stalkwise_isZariskiLocalAtSource_of_respectsIso hP
-  convert of_isZariskiLocalAtSource_of_isZariskiLocalAtTarget
-    (P := AlgebraicGeometry.stalkwise P) with R S _ _ φ
+  convert!
+    of_isZariskiLocalAtSource_of_isZariskiLocalAtTarget (P := AlgebraicGeometry.stalkwise P) with R
+    S _ _ φ
   exact (stalkwise_SpecMap_iff hP (CommRingCat.ofHom φ)).symm
 
 lemma stableUnderComposition (hP : RingHom.StableUnderComposition Q) :
diff --git a/Mathlib/AlgebraicGeometry/Morphisms/Separated.lean b/Mathlib/AlgebraicGeometry/Morphisms/Separated.lean
index a9a5b335ead4cc..1bed75b024ca52 100644
--- a/Mathlib/AlgebraicGeometry/Morphisms/Separated.lean
+++ b/Mathlib/AlgebraicGeometry/Morphisms/Separated.lean
@@ -133,7 +133,7 @@ instance [IsSeparated g] :
   rw [← MorphismProperty.cancel_left_of_respectsIso @IsClosedImmersion (pullback.fst f (𝟙 Y))]
   rw [← MorphismProperty.cancel_right_of_respectsIso @IsClosedImmersion _
     (pullback.congrHom rfl (Category.id_comp g)).inv]
-  convert (inferInstance : IsClosedImmersion (pullback.mapDesc f (𝟙 _) g)) using 1
+  convert! (inferInstance : IsClosedImmersion (pullback.mapDesc f (𝟙 _) g)) using 1
   ext : 1 <;> simp [pullback.condition]
 
 end IsSeparated
@@ -274,7 +274,7 @@ instance isClosedImmersion_equalizer_ι_left {S : Scheme} {X Y : Over S} [IsSepa
     ((Limits.isPullback_equalizer_prod f g).map (Over.forget _)).flip ?_
   rw [← MorphismProperty.cancel_right_of_respectsIso @IsClosedImmersion _
     (Over.prodLeftIsoPullback Y Y).hom]
-  convert (inferInstance : IsClosedImmersion (pullback.diagonal Y.hom))
+  convert! (inferInstance : IsClosedImmersion (pullback.diagonal Y.hom))
   ext1 <;> simp [← Over.comp_left]
 
 set_option backward.isDefEq.respectTransparency false in
@@ -358,7 +358,7 @@ end Scheme
 
 instance IsSeparated.hasAffineProperty :
     HasAffineProperty @IsSeparated fun X _ _ _ ↦ X.IsSeparated := by
-  convert HasAffineProperty.of_isZariskiLocalAtTarget @IsSeparated with X Y f hY
+  convert! HasAffineProperty.of_isZariskiLocalAtTarget @IsSeparated with X Y f hY
   rw [Scheme.isSeparated_iff, ← terminal.comp_from f, IsSeparated.comp_iff]
   rfl
 
diff --git a/Mathlib/AlgebraicGeometry/Morphisms/Smooth.lean b/Mathlib/AlgebraicGeometry/Morphisms/Smooth.lean
index a4691fe0efbde2..90a3aaee05e490 100644
--- a/Mathlib/AlgebraicGeometry/Morphisms/Smooth.lean
+++ b/Mathlib/AlgebraicGeometry/Morphisms/Smooth.lean
@@ -86,7 +86,7 @@ lemma Smooth.iff_forall_exists_isStandardSmooth (f : X ⟶ Y) :
       ∀ (x : X), ∃ (U : Y.Opens) (_ : IsAffineOpen U) (V : X.Opens) (_ : IsAffineOpen V) (_ : x ∈ V)
         (e : V ≤ f ⁻¹ᵁ U), (f.appLE U V e).hom.IsStandardSmooth := by
   have : HasRingHomProperty @Smooth.{u} (Locally IsStandardSmooth) := by
-    convert (inferInstance : HasRingHomProperty @Smooth.{u} RingHom.Smooth)
+    convert! (inferInstance : HasRingHomProperty (@Smooth.{u}) RingHom.Smooth)
     ext f
     rw [RingHom.smooth_iff_locally_isStandardSmooth]
   rw [HasRingHomProperty.iff_exists_appLE_locally (P := @Smooth)]
@@ -279,8 +279,9 @@ lemma exists_smooth_of_formallySmooth_stalk
       IsAffineOpen.isoSpec_hom, IsAffineOpen.toSpecΓ_fromSpec] at hrx
   · have := hV.isLocalization_basicOpen r
     rw [← RingHom.smooth_algebraMap] at hr
-    convert RingHom.Smooth.propertyIsLocal.respectsIso.1 _
-      (IsLocalization.algEquiv (.powers r) _ Γ(X, X.basicOpen r)).toRingEquiv hr
+    convert!
+      RingHom.Smooth.propertyIsLocal.respectsIso.1 _
+        (IsLocalization.algEquiv (.powers r) _ Γ(X, X.basicOpen r)).toRingEquiv hr
     ext
     dsimp
     simp only [IsScalarTower.algebraMap_apply Γ(Y, U) Γ(X, V) (Localization _),
diff --git a/Mathlib/AlgebraicGeometry/Morphisms/SurjectiveOnStalks.lean b/Mathlib/AlgebraicGeometry/Morphisms/SurjectiveOnStalks.lean
index df70ea5e9d912d..3ad7c42378a0c3 100644
--- a/Mathlib/AlgebraicGeometry/Morphisms/SurjectiveOnStalks.lean
+++ b/Mathlib/AlgebraicGeometry/Morphisms/SurjectiveOnStalks.lean
@@ -121,9 +121,10 @@ lemma isEmbedding_pullback {X Y S : Scheme.{u}} (f : X ⟶ S) (g : Y ⟶ S) [Sur
     obtain ⟨ψ, rfl⟩ : ∃ ψ, Spec.map ψ = g' := ⟨_, Spec.map_preimage _⟩
     algebraize [φ.hom, ψ.hom]
     rw [HasRingHomProperty.Spec_iff (P := @SurjectiveOnStalks)] at H
-    convert ((iX.isOpenEmbedding.prodMap iY.isOpenEmbedding).isEmbedding.comp
-      (PrimeSpectrum.isEmbedding_tensorProductTo_of_surjectiveOnStalks R A B H)).comp
-      (Scheme.homeoOfIso (pullbackSpecIso R A B)).isEmbedding
+    convert!
+      ((iX.isOpenEmbedding.prodMap iY.isOpenEmbedding).isEmbedding.comp
+            (PrimeSpectrum.isEmbedding_tensorProductTo_of_surjectiveOnStalks R A B H)).comp
+        (Scheme.homeoOfIso (pullbackSpecIso R A B)).isEmbedding
     ext1 x
     obtain ⟨x, rfl⟩ := (Scheme.homeoOfIso (pullbackSpecIso R A B).symm).surjective x
     simp only [Scheme.homeoOfIso_apply, Function.comp_apply]
@@ -194,7 +195,7 @@ lemma isEmbedding_pullback {X Y S : Scheme.{u}} (f : X ⟶ S) (g : Y ⟶ S) [Sur
         ((𝒲 i.1).f i.2.2 ≫ (𝒰.pullback₁ g).f i.1)
         (𝒰.f i.1) (by simp [pullback.condition]) (by simp [pullback.condition])
         inferInstance inferInstance inferInstance
-    convert this using 7
+    convert! this using 7
     apply pullback.hom_ext <;>
       simp [𝓤, Scheme.Cover.pullbackHom]
 
diff --git a/Mathlib/AlgebraicGeometry/Morphisms/UnderlyingMap.lean b/Mathlib/AlgebraicGeometry/Morphisms/UnderlyingMap.lean
index a49107cc73248b..e71b9335da7474 100644
--- a/Mathlib/AlgebraicGeometry/Morphisms/UnderlyingMap.lean
+++ b/Mathlib/AlgebraicGeometry/Morphisms/UnderlyingMap.lean
@@ -258,7 +258,7 @@ lemma IsDominant.of_comp_of_isOpenImmersion
     IsDominant f := by
   rw [isDominant_iff, DenseRange] at H ⊢
   simp only [Scheme.Hom.comp_base, TopCat.coe_comp, Set.range_comp] at H
-  convert H.preimage g.isOpenEmbedding.isOpenMap using 1
+  convert! H.preimage g.isOpenEmbedding.isOpenMap using 1
   rw [Set.preimage_image_eq _ g.isOpenEmbedding.injective]
 
 lemma Opens.isDominant_ι {U : X.Opens} (hU : Dense (X := X) U) : IsDominant U.ι :=
diff --git a/Mathlib/AlgebraicGeometry/Morphisms/UniversallyOpen.lean b/Mathlib/AlgebraicGeometry/Morphisms/UniversallyOpen.lean
index 6aa9ada9c7d9a1..04e00844ee99cf 100644
--- a/Mathlib/AlgebraicGeometry/Morphisms/UniversallyOpen.lean
+++ b/Mathlib/AlgebraicGeometry/Morphisms/UniversallyOpen.lean
@@ -124,7 +124,7 @@ lemma isOpenMap_of_generalizingMap [LocallyOfFinitePresentation f]
   obtain ⟨S, rfl⟩ := hX
   obtain ⟨φ, rfl⟩ := Spec.map_surjective f
   algebraize [φ.hom]
-  convert PrimeSpectrum.isOpenMap_comap_of_hasGoingDown_of_finitePresentation
+  convert! PrimeSpectrum.isOpenMap_comap_of_hasGoingDown_of_finitePresentation
   · rwa [Algebra.HasGoingDown.iff_generalizingMap_primeSpectrumComap]
   · apply (HasRingHomProperty.Spec_iff (P := @LocallyOfFinitePresentation)).mp inferInstance
 
@@ -137,7 +137,7 @@ lemma Flat.generalizingMap [Flat f] : GeneralizingMap f := by
   intro U V e
   algebraize [(f.appLE U V e).hom]
   apply Algebra.HasGoingDown.iff_generalizingMap_primeSpectrumComap.mp
-  convert Algebra.HasGoingDown.of_flat
+  convert! Algebra.HasGoingDown.of_flat
   exact HasRingHomProperty.appLE @Flat f ‹_› U V e
 
 /-- A flat morphism, locally of finite presentation is universally open. -/
diff --git a/Mathlib/AlgebraicGeometry/Noetherian.lean b/Mathlib/AlgebraicGeometry/Noetherian.lean
index 7984fc67b132fb..9e57b460d25af5 100644
--- a/Mathlib/AlgebraicGeometry/Noetherian.lean
+++ b/Mathlib/AlgebraicGeometry/Noetherian.lean
@@ -175,7 +175,7 @@ theorem isLocallyNoetherian_iff_openCover (𝒰 : Scheme.OpenCover X) :
 /-- If `R` is a Noetherian ring, `Spec R` is a Noetherian topological space. -/
 instance {R : CommRingCat} [IsNoetherianRing R] :
     NoetherianSpace (Spec R) := by
-  convert PrimeSpectrum.instNoetherianSpace (R := R)
+  convert! PrimeSpectrum.instNoetherianSpace (R := R)
 
 lemma noetherianSpace_of_isAffine [IsAffine X] [IsNoetherianRing Γ(X, ⊤)] :
     NoetherianSpace X :=
@@ -209,7 +209,7 @@ instance (priority := 100) {Z : Scheme} [IsLocallyNoetherian X]
   rw [Opens.map_coe, ← Set.preimage_inter_range]
   apply f.isOpenEmbedding.isInducing.isCompact_preimage'
   · apply (noetherianSpace_set_iff _).mp
-    · convert noetherianSpace_of_isAffineOpen U hU
+    · convert! noetherianSpace_of_isAffineOpen U hU
       apply IsLocallyNoetherian.component_noetherian ⟨U, hU⟩
     · exact Set.inter_subset_left
   · exact Set.inter_subset_right
@@ -225,7 +225,7 @@ instance (priority := 100) IsLocallyNoetherian.quasiSeparatedSpace [IsLocallyNoe
   · rw [← Set.preimage_inter_range, IsAffineOpen.range_fromSpec, Set.inter_comm]
     apply hInd.isCompact_preimage'
     · apply (noetherianSpace_set_iff _).mp
-      · convert noetherianSpace_of_isAffineOpen U.1 U.2
+      · convert! noetherianSpace_of_isAffineOpen U.1 U.2
         apply IsLocallyNoetherian.component_noetherian
       · exact Set.inter_subset_left
     · rw [IsAffineOpen.range_fromSpec]
@@ -287,14 +287,14 @@ theorem isNoetherian_iff_of_finite_iSup_eq_top {ι} [Finite ι] {S : ι → X.af
     apply (isLocallyNoetherian_iff_of_iSup_eq_top hS).mp
     exact h.toIsLocallyNoetherian
   · intro h
-    convert IsNoetherian.mk
+    convert! IsNoetherian.mk
     · exact isLocallyNoetherian_of_affine_cover hS h
     · constructor
       rw [← Opens.coe_top, ← hS, Opens.iSup_mk]
       apply isCompact_iUnion
       intro i
       apply isCompact_iff_isCompact_univ.mpr
-      convert CompactSpace.isCompact_univ
+      convert! CompactSpace.isCompact_univ
       have : NoetherianSpace (S i) := by
         apply noetherianSpace_of_isAffineOpen (S i).1 (S i).2
       apply NoetherianSpace.compactSpace (S i)
@@ -308,7 +308,7 @@ theorem isNoetherian_iff_of_finite_affine_openCover {𝒰 : Scheme.OpenCover.{v,
     apply (isLocallyNoetherian_iff_of_affine_openCover _).mp
     exact h.toIsLocallyNoetherian
   · intro hNoeth
-    convert IsNoetherian.mk
+    convert! IsNoetherian.mk
     · exact (isLocallyNoetherian_iff_of_affine_openCover _).mpr hNoeth
     · exact Scheme.OpenCover.compactSpace 𝒰
 
@@ -326,7 +326,7 @@ instance (priority := 100) IsNoetherian.noetherianSpace [IsNoetherian X] :
     rw [X.affineCover.finiteSubcover_X]
     apply Scheme.isAffine_affineCover
   let U : X.affineOpens := ⟨Scheme.Hom.opensRange (𝒰.f i), isAffineOpen_opensRange _⟩
-  convert noetherianSpace_of_isAffineOpen U.1 U.2
+  convert! noetherianSpace_of_isAffineOpen U.1 U.2
   apply IsLocallyNoetherian.component_noetherian
 
 /-- Any morphism of schemes `f : X ⟶ Y` with `X` Noetherian is quasi-compact. -/
diff --git a/Mathlib/AlgebraicGeometry/Normalization.lean b/Mathlib/AlgebraicGeometry/Normalization.lean
index 3d1641c5aa46b4..c90633e152413c 100644
--- a/Mathlib/AlgebraicGeometry/Normalization.lean
+++ b/Mathlib/AlgebraicGeometry/Normalization.lean
@@ -205,7 +205,7 @@ instance : IsIntegralHom f.fromNormalization := by
     letI := (f.app U).hom.toAlgebra
     change (algebraMap Γ(Y, U) (integralClosure Γ(Y, U) Γ(X, f ⁻¹ᵁ U))).IsIntegral
     exact algebraMap_isIntegral_iff.mpr inferInstance
-  convert IsIntegralHom.SpecMap_iff.mpr this
+  convert! IsIntegralHom.SpecMap_iff.mpr this
   rw [← cancel_mono U.2.fromSpec]
   simp [IsAffineOpen.isoSpec_hom, e, ι_fromNormalization]
 
@@ -237,7 +237,7 @@ lemma toNormalization_app_preimage (U : Y.affineOpens) :
   have H : f.toNormalization ⁻¹ᵁ f.fromNormalization ⁻¹ᵁ U =
       (f ⁻¹ᵁ U).ι ''ᵁ (((f ⁻¹ᵁ U).ι ≫ f.toNormalization) ⁻¹ᵁ f.fromNormalization ⁻¹ᵁ U) := by
     simp [← Scheme.Hom.comp_preimage]
-  convert congr($(Scheme.Hom.congr_app (f.ι_toNormalization U) (f.fromNormalization ⁻¹ᵁ U)) ≫
+  convert! congr($(Scheme.Hom.congr_app (f.ι_toNormalization U) (f.fromNormalization ⁻¹ᵁ U)) ≫
     X.presheaf.map (eqToHom H).op) using 1
   · simp [Hom.app_eq_appLE]
   dsimp
@@ -350,8 +350,9 @@ instance [IsReduced X] : IsReduced f.normalization :=
 instance [IsIntegral X] : IsIntegral f.normalization :=
   have : IrreducibleSpace f.normalization := by
     rw [irreducibleSpace_def]
-    convert ((IrreducibleSpace.isIrreducible_univ X).image _
-      f.toNormalization.continuous.continuousOn).closure
+    convert!
+      ((IrreducibleSpace.isIrreducible_univ X).image _
+          f.toNormalization.continuous.continuousOn).closure
     simpa using f.toNormalization.denseRange.closure_range.symm
   isIntegral_of_irreducibleSpace_of_isReduced _
 
@@ -641,7 +642,7 @@ instance [Smooth g] : IsIso (f.normalizationPullback g) := by
     ((pullback.snd f g).normalizationObjIso hV).inv ≫
     (pullback.snd f g).normalization.presheaf.map (eqToHom
       (by simp only [W, ← Scheme.Hom.comp_preimage, Scheme.Hom.normalizationPullback_snd])).op
-  convert show IsIso φ by dsimp only [φ]; infer_instance using 1
+  convert! show IsIso φ by dsimp only [φ]; infer_instance using 1
   ext1
   · dsimp [φ]
     simp only [Scheme.Hom.app_eq_appLE, colimit.ι_desc_assoc, span_left, PushoutCocone.mk_pt,
diff --git a/Mathlib/AlgebraicGeometry/OpenImmersion.lean b/Mathlib/AlgebraicGeometry/OpenImmersion.lean
index 33f0bea355d643..3d3d379bb46ecc 100644
--- a/Mathlib/AlgebraicGeometry/OpenImmersion.lean
+++ b/Mathlib/AlgebraicGeometry/OpenImmersion.lean
@@ -654,7 +654,7 @@ theorem isPullback_lift_id
     {X U Y : Scheme.{u}} (f : X ⟶ Y) (g : U ⟶ Y) [IsOpenImmersion g]
     (H : Set.range f ⊆ Set.range g) :
     IsPullback (IsOpenImmersion.lift g f H) (𝟙 _) g f := by
-  convert IsPullback.of_id_snd.paste_horiz (IsKernelPair.id_of_mono g)
+  convert! IsPullback.of_id_snd.paste_horiz (IsKernelPair.id_of_mono g)
   · exact (Category.comp_id _).symm
   · simp
 
@@ -704,8 +704,10 @@ lemma isPullback {U V X Y : Scheme.{u}} (g : U ⟶ V) (iU : U ⟶ X) (iV : V ⟶
     (H' : f ⁻¹ᵁ iV.opensRange = iU.opensRange) : IsPullback g iU iV f := by
   let e := IsOpenImmersion.isoOfRangeEq (pullback.snd iV f) iU
     (by simpa [range_pullbackSnd] using congr(($H').1))
-  convert (IsPullback.of_horiz_isIso (show CommSq e.inv iU (pullback.snd iV f) (𝟙 X) from
-    ⟨by simp [e]⟩)).paste_horiz (IsPullback.of_hasPullback iV f)
+  convert!
+    (IsPullback.of_horiz_isIso
+          (show CommSq e.inv iU (pullback.snd iV f) (𝟙 X) from ⟨by simp [e]⟩)).paste_horiz
+      (IsPullback.of_hasPullback iV f)
   simp [← cancel_mono iV, e, pullback.condition, H]
 
 /-- If `f` is an open immersion `X ⟶ Y`, the global sections of `X`
diff --git a/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Basic.lean b/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Basic.lean
index f3895c978cad52..2597206406c34e 100644
--- a/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Basic.lean
+++ b/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Basic.lean
@@ -79,7 +79,7 @@ theorem basicOpen_eq_iSup_proj (f : A) :
 theorem isBasis_basicOpen :
     TopologicalSpace.Opens.IsBasis (Set.range (basicOpen 𝒜)) := by
   delta TopologicalSpace.Opens.IsBasis
-  convert ProjectiveSpectrum.isTopologicalBasis_basic_opens 𝒜
+  convert! ProjectiveSpectrum.isTopologicalBasis_basic_opens 𝒜
   exact (Set.range_comp _ _).symm
 
 /-- If `{ xᵢ }` spans the irrelevant ideal of `A`, then `D₊(xᵢ)` covers `Proj A`. -/
@@ -117,15 +117,16 @@ lemma iSup_basicOpen_eq_top' {ι : Type*} (f : ι → A)
     · rw [DirectSum.decompose_of_mem_ne 𝒜 hn hn', sub_zero]
       exact Ideal.subset_span ⟨_, rfl⟩
   | algebraMap r =>
-    convert zero_mem (Ideal.span _)
+    convert! zero_mem (Ideal.span _)
     rw [sub_eq_zero]
     exact (DirectSum.decompose_of_mem_same 𝒜 r.2).symm
   | add x y hx hy _ _ =>
     rw [map_add, add_sub_add_comm]
     exact add_mem ‹_› ‹_›
   | mul x y hx hy hx' hy' =>
-    convert add_mem (Ideal.mul_mem_left _ x hy')
-      (Ideal.mul_mem_right (GradedRing.projZeroRingHom 𝒜 y) _ hx') using 1
+    convert!
+      add_mem (Ideal.mul_mem_left _ x hy')
+        (Ideal.mul_mem_right (GradedRing.projZeroRingHom 𝒜 y) _ hx') using 1
     rw [map_mul]
     ring
 
@@ -164,7 +165,7 @@ noncomputable
 def basicOpenIsoSpec : (basicOpen 𝒜 f).toScheme ≅ Spec (.of <| Away 𝒜 f) :=
   have : IsIso (basicOpenToSpec 𝒜 f) := by
     apply (isIso_iff_of_reflects_iso _ Scheme.forgetToLocallyRingedSpace).mp ?_
-    convert ProjectiveSpectrum.Proj.isIso_toSpec 𝒜 f f_deg hm using 1
+    convert! ProjectiveSpectrum.Proj.isIso_toSpec 𝒜 f f_deg hm using 1
     refine Eq.trans ?_ (ΓSpec.locallyRingedSpaceAdjunction.homEquiv_apply _ _ _).symm
     dsimp [basicOpenToSpec, Scheme.Opens.toSpecΓ]
     simp only [eqToHom_op, Category.assoc, ← Spec.map_comp]
@@ -344,7 +345,7 @@ def affineOpenCover : (Proj 𝒜).AffineOpenCover :=
   rw [← DirectSum.sum_support_decompose 𝒜 z]
   refine Ideal.sum_mem _ fun c hc ↦ if hc0 : c = 0 then ?_ else
     Ideal.subset_span ⟨⟨⟨c, Nat.pos_iff_ne_zero.mpr hc0⟩, _⟩, rfl⟩
-  convert Ideal.zero_mem _
+  convert! Ideal.zero_mem _
   subst hc0
   exact hz
 
diff --git a/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Functor.lean b/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Functor.lean
index 1174f931fab343..65b2a377e24f94 100644
--- a/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Functor.lean
+++ b/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Functor.lean
@@ -210,7 +210,7 @@ theorem map_comp : map (g.comp f) (irrelevant_le_map_comp hf hg) = map g hg ≫
 set_option backward.isDefEq.respectTransparency false in
 theorem map_id : map (.id 𝒜) (by simp) = 𝟙 (Proj 𝒜) := by
   refine (affineOpenCover _).openCover.hom_ext _ _ fun s ↦ ?_
-  convert awayι_comp_map (.id 𝒜) _ _ _ s.2.2 using 1
+  convert! awayι_comp_map (.id 𝒜) _ _ _ s.2.2 using 1
   simp
 
 end Proj
diff --git a/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Proper.lean b/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Proper.lean
index 29825cc7cd11c4..046a7827b71b73 100644
--- a/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Proper.lean
+++ b/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Proper.lean
@@ -46,24 +46,24 @@ lemma lift_awayMapₐ_awayMapₐ_surjective {d e : ℕ} {f : A} (hf : f ∈ 𝒜
     exact this.elim _ _
   have : n = j * (d + e) := by
     apply DirectSum.degree_eq_of_mem_mem 𝒜 hb'
-    · convert SetLike.pow_mem_graded _ _ using 2
+    · convert! SetLike.pow_mem_graded _ _ using 2
       · infer_instance
       · exact hx ▸ SetLike.mul_mem_graded hf hg
     · exact hx ▸ hfg
   let x0 : NumDenSameDeg 𝒜 (.powers f) :=
   { deg := j * (d * (e + 1))
     num := ⟨a * g ^ (j * (d - 1)), by
-      convert SetLike.mul_mem_graded ha (SetLike.pow_mem_graded _ hg) using 2
+      convert! SetLike.mul_mem_graded ha (SetLike.pow_mem_graded _ hg) using 2
       rw [this]
       cases d
       · contradiction
       · simp; ring⟩
-    den := ⟨f ^ (j * (e + 1)), by convert SetLike.pow_mem_graded _ hf using 2; ring⟩
+    den := ⟨f ^ (j * (e + 1)), by convert! SetLike.pow_mem_graded _ hf using 2; ring⟩
     den_mem := ⟨_,rfl⟩ }
   let y0 : NumDenSameDeg 𝒜 (.powers g) :=
   { deg := j * (d * e)
-    num := ⟨f ^ (j * e), by convert SetLike.pow_mem_graded _ hf using 2; ring⟩
-    den := ⟨g ^ (j * d), by convert SetLike.pow_mem_graded _ hg using 2; ring⟩
+    num := ⟨f ^ (j * e), by convert! SetLike.pow_mem_graded _ hf using 2; ring⟩
+    den := ⟨g ^ (j * d), by convert! SetLike.pow_mem_graded _ hg using 2; ring⟩
     den_mem := ⟨_,rfl⟩ }
   use mk x0 ⊗ₜ mk y0
   ext
@@ -101,8 +101,9 @@ instance isSeparated : IsSeparated (toSpecZero 𝒜) := by
     (Algebra.TensorProduct.lift (awayMapₐ 𝒜 j.2.2 rfl) (awayMapₐ 𝒜 i.2.2 (mul_comm _ _))
       (fun _ _ ↦ .all _ _)).toRingHom
   have : Function.Surjective F := lift_awayMapₐ_awayMapₐ_surjective 𝒜 i.2.2 j.2.2 rfl i.1.2
-  convert IsClosedImmersion.spec_of_surjective
-    (CommRingCat.ofHom (R := Away 𝒜 i.2.1 ⊗[𝒜 0] Away 𝒜 j.2.1) F) this using 1
+  convert!
+    IsClosedImmersion.spec_of_surjective
+      (CommRingCat.ofHom (R := Away 𝒜 i.2.1 ⊗[𝒜 0] Away 𝒜 j.2.1) F) this using 1
   rw [← cancel_mono (pullbackSpecIso ..).inv]
   apply pullback.hom_ext
   · simp only [Iso.trans_hom, congrHom_hom, Category.assoc, Iso.hom_inv_id, Category.comp_id,
@@ -215,7 +216,7 @@ theorem valuativeCriterion_existence_aux
     refine zero_lt_iff.mpr fun hKmax ↦ ?_
     have (i : _) : ψ i = 0 := le_zero_iff.mp (hKmax ▸ Finset.le_max' _ _ (by simp))
     simp only [ψ, map_pow, pow_eq_zero_iff', map_eq_zero, ne_eq] at this
-    have : φ 1 = 0 := by convert (this j).1; ext; simp
+    have : φ 1 = 0 := by convert! (this j).1; ext; simp
     simp only [map_one, one_ne_zero] at this
   letI := (awayMap 𝒜 (f := x j) (hxdi i₀) rfl).toAlgebra
   have := Away.isLocalization_mul (hxdi j) (hxdi i₀) rfl (hdi _).ne'
@@ -244,15 +245,16 @@ theorem valuativeCriterion_existence_aux
     obtain ⟨a, ai, hai, rfl⟩ := h
     simp only [smul_eq_mul] at hai
     have H : (∏ i, x i ^ ai i) * x i₀ ^ (a * (d j - 1)) ∈ 𝒜 ((a * d i₀) • d j) := by
-      convert SetLike.mul_mem_graded (SetLike.prod_pow_mem_graded 𝒜 d x ai fun _ _ ↦ hxdi _)
-        (SetLike.pow_mem_graded (a * (d j - 1)) (hxdi i₀)) using 2
+      convert!
+        SetLike.mul_mem_graded (SetLike.prod_pow_mem_graded 𝒜 d x ai fun _ _ ↦ hxdi _)
+          (SetLike.pow_mem_graded (a * (d j - 1)) (hxdi i₀)) using 2
       simp only [smul_eq_mul, hai]
       cases h : d j
       · cases (hdi j).ne' h
       · simp only [add_tsub_cancel_right]; ring
     suffices valuation O K (φ (Away.mk 𝒜 (hxdi j) _ _ H) /
           φ (Away.isLocalizationElem (hxdi j) (hxdi i₀)) ^ a) ≤ 1 by
-      convert this
+      convert! this
       rw [eq_div_iff (pow_ne_zero _ hunit.ne_zero), ← hφ'1, ← hφ'1, RingHom.comp_apply,
         ← map_pow, ← map_mul]
       congr
@@ -341,7 +343,7 @@ lemma valuativeCriterion_existence [Algebra.FiniteType (𝒜 0) A] :
     exact congr_arg Subtype.val (e.apply_symm_apply _)
   refine ⟨⟨Spec.map (CommRingCat.ofHom φ'') ≫ Proj.awayι 𝒜 _ (hxd _ i₀.2) (hd _ _).bot_lt, ?_, ?_⟩⟩
   · rw [← Spec.map_comp_assoc]
-    convert IsOpenImmersion.lift_fac _ _ this using 1
+    convert! IsOpenImmersion.lift_fac _ _ this using 1
     change _ = φ ≫ _
     rw [← Spec.map_preimage φ, ← CommRingCat.ofHom_hom (Spec.preimage φ), ← hφ,
       ← CommRingCat.ofHom_comp]
diff --git a/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Scheme.lean b/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Scheme.lean
index 2c707a758533b3..0df625c2b1eb3b 100644
--- a/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Scheme.lean
+++ b/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Scheme.lean
@@ -290,7 +290,7 @@ theorem mem_carrier_iff' (q : Spec.T A⁰_ f) (a : A) :
       · rw [Set.mem_image]; refine ⟨_, h, rfl⟩
       · rw [Set.mem_image] at h; rcases h with ⟨x, h, hx⟩
         change x ∈ q.asIdeal at h
-        convert h
+        convert! h
         rw [HomogeneousLocalization.ext_iff_val, HomogeneousLocalization.val_mk]
         dsimp only [Subtype.coe_mk]; rw [← hx]; rfl)
 
@@ -301,7 +301,7 @@ theorem mem_carrier_iff_of_mem (hm : 0 < m) (q : Spec.T A⁰_ f) (a : A) {n} (hn
   trans (HomogeneousLocalization.mk ⟨m * n, ⟨proj 𝒜 n a ^ m, by rw [← smul_eq_mul]; mem_tac⟩,
     ⟨f ^ n, by rw [mul_comm]; mem_tac⟩, ⟨_, rfl⟩⟩ : A⁰_ f) ∈ q.asIdeal
   · refine ⟨fun h ↦ h n, fun h i ↦ if hi : i = n then hi ▸ h else ?_⟩
-    convert zero_mem q.asIdeal
+    convert! zero_mem q.asIdeal
     apply HomogeneousLocalization.val_injective
     simp only [proj_apply, decompose_of_mem_ne _ hn (Ne.symm hi), zero_pow hm.ne',
       HomogeneousLocalization.val_mk, Localization.mk_zero, HomogeneousLocalization.val_zero]
@@ -326,7 +326,7 @@ theorem num_mem_carrier_iff (hm : 0 < m) (q : Spec.T A⁰_ f)
   have : f ^ n ≠ 0 := fun e ↦ by
     have := HomogeneousLocalization.subsingleton 𝒜 (x := .powers f) ⟨n, e⟩
     exact IsEmpty.elim (inferInstanceAs (IsEmpty (PrimeSpectrum (A⁰_ f)))) q
-  convert mem_carrier_iff_of_mem_mul f_deg hm q z.num.1 (n := n) ?_ using 2
+  convert! mem_carrier_iff_of_mem_mul f_deg hm q z.num.1 (n := n) ?_ using 2
   · apply HomogeneousLocalization.val_injective; simp only [hn, HomogeneousLocalization.val_mk]
   · have := degree_eq_of_mem_mem 𝒜 (SetLike.pow_mem_graded n f_deg) (hn.symm ▸ z.den.2) this
     rw [← smul_eq_mul, this]; exact z.num.2
@@ -383,10 +383,10 @@ variable (hm : 0 < m) (q : Spec.T A⁰_ f)
 include hm
 
 theorem carrier.zero_mem : (0 : A) ∈ carrier f_deg q := fun i => by
-  convert Submodule.zero_mem q.1 using 1
+  convert! Submodule.zero_mem q.1 using 1
   rw [HomogeneousLocalization.ext_iff_val, HomogeneousLocalization.val_mk,
     HomogeneousLocalization.val_zero]; simp_rw [map_zero, zero_pow hm.ne']
-  convert Localization.mk_zero (S := Submonoid.powers f) _ using 1
+  convert! Localization.mk_zero (S := Submonoid.powers f) _ using 1
 
 theorem carrier.smul_mem (c x : A) (hx : x ∈ carrier f_deg q) : c • x ∈ carrier f_deg q := by
   revert c
@@ -442,7 +442,7 @@ theorem carrier.denom_notMem : f ∉ carrier.asIdeal f_deg hm q := fun rid =>
   q.isPrime.ne_top <|
     (Ideal.eq_top_iff_one _).mpr
       (by
-        convert rid m
+        convert! rid m
         rw [HomogeneousLocalization.ext_iff_val, HomogeneousLocalization.val_one,
           HomogeneousLocalization.val_mk]
         dsimp
@@ -460,7 +460,7 @@ theorem carrier.asIdeal.prime : (carrier.asIdeal f_deg hm q).IsPrime :=
     (carrier.asIdeal.ne_top f_deg hm q) fun {x y} ⟨nx, hnx⟩ ⟨ny, hny⟩ hxy =>
     show (∀ _, _ ∈ _) ∨ ∀ _, _ ∈ _ by
       rw [← and_forall_ne nx, and_iff_left, ← and_forall_ne ny, and_iff_left]
-      · apply q.2.mem_or_mem; convert hxy (nx + ny) using 1
+      · apply q.2.mem_or_mem; convert! hxy (nx + ny) using 1
         dsimp
         simp_rw [decompose_of_mem_same 𝒜 hnx, decompose_of_mem_same 𝒜 hny,
           decompose_of_mem_same 𝒜 (SetLike.GradedMonoid.toGradedMul.mul_mem hnx hny),
@@ -469,10 +469,10 @@ theorem carrier.asIdeal.prime : (carrier.asIdeal f_deg hm q).IsPrime :=
           HomogeneousLocalization.val_mul, Localization.mk_mul]
         simp only [Submonoid.mk_mul_mk, mk_eq_monoidOf_mk']
       all_goals
-        intro n hn; convert q.1.zero_mem using 1
+        intro n hn; convert! q.1.zero_mem using 1
         rw [HomogeneousLocalization.ext_iff_val, HomogeneousLocalization.val_mk,
           HomogeneousLocalization.val_zero]; simp_rw [proj_apply]
-        convert mk_zero (S := Submonoid.powers f) _
+        convert! mk_zero (S := Submonoid.powers f) _
         rw [decompose_of_mem_ne 𝒜 _ hn.symm, zero_pow hm.ne']
         · first | exact hnx | exact hny
 
@@ -680,7 +680,7 @@ lemma toSpec_base_apply_eq {f} (x : Proj| pbo f) :
 
 lemma toSpec_base_isIso {f} {m} (f_deg : f ∈ 𝒜 m) (hm : 0 < m) :
     IsIso (toSpec 𝒜 f).base := by
-  convert (projIsoSpecTopComponent f_deg hm).isIso_hom
+  convert! (projIsoSpecTopComponent f_deg hm).isIso_hom
   exact ConcreteCategory.hom_ext _ _ <| toSpec_base_apply_eq 𝒜
 
 lemma mk_mem_toSpec_base_apply {f} (x : Proj| pbo f)
@@ -694,7 +694,7 @@ lemma toSpec_preimage_basicOpen {f}
     (Opens.map (toSpec 𝒜 f).base).obj (sbo (HomogeneousLocalization.mk t)) =
       Opens.comap ⟨_, continuous_subtype_val⟩ (pbo t.num.1) :=
   Opens.ext <| Opens.map_coe _ _ ▸ by
-  convert (ProjIsoSpecTopComponent.ToSpec.preimage_basicOpen f t)
+  convert! (ProjIsoSpecTopComponent.ToSpec.preimage_basicOpen f t)
   exact funext fun _ => toSpec_base_apply_eq _ _
 
 @[reassoc]
@@ -742,7 +742,7 @@ lemma isLocalization_atPrime (f) (x : pbo f) {m} (f_deg : f ∈ 𝒜 m) (hm : 0
         ⟨f ^ i, SetLike.pow_mem_graded _ f_deg⟩, ⟨_, rfl⟩⟩,
         (mk_mem_toSpec_base_apply _ _ _).not.mpr <| x.1.1.toIdeal.primeCompl.pow_mem hb' m⟩⟩,
         val_injective _ ?_⟩
-    · convert SetLike.mul_mem_graded a.2 (SetLike.pow_mem_graded (m - 1) hb) using 2
+    · convert! SetLike.mul_mem_graded a.2 (SetLike.pow_mem_graded (m - 1) hb) using 2
       rw [← succ_nsmul', tsub_add_cancel_of_le (by lia), mul_comm, smul_eq_mul]
     · simp only [RingHom.algebraMap_toAlgebra, map_mk, GradedRingHom.id_apply, val_mul, val_mk,
         mk_eq_mk', ← IsLocalization.mk'_mul, Submonoid.mk_mul_mk, IsLocalization.mk'_eq_iff_eq]
diff --git a/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean b/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean
index b756f0661b51ec..bdb664d7556e7f 100644
--- a/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean
+++ b/Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean
@@ -236,7 +236,7 @@ theorem zeroLocus_bUnion (s : Set (Set A)) :
 theorem vanishingIdeal_iUnion {γ : Sort*} (t : γ → Set (ProjectiveSpectrum 𝒜)) :
     vanishingIdeal (⋃ i, t i) = ⨅ i, vanishingIdeal (t i) :=
   HomogeneousIdeal.toIdeal_injective <| by
-    convert (gc_ideal 𝒜).u_iInf; exact HomogeneousIdeal.toIdeal_iInf _
+    convert! (gc_ideal 𝒜).u_iInf; exact HomogeneousIdeal.toIdeal_iInf _
 
 theorem zeroLocus_inf (I J : Ideal A) :
     zeroLocus 𝒜 ((I ⊓ J : Ideal A) : Set A) = zeroLocus 𝒜 I ∪ zeroLocus 𝒜 J :=
@@ -287,7 +287,7 @@ instance zariskiTopology : TopologicalSpace (ProjectiveSpectrum 𝒜) :=
       let f : Zs → Set _ := fun i => Classical.choose (h i.2)
       have H : (Set.iInter fun i ↦ zeroLocus 𝒜 (f i)) ∈ Set.range (zeroLocus 𝒜) :=
         ⟨_, zeroLocus_iUnion 𝒜 _⟩
-      convert H using 2
+      convert! H using 2
       funext i
       exact (Classical.choose_spec (h i.2)).symm)
     (by
diff --git a/Mathlib/AlgebraicGeometry/Properties.lean b/Mathlib/AlgebraicGeometry/Properties.lean
index f47654840db6e2..61bd12ec15f0da 100644
--- a/Mathlib/AlgebraicGeometry/Properties.lean
+++ b/Mathlib/AlgebraicGeometry/Properties.lean
@@ -161,7 +161,7 @@ theorem reduce_to_affine_nbhd (P : ∀ (X : Scheme) (_ : X), Prop)
     ∀ (X : Scheme) (x : X), P X x := by
   intro X x
   obtain ⟨y, e⟩ := X.affineCover.covers x
-  convert h₂ (X.affineCover.f (X.affineCover.idx x)) y _
+  convert! h₂ (X.affineCover.f (X.affineCover.idx x)) y _
   · rw [e]
   apply h₁
 
@@ -289,7 +289,7 @@ theorem isIntegral_of_irreducibleSpace_of_isReduced [IsReduced X] [H : Irreducib
     replace e := congr_arg (X.presheaf.germ U x hxU) e
     rw [map_mul, map_zero] at e
     refine zero_ne_one' (X.presheaf.stalk x) (isUnit_zero_iff.1 ?_)
-    convert hx₁.mul hx₂
+    convert! hx₁.mul hx₂
     exact e.symm
   exact NoZeroDivisors.to_isDomain _
 
@@ -315,7 +315,7 @@ lemma IsIntegral.of_isIso {X Y : Scheme.{u}} [h : IsIntegral X] (f : X ⟶ Y) [I
   exact Nonempty.map f inferInstance
 
 instance {R : CommRingCat} [IsDomain R] : IrreducibleSpace (Spec R) := by
-  convert PrimeSpectrum.irreducibleSpace (R := R)
+  convert! PrimeSpectrum.irreducibleSpace (R := R)
 
 instance {R : CommRingCat} [IsDomain R] : IsIntegral (Spec R) :=
   isIntegral_of_irreducibleSpace_of_isReduced _
diff --git a/Mathlib/AlgebraicGeometry/Pullbacks.lean b/Mathlib/AlgebraicGeometry/Pullbacks.lean
index a78cb1086037af..a6e1ef33885911 100644
--- a/Mathlib/AlgebraicGeometry/Pullbacks.lean
+++ b/Mathlib/AlgebraicGeometry/Pullbacks.lean
@@ -605,7 +605,7 @@ lemma _root_.AlgebraicGeometry.Scheme.isPullback_of_openCover
         (lift fWX fWY h) f := by
       rw [← IsPullback.paste_vert_iff this.flip (by ext <;> simp [f])]
       simpa using .of_hasPullback _ _
-    convert (inferInstance : IsIso (H'.isoPullback.inv ≫ (H i).isoPullback.hom))
+    convert! (inferInstance : IsIso (H'.isoPullback.inv ≫ (H i).isoPullback.hom))
     aesop (add simp [Iso.eq_inv_comp, Scheme.Cover.pullbackHom])
   exact MorphismProperty.of_zeroHypercover_target (P := .isomorphisms Scheme)
     (Scheme.Pullback.openCoverOfLeft 𝒰 fXZ fYZ) H₁
diff --git a/Mathlib/AlgebraicGeometry/QuasiAffine.lean b/Mathlib/AlgebraicGeometry/QuasiAffine.lean
index b90fc50db99ff3..c31781fe196c03 100644
--- a/Mathlib/AlgebraicGeometry/QuasiAffine.lean
+++ b/Mathlib/AlgebraicGeometry/QuasiAffine.lean
@@ -65,7 +65,7 @@ lemma IsQuasiAffine.isBasis_basicOpen (X : Scheme.{u}) [IsQuasiAffine X] :
   refine ⟨_, ⟨r, ?_, rfl⟩, hxr, (Set.preimage_mono hrU).trans_eq
     (Set.preimage_image_eq _ X.toSpecΓ.isEmbedding.injective)⟩
   rw [← Hom.isAffineOpen_iff_of_isOpenImmersion X.toSpecΓ]
-  convert IsAffineOpen.Spec_basicOpen r
+  convert! IsAffineOpen.Spec_basicOpen r
   exact SetLike.coe_injective (Set.image_preimage_eq_of_subset
     (hrU.trans (Set.image_subset_range _ _)))
 
@@ -84,7 +84,7 @@ lemma IsQuasiAffine.of_forall_exists_mem_basicOpen (X : Scheme.{u}) [CompactSpac
   obtain ⟨r, hr, hxr⟩ := H x
   refine ⟨PrimeSpectrum.basicOpen r, (X.toSpecΓ_preimage_basicOpen r).ge hxr, ?_⟩
   suffices IsOpenImmersion ((X.basicOpen r).ι ≫ X.toSpecΓ) by
-    convert this <;> rw [toSpecΓ_preimage_basicOpen]
+    convert! this <;> rw [toSpecΓ_preimage_basicOpen]
   rw [← Opens.toSpecΓ_SpecMap_presheaf_map_top]
   have := isLocalization_basicOpen_of_qcqs isCompact_univ isQuasiSeparated_univ r
   exact MorphismProperty.comp_mem _ hr.isoSpec.hom _ inferInstance (.of_isLocalization r)
diff --git a/Mathlib/AlgebraicGeometry/Restrict.lean b/Mathlib/AlgebraicGeometry/Restrict.lean
index 4af3250749b579..89ab8d83468aa4 100644
--- a/Mathlib/AlgebraicGeometry/Restrict.lean
+++ b/Mathlib/AlgebraicGeometry/Restrict.lean
@@ -168,7 +168,7 @@ lemma stalkIso_inv {X : Scheme.{u}} (U : X.Opens) (x : U) :
   apply TopCat.Presheaf.stalk_hom_ext
   intro W hxW
   simp only [Category.comp_id, U.germ_stalkIso_hom_assoc]
-  convert (Scheme.Hom.germ_stalkMap U.ι (U.ι ''ᵁ W) x ⟨_, hxW, rfl⟩).symm
+  convert! (Scheme.Hom.germ_stalkMap U.ι (U.ι ''ᵁ W) x ⟨_, hxW, rfl⟩).symm
   refine (U.toScheme.presheaf.germ_res (homOfLE ?_) _ _).symm
   exact (Set.preimage_image_eq _ Subtype.val_injective).le
 
diff --git a/Mathlib/AlgebraicGeometry/Scheme.lean b/Mathlib/AlgebraicGeometry/Scheme.lean
index b4f0a2c51f3453..b5b8a5122dd60b 100644
--- a/Mathlib/AlgebraicGeometry/Scheme.lean
+++ b/Mathlib/AlgebraicGeometry/Scheme.lean
@@ -449,7 +449,7 @@ def copyBase {X Y : Scheme} (f : X.Hom Y) (g : X → Y) (h : f.base = g) : X ⟶
   c := f.c ≫ (TopCat.Presheaf.pushforwardEq (by subst h; rfl) _).hom
   prop x := by
     subst h
-    convert f.prop x using 4
+    convert! f.prop x using 4
     cat_disch
 
 lemma copyBase_eq {X Y : Scheme} (f : X.Hom Y) (g : X → Y) (h : f.base = g) :
@@ -862,7 +862,7 @@ theorem basicOpen_eq_of_affine {R : CommRingCat} (f : R) :
 @[simp]
 theorem basicOpen_eq_of_affine' {R : CommRingCat} (f : Γ(Spec R, ⊤)) :
     (Spec R).basicOpen f = PrimeSpectrum.basicOpen ((Scheme.ΓSpecIso R).hom f) := by
-  convert basicOpen_eq_of_affine ((Scheme.ΓSpecIso R).hom f)
+  convert! basicOpen_eq_of_affine ((Scheme.ΓSpecIso R).hom f)
   exact (Iso.hom_inv_id_apply (Scheme.ΓSpecIso R) f).symm
 
 set_option backward.isDefEq.respectTransparency false in
@@ -913,7 +913,7 @@ theorem Spec_zeroLocus_eq_zeroLocus {R : CommRingCat} (s : Set R) :
 
 theorem Spec_zeroLocus {R : CommRingCat} (s : Set Γ(Spec R, ⊤)) :
     (Spec R).zeroLocus s = PrimeSpectrum.zeroLocus ((Scheme.ΓSpecIso R).inv ⁻¹' s) := by
-  convert Spec_zeroLocus_eq_zeroLocus ((Scheme.ΓSpecIso R).inv ⁻¹' s)
+  convert! Spec_zeroLocus_eq_zeroLocus ((Scheme.ΓSpecIso R).inv ⁻¹' s)
   rw [Set.image_preimage_eq]
   exact (ConcreteCategory.bijective_of_isIso (C := CommRingCat) _).2
 section Stalks
diff --git a/Mathlib/AlgebraicGeometry/Sites/BigZariski.lean b/Mathlib/AlgebraicGeometry/Sites/BigZariski.lean
index 8e3567745f550a..ae82a05062643d 100644
--- a/Mathlib/AlgebraicGeometry/Sites/BigZariski.lean
+++ b/Mathlib/AlgebraicGeometry/Sites/BigZariski.lean
@@ -110,7 +110,7 @@ lemma preservesLimitsOfShape_discrete_of_isSheaf_zariskiTopology {F : Scheme.{u}
   refine Presieve.preservesProduct_of_isSheafFor F ?_ initialIsInitial
       (Sigma.cocone (Discrete.functor <| unop ∘ X)) (coproductIsCoproduct' _) ?_ ?_
   · apply hF.isSheafFor
-    convert (⊥_ Scheme).bot_mem_grothendieckTopology
+    convert! (⊥_ Scheme).bot_mem_grothendieckTopology
     rw [eq_bot_iff]
     rintro Y f ⟨g, _, _, ⟨i⟩, _⟩
     exact i.elim
diff --git a/Mathlib/AlgebraicGeometry/Sites/Small.lean b/Mathlib/AlgebraicGeometry/Sites/Small.lean
index 48e6a2ebd8e39a..05562694f4777b 100644
--- a/Mathlib/AlgebraicGeometry/Sites/Small.lean
+++ b/Mathlib/AlgebraicGeometry/Sites/Small.lean
@@ -93,8 +93,9 @@ def overPretopology : Pretopology (Over S) where
     rintro X _ T ⟨𝒰, h, rfl⟩ H
     choose V h hV using H
     refine ⟨𝒰.bind (fun j => V ((𝒰.f j).asOver S) ⟨j⟩), inferInstance, ?_⟩
-    convert Presieve.ofArrows_bind _ (fun j ↦ (𝒰.f j).asOver S) _
-      (fun Y f H j ↦ ((V f H).X j).asOver S) (fun Y f H j ↦ ((V f H).f j).asOver S)
+    convert!
+      Presieve.ofArrows_bind _ (fun j ↦ (𝒰.f j).asOver S) _ (fun Y f H j ↦ ((V f H).X j).asOver S)
+        (fun Y f H j ↦ ((V f H).f j).asOver S)
     apply hV
 
 /-- The topology on `Over S` induced from the topology on `Scheme` defined by `P`.
@@ -196,9 +197,10 @@ def smallPretopology : Pretopology (Q.Over ⊤ S) where
     let 𝒱j (j : 𝒰.I₀) : (Cover (precoverage P) ((𝒰.X j).asOverProp S (p j)).left) :=
       V ((𝒰.f j).asOverProp S) ⟨j⟩
     refine ⟨𝒰.bind (fun j ↦ 𝒱j j), inferInstance, fun j ↦ pV _ _ _, ?_⟩
-    convert Presieve.ofArrows_bind _ (fun j ↦ ((𝒰.f j).asOverProp S)) _
-      (fun Y f H j ↦ ((V f H).X j).asOverProp S (pV _ _ _))
-      (fun Y f H j ↦ ((V f H).f j).asOverProp S)
+    convert!
+      Presieve.ofArrows_bind _ (fun j ↦ ((𝒰.f j).asOverProp S)) _
+        (fun Y f H j ↦ ((V f H).X j).asOverProp S (pV _ _ _))
+        (fun Y f H j ↦ ((V f H).f j).asOverProp S)
     apply hV
 
 set_option backward.isDefEq.respectTransparency false in
diff --git a/Mathlib/AlgebraicGeometry/Sites/SmallAffineZariski.lean b/Mathlib/AlgebraicGeometry/Sites/SmallAffineZariski.lean
index 1e641cd065ca97..7e0512859ee737 100644
--- a/Mathlib/AlgebraicGeometry/Sites/SmallAffineZariski.lean
+++ b/Mathlib/AlgebraicGeometry/Sites/SmallAffineZariski.lean
@@ -355,12 +355,12 @@ noncomputable def isColimitCocone : IsColimit (cocone X) :=
       (U.2.isoSpec.hom ≫ colimit.ι F U) <| by
       rw [Pullback.range_fst, Opens.range_ι, ← Hom.coe_opensRange, Hom.opensRange_comp_of_isIso,
         ← Scheme.Hom.coe_preimage]
-      convert congr($(D.toBase_preimage_eq_opensRange_ι U).1)
+      convert! congr($(D.toBase_preimage_eq_opensRange_ι U).1)
       · delta cocone
         congr with U
         simp [D, relativeGluingData, restrictIsoSpec]
       · simp
-    convert (inferInstance : IsIso e.hom)
+    convert! (inferInstance : IsIso e.hom)
     rw [← cancel_mono U.1.ι, ← Iso.inv_comp_eq]
     simp [e, ← pullback.condition, IsAffineOpen.isoSpec_hom]
   .ofPointIso (colimit.isColimit F)
diff --git a/Mathlib/AlgebraicGeometry/Spec.lean b/Mathlib/AlgebraicGeometry/Spec.lean
index e0efd2553c4ba5..e312d427ededc6 100644
--- a/Mathlib/AlgebraicGeometry/Spec.lean
+++ b/Mathlib/AlgebraicGeometry/Spec.lean
@@ -291,7 +291,7 @@ theorem Spec_Γ_naturality {R S : CommRingCat.{u}} (f : R ⟶ S) :
 @[simps! hom_app inv_app]
 def LocallyRingedSpace.SpecΓIdentity : Spec.toLocallyRingedSpace.rightOp ⋙ Γ ≅ 𝟭 _ :=
   Iso.symm <| NatIso.ofComponents.{u, u, u + 1, u + 1} (fun R ↦ asIso (toSpecΓ R) :)
-    fun {X Y} f => by convert Spec_Γ_naturality (R := X) (S := Y) f
+    fun {X Y} f => by convert! Spec_Γ_naturality (R := X) (S := Y) f
 
 end SpecΓ
 
diff --git a/Mathlib/AlgebraicGeometry/Stalk.lean b/Mathlib/AlgebraicGeometry/Stalk.lean
index 15f6f4b03d7e74..72a527c40f8f2e 100644
--- a/Mathlib/AlgebraicGeometry/Stalk.lean
+++ b/Mathlib/AlgebraicGeometry/Stalk.lean
@@ -337,7 +337,7 @@ lemma stalkClosedPointTo_fromSpecStalk (x : X) :
   refine TopCat.Presheaf.stalk_hom_ext _ fun U hxU ↦ ?_
   simp only [TopCat.Presheaf.stalkCongr_hom, TopCat.Presheaf.germ_stalkSpecializes]
   have : X.fromSpecStalk x = Spec.map (𝟙 (X.presheaf.stalk x)) ≫ X.fromSpecStalk x := by simp
-  convert germ_stalkClosedPointTo_Spec_fromSpecStalk (𝟙 (X.presheaf.stalk x)) U hxU
+  convert! germ_stalkClosedPointTo_Spec_fromSpecStalk (𝟙 (X.presheaf.stalk x)) U hxU
 
 @[reassoc]
 lemma Spec_stalkClosedPointTo_fromSpecStalk :
diff --git a/Mathlib/AlgebraicGeometry/StructureSheaf.lean b/Mathlib/AlgebraicGeometry/StructureSheaf.lean
index e299ee3e66f5da..053111c9e5155a 100644
--- a/Mathlib/AlgebraicGeometry/StructureSheaf.lean
+++ b/Mathlib/AlgebraicGeometry/StructureSheaf.lean
@@ -395,7 +395,7 @@ lemma isUnit_basicOpen_end (f : R) :
   have := (isUnit_basicOpen f).map
     (algebraMap _ (Module.End Γ(R, basicOpen f) Γ(M, basicOpen f)))
   rw [Module.End.isUnit_iff] at this ⊢
-  convert this
+  convert! this
   ext a
   simp
 
@@ -481,8 +481,8 @@ theorem exists_le_iSup_basicOpen_and_smul_eq_smul_and_eq_const
     have : n i j + 1 ≤ N := (t ×ˢ t).le_sup (f := fun x ↦ n x.1 x.2 + 1) (b := ⟨_, _⟩) (by simp)
     rw [← Nat.sub_add_cancel this, pow_add, mul_smul, mul_smul]
     congr 1
-    convert (hn i j).symm using 1 <;> module
-  · convert congr((structureSheafInType R M).presheaf.map (homOfLE ?_).op $((H i).symm)) using 1
+    convert! (hn i j).symm using 1 <;> module
+  · convert! congr((structureSheafInType R M).presheaf.map (homOfLE ?_).op $((H i).symm)) using 1
     · refine Subtype.ext <| funext fun x ↦ LocalizedModule.mk_eq.mpr ⟨1, ?_⟩
       simp [Submonoid.smul_def, pow_succ', mul_smul]
     · simp
@@ -512,8 +512,9 @@ theorem toBasicOpenₗ_surjective (f : R) : Function.Surjective (toBasicOpenₗ
     ← Finset.sum_smul, hc]
 
 public instance (f : R) : IsLocalizedModule.Away f (toOpenₗ R M (basicOpen f)) := by
-  convert IsLocalizedModule.of_linearEquiv (.powers f) (LocalizedModule.mkLinearMap (.powers f) M)
-    (.ofBijective _ ⟨toBasicOpenₗ_injective _, toBasicOpenₗ_surjective _⟩)
+  convert!
+    IsLocalizedModule.of_linearEquiv (.powers f) (LocalizedModule.mkLinearMap (.powers f) M)
+      (.ofBijective _ ⟨toBasicOpenₗ_injective _, toBasicOpenₗ_surjective _⟩)
   ext x
   simp [toOpenₗ]
 
@@ -524,7 +525,7 @@ instance isIso_toBasicOpenₗ (f : R) :
 set_option backward.isDefEq.respectTransparency false in
 public lemma toOpenₗ_top_bijective : Function.Bijective (toOpenₗ R M ⊤) := by
   have : IsLocalizedModule ⊥ (toOpenₗ R M ⊤) := by
-    convert (inferInstance : IsLocalizedModule (.powers 1) (toOpenₗ R M (basicOpen 1)))
+    convert! (inferInstance : IsLocalizedModule (.powers 1) (toOpenₗ R M (basicOpen 1)))
     rw [PrimeSpectrum.basicOpen_one, Submonoid.powers_one]
   refine ⟨fun x y e ↦ by simpa using (IsLocalizedModule.eq_iff_exists ⊥ _).mp e, fun x ↦ ?_⟩
   obtain ⟨⟨x, _, rfl⟩, rfl⟩ := IsLocalizedModule.mk'_surjective ⊥ (toOpenₗ R M ⊤) x
@@ -643,7 +644,7 @@ theorem toOpenₗ_germ (U : Opens (PrimeSpectrum.Top R)) (x : PrimeSpectrum.Top
 
 theorem isUnit_toStalk (x : PrimeSpectrum.Top R) (f : R) (hf : x ∈ basicOpen f) :
     IsUnit (toStalk R x f) := by
-  convert (isUnit_basicOpen f).map ((structurePresheafInCommRingCat R).germ _ x hf).hom
+  convert! (isUnit_basicOpen f).map ((structurePresheafInCommRingCat R).germ _ x hf).hom
   exact ((structurePresheafInCommRingCat R).germ_res_apply (homOfLE (le_top : basicOpen f ≤ ⊤))
     x hf (algebraMap R Γ(R, ⊤) f)).symm
 
@@ -653,7 +654,7 @@ theorem isUnit_toStalkₗ' (x : PrimeSpectrum.Top R) (f : R) (hf : x ∈ basicOp
     (Module.End ((structurePresheafInCommRingCat R).stalk x)
       ((structurePresheafInModuleCat R M).stalk x)))
   rw [Module.End.isUnit_iff] at this ⊢
-  convert this
+  convert! this
   ext a
   simp only [Module.algebraMap_end_apply]
   rw [toStalk_smul]
@@ -768,8 +769,9 @@ theorem localizationToStalk_stalkToFiberRingHom (x : PrimeSpectrum.Top R) :
 
 instance (x : PrimeSpectrum.Top R) :
     IsLocalizedModule x.asIdeal.primeCompl (toStalkₗ' R M x).hom := by
-  convert IsLocalizedModule.of_linearEquiv x.asIdeal.primeCompl
-    (LocalizedModule.mkLinearMap x.asIdeal.primeCompl M) (stalkIsoₗ R M x).toLinearEquiv.symm
+  convert!
+    IsLocalizedModule.of_linearEquiv x.asIdeal.primeCompl
+      (LocalizedModule.mkLinearMap x.asIdeal.primeCompl M) (stalkIsoₗ R M x).toLinearEquiv.symm
   ext m
   refine .trans ?_ (localizationtoStalkₗ_mk ..).symm
   dsimp +instances [toStalkₗ', toOpenₗ]
@@ -795,8 +797,9 @@ def toStalkₗ (x : PrimeSpectrum.Top R) :
 
 public
 instance (x : PrimeSpectrum.Top R) : IsLocalizedModule x.asIdeal.primeCompl (toStalkₗ R M x) := by
-  convert IsLocalizedModule.of_linearEquiv x.asIdeal.primeCompl
-    (toStalkₗ' R M x).hom (modulePresheafStalkIso R M x).symm
+  convert!
+    IsLocalizedModule.of_linearEquiv x.asIdeal.primeCompl (toStalkₗ' R M x).hom
+      (modulePresheafStalkIso R M x).symm
   ext m
   let α : TopCat.Presheaf.stalk (moduleStructurePresheaf R M).presheaf x ≅
     (forget₂ _ _).obj ((structurePresheafInModuleCat R M).stalk x) :=
@@ -846,8 +849,9 @@ def commRingCatStalkEquivModuleStalk (x : PrimeSpectrum.Top R) :
 public instance (x : PrimeSpectrum.Top R) :
     IsLocalization.AtPrime ((structurePresheafInCommRingCat R).stalk x) x.asIdeal := by
   refine (isLocalizedModule_iff_isLocalization' _ _).mp ?_
-  convert IsLocalizedModule.of_linearEquiv x.asIdeal.primeCompl (toStalkₗ R R x)
-    (commRingCatStalkEquivModuleStalk R x)
+  convert!
+    IsLocalizedModule.of_linearEquiv x.asIdeal.primeCompl (toStalkₗ R R x)
+      (commRingCatStalkEquivModuleStalk R x)
   let α : TopCat.Presheaf.stalk (moduleStructurePresheaf R R).presheaf x ≅
     (forget₂ CommRingCat RingCat ⋙ forget₂ RingCat AddCommGrpCat).obj
       ((structurePresheafInCommRingCat R).stalk x) :=
@@ -969,7 +973,7 @@ def Localizations.comapFun (y : PrimeSpectrum.Top S) :
       have := IsLocalizedModule.map_units (S := y.asIdeal.primeCompl)
         (LocalizedModule.mkLinearMap y.asIdeal.primeCompl N) ⟨σ x, x.2⟩
       rw [Module.End.isUnit_iff] at this ⊢
-      convert this using 2 with a
+      convert! this using 2 with a
       exact (IsScalarTower.algebraMap_smul ..).symm)
   { __ := g,
     map_smul' r x := by simpa [Localizations] using (IsScalarTower.algebraMap_smul ..).symm }
diff --git a/Mathlib/AlgebraicGeometry/ZariskisMainTheorem.lean b/Mathlib/AlgebraicGeometry/ZariskisMainTheorem.lean
index 43c1de99f1bc83..141410f5c3014c 100644
--- a/Mathlib/AlgebraicGeometry/ZariskisMainTheorem.lean
+++ b/Mathlib/AlgebraicGeometry/ZariskisMainTheorem.lean
@@ -103,14 +103,14 @@ theorem exists_etale_isCompl_of_quasiFiniteAt [IsSeparated f]
   refine ⟨Spec (.of R), Spec.map φ ≫ hU.fromSpec, inferInstance,
     ⟨⟨P, ‹_›⟩, ?_⟩, W₁, W₂, ⟨g ⟨P', ‹_›⟩, ?_⟩, ?_, ‹_›, ?_⟩
   · dsimp [Spec.map_apply]
-    convert hU.fromSpec_primeIdealOf ⟨f x, hxU⟩
+    convert! hU.fromSpec_primeIdealOf ⟨f x, hxU⟩
     · exact PrimeSpectrum.ext (Ideal.over_def _ _).symm
     · simp [h]
   · exact ⟨⟨P', ‹_›⟩, heP', rfl⟩
   · simp [isCompl_iff, disjoint_iff, codisjoint_iff, W₂, SetLike.ext'_iff]
   · trans hV.fromSpec ⟨P'.comap Algebra.TensorProduct.includeRight.toRingHom, inferInstance⟩
     · simp [← Scheme.Hom.comp_apply, -Scheme.Hom.comp_base, g, reassoc_of% he₁]; rfl
-    convert hV.fromSpec_primeIdealOf ⟨x, hxV⟩
+    convert! hV.fromSpec_primeIdealOf ⟨x, hxV⟩
 
 variable {X Y S : Scheme.{u}} (f : X ⟶ Y)
 
@@ -154,7 +154,7 @@ lemma Scheme.Hom.exists_mem_and_isIso_morphismRestrict_toNormalization
       · rw [← Scheme.Hom.inv_image, ← SetLike.coe_subset_coe]
         simpa [← Scheme.Hom.opensRange_comp, ι, e, Scheme.Hom.normalizationCoprodIso,
           Set.range_comp] using Set.subset_preimage_image _ _
-    convert (inferInstance : IsIso (Scheme.isoOfEq _ Heq).hom)
+    convert! (inferInstance : IsIso (Scheme.isoOfEq _ Heq).hom)
     rw [Iso.comp_inv_eq, ← Iso.inv_comp_eq, ← cancel_mono (Scheme.Opens.ι _)]
     have : V.ι ≫ (H.coconePointUniqueUpToIso (colimit.isColimit _)).hom = coprod.inl :=
       H.comp_coconePointUniqueUpToIso_hom _ ⟨.left⟩
@@ -214,7 +214,7 @@ lemma Scheme.Hom.exists_isIso_morphismRestrict_toNormalization
       ((morphismRestrictRestrict ..).symm ≪≫ morphismRestrictOpensRange ..)).mp ?_
     have : Opens.ι _ ''ᵁ (𝒰.f x).opensRange = V x := by
       simp only [Opens.iSupOpenCover, 𝒰, ← opensRange_comp, homOfLE_ι, Opens.opensRange_ι]
-    convert hV x
+    convert! hV x
   refine ⟨⨆ x : { x | f.QuasiFiniteAt x }, V x, this, ?_⟩
   ext x
   suffices (∃ i : { x | f.QuasiFiniteAt x }, toNormalization f x ∈ V i) ↔ f.QuasiFiniteAt x by
@@ -265,7 +265,7 @@ lemma Scheme.Hom.exists_isIso_morphismRestrict_toNormalization
     have := (inferInstance : IsIso ((toNormalization f ∣_ V y).app
       (Scheme.homOfLE _ hrV).opensRange))
     simp only [Opens.toScheme_presheaf_obj, app_eq_appLE, morphismRestrict_appLE] at this ⊢
-    convert this <;>
+    convert! this <;>
       simp [Scheme.Hom.image_preimage_eq_opensRange_inf, -Scheme.preimage_basicOpen,
         f.toNormalization.preimage_mono, hrV, H]
   have : (f.appLE U W H).hom.QuasiFinite := by
@@ -275,7 +275,7 @@ lemma Scheme.Hom.exists_isIso_morphismRestrict_toNormalization
     exact .of_isIntegral_of_finiteType (IsIntegralHom.isIntegral_app f.fromNormalization _ hU)
       ⟨r, (hU.preimage f.fromNormalization).isLocalization_basicOpen _⟩ this
   have hxU : f x ∈ U := by
-    convert show _ ∈ U from (normalization f).basicOpen_le _ hxV
+    convert! show _ ∈ U from (normalization f).basicOpen_le _ hxV
     rw [← Scheme.Hom.comp_apply, f.toNormalization_fromNormalization]
   refine .of_comp (g := (Y.presheaf.germ U _ hxU).hom) ?_
   rw [← CommRingCat.hom_comp, f.germ_stalkMap, ← X.presheaf.germ_res (homOfLE H) _ hxV,
@@ -321,8 +321,11 @@ lemma Scheme.Hom.mem_quasiFiniteLocus [LocallyOfFiniteType f]
 instance [LocallyOfFiniteType f] [IsSeparated f] [QuasiCompact f] :
     IsOpenImmersion (f.quasiFiniteLocus.ι ≫ f.toNormalization) := by
   obtain ⟨U, hU, e⟩ := Scheme.Hom.exists_isIso_morphismRestrict_toNormalization f
-  convert (inferInstance : IsOpenImmersion ((X.isoOfEq (U := f.quasiFiniteLocus)
-    (SetLike.coe_injective e.symm)).hom ≫ f.toNormalization ∣_ U ≫ U.ι)) using 1
+  convert!
+    (inferInstance :
+      IsOpenImmersion
+        ((X.isoOfEq (U := f.quasiFiniteLocus) (SetLike.coe_injective e.symm)).hom ≫
+          f.toNormalization ∣_ U ≫ U.ι)) using 1
   simp
 
 lemma Scheme.Hom.quasiFiniteLocus_eq_top [LocallyQuasiFinite f] [LocallyOfFiniteType f] :
@@ -351,8 +354,12 @@ instance [LocallyOfFiniteType f] :
 
 instance [LocallyQuasiFinite f] [LocallyOfFiniteType f] [IsSeparated f] [QuasiCompact f] :
     IsOpenImmersion f.toNormalization := by
-  convert (inferInstance : IsOpenImmersion (X.topIso.inv ≫ (X.isoOfEq
-    f.quasiFiniteLocus_eq_top).inv ≫ f.quasiFiniteLocus.ι ≫ f.toNormalization)) using 1
+  convert!
+    (inferInstance :
+      IsOpenImmersion
+        (X.topIso.inv ≫
+          (X.isoOfEq f.quasiFiniteLocus_eq_top).inv ≫
+            f.quasiFiniteLocus.ι ≫ f.toNormalization)) using 1
   simp
 
 -- In particular it is surjective (by infer_instance), since it is a priori dominant.
diff --git a/Mathlib/AlgebraicTopology/CechNerve.lean b/Mathlib/AlgebraicTopology/CechNerve.lean
index d38ac4b1d73a8d..a9fdcf1b7f7410 100644
--- a/Mathlib/AlgebraicTopology/CechNerve.lean
+++ b/Mathlib/AlgebraicTopology/CechNerve.lean
@@ -306,7 +306,7 @@ def cechConerveEquiv (F : Arrow C) (X : CosimplicialObject.Augmented C) :
       rw [WidePushout.ι_desc]
       nth_rw 2 [← Category.comp_id A.right]
       congr 1
-      convert X.right.map_id _
+      convert! X.right.map_id _
       ext ⟨a, ha⟩
       simp
 
diff --git a/Mathlib/AlgebraicTopology/DoldKan/Faces.lean b/Mathlib/AlgebraicTopology/DoldKan/Faces.lean
index 54107ab3f728b2..6cab6acea43b2e 100644
--- a/Mathlib/AlgebraicTopology/DoldKan/Faces.lean
+++ b/Mathlib/AlgebraicTopology/DoldKan/Faces.lean
@@ -80,7 +80,7 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _⦋n + 1⦌} (v : Highe
   · rintro ⟨k, hk⟩
     suffices φ ≫ X.δ (⟨a + 2 + k, by lia⟩ : Fin (n + 2)) = 0 by
       simp only [this, Fin.natAdd_mk, Fin.cast_mk, zero_comp, smul_zero]
-    convert v ⟨a + k + 1, by lia⟩ (by rw [Fin.val_mk]; lia)
+    convert! v ⟨a + k + 1, by lia⟩ (by rw [Fin.val_mk]; lia)
     dsimp
     lia
   -- cleaning up the second sum
diff --git a/Mathlib/AlgebraicTopology/DoldKan/GammaCompN.lean b/Mathlib/AlgebraicTopology/DoldKan/GammaCompN.lean
index 265f71c3d9cf6c..14a8c7741d4c01 100644
--- a/Mathlib/AlgebraicTopology/DoldKan/GammaCompN.lean
+++ b/Mathlib/AlgebraicTopology/DoldKan/GammaCompN.lean
@@ -144,7 +144,7 @@ lemma N₂Γ₂ToKaroubiIso_inv_app (X : ChainComplex C ℕ) :
   ext n
   dsimp [N₂Γ₂ToKaroubiIso]
   simp only [comp_id, PInfty_f_idem_assoc, AlternatingFaceMapComplex.obj_X, Γ₀_obj_obj]
-  convert comp_id _
+  convert! comp_id _
   apply (Γ₀.splitting X).hom_ext'
   intro A
   rw [Splitting.ι_desc]
diff --git a/Mathlib/AlgebraicTopology/FundamentalGroupoid/InducedMaps.lean b/Mathlib/AlgebraicTopology/FundamentalGroupoid/InducedMaps.lean
index 2c72338fb24bde..1ff39a0d918e88 100644
--- a/Mathlib/AlgebraicTopology/FundamentalGroupoid/InducedMaps.lean
+++ b/Mathlib/AlgebraicTopology/FundamentalGroupoid/InducedMaps.lean
@@ -155,10 +155,10 @@ theorem heq_path_of_eq_image :
   exact hfg
 
 set_option backward.privateInPublic true in
-private theorem start_path : f x₀ = g x₂ := by convert hfg 0 <;> simp only [Path.source]
+private theorem start_path : f x₀ = g x₂ := by convert! hfg 0 <;> simp only [Path.source]
 
 set_option backward.privateInPublic true in
-private theorem end_path : f x₁ = g x₃ := by convert hfg 1 <;> simp only [Path.target]
+private theorem end_path : f x₁ = g x₃ := by convert! hfg 1 <;> simp only [Path.target]
 
 set_option backward.isDefEq.respectTransparency false in
 set_option backward.privateInPublic true in
diff --git a/Mathlib/AlgebraicTopology/FundamentalGroupoid/SimplyConnected.lean b/Mathlib/AlgebraicTopology/FundamentalGroupoid/SimplyConnected.lean
index 0bf5739df1590b..25c8f97db9970d 100644
--- a/Mathlib/AlgebraicTopology/FundamentalGroupoid/SimplyConnected.lean
+++ b/Mathlib/AlgebraicTopology/FundamentalGroupoid/SimplyConnected.lean
@@ -94,7 +94,7 @@ theorem simply_connected_iff_paths_homotopic :
 theorem simply_connected_iff_paths_homotopic' :
     SimplyConnectedSpace Y ↔
       PathConnectedSpace Y ∧ ∀ {x y : Y} (p₁ p₂ : Path x y), Path.Homotopic p₁ p₂ := by
-  convert simply_connected_iff_paths_homotopic (Y := Y)
+  convert! simply_connected_iff_paths_homotopic (Y := Y)
   simp [Path.Homotopic.Quotient, Setoid.eq_top_iff]; rfl
 
 set_option backward.isDefEq.respectTransparency false in
diff --git a/Mathlib/AlgebraicTopology/ModelCategory/FundamentalLemma.lean b/Mathlib/AlgebraicTopology/ModelCategory/FundamentalLemma.lean
index 9181514d9cff64..2c2e7570f012b7 100644
--- a/Mathlib/AlgebraicTopology/ModelCategory/FundamentalLemma.lean
+++ b/Mathlib/AlgebraicTopology/ModelCategory/FundamentalLemma.lean
@@ -77,7 +77,7 @@ lemma bijective_rightHomotopyClassToHom :
       (by rwa [← weakEquivalence_iff])
     rw [← Function.Bijective.of_comp_iff _
       (LeftHomotopyClass.postcomp_bijective_of_fibration_of_weakEquivalence _ p)]
-    convert (Iso.homCongr (Iso.refl (L.obj X)) (asIso (L.map p))).bijective.comp hY'
+    convert! (Iso.homCongr (Iso.refl (L.obj X)) (asIso (L.map p))).bijective.comp hY'
     ext f
     obtain ⟨f, rfl⟩ := f.mk_surjective
     simp
@@ -91,7 +91,7 @@ lemma bijective_rightHomotopyClassToHom :
       (by rwa [← weakEquivalence_iff])
     rw [← Function.Bijective.of_comp_iff _
       (RightHomotopyClass.precomp_bijective_of_cofibration_of_weakEquivalence Y i)]
-    convert (Iso.homCongr (asIso (L.map i)) (Iso.refl (L.obj Y))).symm.bijective.comp hX'
+    convert! (Iso.homCongr (asIso (L.map i)) (Iso.refl (L.obj Y))).symm.bijective.comp hX'
     ext f
     obtain ⟨f, rfl⟩ := f.mk_surjective
     simp
diff --git a/Mathlib/AlgebraicTopology/ModelCategory/Homotopy.lean b/Mathlib/AlgebraicTopology/ModelCategory/Homotopy.lean
index a16d714f750d0f..6481743a905853 100644
--- a/Mathlib/AlgebraicTopology/ModelCategory/Homotopy.lean
+++ b/Mathlib/AlgebraicTopology/ModelCategory/Homotopy.lean
@@ -157,11 +157,11 @@ lemma postcomp_bijective_of_weakEquivalence
   have hi : Function.Bijective (fun (f : LeftHomotopyClass X Y) ↦ f.postcomp h.i) := by
     rw [← Function.Bijective.of_comp_iff'
       (postcomp_bijective_of_fibration_of_weakEquivalence X h.r)]
-    convert Function.bijective_id
+    convert! Function.bijective_id
     ext φ
     obtain ⟨φ, rfl⟩ := φ.mk_surjective
     simp
-  convert (postcomp_bijective_of_fibration_of_weakEquivalence X h.p).comp hi using 1
+  convert! (postcomp_bijective_of_fibration_of_weakEquivalence X h.p).comp hi using 1
   ext φ
   obtain ⟨φ, rfl⟩ := φ.mk_surjective
   simp
@@ -204,11 +204,11 @@ lemma precomp_bijective_of_weakEquivalence
   have hj : Function.Bijective (fun (g : RightHomotopyClass Y Z) ↦ g.precomp h.p) := by
     rw [← Function.Bijective.of_comp_iff'
       (precomp_bijective_of_cofibration_of_weakEquivalence Z h.s)]
-    convert Function.bijective_id
+    convert! Function.bijective_id
     ext φ
     obtain ⟨φ, rfl⟩ := φ.mk_surjective
     simp
-  convert (precomp_bijective_of_cofibration_of_weakEquivalence Z h.i).comp hj using 1
+  convert! (precomp_bijective_of_cofibration_of_weakEquivalence Z h.i).comp hj using 1
   ext φ
   obtain ⟨φ, rfl⟩ := φ.mk_surjective
   simp
diff --git a/Mathlib/AlgebraicTopology/ModelCategory/LeftHomotopy.lean b/Mathlib/AlgebraicTopology/ModelCategory/LeftHomotopy.lean
index 896925077ca3f0..fa71f02f92b853 100644
--- a/Mathlib/AlgebraicTopology/ModelCategory/LeftHomotopy.lean
+++ b/Mathlib/AlgebraicTopology/ModelCategory/LeftHomotopy.lean
@@ -167,7 +167,7 @@ lemma exists_good_cylinder {f g : X ⟶ Y} (h : P.LeftHomotopy f g) :
       i₁ := coprod.inr ≫ d.i
       π := d.p ≫ P.π }, ⟨by
         rw [cofibration_iff]
-        convert d.hi
+        convert! d.hi
         aesop⟩, ⟨{ h := d.p ≫ h.h }⟩⟩
 
 /-- The covering homotopy theorem: if `p : E ⟶ B` is a fibration,
diff --git a/Mathlib/AlgebraicTopology/ModelCategory/RightHomotopy.lean b/Mathlib/AlgebraicTopology/ModelCategory/RightHomotopy.lean
index 51b005600ec4f0..452c95a55f093c 100644
--- a/Mathlib/AlgebraicTopology/ModelCategory/RightHomotopy.lean
+++ b/Mathlib/AlgebraicTopology/ModelCategory/RightHomotopy.lean
@@ -170,7 +170,7 @@ lemma exists_good_pathObject {f g : X ⟶ Y} (h : P.RightHomotopy f g) :
       p₁ := d.p ≫ prod.snd
       ι := P.ι ≫ d.i }, ⟨by
         rw [fibration_iff]
-        convert d.hp
+        convert! d.hp
         aesop⟩, ⟨{ h := h.h ≫ d.i }⟩⟩
 
 /-- The homotopy extension theorem: if `p : A ⟶ X` is a cofibration,
diff --git a/Mathlib/AlgebraicTopology/SimplexCategory/Basic.lean b/Mathlib/AlgebraicTopology/SimplexCategory/Basic.lean
index fae9a62b62afc5..ca5f7ef0d62ce2 100644
--- a/Mathlib/AlgebraicTopology/SimplexCategory/Basic.lean
+++ b/Mathlib/AlgebraicTopology/SimplexCategory/Basic.lean
@@ -660,7 +660,7 @@ instance : (forget SimplexCategory).ReflectsIsomorphisms :=
                 by_cases h' : y₁ < y₂
                 · by_contra h''
                   apply not_le.mpr h'
-                  convert f.toOrderHom.monotone (le_of_not_ge h'')
+                  convert! f.toOrderHom.monotone (le_of_not_ge h'')
                   all_goals
                     exact (ConcreteCategory.congr_hom (Iso.inv_hom_id
                       (asIso ((forget SimplexCategory).map f))) _).symm
diff --git a/Mathlib/AlgebraicTopology/SimplexCategory/GeneratorsRelations/NormalForms.lean b/Mathlib/AlgebraicTopology/SimplexCategory/GeneratorsRelations/NormalForms.lean
index 8059c66eb31537..ca7e85ec11cc33 100644
--- a/Mathlib/AlgebraicTopology/SimplexCategory/GeneratorsRelations/NormalForms.lean
+++ b/Mathlib/AlgebraicTopology/SimplexCategory/GeneratorsRelations/NormalForms.lean
@@ -278,7 +278,7 @@ lemma standardσ_simplicialInsert (hL : IsAdmissible (m + 1) L) (j : ℕ) (hj :
     · have : ∀ (j k : ℕ) (h : j < (k + 1)), Fin.ofNat (k + 1) j = j := by simp -- helps grind below
       have : a < m + 2 := by grind -- helps grind below
       have : σ (Fin.ofNat (m + 2) a) ≫ σ (.ofNat _ j) = σ (.ofNat _ (j + 1)) ≫ σ (.ofNat _ a) := by
-        convert σ_comp_σ_nat (n := m) a j (by grind) (by grind) (by grind) <;> grind
+        convert! σ_comp_σ_nat (n := m) a j (by grind) (by grind) (by grind) <;> grind
       grind [standardσ_cons]
 
 set_option backward.isDefEq.respectTransparency false in
diff --git a/Mathlib/AlgebraicTopology/SimplicialSet/HomotopyCat.lean b/Mathlib/AlgebraicTopology/SimplicialSet/HomotopyCat.lean
index 8e961857e5c6b9..06fa48920be456 100644
--- a/Mathlib/AlgebraicTopology/SimplicialSet/HomotopyCat.lean
+++ b/Mathlib/AlgebraicTopology/SimplicialSet/HomotopyCat.lean
@@ -363,7 +363,7 @@ def lift : V.HomotopyCategory ⥤ D :=
     (Cat.FreeRefl.lift' obj (fun f ↦ map f) map_id) (by
       rintro _ _ _ _ ⟨h⟩
       simp only [Functor.map_comp]
-      convert map_comp h <;> apply Cat.FreeRefl.lift'_map)
+      convert! map_comp h <;> apply Cat.FreeRefl.lift'_map)
 
 @[simp]
 lemma lift_obj_mk (x : V _⦋0⦌₂) : (lift obj map map_id map_comp).obj (mk x) = obj x := rfl
diff --git a/Mathlib/AlgebraicTopology/SimplicialSet/HornColimits.lean b/Mathlib/AlgebraicTopology/SimplicialSet/HornColimits.lean
index 300aab948d5c2e..ad417247be5419 100644
--- a/Mathlib/AlgebraicTopology/SimplicialSet/HornColimits.lean
+++ b/Mathlib/AlgebraicTopology/SimplicialSet/HornColimits.lean
@@ -275,15 +275,15 @@ def desc.multicofork :
       fin_cases x
       · simp only [← cancel_epi (stdSimplex.facePairIso.{u} (n := 3) 1 3 (by simp)).hom,
           ← Category.assoc]
-        convert h₁₃ <;> decide
+        convert! h₁₃ <;> decide
       · dsimp
         simp only [← cancel_epi (stdSimplex.facePairIso.{u} (n := 3) 1 2 (by simp)).hom,
           ← Category.assoc]
-        convert h₁₂ <;> decide
+        convert! h₁₂ <;> decide
       · dsimp
         simp only [← cancel_epi (stdSimplex.facePairIso.{u} (n := 3) 0 1 (by simp)).hom,
           ← Category.assoc]
-        convert h₂₃ <;> decide)
+        convert! h₂₃ <;> decide)
 
 @[simp, reassoc]
 lemma desc.multicofork_π_zero :
@@ -362,15 +362,15 @@ def desc.multicofork :
       · dsimp
         simp only [← cancel_epi (stdSimplex.facePairIso.{u} (n := 3) 2 3 (by simp)).hom,
           ← Category.assoc]
-        convert h₂₃ <;> decide
+        convert! h₂₃ <;> decide
       · dsimp
         simp only [← cancel_epi (stdSimplex.facePairIso.{u} (n := 3) 1 2 (by simp)).hom,
           ← Category.assoc]
-        convert h₁₂ <;> decide
+        convert! h₁₂ <;> decide
       · dsimp
         simp only [← cancel_epi (stdSimplex.facePairIso.{u} (n := 3) 0 2 (by simp)).hom,
           ← Category.assoc]
-        convert h₀₂ <;> decide)
+        convert! h₀₂ <;> decide)
 
 @[simp, reassoc]
 lemma desc.multicofork_π_zero :
diff --git a/Mathlib/AlgebraicTopology/SimplicialSet/Nerve.lean b/Mathlib/AlgebraicTopology/SimplicialSet/Nerve.lean
index 1734cd5bf1dbfa..7a3fdd012330a8 100644
--- a/Mathlib/AlgebraicTopology/SimplicialSet/Nerve.lean
+++ b/Mathlib/AlgebraicTopology/SimplicialSet/Nerve.lean
@@ -234,7 +234,7 @@ lemma homEquiv_comp {x₀ x₁ x₂ : ComposableArrows C 0}
   obtain ⟨f₀₁, rfl⟩ := edgeMk_surjective e₀₁
   obtain ⟨f₁₂, rfl⟩ := edgeMk_surjective e₁₂
   obtain ⟨f₀₂, rfl⟩ := edgeMk_surjective e₀₂
-  convert (nerve.nonempty_compStruct_iff _ _ _).1 ⟨h⟩ <;> apply homEquiv_edgeMk
+  convert! (nerve.nonempty_compStruct_iff _ _ _).1 ⟨h⟩ <;> apply homEquiv_edgeMk
 
 set_option backward.isDefEq.respectTransparency false in
 lemma σ_zero_nerveEquiv_symm (x : C) :
diff --git a/Mathlib/AlgebraicTopology/SimplicialSet/Path.lean b/Mathlib/AlgebraicTopology/SimplicialSet/Path.lean
index d8653e1ddc3406..234a2939fa28db 100644
--- a/Mathlib/AlgebraicTopology/SimplicialSet/Path.lean
+++ b/Mathlib/AlgebraicTopology/SimplicialSet/Path.lean
@@ -373,7 +373,7 @@ def horn.spineId {n : ℕ} (i : Fin (n + 3))
     (h₀ : 0 < i) (hₙ : i < Fin.last (n + 2)) :
     Path (Λ[n + 2, i] : SSet.{u}) (n + 2) :=
   Λ[n + 2, i].liftPath (stdSimplex.spineId (n + 2)) (by simp) (fun j ↦ by
-    convert (horn.primitiveEdge.{u} h₀ hₙ j).2
+    convert! (horn.primitiveEdge.{u} h₀ hₙ j).2
     ext a
     fin_cases a <;> rfl)
 
diff --git a/Mathlib/AlgebraicTopology/SimplicialSet/StrictSegal.lean b/Mathlib/AlgebraicTopology/SimplicialSet/StrictSegal.lean
index 5e2e0a06875543..ce9df0560ff8c1 100644
--- a/Mathlib/AlgebraicTopology/SimplicialSet/StrictSegal.lean
+++ b/Mathlib/AlgebraicTopology/SimplicialSet/StrictSegal.lean
@@ -166,7 +166,7 @@ theorem spineToSimplex_interval (f : Path X m) (j l : ℕ) (hjl : j + l ≤ m) :
   apply sx.spineInjective l
   dsimp only [spineEquiv, Equiv.coe_fn_mk]
   rw [spine_spineToSimplex_apply]
-  convert spine_map_subinterval X m h j l hjl <| sx.spineToSimplex m h f
+  convert! spine_map_subinterval X m h j l hjl <| sx.spineToSimplex m h f
   exact sx.spine_spineToSimplex_apply m h f |>.symm
 
 theorem spineToSimplex_edge (f : Path X m) (j l : ℕ) (hjl : j + l ≤ m) :
diff --git a/Mathlib/Analysis/Analytic/Basic.lean b/Mathlib/Analysis/Analytic/Basic.lean
index 1cd0e0a022d2d3..bd5e66693eb5a2 100644
--- a/Mathlib/Analysis/Analytic/Basic.lean
+++ b/Mathlib/Analysis/Analytic/Basic.lean
@@ -157,7 +157,7 @@ theorem HasFPowerSeriesOnBall.comp_sub (hf : HasFPowerSeriesOnBall f p x r) (y :
   { r_le := hf.r_le
     r_pos := hf.r_pos
     hasSum := fun {z} hz => by
-      convert hf.hasSum hz using 2
+      convert! hf.hasSum hz using 2
       abel }
 
 theorem HasFPowerSeriesWithinOnBall.comp_sub (hf : HasFPowerSeriesWithinOnBall f p s x r) (y : E) :
@@ -169,7 +169,7 @@ theorem HasFPowerSeriesWithinOnBall.comp_sub (hf : HasFPowerSeriesWithinOnBall f
       simp only [add_singleton, image_add_right, mem_insert_iff, add_eq_left, mem_preimage] at hz1 ⊢
       abel_nf at hz1
       assumption
-    convert hf.hasSum this hz2 using 2
+    convert! hf.hasSum this hz2 using 2
     abel
 
 theorem HasFPowerSeriesAt.comp_sub (hf : HasFPowerSeriesAt f p x) (y : E) :
@@ -192,7 +192,7 @@ theorem AnalyticOnNhd.comp_sub (hf : AnalyticOnNhd 𝕜 f s) (y : E) :
   intro x hx
   simp only [add_singleton, image_add_right, mem_preimage] at hx
   rw [show x = (x - y) + y by abel]
-  apply (hf (x - y) (by convert hx using 1; abel)).comp_sub
+  apply (hf (x - y) (by convert! hx using 1; abel)).comp_sub
 
 theorem AnalyticWithinAt.comp_sub (hf : AnalyticWithinAt 𝕜 f s x) (y : E) :
     AnalyticWithinAt 𝕜 (fun z ↦ f (z - y)) (s + {y}) (x + y) := by
@@ -204,7 +204,7 @@ theorem AnalyticOn.comp_sub (hf : AnalyticOn 𝕜 f s) (y : E) :
   intro x hx
   simp only [add_singleton, image_add_right, mem_preimage] at hx
   rw [show x = (x - y) + y by abel]
-  apply (hf (x - y) (by convert hx using 1; abel)).comp_sub
+  apply (hf (x - y) (by convert! hx using 1; abel)).comp_sub
 
 theorem HasFPowerSeriesWithinOnBall.hasSum_sub (hf : HasFPowerSeriesWithinOnBall f p s x r) {y : E}
     (hy : y ∈ (insert x s) ∩ Metric.eball x r) :
@@ -243,7 +243,7 @@ lemma HasFPowerSeriesWithinOnBall.congr {f g : E → F} {p : FormalMultilinearSe
     HasFPowerSeriesWithinOnBall g p s x r := by
   refine ⟨h.r_le, h.r_pos, ?_⟩
   intro y hy h'y
-  convert h.hasSum hy h'y using 1
+  convert! h.hasSum hy h'y using 1
   simp only [mem_insert_iff, add_eq_left] at hy
   rcases hy with rfl | hy
   · simpa using h''
@@ -258,7 +258,7 @@ lemma HasFPowerSeriesWithinOnBall.congr' {f g : E → F} {p : FormalMultilinearS
     (h' : EqOn g f (insert x s ∩ Metric.eball x r)) :
     HasFPowerSeriesWithinOnBall g p s x r := by
   refine ⟨h.r_le, h.r_pos, fun {y} hy h'y ↦ ?_⟩
-  convert h.hasSum hy h'y using 1
+  convert! h.hasSum hy h'y using 1
   exact h' ⟨hy, by simpa [edist_eq_enorm_sub] using h'y⟩
 
 lemma HasFPowerSeriesWithinAt.congr {f g : E → F} {p : FormalMultilinearSeries 𝕜 E F} {s : Set E}
@@ -279,7 +279,7 @@ theorem HasFPowerSeriesOnBall.congr (hf : HasFPowerSeriesOnBall f p x r)
   { r_le := hf.r_le
     r_pos := hf.r_pos
     hasSum := fun {y} hy => by
-      convert hf.hasSum hy using 1
+      convert! hf.hasSum hy using 1
       apply hg.symm
       simpa [edist_eq_enorm_sub] using hy }
 
@@ -798,8 +798,9 @@ theorem HasFPowerSeriesWithinOnBall.isBigO_image_sub_image_sub_deriv_principal
       exact Metric.eball_subset_eball hr.le hy'
     set A : ℕ → F := fun n => (p n fun _ => y.1 - x) - p n fun _ => y.2 - x
     have hA : HasSum (fun n => A (n + 2)) (f y.1 - f y.2 - p 1 fun _ => y.1 - y.2) := by
-      convert (hasSum_nat_add_iff' 2).2
-        ((hf.hasSum_sub ⟨ys.1, hy.1⟩).sub (hf.hasSum_sub ⟨ys.2, hy.2⟩)) using 1
+      convert!
+        (hasSum_nat_add_iff' 2).2
+          ((hf.hasSum_sub ⟨ys.1, hy.1⟩).sub (hf.hasSum_sub ⟨ys.2, hy.2⟩)) using 1
       rw [Finset.sum_range_succ, Finset.sum_range_one, hf.coeff_zero, hf.coeff_zero, sub_self,
         zero_add, ← Subsingleton.pi_single_eq (0 : Fin 1) (y.1 - x), Pi.single,
         ← Subsingleton.pi_single_eq (0 : Fin 1) (y.2 - x), Pi.single, ← (p 1).map_update_sub,
@@ -953,7 +954,7 @@ theorem HasFPowerSeriesWithinOnBall.tendstoUniformlyOn' {r' : ℝ≥0}
     (hf : HasFPowerSeriesWithinOnBall f p s x r) (h : (r' : ℝ≥0∞) < r) :
     TendstoUniformlyOn (fun n y => p.partialSum n (y - x)) f atTop
       (insert x s ∩ Metric.ball (x : E) r') := by
-  convert (hf.tendstoUniformlyOn h).comp fun y => y - x using 1
+  convert! (hf.tendstoUniformlyOn h).comp fun y => y - x using 1
   · simp [Function.comp_def]
   · ext z
     simp [dist_eq_norm]
@@ -975,7 +976,7 @@ theorem HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn'
     TendstoLocallyUniformlyOn (fun n y => p.partialSum n (y - x)) f atTop
       (insert x s ∩ Metric.eball (x : E) r) := by
   have A : ContinuousOn (fun y : E => y - x) (insert x s ∩ Metric.eball (x : E) r) := by fun_prop
-  convert hf.tendstoLocallyUniformlyOn.comp (fun y : E => y - x) _ A using 1
+  convert! hf.tendstoLocallyUniformlyOn.comp (fun y : E => y - x) _ A using 1
   · ext z
     simp
   · intro z
@@ -1115,7 +1116,7 @@ theorem hasFPowerSeriesAt_iff :
     have : (‖z‖₊ : ENNReal) ≤ p.radius := by
       simp only [dist_zero_right] at h
       apply FormalMultilinearSeries.le_radius_of_tendsto
-      convert tendsto_norm.comp (h le_z).summable.tendsto_atTop_zero
+      convert! tendsto_norm.comp (h le_z).summable.tendsto_atTop_zero
       simp [norm_smul, mul_comm]
     refine lt_of_lt_of_le ?_ this
     simp only [ENNReal.coe_pos]
diff --git a/Mathlib/Analysis/Analytic/Binomial.lean b/Mathlib/Analysis/Analytic/Binomial.lean
index 7688f92d8ac58c..f4abdc9dea8ee1 100644
--- a/Mathlib/Analysis/Analytic/Binomial.lean
+++ b/Mathlib/Analysis/Analytic/Binomial.lean
@@ -102,7 +102,7 @@ theorem one_add_cpow_hasFPowerSeriesOnBall_zero {a : ℂ} :
     HasFPowerSeriesOnBall (fun x ↦ (1 + x) ^ a) (binomialSeries ℂ a) 0 1 := by
   suffices (binomialSeries ℂ a = FormalMultilinearSeries.ofScalars ℂ
       fun n ↦ iteratedDeriv n (fun (x : ℂ) ↦ (1 + x) ^ a) 0 / n !) by
-    convert AnalyticOn.hasFPowerSeriesOnSubball _ _ _
+    convert! AnalyticOn.hasFPowerSeriesOnSubball _ _ _
     · norm_num
     · -- TODO: use `fun_prop` for this subgoal
       apply AnalyticOn.cpow (analyticOn_const.add analyticOn_id) analyticOn_const
@@ -171,7 +171,7 @@ theorem one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero (a : ℂ) :
 theorem one_div_one_sub_pow_hasFPowerSeriesOnBall_zero (a : ℕ) :
     HasFPowerSeriesOnBall (fun x ↦ 1 / (1 - x) ^ (a + 1))
       (.ofScalars ℂ (𝕜 := ℂ) fun n ↦ ↑(Nat.choose (a + n) a)) 0 1 := by
-  convert one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero (a + 1) using 3 with z n
+  convert! one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero (a + 1) using 3 with z n
   · norm_cast
   · rw [eq_comm, add_right_comm, add_sub_cancel_right, ← Nat.cast_add,
       Ring.choose_natCast, Nat.choose_symm_add]
@@ -184,7 +184,7 @@ theorem one_div_sub_pow_hasFPowerSeriesOnBall_zero (a : ℕ) {z : ℂ} (hz : z 
   have := this.compContinuousLinearMap
   have H : 1 / ‖(z⁻¹ • 1 : ℂ →L[ℂ] ℂ)‖ₑ = ‖z‖ₑ := by simp [enorm_smul, enorm_inv, hz]
   simp only [one_div, ContinuousLinearMap.coe_smul', H, Function.comp_def] at this
-  convert (this.const_smul (c := (z ^ (a + 1))⁻¹)).congr ?_ using 2
+  convert! (this.const_smul (c := (z ^ (a + 1))⁻¹)).congr ?_ using 2
   · ext n
     simp only [FormalMultilinearSeries.smul_apply, ContinuousMultilinearMap.smul_apply,
       FormalMultilinearSeries.compContinuousLinearMap_apply]
@@ -213,8 +213,9 @@ theorem one_div_one_sub_sq_hasFPowerSeriesOnBall_zero :
 theorem hasFPowerSeriesOnBall_ofScalars_mul_add_zero (a b : ℂ) :
     HasFPowerSeriesOnBall (fun x ↦ (b - a) / (1 - x) + a / (1 - x) ^ 2)
       (.ofScalars ℂ fun n ↦ a * n + b) 0 1 := by
-  convert (one_div_one_sub_hasFPowerSeriesOnBall_zero.const_smul (c := b - a)).add
-    (one_div_one_sub_sq_hasFPowerSeriesOnBall_zero.const_smul (c := a)) using 2
+  convert!
+    (one_div_one_sub_hasFPowerSeriesOnBall_zero.const_smul (c := b - a)).add
+      (one_div_one_sub_sq_hasFPowerSeriesOnBall_zero.const_smul (c := a)) using 2
   · simp [div_eq_mul_inv]
   · ext; simp; ring
 
@@ -226,7 +227,7 @@ lemma one_div_sub_sq_sub_one_div_sq_hasFPowerSeriesOnBall_zero (w x : ℂ) (hw :
   · simpa only [sub_sub_sub_cancel_right, zero_add, sub_sq_comm w, zpow_neg, zpow_natCast, mul_comm]
       using (one_div_sub_sq_hasFPowerSeriesOnBall_zero
         (z := w - x) (by simp [sub_eq_zero, hw])).comp_sub x
-  · convert hasFPowerSeriesOnBall_const.mono _ le_top
+  · convert! hasFPowerSeriesOnBall_const.mono _ le_top
     · ext (_ | _) <;> simp [zpow_ofNat]
     · simpa [sub_eq_zero]
 
@@ -241,7 +242,7 @@ theorem one_add_rpow_hasFPowerSeriesOnBall_zero {a : ℝ} :
   have H : binomialSeries ℂ a = (binomialSeries ℂ (a : ℂ)).restrictScalars (𝕜 := ℝ) := by aesop
   have : HasFPowerSeriesOnBall (fun x ↦ (1 + x) ^ (a : ℂ)) (binomialSeries ℂ a) (.ofRealCLM 0) 1 :=
     Complex.ofRealCLM.map_zero ▸ H ▸ Complex.one_add_cpow_hasFPowerSeriesOnBall_zero.restrictScalars
-  convert (Complex.reCLM.comp_hasFPowerSeriesOnBall this.compContinuousLinearMap).congr ?_
+  convert! (Complex.reCLM.comp_hasFPowerSeriesOnBall this.compContinuousLinearMap).congr ?_
   · ext; simp [Function.comp_def]
   · simp
   · intro x hx; simp_all; norm_cast
@@ -261,7 +262,7 @@ theorem one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero (a : ℝ) :
       (.ofScalars ℝ fun n ↦ Ring.choose (a + n - 1) n) 0 1 := by
   have := (Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero a).restrictScalars (𝕜 := ℝ)
   rw [← Complex.ofRealCLM.map_zero] at this
-  convert (Complex.reCLM.comp_hasFPowerSeriesOnBall this.compContinuousLinearMap).congr ?_ using 1
+  convert! (Complex.reCLM.comp_hasFPowerSeriesOnBall this.compContinuousLinearMap).congr ?_ using 1
   · ext n
     simp only [ContinuousLinearMap.compFormalMultilinearSeries_apply,
       ContinuousLinearMap.compContinuousMultilinearMap_coe, Function.comp_apply,
@@ -280,7 +281,7 @@ theorem one_div_sub_pow_hasFPowerSeriesOnBall_zero (a : ℕ) {r : ℝ} (hr : r 
   have := (Complex.one_div_sub_pow_hasFPowerSeriesOnBall_zero a (z := r)
     (by simpa)).restrictScalars (𝕜 := ℝ)
   rw [← Complex.ofRealCLM.map_zero] at this
-  convert (Complex.reCLM.comp_hasFPowerSeriesOnBall this.compContinuousLinearMap) using 2
+  convert! (Complex.reCLM.comp_hasFPowerSeriesOnBall this.compContinuousLinearMap) using 2
   · simp [-Complex.inv_re, ← Complex.ofReal_pow, ← Complex.ofReal_inv, ← Complex.ofReal_sub]
   · ext n
     simp only [ContinuousLinearMap.compFormalMultilinearSeries_apply,
@@ -310,8 +311,9 @@ theorem one_div_one_sub_sq_hasFPowerSeriesOnBall_zero :
 theorem hasFPowerSeriesOnBall_ofScalars_mul_add_zero (a b : ℝ) :
     HasFPowerSeriesOnBall (fun x ↦ (b - a) / (1 - x) + a / (1 - x) ^ 2)
       (.ofScalars ℝ (a * · + b)) 0 1 := by
-  convert (one_div_one_sub_hasFPowerSeriesOnBall_zero.const_smul (c := b - a)).add
-    (one_div_one_sub_sq_hasFPowerSeriesOnBall_zero.const_smul (c := a)) using 2
+  convert!
+    (one_div_one_sub_hasFPowerSeriesOnBall_zero.const_smul (c := b - a)).add
+      (one_div_one_sub_sq_hasFPowerSeriesOnBall_zero.const_smul (c := a)) using 2
   · simp [div_eq_mul_inv]
   · ext; simp; ring
 
diff --git a/Mathlib/Analysis/Analytic/CPolynomialDef.lean b/Mathlib/Analysis/Analytic/CPolynomialDef.lean
index b70ae678d0d476..bd2d56420786ae 100644
--- a/Mathlib/Analysis/Analytic/CPolynomialDef.lean
+++ b/Mathlib/Analysis/Analytic/CPolynomialDef.lean
@@ -243,7 +243,7 @@ theorem HasFiniteFPowerSeriesOnBall.bound_zero_of_eq_zero (hf : ∀ y ∈ Metric
     exact le_top
   · intro y hy
     rw [hf (x + y)]
-    · convert hasSum_zero
+    · convert! hasSum_zero
       rw [hp, ContinuousMultilinearMap.zero_apply]
     · rwa [Metric.mem_eball, edist_eq_enorm_sub, add_comm, add_sub_cancel_right,
         ← edist_zero_right, ← Metric.mem_eball]
diff --git a/Mathlib/Analysis/Analytic/Composition.lean b/Mathlib/Analysis/Analytic/Composition.lean
index e67f66be85f999..2e5c85c799cb8a 100644
--- a/Mathlib/Analysis/Analytic/Composition.lean
+++ b/Mathlib/Analysis/Analytic/Composition.lean
@@ -121,7 +121,7 @@ theorem applyComposition_single (p : FormalMultilinearSeries 𝕜 E F) {n : ℕ}
   refine p.congr (by simp) fun i hi1 hi2 => ?_
   dsimp
   congr 1
-  convert Composition.single_embedding hn ⟨i, hi2⟩ using 1
+  convert! Composition.single_embedding hn ⟨i, hi2⟩ using 1
   obtain ⟨j_val, j_property⟩ := j
   have : j_val = 0 := le_bot_iff.1 (Nat.lt_succ_iff.1 j_property)
   rw! [this]
@@ -151,7 +151,7 @@ theorem applyComposition_update (p : FormalMultilinearSeries 𝕜 E F) {n : ℕ}
     let j' := c.invEmbedding j
     suffices B : Function.update v j z ∘ r = Function.update (v ∘ r) j' z by rw [B]
     suffices C : Function.update v (r j') z ∘ r = Function.update (v ∘ r) j' z by
-      convert C; exact (c.embedding_comp_inv j).symm
+      convert! C; exact (c.embedding_comp_inv j).symm
     exact Function.update_comp_eq_of_injective _ (c.embedding _).injective _ _
   · simp only [h, Function.update_of_ne, Ne, not_false_iff]
     let r : Fin (c.blocksFun k) → Fin n := c.embedding k
@@ -386,7 +386,7 @@ theorem comp_id (p : FormalMultilinearSeries 𝕜 E F) (x : E) : p.comp (id 𝕜
     obtain ⟨i, hi⟩ : ∃ (i : Fin b.blocks.length), b.blocks[i] = k :=
       List.get_of_mem hk
     let j : Fin b.length := ⟨i.val, b.blocks_length ▸ i.prop⟩
-    have A : 1 < b.blocksFun j := by convert lt_k
+    have A : 1 < b.blocksFun j := by convert! lt_k
     ext v
     rw [compAlongComposition_apply, ContinuousMultilinearMap.zero_apply]
     apply ContinuousMultilinearMap.map_coord_zero _ j
@@ -485,10 +485,10 @@ theorem comp_summable_nnreal (q : FormalMultilinearSeries 𝕜 F G) (p : FormalM
   refine Summable.mul_left _ ?_
   have : ∀ n : ℕ, HasSum (fun c : Composition n => (4 ^ n : ℝ≥0)⁻¹) (2 ^ (n - 1) / 4 ^ n) := by
     intro n
-    convert hasSum_fintype fun c : Composition n => (4 ^ n : ℝ≥0)⁻¹
+    convert! hasSum_fintype fun c : Composition n => (4 ^ n : ℝ≥0)⁻¹
     simp [Finset.card_univ, composition_card, div_eq_mul_inv]
   refine NNReal.summable_sigma.2 ⟨fun n => (this n).summable, (NNReal.summable_nat_add_iff 1).1 ?_⟩
-  convert (NNReal.summable_geometric (NNReal.div_lt_one_of_lt one_lt_two)).mul_left (1 / 4) using 1
+  convert! (NNReal.summable_geometric (NNReal.div_lt_one_of_lt one_lt_two)).mul_left (1 / 4) using 1
   ext1 n
   rw [(this _).tsum_eq, add_tsub_cancel_right]
   simp [field, pow_succ, mul_pow, show (4 : ℝ≥0) = 2 * 2 by norm_num]
@@ -1164,7 +1164,7 @@ theorem sizeUpTo_sizeUpTo_add (a : Composition n) (b : Composition a.length) {i
   | succ j IHj =>
     have A : j < blocksFun b ⟨i, hi⟩ := lt_trans (lt_add_one j) hj
     have B : j < length (sigmaCompositionAux a b ⟨i, (length_gather a b).symm ▸ hi⟩) := by
-      convert A; rw [← length_sigmaCompositionAux]
+      convert! A; rw [← length_sigmaCompositionAux]
     have C : sizeUpTo b i + j < sizeUpTo b (i + 1) := by
       simp only [sizeUpTo_succ b hi, add_lt_add_iff_left]
       exact A
diff --git a/Mathlib/Analysis/Analytic/Constructions.lean b/Mathlib/Analysis/Analytic/Constructions.lean
index b0d3cf783d3c00..b1b63381419934 100644
--- a/Mathlib/Analysis/Analytic/Constructions.lean
+++ b/Mathlib/Analysis/Analytic/Constructions.lean
@@ -794,8 +794,9 @@ lemma formalMultilinearSeries_geometric_apply_norm [NormOneClass A] (n : ℕ) :
 
 lemma one_le_formalMultilinearSeries_geometric_radius :
     1 ≤ (formalMultilinearSeries_geometric 𝕜 A).radius := by
-  convert formalMultilinearSeries_geometric_eq_ofScalars 𝕜 A ▸
-    FormalMultilinearSeries.inv_le_ofScalars_radius_of_tendsto A _ one_ne_zero (by simp)
+  convert!
+    formalMultilinearSeries_geometric_eq_ofScalars 𝕜 A ▸
+      FormalMultilinearSeries.inv_le_ofScalars_radius_of_tendsto A _ one_ne_zero (by simp)
   simp
 
 lemma formalMultilinearSeries_geometric_radius [NormOneClass A] :
@@ -829,7 +830,7 @@ analytic at any unit. -/
 lemma analyticAt_inverse [HasSummableGeomSeries A] (z : Aˣ) :
     AnalyticAt 𝕜 Ring.inverse (z : A) := by
   rcases subsingleton_or_nontrivial A with hA | hA
-  · convert analyticAt_const (v := (0 : A))
+  · convert! analyticAt_const (v := (0 : A))
   · let f1 : A → A := fun a ↦ a * z.inv
     let f2 : A → A := fun b ↦ (1 - b)⁻¹ʳ
     let f3 : A → A := fun c ↦ 1 - z.inv * c
@@ -862,7 +863,7 @@ lemma analyticOnNhd_inverse [HasSummableGeomSeries A] :
 variable (𝕜 𝕝) in
 lemma hasFPowerSeriesOnBall_inv_one_sub :
     HasFPowerSeriesOnBall (fun x : 𝕝 ↦ (1 - x)⁻¹) (formalMultilinearSeries_geometric 𝕜 𝕝) 0 1 := by
-  convert hasFPowerSeriesOnBall_inverse_one_sub 𝕜 𝕝
+  convert! hasFPowerSeriesOnBall_inverse_one_sub 𝕜 𝕝
   exact Ring.inverse_eq_inv'.symm
 
 variable (𝕝) in
@@ -874,7 +875,7 @@ lemma analyticAt_inv_one_sub : AnalyticAt 𝕜 (fun x : 𝕝 ↦ (1 - x)⁻¹) 0
 away from 0. -/
 @[fun_prop]
 lemma analyticAt_inv {z : 𝕝} (hz : z ≠ 0) : AnalyticAt 𝕜 Inv.inv z := by
-  convert analyticAt_inverse (𝕜 := 𝕜) (Units.mk0 _ hz)
+  convert! analyticAt_inverse (𝕜 := 𝕜) (Units.mk0 _ hz)
   exact Ring.inverse_eq_inv'.symm
 
 /-- `x⁻¹` is analytic away from zero -/
@@ -1064,7 +1065,7 @@ theorem Finset.analyticWithinAt_fun_prod {A : Type*} [NormedCommRing A] [NormedA
 theorem Finset.analyticWithinAt_prod {A : Type*} [NormedCommRing A] [NormedAlgebra 𝕜 A]
     {f : α → E → A} {c : E} {s : Set E} (N : Finset α) (h : ∀ n ∈ N, AnalyticWithinAt 𝕜 (f n) s c) :
     AnalyticWithinAt 𝕜 (∏ n ∈ N, f n) s c := by
-  convert N.analyticWithinAt_fun_prod h
+  convert! N.analyticWithinAt_fun_prod h
   simp
 
 /-- Finite products of analytic functions are analytic -/
@@ -1080,7 +1081,7 @@ theorem Finset.analyticAt_fun_prod {A : Type*} [NormedCommRing A] [NormedAlgebra
 theorem Finset.analyticAt_prod {α : Type*} {A : Type*} [NormedCommRing A] [NormedAlgebra 𝕜 A]
     {f : α → E → A} {c : E} (N : Finset α) (h : ∀ n ∈ N, AnalyticAt 𝕜 (f n) c) :
     AnalyticAt 𝕜 (∏ n ∈ N, f n) c := by
-  convert N.analyticAt_fun_prod h
+  convert! N.analyticAt_fun_prod h
   simp
 
 /-- Finite products of analytic functions are analytic -/
@@ -1181,7 +1182,7 @@ theorem HasFPowerSeriesWithinOnBall.compContinuousLinearMap
     simp only [ENNReal.div_pos_iff, ne_eq, enorm_ne_top, not_false_eq_true, and_true]
     exact pos_iff_ne_zero.mp hf.r_pos
   hasSum hy1 hy2 := by
-    convert hf.hasSum _ _
+    convert! hf.hasSum _ _
     · simp
     · simp only [Set.mem_insert_iff, add_eq_left, Set.mem_preimage, map_add] at hy1 ⊢
       rcases hy1 with (hy1 | hy1) <;> simp [hy1]
diff --git a/Mathlib/Analysis/Analytic/ConvergenceRadius.lean b/Mathlib/Analysis/Analytic/ConvergenceRadius.lean
index 06d1363bb19a8e..2419d517f62cd4 100644
--- a/Mathlib/Analysis/Analytic/ConvergenceRadius.lean
+++ b/Mathlib/Analysis/Analytic/ConvergenceRadius.lean
@@ -377,7 +377,7 @@ theorem radius_compContinuousLinearMap_linearIsometryEquiv_eq [Nontrivial E]
     (p.compContinuousLinearMap u.toLinearIsometry.toContinuousLinearMap).radius = p.radius := by
   refine le_antisymm ?_ <| le_radius_compContinuousLinearMap _ _
   have _ : Nontrivial F := u.symm.toEquiv.nontrivial
-  convert radius_compContinuousLinearMap_le p u.toContinuousLinearEquiv
+  convert! radius_compContinuousLinearMap_le p u.toContinuousLinearEquiv
   have : u.toContinuousLinearEquiv.symm.toContinuousLinearMap =
     u.symm.toLinearIsometry.toContinuousLinearMap := rfl
   simp [this]
diff --git a/Mathlib/Analysis/Analytic/Inverse.lean b/Mathlib/Analysis/Analytic/Inverse.lean
index 83e61eff0ea51c..21921fa95cb22d 100644
--- a/Mathlib/Analysis/Analytic/Inverse.lean
+++ b/Mathlib/Analysis/Analytic/Inverse.lean
@@ -135,13 +135,12 @@ theorem leftInv_comp (p : FormalMultilinearSeries 𝕜 E F) (i : E ≃L[𝕜] F)
             (p.leftInv i x c.length) (p.applyComposition c v) := by
       simp only [leftInv, ContinuousMultilinearMap.neg_apply, neg_inj,
         ContinuousMultilinearMap.sum_apply]
-      convert
-        (sum_toFinset_eq_subtype
-          (fun c : Composition (n + 2) => c.length < n + 2)
-          (fun c : Composition (n + 2) =>
-          (ContinuousMultilinearMap.compAlongComposition
-            (p.compContinuousLinearMap (i.symm : F →L[𝕜] E)) c (p.leftInv i x c.length))
-            fun j : Fin (n + 2) => p 1 fun _ : Fin 1 => v j)).symm.trans
+      convert!
+        (sum_toFinset_eq_subtype (fun c : Composition (n + 2) => c.length < n + 2)
+              (fun c : Composition (n + 2) =>
+                (ContinuousMultilinearMap.compAlongComposition
+                    (p.compContinuousLinearMap (i.symm : F →L[𝕜] E)) c (p.leftInv i x c.length))
+                  fun j : Fin (n + 2) => p 1 fun _ : Fin 1 => v j)).symm.trans
           _
       simp only [compContinuousLinearMap_applyComposition,
         ContinuousMultilinearMap.compAlongComposition_apply]
@@ -642,7 +641,7 @@ lemma HasFPowerSeriesAt.eventually_hasSum_of_comp {f : E → F} {g : F → G}
         (partialSum_continuous q a).continuousAt
       apply this.tendsto.comp
       apply Tendsto.sub h'y
-      convert tendsto_const_nhds
+      convert! tendsto_const_nhds
       exact (HasFPowerSeriesAt.coeff_zero hf fun _ ↦ 0).symm
     apply u_closed.mem_of_tendsto this
     filter_upwards [Ici_mem_atTop b₀] with b hb using vu (hab _ _ ha hb)
diff --git a/Mathlib/Analysis/Analytic/IsolatedZeros.lean b/Mathlib/Analysis/Analytic/IsolatedZeros.lean
index 1d2c07aa36a4bf..5c111cc646b8e4 100644
--- a/Mathlib/Analysis/Analytic/IsolatedZeros.lean
+++ b/Mathlib/Analysis/Analytic/IsolatedZeros.lean
@@ -52,7 +52,7 @@ namespace HasSum
 variable {a : ℕ → E}
 
 theorem hasSum_at_zero (a : ℕ → E) : HasSum (fun n => (0 : 𝕜) ^ n • a n) (a 0) := by
-  convert hasSum_single (α := E) 0 fun b h ↦ _ <;> simp [*]
+  convert! hasSum_single (α := E) 0 fun b h ↦ _ <;> simp [*]
 
 theorem exists_hasSum_smul_of_apply_eq_zero (hs : HasSum (fun m => z ^ m • a m) s)
     (ha : ∀ k < n, a k = 0) : ∃ t : E, z ^ n • t = s ∧ HasSum (fun m => z ^ m • a (m + n)) t := by
@@ -66,7 +66,7 @@ theorem exists_hasSum_smul_of_apply_eq_zero (hs : HasSum (fun m => z ^ m • a m
       Finset.sum_eq_zero fun k hk => by simp [ha k (Finset.mem_range.mp hk)]
     have h2 : HasSum (fun m => z ^ (m + n) • a (m + n)) s := by
       simpa [h1] using (hasSum_nat_add_iff' n).mpr hs
-    convert h2.const_smul (z⁻¹ ^ n) using 2 with x
+    convert! h2.const_smul (z⁻¹ ^ n) using 2 with x
     · match_scalars
       simp [field, pow_add]
     · simp only [inv_pow]
@@ -82,7 +82,7 @@ theorem has_fpower_series_dslope_fslope (hp : HasFPowerSeriesAt f p z₀) :
   simp only [hasFPowerSeriesAt_iff, coeff_fslope] at hp ⊢
   refine hp.mono fun x hx => ?_
   by_cases h : x = 0
-  · convert hasSum_single (α := E) 0 _ <;> intros <;> simp [*]
+  · convert! hasSum_single (α := E) 0 _ <;> intros <;> simp [*]
   · have hxx : ∀ n : ℕ, x⁻¹ * x ^ (n + 1) = x ^ n := fun n => by simp [field, _root_.pow_succ]
     suffices HasSum (fun n => x⁻¹ • x ^ (n + 1) • p.coeff (n + 1)) (x⁻¹ • (f (z₀ + x) - f z₀)) by
       simpa [dslope, slope, h, smul_smul, hxx] using this
diff --git a/Mathlib/Analysis/Analytic/OfScalars.lean b/Mathlib/Analysis/Analytic/OfScalars.lean
index 8f8ae97debe2ae..47d7b0d043060d 100644
--- a/Mathlib/Analysis/Analytic/OfScalars.lean
+++ b/Mathlib/Analysis/Analytic/OfScalars.lean
@@ -238,9 +238,9 @@ theorem ofScalars_radius_eq_of_tendsto [NormOneClass E] {r : NNReal} (hr : r ≠
     (hc : Tendsto (fun n ↦ ‖c n‖ / ‖c n.succ‖) atTop (𝓝 r)) :
       (ofScalars E c).radius = ofNNReal r := by
   suffices Tendsto (fun n ↦ ‖c n.succ‖ / ‖c n‖) atTop (𝓝 r⁻¹) by
-    convert ofScalars_radius_eq_inv_of_tendsto E c (inv_ne_zero hr) this
+    convert! ofScalars_radius_eq_inv_of_tendsto E c (inv_ne_zero hr) this
     simp
-  convert hc.inv₀ (NNReal.coe_ne_zero.mpr hr) using 1
+  convert! hc.inv₀ (NNReal.coe_ne_zero.mpr hr) using 1
   simp
 
 /-- The ratio test stating that if `‖c n.succ‖ / ‖c n‖` tends to zero, the radius is unbounded.
@@ -280,7 +280,7 @@ theorem ofScalars_radius_eq_zero_of_tendsto [NormOneClass E]
   · filter_upwards [hc.eventually_ge_atTop (2 * r⁻¹), eventually_ne_atTop 0] with n hc hn
     simp only [ofScalars_norm, norm_mul, norm_norm, norm_pow, NNReal.norm_eq]
     rw [mul_comm ‖c n‖, ← mul_assoc, ← div_le_div_iff₀, mul_div_assoc]
-    · convert hc
+    · convert! hc
       rw [pow_succ, div_mul_cancel_left₀, NNReal.coe_inv]
       aesop
     · simp_all
@@ -317,7 +317,7 @@ theorem ofScalars_radius_eq_inv_of_tendsto_ENNReal [NormOneClass E] {r : ℝ≥0
     simp_all
   · have hr' := toReal_ne_zero.mp hr.ne.symm
     have hr'' := toNNReal_ne_zero.mpr hr' -- this result could go in ENNReal
-    convert ofScalars_radius_eq_inv_of_tendsto E c hr'' ?_
+    convert! ofScalars_radius_eq_inv_of_tendsto E c hr'' ?_
     · simp [ENNReal.coe_inv hr'', ENNReal.coe_toNNReal (toReal_ne_zero.mp hr.ne.symm).2]
     · simp_rw [ENNReal.coe_toNNReal_eq_toReal]
       refine Tendsto.congr' ?_ <| (tendsto_toReal hr'.2).comp hc'
diff --git a/Mathlib/Analysis/Analytic/Order.lean b/Mathlib/Analysis/Analytic/Order.lean
index a740430c245744..00521c72816ac2 100644
--- a/Mathlib/Analysis/Analytic/Order.lean
+++ b/Mathlib/Analysis/Analytic/Order.lean
@@ -385,7 +385,7 @@ lemma AnalyticAt.exists_eventuallyEq_sum_add_pow_mul [CharZero 𝕜] [CompleteSp
       (fun z : 𝕜 ↦ ∑ i ∈ .range n, (z ^ i / i.factorial) • iteratedDeriv i f 0) 0 := by
     refine Finset.analyticAt_fun_sum _ fun i hi ↦ ?_
     fun_prop
-  convert (natCast_le_analyticOrderAt (hf.fun_sub this)).mp ?_
+  convert! (natCast_le_analyticOrderAt (hf.fun_sub this)).mp ?_
   · simp
   · rw [natCast_le_analyticOrderAt_iff_iteratedDeriv_eq_zero (hf.fun_sub this)]
     intro i hi
diff --git a/Mathlib/Analysis/Analytic/Polynomial.lean b/Mathlib/Analysis/Analytic/Polynomial.lean
index e48dc758bfe01c..3636136f585bec 100644
--- a/Mathlib/Analysis/Analytic/Polynomial.lean
+++ b/Mathlib/Analysis/Analytic/Polynomial.lean
@@ -32,7 +32,7 @@ theorem AnalyticWithinAt.aeval_polynomial (hf : AnalyticWithinAt 𝕜 f s z) (p
   refine p.induction_on (fun k ↦ ?_) (fun p q hp hq ↦ ?_) fun p i hp ↦ ?_
   · simp_rw [aeval_C]; apply analyticWithinAt_const
   · simp_rw [aeval_add]; exact hp.add hq
-  · convert hp.mul hf
+  · convert! hp.mul hf
     simp_rw [pow_succ, aeval_mul, ← mul_assoc, aeval_X]
 
 theorem AnalyticAt.aeval_polynomial (hf : AnalyticAt 𝕜 f z) (p : A[X]) :
diff --git a/Mathlib/Analysis/Analytic/Uniqueness.lean b/Mathlib/Analysis/Analytic/Uniqueness.lean
index ff9392fefd0bb9..4b2d69f24953b6 100644
--- a/Mathlib/Analysis/Analytic/Uniqueness.lean
+++ b/Mathlib/Analysis/Analytic/Uniqueness.lean
@@ -167,7 +167,7 @@ theorem eqOn_zero_of_preconnected_of_eventuallyEq_zero_aux [CompleteSpace F] {f
   have A : HasSum (fun n : ℕ => q n fun _ : Fin n => z - y) (f z) := has_series.hasSum_sub hz
   have B : HasSum (fun n : ℕ => q n fun _ : Fin n => z - y) 0 := by
     have : HasFPowerSeriesAt 0 q y := has_series.hasFPowerSeriesAt.congr yu
-    convert hasSum_zero (α := F) using 1
+    convert! hasSum_zero (α := F) using 1
     ext n
     exact this.apply_eq_zero n _
   exact HasSum.unique A B
diff --git a/Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean b/Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean
index 8143012f41d696..efee98d87146b4 100644
--- a/Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean
+++ b/Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean
@@ -76,7 +76,7 @@ nonrec theorem IsEquivalent.isBigO (h : u ~[l] v) : u =O[l] v :=
   (IsBigO.congr_of_sub h.isBigO.symm).mp (isBigO_refl _ _)
 
 theorem IsEquivalent.isBigO_symm (h : u ~[l] v) : v =O[l] u := by
-  convert h.isLittleO.right_isBigO_add
+  convert! h.isLittleO.right_isBigO_add
   simp
 
 theorem IsEquivalent.isTheta (h : u ~[l] v) : u =Θ[l] v :=
@@ -167,7 +167,7 @@ theorem IsLittleO.isEquivalent (huv : (u - v) =o[l] v) : u ~[l] v := huv
 
 theorem IsEquivalent.neg (huv : u ~[l] v) : (fun x ↦ -u x) ~[l] fun x ↦ -v x := by
   rw [IsEquivalent]
-  convert huv.isLittleO.neg_left.neg_right
+  convert! huv.isLittleO.neg_left.neg_right
   simp [neg_add_eq_sub]
 
 end NormedAddCommGroup
@@ -184,10 +184,10 @@ theorem isEquivalent_iff_exists_eq_mul :
   constructor <;> rintro ⟨φ, hφ, h⟩ <;> [refine ⟨φ + 1, ?_, ?_⟩; refine ⟨φ - 1, ?_, ?_⟩]
   · conv in 𝓝 _ => rw [← zero_add (1 : β)]
     exact hφ.add tendsto_const_nhds
-  · convert h.fun_add (EventuallyEq.refl l v) <;> simp [add_mul]
+  · convert! h.fun_add (EventuallyEq.refl l v) <;> simp [add_mul]
   · conv in 𝓝 _ => rw [← sub_self (1 : β)]
     exact hφ.sub tendsto_const_nhds
-  · convert h.fun_sub (EventuallyEq.refl l v); simp [sub_mul]
+  · convert! h.fun_sub (EventuallyEq.refl l v); simp [sub_mul]
 
 theorem IsEquivalent.exists_eq_mul (huv : u ~[l] v) :
     ∃ (φ : α → β) (_ : Tendsto φ l (𝓝 1)), u =ᶠ[l] φ * v :=
@@ -213,7 +213,7 @@ theorem isEquivalent_iff_tendsto_one (hz : ∀ᶠ x in l, v x ≠ 0) :
     simp only [Pi.sub_apply, sub_div] at this
     have key : Tendsto (fun x ↦ v x / v x) l (𝓝 1) :=
       (tendsto_congr' <| hz.mono fun x hnz ↦ @div_self _ _ (v x) hnz).mpr tendsto_const_nhds
-    convert this.add key
+    convert! this.add key
     · simp
     · simp
   · exact isEquivalent_of_tendsto_one
@@ -227,8 +227,9 @@ theorem IsEquivalent.smul {α E 𝕜 : Type*} [NormedField 𝕜] [NormedAddCommG
     (fun x ↦ a x • u x) ~[l] fun x ↦ b x • v x := by
   rcases hab.exists_eq_mul with ⟨φ, hφ, habφ⟩
   have : ((fun x ↦ a x • u x) - (fun x ↦ b x • v x)) =ᶠ[l] fun x ↦ b x • (φ x • u x - v x) := by
-    convert (habφ.comp₂ (· • ·) <| EventuallyEq.refl _ u).fun_sub
-      (EventuallyEq.refl _ fun x ↦ b x • v x) using 1
+    convert!
+      (habφ.comp₂ (· • ·) <| EventuallyEq.refl _ u).fun_sub
+        (EventuallyEq.refl _ fun x ↦ b x • v x) using 1
     ext
     rw [Pi.mul_apply, mul_comm, mul_smul, ← smul_sub]
   refine (isLittleO_congr this.symm <| EventuallyEq.rfl).mp ((isBigO_refl b l).smul_isLittleO ?_)
@@ -286,7 +287,7 @@ protected theorem IsEquivalent.inv (huv : u ~[l] v) : u⁻¹ ~[l] v⁻¹ := by
   rcases huv with ⟨φ, hφ, h⟩
   rw [← inv_one]
   refine ⟨fun x ↦ (φ x)⁻¹, Tendsto.inv₀ hφ (by simp), ?_⟩
-  convert h.fun_inv
+  convert! h.fun_inv
   simp [mul_comm]
 
 protected theorem IsEquivalent.div (htu : t ~[l] u) (hvw : v ~[l] w) :
@@ -321,7 +322,7 @@ theorem IsEquivalent.tendsto_atTop_iff [OrderTopology β] (huv : u ~[l] v) :
 
 theorem IsEquivalent.tendsto_atBot [OrderTopology β] (huv : u ~[l] v) (hu : Tendsto u l atBot) :
     Tendsto v l atBot := by
-  convert tendsto_neg_atTop_atBot.comp (huv.neg.tendsto_atTop <| tendsto_neg_atBot_atTop.comp hu)
+  convert! tendsto_neg_atTop_atBot.comp (huv.neg.tendsto_atTop <| tendsto_neg_atBot_atTop.comp hu)
   ext
   simp
 
diff --git a/Mathlib/Analysis/Asymptotics/Defs.lean b/Mathlib/Analysis/Asymptotics/Defs.lean
index 1b97e119250e7b..51fddaaf99e009 100644
--- a/Mathlib/Analysis/Asymptotics/Defs.lean
+++ b/Mathlib/Analysis/Asymptotics/Defs.lean
@@ -1312,7 +1312,7 @@ theorem IsBigOWith.mul {f₁ f₂ : α → R} {g₁ g₂ : α → S} {c₁ c₂
   simp only [IsBigOWith_def] at *
   filter_upwards [h₁, h₂] with _ hx₁ hx₂
   apply le_trans (norm_mul_le _ _)
-  convert mul_le_mul hx₁ hx₂ (norm_nonneg _) (le_trans (norm_nonneg _) hx₁) using 1
+  convert! mul_le_mul hx₁ hx₂ (norm_nonneg _) (le_trans (norm_nonneg _) hx₁) using 1
   rw [norm_mul, mul_mul_mul_comm]
 
 theorem IsBigO.mul {f₁ f₂ : α → R} {g₁ g₂ : α → S} (h₁ : f₁ =O[l] g₁) (h₂ : f₂ =O[l] g₂) :
@@ -1375,7 +1375,7 @@ theorem IsLittleO.pow {f : α → R} {g : α → S} (h : f =o[l] g) {n : ℕ} (h
   obtain ⟨n, rfl⟩ := Nat.exists_eq_succ_of_ne_zero hn.ne'; clear hn
   induction n with
   | zero => simpa only [pow_one]
-  | succ n ihn => convert ihn.mul h <;> simp [pow_succ]
+  | succ n ihn => convert! ihn.mul h <;> simp [pow_succ]
 
 theorem IsLittleO.of_pow [NormOneClass S] {f : α → S} {g : α → R} {n : ℕ}
     (h : (f ^ n) =o[l] (g ^ n)) (hn : n ≠ 0) : f =o[l] g :=
diff --git a/Mathlib/Analysis/Asymptotics/Lemmas.lean b/Mathlib/Analysis/Asymptotics/Lemmas.lean
index 788c0d0b079715..483261194923fb 100644
--- a/Mathlib/Analysis/Asymptotics/Lemmas.lean
+++ b/Mathlib/Analysis/Asymptotics/Lemmas.lean
@@ -279,7 +279,7 @@ theorem IsBigOWith.smul (h₁ : IsBigOWith c l k₁ k₂) (h₂ : IsBigOWith c'
   simp only [IsBigOWith_def] at *
   filter_upwards [h₁, h₂] with _ hx₁ hx₂
   apply le_trans (norm_smul_le _ _)
-  convert mul_le_mul hx₁ hx₂ (norm_nonneg _) (le_trans (norm_nonneg _) hx₁) using 1
+  convert! mul_le_mul hx₁ hx₂ (norm_nonneg _) (le_trans (norm_nonneg _) hx₁) using 1
   rw [norm_smul, mul_mul_mul_comm]
 
 theorem IsBigO.smul (h₁ : k₁ =O[l] k₂) (h₂ : f' =O[l] g') :
@@ -437,13 +437,13 @@ theorem IsLittleO.of_tendsto_div_atTop (h : Tendsto (fun x ↦ g x / f x) l atTo
     intro x h h0
     simp only [h0, zero_div] at h
     grind
-  · convert Tendsto.comp tendsto_inv_atTop_zero h
+  · convert! Tendsto.comp tendsto_inv_atTop_zero h
     simp
 
 theorem IsLittleO.of_tendsto_div_atBot (h : Tendsto (fun x ↦ g x / f x) l atBot) : f =o[l] g := by
   refine IsLittleO.of_neg_left (IsLittleO.of_tendsto_div_atTop ?_)
   rw [← tendsto_neg_atBot_iff]
-  convert h using 2
+  convert! h using 2
   simp [div_neg_eq_neg_div]
 
 end div_tendsto_infty
@@ -570,7 +570,7 @@ theorem isLittleO_norm_pow_norm_pow {m n : ℕ} (h : m < n) :
   (isLittleO_pow_pow h).comp_tendsto tendsto_norm_zero
 
 theorem isLittleO_pow_id {n : ℕ} (h : 1 < n) : (fun x : 𝕜 => x ^ n) =o[𝓝 0] fun x => x := by
-  convert isLittleO_pow_pow h (𝕜 := 𝕜)
+  convert! isLittleO_pow_pow h (𝕜 := 𝕜)
   simp only [pow_one]
 
 theorem isLittleO_norm_pow_id {n : ℕ} (h : 1 < n) :
diff --git a/Mathlib/Analysis/Asymptotics/SpecificAsymptotics.lean b/Mathlib/Analysis/Asymptotics/SpecificAsymptotics.lean
index 976ec385bd3ad3..9bf8b0f69de378 100644
--- a/Mathlib/Analysis/Asymptotics/SpecificAsymptotics.lean
+++ b/Mathlib/Analysis/Asymptotics/SpecificAsymptotics.lean
@@ -110,7 +110,7 @@ theorem Asymptotics.IsBigO.trans_tendsto_norm_atTop {α : Type*} {u v : α → 
     Tendsto (fun x => ‖v x‖) l atTop := by
   rcases huv.exists_pos with ⟨c, hc, hcuv⟩
   rw [IsBigOWith] at hcuv
-  convert Tendsto.atTop_div_const hc (tendsto_atTop_mono' l hcuv hu)
+  convert! Tendsto.atTop_div_const hc (tendsto_atTop_mono' l hcuv hu)
   rw [mul_div_cancel_left₀ _ hc.ne.symm]
 
 end NormedLinearOrderedField
diff --git a/Mathlib/Analysis/Asymptotics/Theta.lean b/Mathlib/Analysis/Asymptotics/Theta.lean
index ef28392c865f30..9b2bcb74a399f9 100644
--- a/Mathlib/Analysis/Asymptotics/Theta.lean
+++ b/Mathlib/Analysis/Asymptotics/Theta.lean
@@ -284,7 +284,7 @@ theorem isTheta_of_div_tendsto_nhds_ne_zero {c : 𝕜} {f g : α → 𝕜}
     f =Θ[l] g := by
   refine ⟨isBigO_of_div_tendsto_nhds_of_ne_zero h hc,
     isBigO_of_div_tendsto_nhds_of_ne_zero ?_ (inv_ne_zero hc)⟩
-  convert h.inv₀ hc using 1
+  convert! h.inv₀ hc using 1
   ext
   simp
 
diff --git a/Mathlib/Analysis/BoxIntegral/Basic.lean b/Mathlib/Analysis/BoxIntegral/Basic.lean
index 907f94655b6723..9f8867a2600227 100644
--- a/Mathlib/Analysis/BoxIntegral/Basic.lean
+++ b/Mathlib/Analysis/BoxIntegral/Basic.lean
@@ -483,7 +483,10 @@ theorem to_subbox_aux (h : Integrable I l f vol) (hJ : J ≤ I) :
       Tendsto (integralSum f vol) (l.toFilteriUnion I (Prepartition.single I J hJ)) (𝓝 y) := by
   refine (cauchy_map_iff_exists_tendsto.1
     (h.cauchy_map_integralSum_toFilteriUnion (.single I J hJ))).imp fun y hy ↦ ⟨?_, hy⟩
-  convert hy.comp (l.tendsto_embedBox_toFilteriUnion_top hJ) -- faster than `exact` here
+  convert!
+    hy.comp
+      (l.tendsto_embedBox_toFilteriUnion_top hJ) -- faster than `exact` here
+         -- faster than `exact` here
 
 /-- If `f` is integrable on a box `I`, then it is integrable on any subbox of `I`. -/
 theorem to_subbox (h : Integrable I l f vol) (hJ : J ≤ I) : Integrable J l f vol :=
@@ -805,7 +808,7 @@ theorem HasIntegral.of_bRiemann_eq_false_of_forall_isLittleO (hl : l.bRiemann =
       rw [Finset.mem_filter] at hJ; obtain ⟨hJ, hJs⟩ := hJ
       refine Hδ₁ c _ ⟨π.tag_mem_Icc _, hJs⟩ _ (hεs0 _) _ (π.le_of_mem' _ hJ) ?_
         (hπδ.2 hlH J hJ) fun hD => (Finset.le_sup hJ).trans (hπδ.3 hD)
-      convert hπδ.1 J hJ using 3; exact (if_pos hJs).symm
+      convert! hπδ.1 J hJ using 3; exact (if_pos hJs).symm
     refine (dist_sum_sum_le_of_le _ this).trans ?_
     rw [sum_comp]
     refine (sum_le_sum ?_).trans (hεs _ ?_)
@@ -825,7 +828,7 @@ theorem HasIntegral.of_bRiemann_eq_false_of_forall_isLittleO (hl : l.bRiemann =
       rw [Finset.mem_filter] at hJ; obtain ⟨hJ, hJs⟩ := hJ
       refine Hδ₂ c _ ⟨π.tag_mem_Icc _, hJs⟩ _ ε'0 _ (π.le_of_mem' _ hJ) ?_ (fun hH => hπδ.2 hH J hJ)
         fun hD => (Finset.le_sup hJ).trans (hπδ.3 hD)
-      convert hπδ.1 J hJ using 3; exact (if_neg hJs).symm
+      convert! hπδ.1 J hJ using 3; exact (if_neg hJs).symm
     _ ≤ ∑ J ∈ π.boxes, ε' * B J := by
       gcongr
       · exact fun _ _ _ ↦ mul_nonneg ε'0.le (hB0 _)
diff --git a/Mathlib/Analysis/BoxIntegral/Integrability.lean b/Mathlib/Analysis/BoxIntegral/Integrability.lean
index 9f724990366c46..a7e944a69d5371 100644
--- a/Mathlib/Analysis/BoxIntegral/Integrability.lean
+++ b/Mathlib/Analysis/BoxIntegral/Integrability.lean
@@ -274,7 +274,7 @@ theorem IntegrableOn.hasBoxIntegral [CompleteSpace E] {f : (ι → ℝ) → E} {
     have :
         l.MemBaseSet I c ((hfi' n).convergenceR (δ n) c) (π.filter fun J => Nx (π.tag J) = n) :=
       (hπ.filter _).mono' _ le_rfl le_rfl fun J hJ => (hrn J hJ).le
-    convert (hfi' n).dist_integralSum_sum_integral_le_of_memBaseSet (δ0 _) this using 2
+    convert! (hfi' n).dist_integralSum_sum_integral_le_of_memBaseSet (δ0 _) this using 2
     · refine sum_congr rfl fun J hJ => ?_
       simp [hNxn J hJ]
     · refine sum_congr rfl fun J hJ => ?_
@@ -305,7 +305,7 @@ theorem ContinuousOn.hasBoxIntegral [CompleteSpace E] {f : (ι → ℝ) → E} (
     (l : IntegrationParams) :
     HasIntegral.{u, v, v} I l f μ.toBoxAdditive.toSMul (∫ x in I, f x ∂μ) := by
   obtain ⟨y, hy⟩ := BoxIntegral.integrable_of_continuousOn l hc μ
-  convert hy
+  convert! hy
   have : IntegrableOn f I μ :=
     IntegrableOn.mono_set (hc.integrableOn_compact I.isCompact_Icc) Box.coe_subset_Icc
   exact HasIntegral.unique (IntegrableOn.hasBoxIntegral this ⊥ rfl) (HasIntegral.mono hy bot_le)
@@ -317,7 +317,7 @@ theorem AEContinuous.hasBoxIntegral [CompleteSpace E] {f : (ι → ℝ) → E} (
     (hc : ∀ᵐ x ∂μ, ContinuousAt f x) (l : IntegrationParams) :
     HasIntegral.{u, v, v} I l f μ.toBoxAdditive.toSMul (∫ x in I, f x ∂μ) := by
   obtain ⟨y, hy⟩ := integrable_of_bounded_and_ae_continuous l hb μ hc
-  convert hy
+  convert! hy
   refine HasIntegral.unique (IntegrableOn.hasBoxIntegral ?_ ⊥ rfl) (HasIntegral.mono hy bot_le)
   constructor
   · let v := {x : (ι → ℝ) | ContinuousAt f x}
diff --git a/Mathlib/Analysis/BoxIntegral/Partition/Basic.lean b/Mathlib/Analysis/BoxIntegral/Partition/Basic.lean
index 3ae1a413b276e3..e88622d3d35486 100644
--- a/Mathlib/Analysis/BoxIntegral/Partition/Basic.lean
+++ b/Mathlib/Analysis/BoxIntegral/Partition/Basic.lean
@@ -198,7 +198,7 @@ theorem iUnion_def' : π.iUnion = ⋃ J ∈ π.boxes, ↑J := rfl
 
 @[simp]
 theorem mem_iUnion : x ∈ π.iUnion ↔ ∃ J ∈ π, x ∈ J := by
-  convert Set.mem_iUnion₂
+  convert! Set.mem_iUnion₂
   rw [Box.mem_coe, exists_prop]
 
 @[simp]
@@ -329,7 +329,7 @@ theorem biUnionIndex_le (πi : ∀ J, Prepartition J) (J : Box ι) : π.biUnionI
   · rw [biUnionIndex, dif_neg hJ]
 
 theorem mem_biUnionIndex (hJ : J ∈ π.biUnion πi) : J ∈ πi (π.biUnionIndex πi J) := by
-  convert (π.mem_biUnion.1 hJ).choose_spec.2 <;> exact dif_pos hJ
+  convert! (π.mem_biUnion.1 hJ).choose_spec.2 <;> exact dif_pos hJ
 
 theorem le_biUnionIndex (hJ : J ∈ π.biUnion πi) : J ≤ π.biUnionIndex πi J :=
   le_of_mem _ (π.mem_biUnionIndex hJ)
@@ -548,11 +548,11 @@ theorem filter_true : (π.filter fun _ => True) = π :=
 theorem iUnion_filter_not (π : Prepartition I) (p : Box ι → Prop) :
     (π.filter fun J => ¬p J).iUnion = π.iUnion \ (π.filter p).iUnion := by
   simp only [Prepartition.iUnion]
-  convert
+  convert!
     (@Set.biUnion_diff_biUnion_eq (ι → ℝ) (Box ι) π.boxes (π.filter p).boxes (↑) _).symm using 4
   · simp +contextual
   · rw [Set.PairwiseDisjoint]
-    convert π.pairwiseDisjoint
+    convert! π.pairwiseDisjoint
     rw [Set.union_eq_left, filter_boxes, coe_filter]
     exact fun _ ⟨h, _⟩ => h
 
@@ -560,7 +560,7 @@ open scoped Classical in
 theorem sum_fiberwise {α M} [AddCommMonoid M] (π : Prepartition I) (f : Box ι → α) (g : Box ι → M) :
     (∑ y ∈ π.boxes.image f, ∑ J ∈ (π.filter fun J => f J = y).boxes, g J) =
       ∑ J ∈ π.boxes, g J := by
-  convert sum_fiberwise_of_maps_to (fun _ => Finset.mem_image_of_mem f) g
+  convert! sum_fiberwise_of_maps_to (fun _ => Finset.mem_image_of_mem f) g
 
 open scoped Classical in
 /-- Union of two disjoint prepartitions. -/
diff --git a/Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean b/Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean
index 46b58f40fd0212..84e1f0310b0e78 100644
--- a/Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean
+++ b/Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean
@@ -72,7 +72,7 @@ theorem iUnion_toPrepartition : π.toPrepartition.iUnion = π.iUnion := rfl
 
 @[simp]
 theorem mem_iUnion : x ∈ π.iUnion ↔ ∃ J ∈ π, x ∈ J := by
-  convert Set.mem_iUnion₂
+  convert! Set.mem_iUnion₂
   rw [Box.mem_coe, mem_toPrepartition, exists_prop]
 
 theorem subset_iUnion (h : J ∈ π) : ↑J ⊆ π.iUnion :=
diff --git a/Mathlib/Analysis/BoxIntegral/UnitPartition.lean b/Mathlib/Analysis/BoxIntegral/UnitPartition.lean
index bafcb5e7e5ff80..b8f218c8f6b7d6 100644
--- a/Mathlib/Analysis/BoxIntegral/UnitPartition.lean
+++ b/Mathlib/Analysis/BoxIntegral/UnitPartition.lean
@@ -458,7 +458,7 @@ theorem _root_.tendsto_card_div_pow_atTop_volume (hs₁ : IsBounded s)
     (hs₂ : MeasurableSet s) (hs₃ : volume (frontier s) = 0) :
     Tendsto (fun n : ℕ ↦ (Nat.card ↑(s ∩ (n : ℝ)⁻¹ • L) : ℝ) / n ^ card ι)
       atTop (𝓝 (volume.real s)) := by
-  convert tendsto_tsum_div_pow_atTop_integral s (fun _ ↦ 1) continuous_const hs₁ hs₂ hs₃
+  convert! tendsto_tsum_div_pow_atTop_integral s (fun _ ↦ 1) continuous_const hs₁ hs₂ hs₃
   · rw [tsum_const, nsmul_eq_mul, mul_one, Nat.cast_inj]
   · rw [setIntegral_const, smul_eq_mul, mul_one]
 
diff --git a/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Continuity.lean b/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Continuity.lean
index ac8de4fd93f24c..d41724ad722113 100644
--- a/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Continuity.lean
+++ b/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Continuity.lean
@@ -236,8 +236,10 @@ theorem continuousOn_cfc {s : Set 𝕜} (hs : IsCompact s) (f : 𝕜 → 𝕜)
     (hf : ContinuousOn f s := by cfc_cont_tac) :
     ContinuousOn (cfc f) {a | p a ∧ spectrum 𝕜 a ⊆ s} :=
   continuousOn_iff_continuous_restrict.mpr <| by
-    convert continuous_cfcHomSuperset_left hs ⟨_, hf.restrict⟩
-      ((↑) : {a | p a ∧ spectrum 𝕜 a ⊆ s} → A) continuous_subtype_val (fun x ↦ x.2.2) with x
+    convert!
+      continuous_cfcHomSuperset_left hs ⟨_, hf.restrict⟩ ((↑) : {a | p a ∧ spectrum 𝕜 a ⊆ s} → A)
+        continuous_subtype_val (fun x ↦ x.2.2) with
+      x
     rw [cfcHomSuperset_apply, Set.restrict_apply, cfc_apply _ _ x.2.1 (hf.mono x.2.2)]
     congr!
 
@@ -736,11 +738,13 @@ theorem continuousOn_cfcₙ {s : Set 𝕜} (hs : IsCompact s) (f : 𝕜 → 𝕜
     ContinuousOn (cfcₙ f · : A → A) {a | p a ∧ quasispectrum 𝕜 a ⊆ s} := by
   by_cases hs0 : 0 ∈ s
   · rw [continuousOn_iff_continuous_restrict]
-    convert continuous_cfcₙHomSuperset_left hs (hs0 := ⟨hs0⟩) ⟨⟨_, hf.restrict⟩, hf0⟩
-      (X := {a : A | p a ∧ quasispectrum 𝕜 a ⊆ s}) continuous_subtype_val (fun x ↦ x.2.2) with x
+    convert!
+      continuous_cfcₙHomSuperset_left hs (hs0 := ⟨hs0⟩) ⟨⟨_, hf.restrict⟩, hf0⟩ (X :=
+        {a : A | p a ∧ quasispectrum 𝕜 a ⊆ s}) continuous_subtype_val (fun x ↦ x.2.2) with
+      x
     rw [cfcₙHomSuperset_apply, Set.restrict_apply, cfcₙ_apply _ _ (hf.mono x.2.2) hf0 x.2.1]
     congr!
-  · convert continuousOn_empty _
+  · convert! continuousOn_empty _
     rw [Set.eq_empty_iff_forall_notMem]
     exact fun a ha ↦ hs0 <| ha.2 <| quasispectrum.zero_mem 𝕜 a
 
diff --git a/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Instances.lean b/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Instances.lean
index f7597a30199e1b..15ab3086848860 100644
--- a/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Instances.lean
+++ b/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Instances.lean
@@ -118,7 +118,7 @@ lemma cfcₙAux_mem_range_inr (f : C(σₙ 𝕜 a, 𝕜)₀) :
     rw [SetLike.mem_coe, NonUnitalStarSubalgebra.mem_comap, cfcₙAux_id hp₁ a ha]
     exact ⟨a, rfl⟩
   · simp only [NonUnitalStarAlgHom.coe_range]
-    convert IsClosed.preimage (Unitization.continuous_fst (𝕜 := 𝕜)) isClosed_singleton
+    convert! IsClosed.preimage (Unitization.continuous_fst (𝕜 := 𝕜)) isClosed_singleton
     aesop
 
 variable [CStarRing A]
@@ -170,7 +170,7 @@ theorem RCLike.nonUnitalContinuousFunctionalCalculusIsClosedEmbedding :
   toNonUnitalContinuousFunctionalCalculus := RCLike.nonUnitalContinuousFunctionalCalculus hp₁
   isClosedEmbedding a ha := by
     apply isometry_inr (𝕜 := 𝕜) (A := A) |>.isClosedEmbedding |>.of_comp_iff.mp
-    convert isClosedEmbedding_cfcₙAux hp₁ a ha
+    convert! isClosedEmbedding_cfcₙAux hp₁ a ha
     congrm (⇑$(inrNonUnitalStarAlgHom_comp_cfcₙHom_eq_cfcₙAux hp₁ a ha))
 
 end RCLike
diff --git a/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Isometric.lean b/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Isometric.lean
index 85ebd14b8493a3..55669d08594c0a 100644
--- a/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Isometric.lean
+++ b/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Isometric.lean
@@ -74,7 +74,7 @@ lemma IsGreatest.norm_cfc [Nontrivial A] (f : 𝕜 → 𝕜) (a : A)
     |>.image_of_continuousOn hf.norm |>.exists_isGreatest <|
     (ContinuousFunctionalCalculus.spectrum_nonempty a ha).image _
   obtain ⟨x, hx', rfl⟩ := hx.1
-  convert hx
+  convert! hx
   rw [cfc_apply f a, norm_cfcHom a _]
   apply le_antisymm
   · apply ContinuousMap.norm_le _ (norm_nonneg _) |>.mpr
@@ -85,7 +85,7 @@ lemma IsGreatest.norm_cfc [Nontrivial A] (f : 𝕜 → 𝕜) (a : A)
 lemma IsGreatest.nnnorm_cfc [Nontrivial A] (f : 𝕜 → 𝕜) (a : A)
     (hf : ContinuousOn f (σ 𝕜 a) := by cfc_cont_tac) (ha : p a := by cfc_tac) :
     IsGreatest ((fun x ↦ ‖f x‖₊) '' σ 𝕜 a) ‖cfc f a‖₊ := by
-  convert Real.toNNReal_monotone.map_isGreatest (.norm_cfc f a)
+  convert! Real.toNNReal_monotone.map_isGreatest (.norm_cfc f a)
   all_goals simp [Set.image_image, norm_toNNReal]
 
 lemma norm_apply_le_norm_cfc (f : 𝕜 → 𝕜) (a : A) ⦃x : 𝕜⦄ (hx : x ∈ σ 𝕜 a)
@@ -264,7 +264,7 @@ lemma IsGreatest.norm_cfcₙ (f : 𝕜 → 𝕜) (a : A)
       |>.image_of_continuousOn hf.norm |>.exists_isGreatest <|
       (quasispectrum.nonempty 𝕜 a).image _
   obtain ⟨x, hx', rfl⟩ := hx.1
-  convert hx
+  convert! hx
   rw [cfcₙ_apply f a, norm_cfcₙHom a _]
   apply le_antisymm
   · apply ContinuousMap.norm_le _ (norm_nonneg _) |>.mpr
@@ -275,7 +275,7 @@ lemma IsGreatest.norm_cfcₙ (f : 𝕜 → 𝕜) (a : A)
 lemma IsGreatest.nnnorm_cfcₙ (f : 𝕜 → 𝕜) (a : A)
     (hf : ContinuousOn f (σₙ 𝕜 a) := by cfc_cont_tac) (hf₀ : f 0 = 0 := by cfc_zero_tac)
     (ha : p a := by cfc_tac) : IsGreatest ((fun x ↦ ‖f x‖₊) '' σₙ 𝕜 a) ‖cfcₙ f a‖₊ := by
-  convert Real.toNNReal_monotone.map_isGreatest (.norm_cfcₙ f a)
+  convert! Real.toNNReal_monotone.map_isGreatest (.norm_cfcₙ f a)
   all_goals simp [Set.image_image, norm_toNNReal]
 
 lemma norm_apply_le_norm_cfcₙ (f : 𝕜 → 𝕜) (a : A) ⦃x : 𝕜⦄ (hx : x ∈ σₙ 𝕜 a)
@@ -455,7 +455,7 @@ lemma IsGreatest.nnnorm_cfc_nnreal [Nontrivial A] (f : ℝ≥0 → ℝ≥0) (a :
   rw [cfc_nnreal_eq_real ..]
   obtain ⟨-, ha'⟩ := nonneg_iff_isSelfAdjoint_and_quasispectrumRestricts.mp ha
   rw [← SpectrumRestricts] at ha'
-  convert IsGreatest.nnnorm_cfc (fun x : ℝ ↦ (f x.toNNReal : ℝ)) a ?hf_cont
+  convert! IsGreatest.nnnorm_cfc (fun x : ℝ ↦ (f x.toNNReal : ℝ)) a ?hf_cont
   case hf_cont => exact continuous_subtype_val.comp_continuousOn <|
     ContinuousOn.comp ‹_› continuous_real_toNNReal.continuousOn <| ha'.image ▸ Set.mapsTo_image ..
   simp [Set.image_image, ← ha'.image]
@@ -529,7 +529,7 @@ lemma IsGreatest.nnnorm_cfcₙ_nnreal (f : ℝ≥0 → ℝ≥0) (a : A)
     (ha : 0 ≤ a := by cfc_tac) : IsGreatest (f '' σₙ ℝ≥0 a) ‖cfcₙ f a‖₊ := by
   rw [cfcₙ_nnreal_eq_real ..]
   obtain ⟨-, ha'⟩ := nonneg_iff_isSelfAdjoint_and_quasispectrumRestricts.mp ha
-  convert IsGreatest.nnnorm_cfcₙ (fun x : ℝ ↦ (f x.toNNReal : ℝ)) a ?hf_cont (by simpa)
+  convert! IsGreatest.nnnorm_cfcₙ (fun x : ℝ ↦ (f x.toNNReal : ℝ)) a ?hf_cont (by simpa)
   case hf_cont => exact continuous_subtype_val.comp_continuousOn <|
     ContinuousOn.comp ‹_› continuous_real_toNNReal.continuousOn <| ha'.image ▸ Set.mapsTo_image ..
   simp [Set.image_image, ← ha'.image]
diff --git a/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/NonUnital.lean b/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/NonUnital.lean
index daaf1353034ccd..8e874f08aa4074 100644
--- a/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/NonUnital.lean
+++ b/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/NonUnital.lean
@@ -475,7 +475,7 @@ lemma cfcₙ_comp (g f : R → R) (a : A)
     ext
     simp
   rw [cfcₙ_apply .., cfcₙ_apply f a,
-    cfcₙ_apply _ _ (by convert hg) (ha := cfcₙHom_predicate (show p a from ha) _),
+    cfcₙ_apply _ _ (by convert! hg) (ha := cfcₙHom_predicate (show p a from ha) _),
     ← cfcₙHom_comp _ _]
   swap
   · exact ⟨.mk _ <| hf.restrict.codRestrict fun x ↦ by rw [sp_eq]; use x.1; simp, Subtype.ext hf0⟩
@@ -840,7 +840,7 @@ lemma isClosedEmbedding_cfcₙHom_of_cfcHom [ClosedEmbeddingContinuousFunctional
     Filter.comap_comap]
   refine .symm <| inf_eq_left.mpr <| le_top.trans <| eq_top_iff.mp ?_
   have : ∀ U ∈ 𝓤 (C(Unit, R)), (0, 0) ∈ U := fun U hU ↦ refl_mem_uniformity hU
-  convert Filter.comap_const_of_mem this with ⟨u, v⟩ <;>
+  convert! Filter.comap_const_of_mem this with ⟨u, v⟩ <;>
   ext ⟨x, rfl⟩ <;> [exact map_zero u; exact map_zero v]
 
 instance ContinuousFunctionalCalculus.toNonUnital [ContinuousFunctionalCalculus R A p] :
diff --git a/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Order.lean b/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Order.lean
index 1c620b900e2bae..f0ad4b5961e47b 100644
--- a/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Order.lean
+++ b/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Order.lean
@@ -221,7 +221,7 @@ variable [PartialOrder A] [StarOrderedRing A]
 lemma nnnorm_mem_spectrum_of_nonneg [Nontrivial A] {a : A} (ha : 0 ≤ a := by cfc_tac) :
     ‖a‖₊ ∈ spectrum ℝ≥0 a := by
   have : IsSelfAdjoint a := .of_nonneg ha
-  convert NNReal.spectralRadius_mem_spectrum (a := a) ?_ (.nnreal_of_nonneg ha)
+  convert! NNReal.spectralRadius_mem_spectrum (a := a) ?_ (.nnreal_of_nonneg ha)
   · simp [this.spectrumRestricts.spectralRadius_eq, this.spectralRadius_eq_nnnorm]
   · exact this.spectrumRestricts.image ▸ (spectrum.nonempty a).image _
 
@@ -480,7 +480,7 @@ lemma star_right_conjugate_le_norm_smul {a b : A} (hb : IsSelfAdjoint b := by cf
 lemma isClosed_nonneg : IsClosed {a : A | 0 ≤ a} := by
   suffices IsClosed {a : A⁺¹ | 0 ≤ a} by
     rw [Unitization.isometry_inr (𝕜 := ℂ) |>.isClosedEmbedding.isClosed_iff_image_isClosed]
-    convert this.inter <| (Unitization.isometry_inr (𝕜 := ℂ)).isClosedEmbedding.isClosed_range
+    convert! this.inter <| (Unitization.isometry_inr (𝕜 := ℂ)).isClosedEmbedding.isClosed_range
     ext a
     simp only [Set.mem_image, Set.mem_setOf_eq, Set.mem_inter_iff, Set.mem_range, ← exists_and_left]
     congr! 2 with x
diff --git a/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Restrict.lean b/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Restrict.lean
index 53cb75a105c542..ae98b71f0e4926 100644
--- a/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Restrict.lean
+++ b/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Restrict.lean
@@ -76,7 +76,7 @@ lemma starAlgHom_id {a : A} {φ : C(spectrum S a, S) →⋆ₐ[S] A} {f : C(S, R
     (h : SpectrumRestricts a f) (h_id : φ (.restrict (spectrum S a) <| .id S) = a) :
     h.starAlgHom φ (.restrict (spectrum R a) <| .id R) = a := by
   simp only [SpectrumRestricts.starAlgHom_apply]
-  convert h_id
+  convert! h_id
   ext x
   exact h.rightInvOn x.2
 
@@ -239,7 +239,7 @@ lemma nonUnitalStarAlgHom_id {a : A} {φ : C(σₙ S a, S)₀ →⋆ₙₐ[S] A}
     (h : QuasispectrumRestricts a f) (h_id : φ (.id _) = a) :
     h.nonUnitalStarAlgHom φ (.id _) = a := by
   simp only [QuasispectrumRestricts.nonUnitalStarAlgHom_apply]
-  convert h_id
+  convert! h_id
   ext x
   exact h.rightInvOn x.2
 
diff --git a/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Unique.lean b/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Unique.lean
index 91c04a0b1a975a..d9cb6432619780 100644
--- a/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Unique.lean
+++ b/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Unique.lean
@@ -41,7 +41,7 @@ instance (priority := 100) RCLike.instContinuousMapUniqueHom [TopologicalSpace A
     ContinuousMap.UniqueHom 𝕜 A where
   eq_of_continuous_of_map_id s _ φ ψ hφ hψ h :=
     ContinuousMap.starAlgHom_ext_map_X hφ hψ <| by
-      convert h using 1
+      convert! h using 1
       all_goals exact congr_arg _ (by ext; simp)
 
 instance Real.instContinuousMapUniqueHom [TopologicalSpace A]
@@ -123,13 +123,13 @@ noncomputable def realContinuousMapOfNNReal (φ : C(X, ℝ≥0) →⋆ₐ[ℝ≥
     have := congr(φ $(f.toNNReal_mul_add_neg_mul_add_mul_neg_eq g))
     simp only [map_add, map_mul, sub_mul, mul_sub] at this ⊢
     rw [← sub_eq_zero] at this ⊢
-    convert this using 1
+    convert! this using 1
     abel
   map_add' f g := by
     have := congr(φ $(f.toNNReal_add_add_neg_add_neg_eq g))
     simp only [map_add] at this ⊢
     rw [← sub_eq_zero] at this ⊢
-    convert this using 1
+    convert! this using 1
     abel
   commutes' r := by
     obtain (hr | hr) := le_total 0 r
diff --git a/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Unital.lean b/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Unital.lean
index 65594cdafcbad2..ae87b6c4067a91 100644
--- a/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Unital.lean
+++ b/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Unital.lean
@@ -610,7 +610,7 @@ lemma cfc_comp (g f : R → R) (a : A) (ha : p a := by cfc_tac)
     ext
     simp
   rw [cfc_apply .., cfc_apply f a,
-    cfc_apply _ _ (cfcHom_predicate (show p a from ha) _) (by convert hg), ← cfcHom_comp _ _]
+    cfc_apply _ _ (cfcHom_predicate (show p a from ha) _) (by convert! hg), ← cfcHom_comp _ _]
   swap
   · exact ContinuousMap.mk _ <| hf.restrict.codRestrict fun x ↦ by rw [sp_eq]; use x.1; simp
   · congr
@@ -784,7 +784,7 @@ lemma cfc_inv (hf' : ∀ x ∈ spectrum R a, f x ≠ 0)
 lemma cfc_inv_id (a : Aˣ) (ha : p a := by cfc_tac) :
     cfc (fun x ↦ x⁻¹ : R → R) (a : A) = a⁻¹ := by
   rw [← Ring.inverse_unit]
-  convert cfc_inv (id : R → R) (a : A) ?_
+  convert! cfc_inv (id : R → R) (a : A) ?_
   · exact (cfc_id R (a : A)).symm
   · rintro x hx rfl
     exact spectrum.zero_notMem R a.isUnit hx
diff --git a/Mathlib/Analysis/CStarAlgebra/Fuglede.lean b/Mathlib/Analysis/CStarAlgebra/Fuglede.lean
index e8df875edb5f3b..d3fd6ac3d9857e 100644
--- a/Mathlib/Analysis/CStarAlgebra/Fuglede.lean
+++ b/Mathlib/Analysis/CStarAlgebra/Fuglede.lean
@@ -132,7 +132,7 @@ public lemma isStarNormal_iff_forall_exp_mul_exp_mem_unitary {a : A} :
   refine ⟨fun ha x ↦ ?_, fun ha ↦ ?_⟩
   /- If `a` is normal, then clearly `exp (x • a) * exp (- x • star a) = exp (I • x • 2 • ℑ a)`
   and the latter is clearly an exponential unitary. -/
-  · convert (selfAdjoint.expUnitary (x • (2 : ℝ) • ℑ a)).2
+  · convert! (selfAdjoint.expUnitary (x • (2 : ℝ) • ℑ a)).2
     have hcomm := star_comm_self (x := a) |>.symm.smul_left x |>.smul_right (-x)
     rw [← exp_add_of_commute hcomm]
     simp [imaginaryPart_apply_coe, smul_comm (2 : ℝ) I, smul_comm x I, smul_smul I I, smul_add x,
@@ -142,7 +142,7 @@ public lemma isStarNormal_iff_forall_exp_mul_exp_mem_unitary {a : A} :
   · have key : ∀ x : ℝ, exp (- x • a) * exp (x • star a) = exp (x • star a) * exp (- x • a) := by
       intro x
       let u : unitary A := ⟨_, ha x⟩
-      convert congr(($(Unitary.star_eq_inv u) : A))
+      convert! congr(($(Unitary.star_eq_inv u) : A))
       · simp [u, star_exp]
       · simp_rw [u, ← Unitary.val_inv_toUnits_apply, neg_smul, ← Units.mul_eq_one_iff_eq_inv,
           Unitary.val_toUnits_apply]
diff --git a/Mathlib/Analysis/CStarAlgebra/Matrix.lean b/Mathlib/Analysis/CStarAlgebra/Matrix.lean
index 19583896a8fc29..c304aa4b11eae3 100644
--- a/Mathlib/Analysis/CStarAlgebra/Matrix.lean
+++ b/Mathlib/Analysis/CStarAlgebra/Matrix.lean
@@ -218,7 +218,7 @@ lemma l2_opNorm_mul (A : Matrix m n 𝕜) (B : Matrix n l 𝕜) :
   simp only [l2_opNorm_def]
   have := (toEuclideanLin (n := n) (m := m) (𝕜 := 𝕜) ≪≫ₗ toContinuousLinearMap) A
     |>.opNorm_comp_le <| (toEuclideanLin (n := l) (m := n) (𝕜 := 𝕜) ≪≫ₗ toContinuousLinearMap) B
-  convert this
+  convert! this
   ext1 x
   exact congr(toLp 2 ($(Matrix.toLin'_mul A B) x))
 
diff --git a/Mathlib/Analysis/CStarAlgebra/Multiplier.lean b/Mathlib/Analysis/CStarAlgebra/Multiplier.lean
index 2a9c2a448bf523..77def5fd570085 100644
--- a/Mathlib/Analysis/CStarAlgebra/Multiplier.lean
+++ b/Mathlib/Analysis/CStarAlgebra/Multiplier.lean
@@ -533,7 +533,7 @@ theorem norm_fst_eq_snd (a : 𝓜(𝕜, A)) : ‖a.fst‖ = ‖a.snd‖ := by
     have h1 b : C * ‖f b‖₊ * ‖b‖₊ ≤ C * ‖f‖₊ * ‖b‖₊ ^ 2 := by grw [f.le_opNNNorm b]; ring_nf; rfl
     have := NNReal.div_le_of_le_mul <| f.opNNNorm_le_bound _ <| by
       simpa only [sqrt_sq, sqrt_mul] using fun b ↦ sqrt_le_sqrt.2 <| (h b).trans (h1 b)
-    convert NNReal.rpow_le_rpow this two_pos.le
+    convert! NNReal.rpow_le_rpow this two_pos.le
     · simp only [NNReal.rpow_two, div_pow, sq_sqrt]
       simp only [sq, mul_self_div_self]
     · simp only [NNReal.rpow_two, sq_sqrt]
diff --git a/Mathlib/Analysis/CStarAlgebra/Spectrum.lean b/Mathlib/Analysis/CStarAlgebra/Spectrum.lean
index 7ceef869235773..35ad0d20dc6c20 100644
--- a/Mathlib/Analysis/CStarAlgebra/Spectrum.lean
+++ b/Mathlib/Analysis/CStarAlgebra/Spectrum.lean
@@ -118,7 +118,7 @@ theorem IsSelfAdjoint.spectralRadius_eq_nnnorm {a : A} (ha : IsSelfAdjoint a) :
     spectralRadius ℂ a = ‖a‖₊ := by
   have hconst : Tendsto (fun _n : ℕ => (‖a‖₊ : ℝ≥0∞)) atTop _ := tendsto_const_nhds
   refine tendsto_nhds_unique ?_ hconst
-  convert
+  convert!
     (spectrum.pow_nnnorm_pow_one_div_tendsto_nhds_spectralRadius (a : A)).comp
       (tendsto_pow_atTop_atTop_of_one_lt one_lt_two) using 1
   refine funext fun n => ?_
@@ -145,7 +145,7 @@ theorem IsStarNormal.spectralRadius_eq_nnnorm (a : A) [IsStarNormal a] :
     ((ENNReal.continuous_pow 2).tendsto (spectralRadius ℂ a)).comp
       (spectrum.pow_nnnorm_pow_one_div_tendsto_nhds_spectralRadius a)
   rw [← heq] at h₂
-  convert tendsto_nhds_unique h₂ (pow_nnnorm_pow_one_div_tendsto_nhds_spectralRadius (a⋆ * a))
+  convert! tendsto_nhds_unique h₂ (pow_nnnorm_pow_one_div_tendsto_nhds_spectralRadius (a⋆ * a))
   rw [(IsSelfAdjoint.star_mul_self a).spectralRadius_eq_nnnorm, sq, nnnorm_star_mul_self, coe_mul]
 
 namespace CStarAlgebra
@@ -213,7 +213,7 @@ lemma IsSelfAdjoint.isConnected_spectrum_compl {a : A} (ha : IsSelfAdjoint a) :
   suffices IsConnected (((σ ℂ a)ᶜ ∩ {z | 0 ≤ z.im}) ∪ (σ ℂ a)ᶜ ∩ {z | z.im ≤ 0}) by
     rw [← Set.inter_union_distrib_left, ← Set.setOf_or] at this
     rw [← Set.inter_univ (σ ℂ a)ᶜ]
-    convert this using 2
+    convert! this using 2
     exact Eq.symm <| Set.eq_univ_of_forall (fun z ↦ le_total 0 z.im)
   refine IsConnected.union ?nonempty ?upper ?lower
   case nonempty =>
diff --git a/Mathlib/Analysis/CStarAlgebra/Unitary/Connected.lean b/Mathlib/Analysis/CStarAlgebra/Unitary/Connected.lean
index eeaa9842871cdd..41a18371763e21 100644
--- a/Mathlib/Analysis/CStarAlgebra/Unitary/Connected.lean
+++ b/Mathlib/Analysis/CStarAlgebra/Unitary/Connected.lean
@@ -67,7 +67,7 @@ lemma Unitary.two_mul_one_sub_le_norm_sub_one_sq {u : A} (hu : u ∈ unitary A)
   have := spectrum.subset_circle_of_unitary hu hz
   simp only [mem_sphere_iff_norm, sub_zero] at this
   rw [← cfc_id' ℂ u, ← cfc_one ℂ u, ← cfc_sub ..]
-  convert norm_apply_le_norm_cfc (fun z ↦ z - 1) u hz
+  convert! norm_apply_le_norm_cfc (fun z ↦ z - 1) u hz
   simpa using congr(Real.sqrt $(norm_sub_one_sq_eq_of_norm_eq_one this)).symm
 
 lemma Unitary.norm_sub_one_sq_eq {u : A} (hu : u ∈ unitary A) {x : ℝ}
@@ -315,7 +315,7 @@ lemma Unitary.joined (u v : unitary A) (huv : ‖(v - u : A)‖ < 2) :
 lemma Unitary.isPathConnected_ball (u : unitary A) (δ : ℝ) (hδ₀ : 0 < δ) (hδ₂ : δ < 2) :
     IsPathConnected (ball (u : unitary A) δ) := by
   suffices IsPathConnected (ball (1 : unitary A) δ) by
-    convert this |>.image (f := (u * ·)) (by fun_prop)
+    convert! this |>.image (f := (u * ·)) (by fun_prop)
     ext v
     rw [← inv_mul_cancel u]
     simp [-inv_mul_cancel, Subtype.dist_eq, dist_eq_norm, ← mul_sub]
diff --git a/Mathlib/Analysis/Calculus/ContDiff/Basic.lean b/Mathlib/Analysis/Calculus/ContDiff/Basic.lean
index 9ccf558790591a..8782686073b4aa 100644
--- a/Mathlib/Analysis/Calculus/ContDiff/Basic.lean
+++ b/Mathlib/Analysis/Calculus/ContDiff/Basic.lean
@@ -372,7 +372,8 @@ theorem HasFTaylorSeriesUpToOn.comp_continuousAffineMap
     rw [map_zero]
     rfl
   · intro m hm x hx
-    convert (hA m).hasFDerivAt.comp_hasFDerivWithinAt x
+    convert!
+      (hA m).hasFDerivAt.comp_hasFDerivWithinAt x
         ((hf.fderivWithin m hm (g x) hx).comp x g.hasFDerivWithinAt (Subset.refl _))
     ext y v
     change p (g x) (Nat.succ m) (g.contLinear ∘ cons y v)
@@ -530,7 +531,8 @@ theorem HasFTaylorSeriesUpToOn.prodMk {n : ℕ∞ω}
   constructor
   · intro x hx; rw [← hf.zero_eq x hx, ← hg.zero_eq x hx]; rfl
   · intro m hm x hx
-    convert (L m).hasFDerivAt.comp_hasFDerivWithinAt x
+    convert!
+      (L m).hasFDerivAt.comp_hasFDerivWithinAt x
         ((hf.fderivWithin m hm x hx).prodMk (hg.fderivWithin m hm x hx))
   · intro m hm
     exact (L m).continuous.comp_continuousOn ((hf.cont m hm).prodMk (hg.cont m hm))
diff --git a/Mathlib/Analysis/Calculus/ContDiff/Convolution.lean b/Mathlib/Analysis/Calculus/ContDiff/Convolution.lean
index 4ba4b0ebc9d423..eee8c3b135d650 100644
--- a/Mathlib/Analysis/Calculus/ContDiff/Convolution.lean
+++ b/Mathlib/Analysis/Calculus/ContDiff/Convolution.lean
@@ -115,7 +115,7 @@ variable [IsAddLeftInvariant μ] [SFinite μ]
 theorem _root_.HasCompactSupport.hasDerivAt_convolution_right (hf : LocallyIntegrable f₀ μ)
     (hcg : HasCompactSupport g₀) (hg : ContDiff 𝕜 1 g₀) (x₀ : 𝕜) :
     HasDerivAt (f₀ ⋆[L, μ] g₀) ((f₀ ⋆[L, μ] deriv g₀) x₀) x₀ := by
-  convert (hcg.hasFDerivAt_convolution_right L hf hg x₀).hasDerivAt using 1
+  convert! (hcg.hasFDerivAt_convolution_right L hf hg x₀).hasDerivAt using 1
   rw [convolution_precompR_apply L hf (hcg.fderiv 𝕜) (hg.continuous_fderiv one_ne_zero)]
   rfl
 
@@ -322,7 +322,7 @@ theorem contDiffOn_convolution_right_with_param_aux {G : Type uP} {E' : Type uP}
         rintro ⟨p, y⟩ ⟨hp, hy⟩
         exact hgs p y hp hy
       apply ih (L.precompR (P × G) :) B
-      convert hg.2.2
+      convert! hg.2.2
   | top ih =>
     rw [contDiffOn_infty] at hg ⊢
     exact fun n ↦ ih n L hgs (hg n)
diff --git a/Mathlib/Analysis/Calculus/ContDiff/Defs.lean b/Mathlib/Analysis/Calculus/ContDiff/Defs.lean
index 2c96fd557ada1f..9a5802b7534894 100644
--- a/Mathlib/Analysis/Calculus/ContDiff/Defs.lean
+++ b/Mathlib/Analysis/Calculus/ContDiff/Defs.lean
@@ -366,7 +366,7 @@ theorem contDiffWithinAt_succ_iff_hasFDerivWithinAt (hn : n ≠ ∞) :
       exact Hp.analyticOn (H'p rfl 0)
     apply (contDiffWithinAt_iff_of_ne_infty hn).2
     refine ⟨u, ?_, fun y : E => (p y).shift, ?_⟩
-    · convert @self_mem_nhdsWithin _ _ x u
+    · convert! @self_mem_nhdsWithin _ _ x u
       have : x ∈ insert x s := by simp
       exact insert_eq_of_mem (mem_of_mem_nhdsWithin this hu)
     · rw [hasFTaylorSeriesUpToOn_succ_iff_right] at Hp
@@ -390,14 +390,14 @@ theorem contDiffWithinAt_succ_iff_hasFDerivWithinAt (hn : n ≠ ∞) :
           HasFDerivWithinAt (fun z => (continuousMultilinearCurryFin0 𝕜 E F).symm (f z))
             (FormalMultilinearSeries.unshift (p' y) (f y) 1).curryLeft (v ∩ u) y
         rw [← Function.comp_def _ f, LinearIsometryEquiv.comp_hasFDerivWithinAt_iff']
-        convert (f'_eq_deriv y hy.2).mono inter_subset_right
+        convert! (f'_eq_deriv y hy.2).mono inter_subset_right
         rw [← Hp'.zero_eq y hy.1]
         ext z
         change ((p' y 0) (init (@cons 0 (fun _ => E) z 0))) (@cons 0 (fun _ => E) z 0 (last 0)) =
           ((p' y 0) 0) z
         congr
         norm_num [eq_iff_true_of_subsingleton]
-      · convert (Hp'.mono inter_subset_left).congr fun x hx => Hp'.zero_eq x hx.1 using 1
+      · convert! (Hp'.mono inter_subset_left).congr fun x hx => Hp'.zero_eq x hx.1 using 1
         · ext x y
           change p' x 0 (init (@snoc 0 (fun _ : Fin 1 => E) 0 y)) y = p' x 0 0 y
           rw [init_snoc]
@@ -731,7 +731,7 @@ theorem contDiffOn_of_continuousOn_differentiableOn {n : ℕ∞}
     simp only [ftaylorSeriesWithin, ContinuousMultilinearMap.curry0_apply,
       iteratedFDerivWithin_zero_apply]
   · intro k hk y hy
-    convert (Hdiff k (lt_of_lt_of_le (mod_cast hk) (mod_cast hm)) y hy).hasFDerivWithinAt
+    convert! (Hdiff k (lt_of_lt_of_le (mod_cast hk) (mod_cast hm)) y hy).hasFDerivWithinAt
   · intro k hk
     exact Hcont k (le_trans (mod_cast hk) (mod_cast hm))
 
@@ -993,7 +993,7 @@ theorem ContDiffAt.differentiableAt_iteratedFDeriv
     {f : E → F} {n : ℕ∞ω} {m : ℕ} {x : E} (h : ContDiffAt 𝕜 n f x) (hmn : ↑m < n) :
     DifferentiableAt 𝕜 (iteratedFDeriv 𝕜 m f) x := by
   rw [← differentiableWithinAt_univ]
-  convert (h.differentiableWithinAt_iteratedFDerivWithin hmn (by simp [uniqueDiffOn_univ]))
+  convert! (h.differentiableWithinAt_iteratedFDerivWithin hmn (by simp [uniqueDiffOn_univ]))
   exact iteratedFDerivWithin_univ.symm
 
 @[fun_prop]
@@ -1168,7 +1168,7 @@ theorem contDiff_succ_iff_hasFDerivAt {n : ℕ} :
 
 theorem contDiff_one_iff_hasFDerivAt : ContDiff 𝕜 1 f ↔
     ∃ f' : E → E →L[𝕜] F, Continuous f' ∧ ∀ x, HasFDerivAt f (f' x) x := by
-  convert contDiff_succ_iff_hasFDerivAt using 4; simp
+  convert! contDiff_succ_iff_hasFDerivAt using 4; simp
 
 theorem AnalyticOn.contDiff (hf : AnalyticOn 𝕜 f univ) : ContDiff 𝕜 n f := by
   rw [← contDiffOn_univ]
diff --git a/Mathlib/Analysis/Calculus/ContDiff/FTaylorSeries.lean b/Mathlib/Analysis/Calculus/ContDiff/FTaylorSeries.lean
index 2f15c0d70dc234..53ded4d8e91d6e 100644
--- a/Mathlib/Analysis/Calculus/ContDiff/FTaylorSeries.lean
+++ b/Mathlib/Analysis/Calculus/ContDiff/FTaylorSeries.lean
@@ -232,7 +232,7 @@ theorem HasFTaylorSeriesUpToOn.hasFDerivWithinAt (h : HasFTaylorSeriesUpToOn n f
     (continuousMultilinearCurryFin1 𝕜 E F (p x 1)) s x from H.congr A (A x hx)
   rw [LinearIsometryEquiv.comp_hasFDerivWithinAt_iff']
   have : ((0 : ℕ) : ℕ∞) < n := pos_iff_ne_zero.mpr hn
-  convert h.fderivWithin _ this x hx
+  convert! h.fderivWithin _ this x hx
   ext y v
   change (p x 1) (snoc 0 y) = (p x 1) (cons y v)
   congr with i
@@ -301,7 +301,7 @@ theorem HasFTaylorSeriesUpToOn.shift_of_succ
     change HasFDerivWithinAt (continuousMultilinearCurryRightEquiv' 𝕜 m E F ∘ (p · m.succ))
       (p x m.succ.succ).curryRight.curryLeft s x
     rw [(continuousMultilinearCurryRightEquiv' 𝕜 m E F).comp_hasFDerivWithinAt_iff']
-    convert H.fderivWithin _ A x hx
+    convert! H.fderivWithin _ A x hx
     ext y v
     change p x (m + 2) (snoc (cons y (init v)) (v (last _))) = p x (m + 2) (cons y v)
     rw [← cons_snoc_eq_snoc_cons, snoc_init_self]
@@ -338,7 +338,7 @@ theorem hasFTaylorSeriesUpToOn_succ_nat_iff_right {n : ℕ} :
             ((p x).shift m.succ).curryLeft s x := Htaylor.fderivWithin _ A x hx
         rw [LinearIsometryEquiv.comp_hasFDerivWithinAt_iff'
             (f' := ((p x).shift m.succ).curryLeft)] at this
-        convert this
+        convert! this
         ext y v
         change
           (p x (Nat.succ (Nat.succ m))) (cons y v) =
diff --git a/Mathlib/Analysis/Calculus/ContDiff/FaaDiBruno.lean b/Mathlib/Analysis/Calculus/ContDiff/FaaDiBruno.lean
index a48e0ab31bdaff..c8d5ce06b8d54e 100644
--- a/Mathlib/Analysis/Calculus/ContDiff/FaaDiBruno.lean
+++ b/Mathlib/Analysis/Calculus/ContDiff/FaaDiBruno.lean
@@ -267,7 +267,7 @@ lemma one_lt_partSize_index_zero (c : OrderedFinpartition (n + 1)) (hc : range (
         c.emb (c.index 0) ⟨c.partSize (c.index 0) - 1, Nat.sub_one_lt_of_lt (c.partSize_pos _)⟩}
           ⊆ range (c.emb (c.index 0)) := by simp [insert_subset]
     simp only [emb_zero] at this
-    convert Nat.card_mono Subtype.finite this
+    convert! Nat.card_mono Subtype.finite this
     simp only [Nat.card_eq_fintype_card, Fintype.card_ofFinset, toFinset_singleton]
     apply (Finset.card_pair ?_).symm
     exact ((Fin.zero_le _).trans_lt (c.parts_strictMono ((pos_iff_ne_zero' (c.index 0)).mpr h))).ne
@@ -383,7 +383,7 @@ def extendMiddle (c : OrderedFinpartition n) (k : Fin c.length) : OrderedFinpart
     · simp only [hm, ↓reduceDIte]
       exact strictMono_succ.comp ((c.emb_strictMono m).comp (by exact fun ⦃a b⦄ h ↦ h))
   parts_strictMono := by
-    convert strictMono_succ.comp c.parts_strictMono with m
+    convert! strictMono_succ.comp c.parts_strictMono with m
     rcases eq_or_ne m k with rfl | hm
     · simp only [↓reduceDIte, update_self, add_tsub_cancel_right, comp_apply, cast_mk]
       let a : Fin (c.partSize m + 1) := ⟨c.partSize m, lt_add_one (c.partSize m)⟩
@@ -549,7 +549,7 @@ def eraseMiddle (c : OrderedFinpartition (n + 1)) (hc : range (c.emb 0) ≠ {0})
   parts_strictMono i j hij := by
     simp only [Fin.lt_def]
     rw [← Nat.add_lt_add_iff_right (k := 1)]
-    convert Fin.lt_def.1 (c.parts_strictMono hij)
+    convert! Fin.lt_def.1 (c.parts_strictMono hij)
     · rcases eq_or_ne i (c.index 0) with rfl | hi
       -- We do not yet replace `omega` with `lia` here, as it is measurably slower.
       · simp only [↓reduceDIte, update_self, succ_mk, cast_mk, val_pred]
@@ -1084,7 +1084,7 @@ theorem HasFTaylorSeriesUpToOn.comp {n : WithTop ℕ∞} {g : F → G} {f : E 
         t (f x) := hg.fderivWithin c.length (cm.trans_lt hm) (f x) (h hx)
       have K : HasFDerivWithinAt f ((continuousMultilinearCurryFin1 𝕜 E F) (p x 1)) s x :=
         hf.hasFDerivWithinAt hm.ne_bot hx
-      convert HasFDerivWithinAt.linear_multilinear_comp (J.comp x K h) I B
+      convert! HasFDerivWithinAt.linear_multilinear_comp (J.comp x K h) I B
       simp only [B, Nat.succ_eq_add_one, Fintype.sum_option, comp_apply, faaDiBruno_aux1,
         faaDiBruno_aux2]
     have B : HasFDerivWithinAt (fun x ↦ (q (f x)).taylorComp (p x) m)
@@ -1095,7 +1095,7 @@ theorem HasFTaylorSeriesUpToOn.comp {n : WithTop ℕ∞} {g : F → G} {f : E 
           ((q (f x)).compAlongOrderedFinpartition (p x) (c.extend i)) =
         (q (f x)).taylorComp (p x) (m + 1) by
       rw [← this]
-      convert B
+      convert! B
       ext v
       simp only [Nat.succ_eq_add_one, Fintype.sum_option, ContinuousMultilinearMap.curryLeft_apply,
         ContinuousMultilinearMap.sum_apply, ContinuousMultilinearMap.add_apply,
diff --git a/Mathlib/Analysis/Calculus/ContDiff/Operations.lean b/Mathlib/Analysis/Calculus/ContDiff/Operations.lean
index 0005b8008d5480..d58073bb7ec730 100644
--- a/Mathlib/Analysis/Calculus/ContDiff/Operations.lean
+++ b/Mathlib/Analysis/Calculus/ContDiff/Operations.lean
@@ -80,7 +80,7 @@ theorem hasFTaylorSeriesUpToOn_pi' {n : ℕ∞ω} :
       ∀ i, HasFTaylorSeriesUpToOn n (fun x => Φ x i)
         (fun x m => (@ContinuousLinearMap.proj 𝕜 _ ι F' _ _ _ i).compContinuousMultilinearMap
           (P' x m)) s := by
-  convert hasFTaylorSeriesUpToOn_pi (𝕜 := 𝕜) (φ := fun i x ↦ Φ x i); ext; rfl
+  convert! hasFTaylorSeriesUpToOn_pi (𝕜 := 𝕜) (φ := fun i x ↦ Φ x i); ext; rfl
 
 theorem contDiffWithinAt_pi :
     ContDiffWithinAt 𝕜 n Φ s x ↔ ∀ i, ContDiffWithinAt 𝕜 n (fun x => Φ x i) s x := by
@@ -405,7 +405,7 @@ theorem iteratedFDerivWithin_fun_sum_apply {ι : Type*} {f : ι → E → F} {u
     {x : E} (hs : UniqueDiffOn 𝕜 s) (hx : x ∈ s) (h : ∀ j ∈ u, ContDiffWithinAt 𝕜 i (f j) s x) :
     iteratedFDerivWithin 𝕜 i (fun z ↦ ∑ j ∈ u, f j z) s x =
       ∑ j ∈ u, iteratedFDerivWithin 𝕜 i (f j) s x := by
-  convert iteratedFDerivWithin_sum_apply hs hx h
+  convert! iteratedFDerivWithin_sum_apply hs hx h
   rw [Finset.sum_apply]
 
 theorem iteratedFDeriv_sum_apply {ι : Type*} {f : ι → E → F} {u : Finset ι} {n : ℕ} {x : E}
@@ -418,7 +418,7 @@ theorem iteratedFDeriv_sum_apply {ι : Type*} {f : ι → E → F} {u : Finset 
 theorem iteratedFDeriv_fun_sum_apply {ι : Type*} {f : ι → E → F} {u : Finset ι} {n : ℕ} {x : E}
     (h : ∀ j ∈ u, ContDiffAt 𝕜 n (f j) x) :
     iteratedFDeriv 𝕜 n (fun z ↦ ∑ j ∈ u, f j z) x = ∑ j ∈ u, iteratedFDeriv 𝕜 n (f j) x := by
-  convert iteratedFDeriv_sum_apply h
+  convert! iteratedFDeriv_sum_apply h
   rw [Finset.sum_apply]
 
 theorem iteratedFDeriv_sum {ι : Type*} {f : ι → E → F} {u : Finset ι} {i : ℕ}
@@ -867,7 +867,7 @@ theorem contDiffAt_map_inverse [CompleteSpace E] (e : E ≃L[𝕜] F) :
   have h₁ : ContDiff 𝕜 n O₁ := contDiff_id.clm_comp contDiff_const
   have h₂ : ContDiff 𝕜 n O₂ := contDiff_const.clm_comp contDiff_id
   refine h₁.contDiffAt.comp _ (ContDiffAt.comp _ ?_ h₂.contDiffAt)
-  convert contDiffAt_ringInverse 𝕜 (1 : (E →L[𝕜] E)ˣ)
+  convert! contDiffAt_ringInverse 𝕜 (1 : (E →L[𝕜] E)ˣ)
   simp [O₂, one_def]
 
 /-- At an invertible map `e : M →L[R] M₂` between Banach spaces, the operation of
@@ -929,7 +929,7 @@ theorem OpenPartialHomeomorph.contDiffAt_symm [CompleteSpace E] (f : OpenPartial
         have h_deriv : HasFDerivAt f (e : E →L[𝕜] F) (f.symm x) := by
           rw [he]
           exact hff' (f.symm x) hxu
-        convert f.hasFDerivAt_symm hx.1 h_deriv
+        convert! f.hasFDerivAt_symm hx.1 h_deriv
         simp [← he]
       · -- Then we check that the formula, being a composition of `ContDiff` pieces, is
         -- itself `ContDiff`
diff --git a/Mathlib/Analysis/Calculus/ContDiff/RestrictScalars.lean b/Mathlib/Analysis/Calculus/ContDiff/RestrictScalars.lean
index 2e9c81530c8f24..a5c18a1e804903 100644
--- a/Mathlib/Analysis/Calculus/ContDiff/RestrictScalars.lean
+++ b/Mathlib/Analysis/Calculus/ContDiff/RestrictScalars.lean
@@ -80,7 +80,7 @@ to `𝕜'`.
 theorem ContDiffAt.restrictScalars_iteratedFDeriv_eventuallyEq (h : ContDiffAt 𝕜' n f x) :
     (restrictScalars 𝕜) ∘ (iteratedFDeriv 𝕜' n f) =ᶠ[𝓝 x] iteratedFDeriv 𝕜 n f := by
   have h' : ContDiffWithinAt 𝕜' n f Set.univ x := h
-  convert (h'.restrictScalars_iteratedFDerivWithin_eventuallyEq _ trivial)
+  convert! (h'.restrictScalars_iteratedFDerivWithin_eventuallyEq _ trivial)
   <;> simp [iteratedFDerivWithin_univ.symm, uniqueDiffOn_univ]
 
 /--
diff --git a/Mathlib/Analysis/Calculus/Deriv/Abs.lean b/Mathlib/Analysis/Calculus/Deriv/Abs.lean
index d1c6735bbcc1db..52c70a137aea08 100644
--- a/Mathlib/Analysis/Calculus/Deriv/Abs.lean
+++ b/Mathlib/Analysis/Calculus/Deriv/Abs.lean
@@ -75,37 +75,37 @@ theorem hasDerivAt_abs {x : ℝ} (hx : x ≠ 0) :
 
 theorem HasStrictFDerivAt.abs_of_neg (hf : HasStrictFDerivAt f f' x)
     (h₀ : f x < 0) : HasStrictFDerivAt (fun x ↦ |f x|) (-f') x := by
-  convert (hasStrictDerivAt_abs_neg h₀).hasStrictFDerivAt.comp x hf using 1
+  convert! (hasStrictDerivAt_abs_neg h₀).hasStrictFDerivAt.comp x hf using 1
   ext y
   simp
 
 theorem HasFDerivAt.abs_of_neg (hf : HasFDerivAt f f' x)
     (h₀ : f x < 0) : HasFDerivAt (fun x ↦ |f x|) (-f') x := by
-  convert (hasDerivAt_abs_neg h₀).hasFDerivAt.comp x hf using 1
+  convert! (hasDerivAt_abs_neg h₀).hasFDerivAt.comp x hf using 1
   ext y
   simp
 
 theorem HasStrictFDerivAt.abs_of_pos (hf : HasStrictFDerivAt f f' x)
     (h₀ : 0 < f x) : HasStrictFDerivAt (fun x ↦ |f x|) f' x := by
-  convert (hasStrictDerivAt_abs_pos h₀).hasStrictFDerivAt.comp x hf using 1
+  convert! (hasStrictDerivAt_abs_pos h₀).hasStrictFDerivAt.comp x hf using 1
   ext y
   simp
 
 theorem HasFDerivAt.abs_of_pos (hf : HasFDerivAt f f' x)
     (h₀ : 0 < f x) : HasFDerivAt (fun x ↦ |f x|) f' x := by
-  convert (hasDerivAt_abs_pos h₀).hasFDerivAt.comp x hf using 1
+  convert! (hasDerivAt_abs_pos h₀).hasFDerivAt.comp x hf using 1
   ext y
   simp
 
 theorem HasStrictFDerivAt.abs (hf : HasStrictFDerivAt f f' x)
     (h₀ : f x ≠ 0) : HasStrictFDerivAt (fun x ↦ |f x|) ((SignType.sign (f x) : ℝ) • f') x := by
-  convert (hasStrictDerivAt_abs h₀).hasStrictFDerivAt.comp x hf using 1
+  convert! (hasStrictDerivAt_abs h₀).hasStrictFDerivAt.comp x hf using 1
   ext y
   simp [mul_comm]
 
 theorem HasFDerivAt.abs (hf : HasFDerivAt f f' x)
     (h₀ : f x ≠ 0) : HasFDerivAt (fun x ↦ |f x|) ((SignType.sign (f x) : ℝ) • f') x := by
-  convert (hasDerivAt_abs h₀).hasFDerivAt.comp x hf using 1
+  convert! (hasDerivAt_abs h₀).hasFDerivAt.comp x hf using 1
   ext y
   simp [mul_comm]
 
@@ -120,12 +120,12 @@ theorem hasDerivWithinAt_abs (s : Set ℝ) {x : ℝ} (hx : x ≠ 0) :
 
 theorem HasFDerivWithinAt.abs_of_neg (hf : HasFDerivWithinAt f f' s x)
     (h₀ : f x < 0) : HasFDerivWithinAt (fun x ↦ |f x|) (-f') s x := by
-  convert (hasDerivAt_abs_neg h₀).comp_hasFDerivWithinAt x hf using 1
+  convert! (hasDerivAt_abs_neg h₀).comp_hasFDerivWithinAt x hf using 1
   simp
 
 theorem HasFDerivWithinAt.abs_of_pos (hf : HasFDerivWithinAt f f' s x)
     (h₀ : 0 < f x) : HasFDerivWithinAt (fun x ↦ |f x|) f' s x := by
-  convert (hasDerivAt_abs_pos h₀).comp_hasFDerivWithinAt x hf using 1
+  convert! (hasDerivAt_abs_pos h₀).comp_hasFDerivWithinAt x hf using 1
   simp
 
 theorem HasFDerivWithinAt.abs (hf : HasFDerivWithinAt f f' s x)
diff --git a/Mathlib/Analysis/Calculus/Deriv/Add.lean b/Mathlib/Analysis/Calculus/Deriv/Add.lean
index c208e50a2b6c5a..456dcd8510a1df 100644
--- a/Mathlib/Analysis/Calculus/Deriv/Add.lean
+++ b/Mathlib/Analysis/Calculus/Deriv/Add.lean
@@ -196,7 +196,7 @@ theorem HasDerivAtFilter.fun_sum (h : ∀ i ∈ u, HasDerivAtFilter (A i) (A' i)
 
 theorem HasDerivAtFilter.sum (h : ∀ i ∈ u, HasDerivAtFilter (A i) (A' i) L) :
     HasDerivAtFilter (∑ i ∈ u, A i) (∑ i ∈ u, A' i) L := by
-  convert HasDerivAtFilter.fun_sum h
+  convert! HasDerivAtFilter.fun_sum h
   simp
 
 theorem HasStrictDerivAt.fun_sum (h : ∀ i ∈ u, HasStrictDerivAt (A i) (A' i) x) :
@@ -328,7 +328,7 @@ theorem differentiableOn_neg : DifferentiableOn 𝕜 (Neg.neg : 𝕜 → 𝕜) s
 lemma differentiableAt_comp_neg {a : 𝕜} :
     DifferentiableAt 𝕜 (fun x ↦ f (-x)) a ↔ DifferentiableAt 𝕜 f (-a) := by
   refine ⟨fun H ↦ ?_, fun H ↦ H.comp a differentiable_neg.differentiableAt⟩
-  convert ((neg_neg a).symm ▸ H).comp (-a) differentiable_neg.differentiableAt
+  convert! ((neg_neg a).symm ▸ H).comp (-a) differentiable_neg.differentiableAt
   ext
   simp only [Function.comp_apply, neg_neg]
 
@@ -460,8 +460,8 @@ lemma differentiableAt_comp_sub_const {a b : 𝕜} :
 lemma differentiableAt_comp_const_sub {a b : 𝕜} :
     DifferentiableAt 𝕜 (fun x ↦ f (b - x)) a ↔ DifferentiableAt 𝕜 f (b - a) := by
   refine ⟨fun H ↦ ?_, fun H ↦ H.comp a (differentiable_id.const_sub _).differentiableAt⟩
-  convert ((sub_sub_cancel _ a).symm ▸ H).comp (b - a)
-    (differentiable_id.const_sub _).differentiableAt
+  convert!
+    ((sub_sub_cancel _ a).symm ▸ H).comp (b - a) (differentiable_id.const_sub _).differentiableAt
   ext
   simp
 
diff --git a/Mathlib/Analysis/Calculus/Deriv/Basic.lean b/Mathlib/Analysis/Calculus/Deriv/Basic.lean
index 99f63e9aa8d90e..19085c55985bb8 100644
--- a/Mathlib/Analysis/Calculus/Deriv/Basic.lean
+++ b/Mathlib/Analysis/Calculus/Deriv/Basic.lean
@@ -922,7 +922,7 @@ lemma HasDerivAt.comp_semilinear (hf : HasDerivAt f f' x) :
   let R : 𝕜 →SL[σ'] 𝕜 := ⟨σ'.toSemilinearMap, σ'.isometry.continuous⟩
   have hR (k : 𝕜) : R k = σ' k := rfl
   rw [hasDerivAt_iff_hasFDerivAt]
-  convert HasFDerivAt.comp_semilinear L R (f' := toSpanSingleton 𝕜 f') ?_
+  convert! HasFDerivAt.comp_semilinear L R (f' := toSpanSingleton 𝕜 f') ?_
   · ext
     simp [R]
   · rwa [← hasDerivAt_iff_hasFDerivAt, hR, RingHomInvPair.comp_apply_eq]
diff --git a/Mathlib/Analysis/Calculus/Deriv/Comp.lean b/Mathlib/Analysis/Calculus/Deriv/Comp.lean
index 5817329ccc094e..8904a0bd28c6d9 100644
--- a/Mathlib/Analysis/Calculus/Deriv/Comp.lean
+++ b/Mathlib/Analysis/Calculus/Deriv/Comp.lean
@@ -161,7 +161,7 @@ theorem HasDerivAtFilter.comp_hasFDerivAtFilter {f : E → 𝕜'} {f' : E →L[
     {L'' : Filter (E × E)} (hh₂ : HasDerivAtFilter h₂ h₂' L') (hf : HasFDerivAtFilter f f' L'')
     (hL : Tendsto (Prod.map f f) L'' L') :
     HasFDerivAtFilter (h₂ ∘ f) (h₂' • f') L'' := by
-  convert (hh₂.restrictScalars 𝕜).comp hf hL
+  convert! (hh₂.restrictScalars 𝕜).comp hf hL
   ext x
   simp [mul_comm]
 
diff --git a/Mathlib/Analysis/Calculus/Deriv/Inv.lean b/Mathlib/Analysis/Calculus/Deriv/Inv.lean
index 4f6215baaf24da..d2ef70ed083d9a 100644
--- a/Mathlib/Analysis/Calculus/Deriv/Inv.lean
+++ b/Mathlib/Analysis/Calculus/Deriv/Inv.lean
@@ -103,7 +103,7 @@ variable {c : 𝕜 → 𝕜} {c' : 𝕜}
 @[to_fun]
 theorem HasDerivWithinAt.inv (hc : HasDerivWithinAt c c' s x) (hx : c x ≠ 0) :
     HasDerivWithinAt (c⁻¹) (-c' / c x ^ 2) s x := by
-  convert (hasDerivAt_inv hx).comp_hasDerivWithinAt x hc using 1
+  convert! (hasDerivAt_inv hx).comp_hasDerivWithinAt x hc using 1
   ring
 
 @[to_fun]
@@ -143,7 +143,7 @@ variable {𝕜' : Type*} [NontriviallyNormedField 𝕜'] [NormedAlgebra 𝕜 
 theorem HasDerivWithinAt.fun_div (hc : HasDerivWithinAt c c' s x) (hd : HasDerivWithinAt d d' s x)
     (hx : d x ≠ 0) :
     HasDerivWithinAt (fun y => c y / d y) ((c' * d x - c x * d') / d x ^ 2) s x := by
-  convert hc.fun_mul ((hasDerivAt_inv hx).comp_hasDerivWithinAt x hd) using 1
+  convert! hc.fun_mul ((hasDerivAt_inv hx).comp_hasDerivWithinAt x hd) using 1
   · simp only [div_eq_mul_inv, (· ∘ ·)]
   · simp [field]
     ring
@@ -155,7 +155,7 @@ theorem HasDerivWithinAt.div (hc : HasDerivWithinAt c c' s x) (hd : HasDerivWith
 
 theorem HasStrictDerivAt.fun_div (hc : HasStrictDerivAt c c' x) (hd : HasStrictDerivAt d d' x)
     (hx : d x ≠ 0) : HasStrictDerivAt (fun y => c y / d y) ((c' * d x - c x * d') / d x ^ 2) x := by
-  convert hc.fun_mul ((hasStrictDerivAt_inv hx).comp x hd) using 1
+  convert! hc.fun_mul ((hasStrictDerivAt_inv hx).comp x hd) using 1
   · simp only [div_eq_mul_inv, (· ∘ ·)]
   · simp [field]
     ring
diff --git a/Mathlib/Analysis/Calculus/Deriv/MeanValue.lean b/Mathlib/Analysis/Calculus/Deriv/MeanValue.lean
index a996d804ec797b..2da41777d06175 100644
--- a/Mathlib/Analysis/Calculus/Deriv/MeanValue.lean
+++ b/Mathlib/Analysis/Calculus/Deriv/MeanValue.lean
@@ -103,12 +103,12 @@ theorem exists_ratio_hasDerivAt_eq_ratio_slope' {lfa lga lfb lgb : ℝ}
   have hha : Tendsto h (𝓝[>] a) (𝓝 <| lgb * lfa - lfb * lga) := by
     have : Tendsto h (𝓝[>] a) (𝓝 <| (lgb - lga) * lfa - (lfb - lfa) * lga) :=
       (tendsto_const_nhds.mul hfa).sub (tendsto_const_nhds.mul hga)
-    convert this using 2
+    convert! this using 2
     ring
   have hhb : Tendsto h (𝓝[<] b) (𝓝 <| lgb * lfa - lfb * lga) := by
     have : Tendsto h (𝓝[<] b) (𝓝 <| (lgb - lga) * lfb - (lfb - lfa) * lgb) :=
       (tendsto_const_nhds.mul hfb).sub (tendsto_const_nhds.mul hgb)
-    convert this using 2
+    convert! this using 2
     ring
   let h' x := (lgb - lga) * f' x - (lfb - lfa) * g' x
   have hhh' : ∀ x ∈ Ioo a b, HasDerivAt h (h' x) x := by
diff --git a/Mathlib/Analysis/Calculus/Deriv/Mul.lean b/Mathlib/Analysis/Calculus/Deriv/Mul.lean
index 931cd244bab57f..64ab0635d2cedf 100644
--- a/Mathlib/Analysis/Calculus/Deriv/Mul.lean
+++ b/Mathlib/Analysis/Calculus/Deriv/Mul.lean
@@ -65,11 +65,11 @@ theorem hasDerivAt_of_bilinear (hu : x ∈ tsupport v → HasDerivAt u u' x)
     · simpa using (B.hasFDerivAt_of_bilinear (hu hxv).hasFDerivAt (hv hxu).hasFDerivAt).hasDerivAt
     · have hx : x ∉ tsupport fun x ↦ B (u x) (v x) :=
         mt (closure_mono (fun x ↦ mt fun h ↦ by simp [h]) ·) hxv
-      convert HasDerivAt.of_notMem_tsupport hx
+      convert! HasDerivAt.of_notMem_tsupport hx
       simp [(hv hxu).unique <| .of_notMem_tsupport hxv, image_eq_zero_of_notMem_tsupport hxv]
   · have hx : x ∉ tsupport fun x ↦ B (u x) (v x) :=
       mt (closure_mono (fun x ↦ mt fun h ↦ by simp [h]) ·) hxu
-    convert HasDerivAt.of_notMem_tsupport hx
+    convert! HasDerivAt.of_notMem_tsupport hx
     by_cases hxv : x ∈ tsupport v
     · simp [image_eq_zero_of_notMem_tsupport hxu, (hu hxv).unique <| .of_notMem_tsupport hxu]
     · simp [image_eq_zero_of_notMem_tsupport hxu, image_eq_zero_of_notMem_tsupport hxv]
@@ -299,7 +299,7 @@ theorem deriv_mul (hc : DifferentiableAt 𝕜 c x) (hd : DifferentiableAt 𝕜 d
 
 theorem HasDerivWithinAt.mul_const (hc : HasDerivWithinAt c c' s x) (d : 𝔸) :
     HasDerivWithinAt (fun y => c y * d) (c' * d) s x := by
-  convert hc.mul (hasDerivWithinAt_const x s d) using 1
+  convert! hc.mul (hasDerivWithinAt_const x s d) using 1
   rw [mul_zero, add_zero]
 
 theorem HasDerivAt.mul_const (hc : HasDerivAt c c' x) (d : 𝔸) :
@@ -312,7 +312,7 @@ theorem hasDerivAt_mul_const (c : 𝕜) : HasDerivAt (fun x => x * c) c x := by
 
 theorem HasStrictDerivAt.mul_const (hc : HasStrictDerivAt c c' x) (d : 𝔸) :
     HasStrictDerivAt (fun y => c y * d) (c' * d) x := by
-  convert hc.mul (hasStrictDerivAt_const x d) using 1
+  convert! hc.mul (hasStrictDerivAt_const x d) using 1
   rw [mul_zero, add_zero]
 
 theorem derivWithin_mul_const (hc : DifferentiableWithinAt 𝕜 c s x) (d : 𝔸) :
@@ -351,7 +351,7 @@ theorem deriv_mul_const_field' (v : 𝕜') : (deriv fun x => u x * v) = fun x =>
 
 theorem HasDerivWithinAt.const_mul (c : 𝔸) (hd : HasDerivWithinAt d d' s x) :
     HasDerivWithinAt (fun y => c * d y) (c * d') s x := by
-  convert (hasDerivWithinAt_const x s c).mul hd using 1
+  convert! (hasDerivWithinAt_const x s c).mul hd using 1
   rw [zero_mul, zero_add]
 
 theorem HasDerivAt.const_mul (c : 𝔸) (hd : HasDerivAt d d' x) :
@@ -364,7 +364,7 @@ theorem hasDerivAt_const_mul (c : 𝕜) : HasDerivAt (fun y => c * y) c x := by
 
 theorem HasStrictDerivAt.const_mul (c : 𝔸) (hd : HasStrictDerivAt d d' x) :
     HasStrictDerivAt (fun y => c * d y) (c * d') x := by
-  convert (hasStrictDerivAt_const _ _).mul hd using 1
+  convert! (hasStrictDerivAt_const _ _).mul hd using 1
   rw [zero_mul, zero_add]
 
 theorem derivWithin_const_mul (c : 𝔸) (hd : DifferentiableWithinAt 𝕜 d s x) :
@@ -417,7 +417,7 @@ theorem HasDerivAt.fun_finsetProd (hf : ∀ i ∈ u, HasDerivAt (f i) (f' i) x)
 
 theorem HasDerivAt.finsetProd (hf : ∀ i ∈ u, HasDerivAt (f i) (f' i) x) :
     HasDerivAt (∏ i ∈ u, f i) (∑ i ∈ u, (∏ j ∈ u.erase i, f j x) • f' i) x := by
-  convert HasDerivAt.fun_finsetProd hf; simp
+  convert! HasDerivAt.fun_finsetProd hf; simp
 
 @[deprecated (since := "2026-04-08")] alias HasDerivAt.finset_prod := HasDerivAt.finsetProd
 
@@ -431,7 +431,7 @@ alias HasDerivWithinAt.fun_finset_prod := HasDerivWithinAt.fun_finsetProd
 
 theorem HasDerivWithinAt.finsetProd (hf : ∀ i ∈ u, HasDerivWithinAt (f i) (f' i) s x) :
     HasDerivWithinAt (∏ i ∈ u, f i) (∑ i ∈ u, (∏ j ∈ u.erase i, f j x) • f' i) s x := by
-  convert HasDerivWithinAt.fun_finsetProd hf; simp
+  convert! HasDerivWithinAt.fun_finsetProd hf; simp
 
 @[deprecated (since := "2026-04-08")]
 alias HasDerivWithinAt.finset_prod := HasDerivWithinAt.finsetProd
@@ -446,7 +446,7 @@ alias HasStrictDerivAt.fun_finset_prod := HasStrictDerivAt.fun_finsetProd
 
 theorem HasStrictDerivAt.finsetProd (hf : ∀ i ∈ u, HasStrictDerivAt (f i) (f' i) x) :
     HasStrictDerivAt (∏ i ∈ u, f i) (∑ i ∈ u, (∏ j ∈ u.erase i, f j x) • f' i) x := by
-  convert HasStrictDerivAt.fun_finsetProd hf; simp
+  convert! HasStrictDerivAt.fun_finsetProd hf; simp
 
 @[deprecated (since := "2026-04-08")]
 alias HasStrictDerivAt.finset_prod := HasStrictDerivAt.finsetProd
@@ -476,7 +476,7 @@ alias derivWithin_fun_finset_prod := derivWithin_fun_finsetProd
 theorem derivWithin_finsetProd (hf : ∀ i ∈ u, DifferentiableWithinAt 𝕜 (f i) s x) :
     derivWithin (∏ i ∈ u, f i) s x =
       ∑ i ∈ u, (∏ j ∈ u.erase i, f j x) • derivWithin (f i) s x := by
-  convert derivWithin_fun_finsetProd hf; simp
+  convert! derivWithin_fun_finsetProd hf; simp
 
 @[deprecated (since := "2026-04-08")] alias derivWithin_finset_prod := derivWithin_finsetProd
 
@@ -498,7 +498,7 @@ alias DifferentiableAt.fun_finset_prod := DifferentiableAt.fun_finsetProd
 @[fun_prop]
 theorem DifferentiableAt.finsetProd (hd : ∀ i ∈ u, DifferentiableAt 𝕜 (f i) x) :
     DifferentiableAt 𝕜 (∏ i ∈ u, f i) x := by
-  convert DifferentiableAt.fun_finsetProd hd; simp
+  convert! DifferentiableAt.fun_finsetProd hd; simp
 
 @[deprecated (since := "2026-04-08")]
 alias DifferentiableAt.finset_prod := DifferentiableAt.finsetProd
@@ -516,7 +516,7 @@ alias DifferentiableWithinAt.fun_finset_prod := DifferentiableWithinAt.fun_finse
 @[fun_prop]
 theorem DifferentiableWithinAt.finsetProd (hd : ∀ i ∈ u, DifferentiableWithinAt 𝕜 (f i) s x) :
     DifferentiableWithinAt 𝕜 (∏ i ∈ u, f i) s x := by
-  convert DifferentiableWithinAt.fun_finsetProd hd; simp
+  convert! DifferentiableWithinAt.fun_finsetProd hd; simp
 
 @[deprecated (since := "2026-04-08")]
 alias DifferentiableWithinAt.finset_prod := DifferentiableWithinAt.finsetProd
diff --git a/Mathlib/Analysis/Calculus/Deriv/Pi.lean b/Mathlib/Analysis/Calculus/Deriv/Pi.lean
index 47d8d0e7533d1c..17a2428521779d 100644
--- a/Mathlib/Analysis/Calculus/Deriv/Pi.lean
+++ b/Mathlib/Analysis/Calculus/Deriv/Pi.lean
@@ -18,7 +18,7 @@ variable {𝕜 ι : Type*} [DecidableEq ι] [NontriviallyNormedField 𝕜]
 
 theorem hasDerivAt_update (x : ι → 𝕜) (i : ι) (y : 𝕜) :
     HasDerivAt (Function.update x i) (Pi.single i (1 : 𝕜)) y := by
-  convert (hasFDerivAt_update x y).hasDerivAt
+  convert! (hasFDerivAt_update x y).hasDerivAt
   ext z j
   rw [Pi.single, Function.update_apply]
   split_ifs with h
diff --git a/Mathlib/Analysis/Calculus/Deriv/Star.lean b/Mathlib/Analysis/Calculus/Deriv/Star.lean
index 0c49359f807a05..1d0a0f93e6b796 100644
--- a/Mathlib/Analysis/Calculus/Deriv/Star.lean
+++ b/Mathlib/Analysis/Calculus/Deriv/Star.lean
@@ -76,7 +76,7 @@ open scoped ComplexConjugate
 lemma HasDerivAt.star_conj {f : 𝕜 → F} {f' : F} (hf : HasDerivAt f f' x) :
     HasDerivAt (star ∘ f ∘ conj) (star f') (conj x) := by
   rw [hasDerivAt_iff_hasFDerivAt]
-  convert hf.hasFDerivAt.star_star
+  convert! hf.hasFDerivAt.star_star
   ext
   simp
 
@@ -85,8 +85,8 @@ lemma HasDerivAt.star_conj {f : 𝕜 → F} {f' : F} (hf : HasDerivAt f f' x) :
 @[simp]
 lemma hasDerivAt_star_conj_iff {f : 𝕜 → F} {x : 𝕜} {f' : F} :
     HasDerivAt (star ∘ f ∘ conj) f' x ↔ HasDerivAt f (star f') (conj x) :=
-  ⟨fun hf ↦ by convert hf.star_conj; simp [Function.comp_def],
-    fun hf ↦ by convert hf.star_conj <;> simp⟩
+  ⟨fun hf ↦ by convert! hf.star_conj; simp [Function.comp_def],
+    fun hf ↦ by convert! hf.star_conj <;> simp⟩
 
 /-- If `f` has derivative `f'` at `z`, then `conj ∘ f ∘ conj` has derivative `conj f'` at
 `conj z`. -/
@@ -110,8 +110,8 @@ lemma DifferentiableAt.star_conj {f : 𝕜 → F} (hf : DifferentiableAt 𝕜 f
 @[simp]
 lemma differentiableAt_star_conj_iff {f : 𝕜 → F} :
     DifferentiableAt 𝕜 (star ∘ f ∘ conj) x ↔ DifferentiableAt 𝕜 f (conj x) :=
-  ⟨fun hf ↦ by convert hf.star_conj; simp [Function.comp_def],
-    fun hf ↦ by convert hf.star_conj; simp⟩
+  ⟨fun hf ↦ by convert! hf.star_conj; simp [Function.comp_def],
+    fun hf ↦ by convert! hf.star_conj; simp⟩
 
 /-- If `f` is differentiable at `conj z`, then `conj ∘ f ∘ conj` is differentiable at `z`. -/
 lemma DifferentiableAt.conj_conj {f : 𝕜 → 𝕜} (hf : DifferentiableAt 𝕜 f x) :
@@ -130,7 +130,7 @@ lemma deriv_star_conj {f : 𝕜 → F} :
     deriv (star ∘ f ∘ conj) = star ∘ deriv f ∘ conj := by
   ext z
   by_cases hf : DifferentiableAt 𝕜 f (conj z)
-  · convert hf.hasDerivAt.star_conj.deriv; simp
+  · convert! hf.hasDerivAt.star_conj.deriv; simp
   · have := differentiableAt_star_conj_iff.not.2 hf
     simp_all [deriv_zero_of_not_differentiableAt]
 
diff --git a/Mathlib/Analysis/Calculus/Deriv/ZPow.lean b/Mathlib/Analysis/Calculus/Deriv/ZPow.lean
index a9c2cda0c75897..4f3d64e754953d 100644
--- a/Mathlib/Analysis/Calculus/Deriv/ZPow.lean
+++ b/Mathlib/Analysis/Calculus/Deriv/ZPow.lean
@@ -42,7 +42,7 @@ theorem hasStrictDerivAt_zpow (m : ℤ) (x : 𝕜) (h : x ≠ 0 ∨ 0 ≤ m) :
   have : ∀ m : ℤ, 0 < m → HasStrictDerivAt (· ^ m) ((m : 𝕜) * x ^ (m - 1)) x := fun m hm ↦ by
     lift m to ℕ using hm.le
     simp only [zpow_natCast, Int.cast_natCast]
-    convert hasStrictDerivAt_pow m x using 2
+    convert! hasStrictDerivAt_pow m x using 2
     rw [← Int.ofNat_one, ← Int.ofNat_sub, zpow_natCast]
     norm_cast at hm
   rcases lt_trichotomy m 0 with (hm | hm | hm)
@@ -50,7 +50,7 @@ theorem hasStrictDerivAt_zpow (m : ℤ) (x : 𝕜) (h : x ≠ 0 ∨ 0 ≤ m) :
     have := (hasStrictDerivAt_inv ?_).scomp _ (this (-m) (neg_pos.2 hm)) <;>
       [skip; exact zpow_ne_zero _ hx]
     simp only [Function.comp_def, zpow_neg, inv_inv, smul_eq_mul] at this
-    convert this using 1
+    convert! this using 1
     rw [sq, mul_inv, inv_inv, Int.cast_neg, neg_mul, neg_mul_neg, ← zpow_add₀ hx, mul_assoc, ←
       zpow_add₀ hx]
     congr
diff --git a/Mathlib/Analysis/Calculus/FDeriv/Add.lean b/Mathlib/Analysis/Calculus/FDeriv/Add.lean
index 87d70486e27ee5..c8f870d8d1f8bd 100644
--- a/Mathlib/Analysis/Calculus/FDeriv/Add.lean
+++ b/Mathlib/Analysis/Calculus/FDeriv/Add.lean
@@ -402,23 +402,23 @@ variable {ι : Type*} {u : Finset ι} {A : ι → E → F} {A' : ι → E →L[
 theorem HasStrictFDerivAt.fun_sum (h : ∀ i ∈ u, HasStrictFDerivAt (A i) (A' i) x) :
     HasStrictFDerivAt (fun y => ∑ i ∈ u, A i y) (∑ i ∈ u, A' i) x := by
   simp only [hasStrictFDerivAt_iff_isLittleO] at *
-  convert IsLittleO.sum h
+  convert! IsLittleO.sum h
   simp [Finset.sum_sub_distrib, ContinuousLinearMap.sum_apply]
 
 @[fun_prop]
 theorem HasStrictFDerivAt.sum (h : ∀ i ∈ u, HasStrictFDerivAt (A i) (A' i) x) :
     HasStrictFDerivAt (∑ i ∈ u, A i) (∑ i ∈ u, A' i) x := by
-  convert HasStrictFDerivAt.fun_sum h; simp
+  convert! HasStrictFDerivAt.fun_sum h; simp
 
 theorem HasFDerivAtFilter.fun_sum (h : ∀ i ∈ u, HasFDerivAtFilter (A i) (A' i) L) :
     HasFDerivAtFilter (fun y => ∑ i ∈ u, A i y) (∑ i ∈ u, A' i) L := by
   simp only [hasFDerivAtFilter_iff_isLittleO] at *
-  convert IsLittleO.sum h
+  convert! IsLittleO.sum h
   simp [ContinuousLinearMap.sum_apply]
 
 theorem HasFDerivAtFilter.sum (h : ∀ i ∈ u, HasFDerivAtFilter (A i) (A' i) L) :
     HasFDerivAtFilter (∑ i ∈ u, A i) (∑ i ∈ u, A' i) L := by
-  convert HasFDerivAtFilter.fun_sum h; simp
+  convert! HasFDerivAtFilter.fun_sum h; simp
 
 @[fun_prop]
 theorem HasFDerivWithinAt.fun_sum (h : ∀ i ∈ u, HasFDerivWithinAt (A i) (A' i) s x) :
diff --git a/Mathlib/Analysis/Calculus/FDeriv/Analytic.lean b/Mathlib/Analysis/Calculus/FDeriv/Analytic.lean
index 927f191ab2c285..a2f38ed508b71f 100644
--- a/Mathlib/Analysis/Calculus/FDeriv/Analytic.lean
+++ b/Mathlib/Analysis/Calculus/FDeriv/Analytic.lean
@@ -182,7 +182,7 @@ theorem HasFPowerSeriesWithinOnBall.hasFDerivWithinAt [CompleteSpace F]
     HasFDerivWithinAt f (continuousMultilinearCurryFin1 𝕜 E F (p.changeOrigin y 1))
       (insert x s) (x + y) := by
   rcases eq_or_ne y 0 with rfl | h''y
-  · convert (h.changeOrigin hy h'y).hasFPowerSeriesWithinAt.hasFDerivWithinAt
+  · convert! (h.changeOrigin hy h'y).hasFPowerSeriesWithinAt.hasFDerivWithinAt
     simp
   · have Z := (h.changeOrigin hy h'y).hasFPowerSeriesWithinAt.hasFDerivWithinAt
     apply (Z.mono (subset_insert _ _)).mono_of_mem_nhdsWithin
@@ -245,7 +245,7 @@ protected theorem HasFPowerSeriesWithinOnBall.fderivWithin_of_mem [CompleteSpace
     HasFPowerSeriesWithinOnBall (fderivWithin 𝕜 f s) p.derivSeries s x r := by
   have : insert x s = s := insert_eq_of_mem hx
   rw [← this] at hu
-  convert h.fderivWithin hu
+  convert! h.fderivWithin hu
   exact this.symm
 
 /-- If a function is analytic on a set `s`, so is its Fréchet derivative. -/
@@ -274,7 +274,7 @@ protected theorem AnalyticOnNhd.iteratedFDeriv [CompleteSpace F] (h : AnalyticOn
   | succ n IH =>
     rw [iteratedFDeriv_succ_eq_comp_left]
     -- Porting note: for reasons that I do not understand at all, `?g` cannot be inlined.
-    convert ContinuousLinearMap.comp_analyticOnNhd ?g IH.fderiv
+    convert! ContinuousLinearMap.comp_analyticOnNhd ?g IH.fderiv
     case g => exact ↑(continuousMultilinearCurryLeftEquiv 𝕜 (fun _ : Fin (n + 1) ↦ E) F).symm
     simp
 
@@ -328,7 +328,7 @@ theorem HasFPowerSeriesWithinOnBall.hasSum_derivSeries_of_hasFDerivWithinAt
     apply HasFDerivWithinAt.fderivWithin _ (hu _ h'y)
     exact a.hasFDerivAt.comp_hasFDerivWithinAt (x + y) hf'
   rw [this] at Z
-  convert Z with n
+  convert! Z with n
   ext v
   simp only [FormalMultilinearSeries.derivSeries, ContinuousLinearMap.coe_sum', Finset.sum_apply,
     ContinuousLinearMap.compFormalMultilinearSeries_apply,
@@ -542,7 +542,7 @@ theorem CPolynomialOn.iteratedFDeriv (h : CPolynomialOn 𝕜 f s) (n : ℕ) :
     exact ((continuousMultilinearCurryFin0 𝕜 E F).symm : F →L[𝕜] E [×0]→L[𝕜] F).comp_cpolynomialOn h
   | succ n IH =>
     rw [iteratedFDeriv_succ_eq_comp_left]
-    convert ContinuousLinearMap.comp_cpolynomialOn ?g IH.fderiv
+    convert! ContinuousLinearMap.comp_cpolynomialOn ?g IH.fderiv
     case g => exact ↑(continuousMultilinearCurryLeftEquiv 𝕜 (fun _ : Fin (n + 1) ↦ E) F).symm
     simp
 
@@ -616,7 +616,7 @@ theorem changeOrigin_toFormalMultilinearSeries [DecidableEq ι] :
 
 protected theorem hasStrictFDerivAt [DecidableEq ι] : HasStrictFDerivAt f (f.linearDeriv x) x := by
   rw [← changeOrigin_toFormalMultilinearSeries]
-  convert f.hasFiniteFPowerSeriesOnBall.hasStrictFDerivAt (y := x) ENNReal.coe_lt_top
+  convert! f.hasFiniteFPowerSeriesOnBall.hasStrictFDerivAt (y := x) ENNReal.coe_lt_top
   rw [zero_add]
 
 protected theorem hasFDerivAt [DecidableEq ι] : HasFDerivAt f (f.linearDeriv x) x :=
@@ -630,7 +630,7 @@ protected theorem hasStrictFDerivAt_uncurry [DecidableEq ι]
     |>.continuousMultilinearMapOption
   have Hf := (f.hasStrictFDerivAt (fun _ ↦ fa)).comp (f := fun fx _ ↦ fx) fa
     (hasStrictFDerivAt_pi.2 fun _ ↦ hasStrictFDerivAt_id _)
-  convert Hf using 1
+  convert! Hf using 1
   ext g
   · suffices ∑ i, fa.1 (Function.update fa.2 i 0) =
         ∑ i, fa.1 fun j ↦ (Function.update (fun _ ↦ fa) (some i) (g, 0) (some j)).2 j by
@@ -653,8 +653,9 @@ theorem _root_.HasStrictFDerivAt.continuousMultilinearMap_apply {G : Type*}
     HasStrictFDerivAt (fun x ↦ f x (g · x))
       (ContinuousMultilinearMap.apply 𝕜 E F (g · x) ∘L f' +
         ∑ i, (f x).toContinuousLinearMap (g · x) i ∘L g' i) x := by
-  convert ContinuousMultilinearMap.hasStrictFDerivAt_uncurry (f x, (g · x))
-    |>.comp x (hf.prodMk (hasStrictFDerivAt_pi.2 hg))
+  convert!
+    ContinuousMultilinearMap.hasStrictFDerivAt_uncurry (f x, (g · x)) |>.comp x
+      (hf.prodMk (hasStrictFDerivAt_pi.2 hg))
   ext
   simp
 
@@ -666,8 +667,10 @@ theorem _root_.HasFDerivWithinAt.continuousMultilinearMap_apply {G : Type*}
     HasFDerivWithinAt (fun x ↦ f x (g · x))
       (ContinuousMultilinearMap.apply 𝕜 E F (g · x) ∘L f' +
         ∑ i, (f x).toContinuousLinearMap (g · x) i ∘L g' i) s x := by
-  convert ContinuousMultilinearMap.hasStrictFDerivAt_uncurry (f x, (g · x))
-    |>.hasFDerivAt.comp_hasFDerivWithinAt x (hf.prodMk (hasFDerivWithinAt_pi.2 hg))
+  convert!
+    ContinuousMultilinearMap.hasStrictFDerivAt_uncurry
+        (f x, (g · x)) |>.hasFDerivAt.comp_hasFDerivWithinAt
+      x (hf.prodMk (hasFDerivWithinAt_pi.2 hg))
   ext
   simp
 
@@ -794,7 +797,7 @@ theorem derivSeries_apply_diag (n : ℕ) (x : E) :
     compContinuousMultilinearMap_coe, ContinuousLinearEquiv.coe_coe, LinearIsometryEquiv.coe_coe,
     Function.comp_apply, ContinuousMultilinearMap.sum_apply, map_sum, coe_sum', Finset.sum_apply,
     continuousMultilinearCurryFin1_apply, Matrix.zero_empty]
-  convert Finset.sum_const _
+  convert! Finset.sum_const _
   · rw [Fin.snoc_zero, changeOriginSeriesTerm_apply, Finset.piecewise_same, add_comm]
   · rw [← card, card_subtype, ← Finset.powerset_univ, ← Finset.powersetCard_eq_filter,
       Finset.card_powersetCard, ← card, card_fin, eq_comm, add_comm, Nat.choose_succ_self_right]
@@ -847,7 +850,7 @@ theorem factorial_smul (n : ℕ) :
 
 theorem hasSum_iteratedFDeriv [CharZero 𝕜] {y : E} (hy : y ∈ Metric.eball 0 r) :
     HasSum (fun n ↦ (n ! : 𝕜)⁻¹ • iteratedFDeriv 𝕜 n f x fun _ ↦ y) (f (x + y)) := by
-  convert h.hasSum hy with n
+  convert! h.hasSum hy with n
   rw [← h.factorial_smul y n, smul_comm, ← smul_assoc, nsmul_eq_mul,
     mul_inv_cancel₀ <| cast_ne_zero.mpr n.factorial_ne_zero, one_smul]
 
diff --git a/Mathlib/Analysis/Calculus/FDeriv/ContinuousAlternatingMap.lean b/Mathlib/Analysis/Calculus/FDeriv/ContinuousAlternatingMap.lean
index 80d8efd9fab5e1..51b8a804c12d29 100644
--- a/Mathlib/Analysis/Calculus/FDeriv/ContinuousAlternatingMap.lean
+++ b/Mathlib/Analysis/Calculus/FDeriv/ContinuousAlternatingMap.lean
@@ -86,16 +86,17 @@ theorem HasFDerivAt.continuousAlternatingMapCompContinuousLinearMap
     HasFDerivAt (fun x ↦ (f x).compContinuousLinearMap (g x))
       (compContinuousLinearMapCLM (g x) ∘L f' +
         (f x).fderivCompContinuousLinearMap (g x) ∘L g') x := by
-  convert hasStrictFDerivAt_compContinuousLinearMap (f x, (g x)) |>.hasFDerivAt
-    |>.comp x (hf.prodMk hg)
+  convert!
+    hasStrictFDerivAt_compContinuousLinearMap (f x, (g x)) |>.hasFDerivAt |>.comp x (hf.prodMk hg)
 
 theorem HasFDerivWithinAt.continuousAlternatingMapCompContinuousLinearMap
     (hf : HasFDerivWithinAt f f' s x) (hg : HasFDerivWithinAt g g' s x) :
     HasFDerivWithinAt (fun x ↦ (f x).compContinuousLinearMap (g x))
       (compContinuousLinearMapCLM (g x) ∘L f' +
         (f x).fderivCompContinuousLinearMap (g x) ∘L g') s x := by
-  convert hasStrictFDerivAt_compContinuousLinearMap (f x, (g x)) |>.hasFDerivAt
-    |>.comp_hasFDerivWithinAt x (hf.prodMk hg)
+  convert!
+    hasStrictFDerivAt_compContinuousLinearMap (f x, (g x)) |>.hasFDerivAt |>.comp_hasFDerivWithinAt
+      x (hf.prodMk hg)
 
 theorem fderivWithin_continuousAlternatingMapCompContinuousLinearMap
     (hf : DifferentiableWithinAt 𝕜 f s x) (hg : DifferentiableWithinAt 𝕜 g s x)
diff --git a/Mathlib/Analysis/Calculus/FDeriv/ContinuousMultilinearMap.lean b/Mathlib/Analysis/Calculus/FDeriv/ContinuousMultilinearMap.lean
index 1a0341c1b2ef17..09fe25ff901c5f 100644
--- a/Mathlib/Analysis/Calculus/FDeriv/ContinuousMultilinearMap.lean
+++ b/Mathlib/Analysis/Calculus/FDeriv/ContinuousMultilinearMap.lean
@@ -65,7 +65,7 @@ theorem ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap
         fg.1.fderivCompContinuousLinearMap fg.2 ∘L .snd _ _ _)
       fg := by
   have := (compContinuousLinearMapContinuousMultilinear 𝕜 F G H).hasStrictFDerivAt fg.2
-  convert this.comp fg hasStrictFDerivAt_snd |>.clm_apply hasStrictFDerivAt_fst
+  convert! this.comp fg hasStrictFDerivAt_snd |>.clm_apply hasStrictFDerivAt_fst
   ext <;> simp [fderivCompContinuousLinearMap]
 
 theorem HasStrictFDerivAt.continuousMultilinearMapCompContinuousLinearMap
@@ -81,16 +81,19 @@ theorem HasFDerivAt.continuousMultilinearMapCompContinuousLinearMap
     HasFDerivAt (fun x ↦ (f x).compContinuousLinearMap (g · x))
       (compContinuousLinearMapL (g · x) ∘L f' +
         (f x).fderivCompContinuousLinearMap (g · x) ∘L .pi g') x := by
-  convert hasStrictFDerivAt_compContinuousLinearMap (f x, (g · x)) |>.hasFDerivAt
-    |>.comp x (hf.prodMk (hasFDerivAt_pi.2 hg))
+  convert!
+    hasStrictFDerivAt_compContinuousLinearMap (f x, (g · x)) |>.hasFDerivAt |>.comp x
+      (hf.prodMk (hasFDerivAt_pi.2 hg))
 
 theorem HasFDerivWithinAt.continuousMultilinearMapCompContinuousLinearMap
     (hf : HasFDerivWithinAt f f' s x) (hg : ∀ i, HasFDerivWithinAt (g i) (g' i) s x) :
     HasFDerivWithinAt (fun x ↦ (f x).compContinuousLinearMap (g · x))
       (compContinuousLinearMapL (g · x) ∘L f' +
         (f x).fderivCompContinuousLinearMap (g · x) ∘L .pi g') s x := by
-  convert hasStrictFDerivAt_compContinuousLinearMap (f x, (g · x)) |>.hasFDerivAt
-    |>.comp_hasFDerivWithinAt x (hf.prodMk (hasFDerivWithinAt_pi.2 hg))
+  convert!
+    hasStrictFDerivAt_compContinuousLinearMap
+          (f x, (g · x)) |>.hasFDerivAt |>.comp_hasFDerivWithinAt
+      x (hf.prodMk (hasFDerivWithinAt_pi.2 hg))
 
 theorem fderivWithin_continuousMultilinearMapCompContinuousLinearMap
     (hf : DifferentiableWithinAt 𝕜 f s x) (hg : ∀ i, DifferentiableWithinAt 𝕜 (g i) s x)
diff --git a/Mathlib/Analysis/Calculus/FDeriv/Equiv.lean b/Mathlib/Analysis/Calculus/FDeriv/Equiv.lean
index ebc8b559e4cd49..d383e0571d7875 100644
--- a/Mathlib/Analysis/Calculus/FDeriv/Equiv.lean
+++ b/Mathlib/Analysis/Calculus/FDeriv/Equiv.lean
@@ -107,7 +107,7 @@ theorem comp_hasFDerivWithinAt_iff {f : G → E} {s : Set G} {x : G} {f' : G →
 theorem comp_hasStrictFDerivAt_iff {f : G → E} {x : G} {f' : G →L[𝕜] E} :
     HasStrictFDerivAt (iso ∘ f) ((iso : E →L[𝕜] F).comp f') x ↔ HasStrictFDerivAt f f' x := by
   refine ⟨fun H => ?_, fun H => iso.hasStrictFDerivAt.comp x H⟩
-  convert iso.symm.hasStrictFDerivAt.comp x H using 1 <;>
+  convert! iso.symm.hasStrictFDerivAt.comp x H using 1 <;>
     ext z <;> apply (iso.symm_apply_apply _).symm
 
 theorem comp_hasFDerivAt_iff {f : G → E} {x : G} {f' : G →L[𝕜] E} :
diff --git a/Mathlib/Analysis/Calculus/FDeriv/Measurable.lean b/Mathlib/Analysis/Calculus/FDeriv/Measurable.lean
index 84564b73eab3b1..605dd565d39f79 100644
--- a/Mathlib/Analysis/Calculus/FDeriv/Measurable.lean
+++ b/Mathlib/Analysis/Calculus/FDeriv/Measurable.lean
@@ -373,7 +373,7 @@ variable [CompleteSpace F]
 Borel-measurable. -/
 theorem measurableSet_of_differentiableAt : MeasurableSet { x | DifferentiableAt 𝕜 f x } := by
   have : IsComplete (univ : Set (E →L[𝕜] F)) := complete_univ
-  convert measurableSet_of_differentiableAt_of_isComplete 𝕜 f this
+  convert! measurableSet_of_differentiableAt_of_isComplete 𝕜 f this
   simp
 
 @[fun_prop]
@@ -701,7 +701,7 @@ Borel-measurable. -/
 theorem measurableSet_of_differentiableWithinAt_Ici :
     MeasurableSet { x | DifferentiableWithinAt ℝ f (Ici x) x } := by
   have : IsComplete (univ : Set F) := complete_univ
-  convert measurableSet_of_differentiableWithinAt_Ici_of_isComplete f this
+  convert! measurableSet_of_differentiableWithinAt_Ici_of_isComplete f this
   simp
 
 @[fun_prop]
@@ -859,7 +859,7 @@ lemma isOpen_B_with_param {r s t : ℝ} (hf : Continuous f.uncurry) (K : Set (E
     IsOpen {p : α × E | p.2 ∈ B (f p.1) K r s t} := by
   suffices H : IsOpen (⋃ L ∈ K,
       {p : α × E | p.2 ∈ A (f p.1) L r t ∧ p.2 ∈ A (f p.1) L s t}) by
-    convert H; ext p; simp [B]
+    convert! H; ext p; simp [B]
   refine isOpen_biUnion (fun L _ ↦ ?_)
   exact (isOpen_A_with_param hf L).inter (isOpen_A_with_param hf L)
 
@@ -894,7 +894,7 @@ values in a complete space is Borel-measurable. -/
 theorem measurableSet_of_differentiableAt_with_param (hf : Continuous f.uncurry) :
     MeasurableSet {p : α × E | DifferentiableAt 𝕜 (f p.1) p.2} := by
   have : IsComplete (univ : Set (E →L[𝕜] F)) := complete_univ
-  convert measurableSet_of_differentiableAt_of_isComplete_with_param hf this
+  convert! measurableSet_of_differentiableAt_of_isComplete_with_param hf this
   simp
 
 theorem measurable_fderiv_with_param (hf : Continuous f.uncurry) :
diff --git a/Mathlib/Analysis/Calculus/FDeriv/Mul.lean b/Mathlib/Analysis/Calculus/FDeriv/Mul.lean
index 7f4a5277b96fff..221f2d046450c0 100644
--- a/Mathlib/Analysis/Calculus/FDeriv/Mul.lean
+++ b/Mathlib/Analysis/Calculus/FDeriv/Mul.lean
@@ -176,7 +176,7 @@ theorem HasStrictFDerivAt.mul' {x : E} (ha : HasStrictFDerivAt a a' x)
 @[to_fun (attr := fun_prop)]
 theorem HasStrictFDerivAt.mul (hc : HasStrictFDerivAt c c' x) (hd : HasStrictFDerivAt d d' x) :
     HasStrictFDerivAt (c * d) (c x • d' + d x • c') x := by
-  convert hc.mul' hd
+  convert! hc.mul' hd
   ext z
   apply mul_comm
 
@@ -190,7 +190,7 @@ theorem HasFDerivWithinAt.mul' (ha : HasFDerivWithinAt a a' s x) (hb : HasFDeriv
 @[to_fun (attr := fun_prop)]
 theorem HasFDerivWithinAt.mul (hc : HasFDerivWithinAt c c' s x) (hd : HasFDerivWithinAt d d' s x) :
     HasFDerivWithinAt (c * d) (c x • d' + d x • c') s x := by
-  convert hc.mul' hd
+  convert! hc.mul' hd
   ext z
   apply mul_comm
 
@@ -204,7 +204,7 @@ theorem HasFDerivAt.mul' (ha : HasFDerivAt a a' x) (hb : HasFDerivAt b b' x) :
 @[to_fun (attr := fun_prop)]
 theorem HasFDerivAt.mul (hc : HasFDerivAt c c' x) (hd : HasFDerivAt d d' x) :
     HasFDerivAt (c * d) (c x • d' + d x • c') x := by
-  convert hc.mul' hd
+  convert! hc.mul' hd
   ext z
   apply mul_comm
 
@@ -274,7 +274,7 @@ theorem HasStrictFDerivAt.mul_const' (ha : HasStrictFDerivAt a a' x) (b : 𝔸)
 @[fun_prop]
 theorem HasStrictFDerivAt.mul_const (hc : HasStrictFDerivAt c c' x) (d : 𝔸') :
     HasStrictFDerivAt (fun y => c y * d) (d • c') x := by
-  convert hc.mul_const' d
+  convert! hc.mul_const' d
   ext z
   apply mul_comm
 
@@ -286,7 +286,7 @@ theorem HasFDerivWithinAt.mul_const' (ha : HasFDerivWithinAt a a' s x) (b : 𝔸
 @[fun_prop]
 theorem HasFDerivWithinAt.mul_const (hc : HasFDerivWithinAt c c' s x) (d : 𝔸') :
     HasFDerivWithinAt (fun y => c y * d) (d • c') s x := by
-  convert hc.mul_const' d
+  convert! hc.mul_const' d
   ext z
   apply mul_comm
 
@@ -298,7 +298,7 @@ theorem HasFDerivAt.mul_const' (ha : HasFDerivAt a a' x) (b : 𝔸) :
 @[fun_prop]
 theorem HasFDerivAt.mul_const (hc : HasFDerivAt c c' x) (d : 𝔸') :
     HasFDerivAt (fun y => c y * d) (d • c') x := by
-  convert hc.mul_const' d
+  convert! hc.mul_const' d
   ext z
   apply mul_comm
 
@@ -683,7 +683,7 @@ theorem fderiv_inverse (x : Rˣ) : fderiv 𝕜 (@Ring.inverse R _) x = -mulLeftR
 
 theorem hasStrictFDerivAt_ringInverse (x : Rˣ) :
     HasStrictFDerivAt Ring.inverse (-mulLeftRight 𝕜 R ↑x⁻¹ ↑x⁻¹) x := by
-  convert (analyticAt_inverse (𝕜 := 𝕜) x).hasStrictFDerivAt
+  convert! (analyticAt_inverse (𝕜 := 𝕜) x).hasStrictFDerivAt
   exact (fderiv_inverse x).symm
 
 variable {h : E → R} {z : E} {S : Set E}
diff --git a/Mathlib/Analysis/Calculus/FDeriv/Norm.lean b/Mathlib/Analysis/Calculus/FDeriv/Norm.lean
index b6bcdb7896031e..e2d0003e6a7904 100644
--- a/Mathlib/Analysis/Calculus/FDeriv/Norm.lean
+++ b/Mathlib/Analysis/Calculus/FDeriv/Norm.lean
@@ -62,7 +62,7 @@ theorem ContDiffAt.contDiffAt_norm_smul (ht : t ≠ 0) (h : ContDiffAt ℝ n (
   have h1 : ContDiffAt ℝ n (fun y ↦ t⁻¹ • y) (t • x) := (contDiff_const_smul t⁻¹).contDiffAt
   have h2 : ContDiffAt ℝ n (fun y ↦ |t| * ‖y‖) x := h.const_smul |t|
   conv at h2 => enter [4]; rw [← one_smul ℝ x, ← inv_mul_cancel₀ ht, mul_smul]
-  convert h2.comp (t • x) h1 using 1
+  convert! h2.comp (t • x) h1 using 1
   ext y
   simp only [Function.comp_apply]
   rw [norm_smul, ← mul_assoc, norm_eq_abs, ← abs_mul, mul_inv_cancel₀ ht, abs_one, one_mul]
@@ -71,7 +71,7 @@ theorem contDiffAt_norm_smul_iff (ht : t ≠ 0) :
     ContDiffAt ℝ n (‖·‖) x ↔ ContDiffAt ℝ n (‖·‖) (t • x) where
   mp h := h.contDiffAt_norm_smul ht
   mpr hd := by
-    convert hd.contDiffAt_norm_smul (inv_ne_zero ht)
+    convert! hd.contDiffAt_norm_smul (inv_ne_zero ht)
     rw [smul_smul, inv_mul_cancel₀ ht, one_smul]
 
 theorem ContDiffAt.contDiffAt_norm_of_smul (h : ContDiffAt ℝ n (‖·‖) (t • x)) :
@@ -95,7 +95,7 @@ theorem HasStrictFDerivAt.hasStrictFDerivAt_norm_smul
     hasStrictFDerivAt_id (t • x) |>.const_smul t⁻¹
   have h2 : HasStrictFDerivAt (fun y ↦ |t| * ‖y‖) (|t| • f) x := h.const_smul |t|
   conv at h2 => enter [3]; rw [← one_smul ℝ x, ← inv_mul_cancel₀ ht, mul_smul]
-  convert h2.comp (t • x) h1 with y
+  convert! h2.comp (t • x) h1 with y
   · rw [norm_smul, ← mul_assoc, norm_eq_abs, ← abs_mul, mul_inv_cancel₀ ht, abs_one, one_mul]
   ext y
   simp only [coe_smul', Pi.smul_apply, smul_eq_mul, comp_smulₛₗ, map_inv₀, RingHom.id_apply,
@@ -119,7 +119,7 @@ theorem HasFDerivAt.hasFDerivAt_norm_smul
     hasFDerivAt_id (t • x) |>.const_smul t⁻¹
   have h2 : HasFDerivAt (fun y ↦ |t| * ‖y‖) (|t| • f) x := h.const_smul |t|
   conv at h2 => enter [3]; rw [← one_smul ℝ x, ← inv_mul_cancel₀ ht, mul_smul]
-  convert h2.comp (t • x) h1 using 2 with y
+  convert! h2.comp (t • x) h1 using 2 with y
   · simp only [Function.comp_apply]
     rw [norm_smul, ← mul_assoc, norm_eq_abs, ← abs_mul, mul_inv_cancel₀ ht, abs_one, one_mul]
   · ext y
@@ -141,7 +141,7 @@ theorem differentiableAt_norm_smul (ht : t ≠ 0) :
     DifferentiableAt ℝ (‖·‖) x ↔ DifferentiableAt ℝ (‖·‖) (t • x) where
   mp hd := (hd.hasFDerivAt.hasFDerivAt_norm_smul ht).differentiableAt
   mpr hd := by
-    convert (hd.hasFDerivAt.hasFDerivAt_norm_smul (inv_ne_zero ht)).differentiableAt
+    convert! (hd.hasFDerivAt.hasFDerivAt_norm_smul (inv_ne_zero ht)).differentiableAt
     rw [smul_smul, inv_mul_cancel₀ ht, one_smul]
 
 theorem DifferentiableAt.differentiableAt_norm_of_smul (h : DifferentiableAt ℝ (‖·‖) (t • x)) :
diff --git a/Mathlib/Analysis/Calculus/FDeriv/Symmetric.lean b/Mathlib/Analysis/Calculus/FDeriv/Symmetric.lean
index 5cb50a282a9eb6..97ce608ae1fb7e 100644
--- a/Mathlib/Analysis/Calculus/FDeriv/Symmetric.lean
+++ b/Mathlib/Analysis/Calculus/FDeriv/Symmetric.lean
@@ -178,7 +178,7 @@ theorem IsSymmSndFDerivWithinAt.iteratedFDerivWithin_cons {x v w : E}
     iteratedFDerivWithin 𝕜 2 f s x ![v, w] = iteratedFDerivWithin 𝕜 2 f s x ![w, v] := by
   simp_rw [isSymmSndFDerivWithinAt_iff_iteratedFDerivWithin hs hx, ContinuousMultilinearMap.ext_iff,
     ContinuousMultilinearMap.domDomCongr_apply] at hf
-  convert hf ![w, v] using 2
+  convert! hf ![w, v] using 2
   ext i
   fin_cases i <;> simp
 
@@ -249,7 +249,7 @@ theorem Convex.taylor_approx_two_segment {v w : E} (hv : x + v ∈ interior s)
     rw [← smul_smul]
     apply s_conv.interior.add_smul_mem this _ ht
     rw [add_assoc] at hw
-    convert s_conv.add_smul_mem_interior xs hw ⟨hpos, h_lt_1.le⟩ using 1
+    convert! s_conv.add_smul_mem_interior xs hw ⟨hpos, h_lt_1.le⟩ using 1
     module
   -- define a function `g` on `[0,1]` (identified with `[v, v + w]`) such that `g 1 - g 0` is the
   -- quantity to be estimated. We will check that its derivative is given by an explicit
@@ -273,7 +273,7 @@ theorem Convex.taylor_approx_two_segment {v w : E} (hv : x + v ∈ interior s)
     · apply_rules [HasDerivAt.hasDerivWithinAt, HasDerivAt.smul_const, hasDerivAt_mul_const]
     · suffices H : HasDerivWithinAt (fun u => ((u * h) ^ 2 / 2) • f'' w w)
           ((((2 : ℕ) : ℝ) * (t * h) ^ (2 - 1) * (1 * h) / 2) • f'' w w) (Icc 0 1) t by
-        convert H using 2
+        convert! H using 2
         ring
       apply_rules [HasDerivAt.hasDerivWithinAt, HasDerivAt.smul_const, hasDerivAt_id',
         HasDerivAt.pow, HasDerivAt.mul_const]
@@ -316,7 +316,7 @@ theorem Convex.taylor_approx_two_segment {v w : E} (hv : x + v ∈ interior s)
   have I : ‖g 1 - g 0‖ ≤ ε * ((‖v‖ + ‖w‖) * ‖w‖) * h ^ 2 := by
     simpa only [mul_one, sub_zero] using
       norm_image_sub_le_of_norm_deriv_le_segment' g_deriv g'_bound 1 (right_mem_Icc.2 zero_le_one)
-  convert I using 1
+  convert! I using 1
   · congr 1
     simp only [g, add_zero, one_mul, zero_div, zero_mul, sub_zero,
       zero_smul, Ne, not_false_iff, zero_pow, reduceCtorEq]
@@ -336,29 +336,29 @@ theorem Convex.isLittleO_alternate_sum_square {v w : E} (h4v : x + (4 : ℝ) •
   have A : (1 : ℝ) / 2 ∈ Ioc (0 : ℝ) 1 := ⟨by simp, by norm_num⟩
   have B : (1 : ℝ) / 2 ∈ Icc (0 : ℝ) 1 := ⟨by simp, by norm_num⟩
   have h2v2w : x + (2 : ℝ) • v + (2 : ℝ) • w ∈ interior s := by
-    convert s_conv.interior.add_smul_sub_mem h4v h4w B using 1
+    convert! s_conv.interior.add_smul_sub_mem h4v h4w B using 1
     module
   have h2vww : x + (2 • v + w) + w ∈ interior s := by
-    convert h2v2w using 1
+    convert! h2v2w using 1
     module
   have h2v : x + (2 : ℝ) • v ∈ interior s := by
-    convert s_conv.add_smul_sub_mem_interior xs h4v A using 1
+    convert! s_conv.add_smul_sub_mem_interior xs h4v A using 1
     module
   have h2w : x + (2 : ℝ) • w ∈ interior s := by
-    convert s_conv.add_smul_sub_mem_interior xs h4w A using 1
+    convert! s_conv.add_smul_sub_mem_interior xs h4w A using 1
     module
   have hvw : x + (v + w) ∈ interior s := by
-    convert s_conv.add_smul_sub_mem_interior xs h2v2w A using 1
+    convert! s_conv.add_smul_sub_mem_interior xs h2v2w A using 1
     module
   have h2vw : x + (2 • v + w) ∈ interior s := by
-    convert s_conv.interior.add_smul_sub_mem h2v h2v2w B using 1
+    convert! s_conv.interior.add_smul_sub_mem h2v h2v2w B using 1
     module
   have hvww : x + (v + w) + w ∈ interior s := by
-    convert s_conv.interior.add_smul_sub_mem h2w h2v2w B using 1
+    convert! s_conv.interior.add_smul_sub_mem h2w h2v2w B using 1
     module
   have TA1 := s_conv.taylor_approx_two_segment hf xs hx h2vw h2vww
   have TA2 := s_conv.taylor_approx_two_segment hf xs hx hvw hvww
-  convert TA1.sub TA2 using 1
+  convert! TA1.sub TA2 using 1
   ext h
   simp only [two_smul, smul_add, ← add_assoc, map_add,
     ContinuousLinearMap.add_apply]
@@ -372,8 +372,9 @@ theorem Convex.second_derivative_within_at_symmetric_of_mem_interior {v w : E}
     (h4v : x + (4 : ℝ) • v ∈ interior s) (h4w : x + (4 : ℝ) • w ∈ interior s) :
     f'' w v = f'' v w := by
   have A : (fun h : ℝ => h ^ 2 • (f'' w v - f'' v w)) =o[𝓝[>] 0] fun h => h ^ 2 := by
-    convert (s_conv.isLittleO_alternate_sum_square hf xs hx h4v h4w).sub
-      (s_conv.isLittleO_alternate_sum_square hf xs hx h4w h4v) using 1
+    convert!
+      (s_conv.isLittleO_alternate_sum_square hf xs hx h4v h4w).sub
+        (s_conv.isLittleO_alternate_sum_square hf xs hx h4w h4v) using 1
     ext h
     simp only [add_comm, smul_add, smul_sub]
     abel
diff --git a/Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean b/Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean
index d583ba95bba822..abe0d80a50dcb9 100644
--- a/Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean
+++ b/Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean
@@ -280,7 +280,7 @@ theorem order_zero : (0 : FormalMultilinearSeries 𝕜 E F).order = 0 := by simp
 theorem ne_zero_of_order_ne_zero (hp : p.order ≠ 0) : p ≠ 0 := fun h => by simp [h] at hp
 
 theorem order_eq_find [DecidablePred fun n => p n ≠ 0] (hp : ∃ n, p n ≠ 0) :
-    p.order = Nat.find hp := by convert Nat.sInf_def hp
+    p.order = Nat.find hp := by convert! Nat.sInf_def hp
 
 theorem order_eq_find' [DecidablePred fun n => p n ≠ 0] (hp : p ≠ 0) :
     p.order = Nat.find (FormalMultilinearSeries.ne_iff.mp hp) :=
@@ -319,7 +319,7 @@ theorem mkPiRing_coeff_eq (p : FormalMultilinearSeries 𝕜 𝕜 E) (n : ℕ) :
 
 @[simp]
 theorem apply_eq_prod_smul_coeff : p n y = (∏ i, y i) • p.coeff n := by
-  convert (p n).toMultilinearMap.map_smul_univ y 1
+  convert! (p n).toMultilinearMap.map_smul_univ y 1
   simp only [Pi.one_apply, smul_eq_mul, mul_one]
 
 theorem coeff_eq_zero : p.coeff n = 0 ↔ p n = 0 := by
diff --git a/Mathlib/Analysis/Calculus/Implicit.lean b/Mathlib/Analysis/Calculus/Implicit.lean
index 6ec8a5cd2b6d28..a299b7bfd3802b 100644
--- a/Mathlib/Analysis/Calculus/Implicit.lean
+++ b/Mathlib/Analysis/Calculus/Implicit.lean
@@ -230,7 +230,7 @@ theorem hasStrictFDerivAt_implicitFunction_fderiv :
       (fderiv 𝕜 (φ.implicitFunction (φ.leftFun φ.pt)) (φ.rightFun φ.pt)) (φ.rightFun φ.pt) := by
   have := φ.hasStrictFDerivAt.to_localInverse.comp (φ.rightFun φ.pt)
     ((hasStrictFDerivAt_const _ _).prodMk (hasStrictFDerivAt_id _))
-  convert this
+  convert! this
   exact this.hasFDerivAt.fderiv
 
 theorem differentiableAt_implicitFunction (φ : ImplicitFunctionData 𝕜 E F G) :
@@ -261,7 +261,7 @@ theorem hasStrictFDerivAt_implicitFunction (g'inv : G →L[𝕜] E)
     (hg'inv : φ.rightDeriv.comp g'inv = ContinuousLinearMap.id 𝕜 G)
     (hg'invf : φ.leftDeriv.comp g'inv = 0) :
     HasStrictFDerivAt (φ.implicitFunction (φ.leftFun φ.pt)) g'inv (φ.rightFun φ.pt) := by
-  convert φ.hasStrictFDerivAt_implicitFunction_fderiv
+  convert! φ.hasStrictFDerivAt_implicitFunction_fderiv
   ext1 x
   rw [eq_comm, fderiv_implicitFunction_apply_eq_iff]
   simp_all [DFunLike.ext_iff]
@@ -423,8 +423,9 @@ theorem to_implicitFunctionOfComplemented (hf : HasStrictFDerivAt f f' a) (hf' :
     (hker : f'.ker.ClosedComplemented) :
     HasStrictFDerivAt (hf.implicitFunctionOfComplemented f f' hf' hker (f a))
       f'.ker.subtypeL 0 := by
-  convert (implicitFunctionDataOfComplemented f f' hf hf' hker).hasStrictFDerivAt_implicitFunction
-    f'.ker.subtypeL _ _
+  convert!
+    (implicitFunctionDataOfComplemented f f' hf hf' hker).hasStrictFDerivAt_implicitFunction
+      f'.ker.subtypeL _ _
   swap
   · ext
     simp only [Classical.choose_spec hker, implicitFunctionDataOfComplemented,
diff --git a/Mathlib/Analysis/Calculus/ImplicitContDiff.lean b/Mathlib/Analysis/Calculus/ImplicitContDiff.lean
index 61878e05e24336..e0bdd104a1df87 100644
--- a/Mathlib/Analysis/Calculus/ImplicitContDiff.lean
+++ b/Mathlib/Analysis/Calculus/ImplicitContDiff.lean
@@ -43,7 +43,7 @@ theorem contDiffAt_implicitFunction {φ : ImplicitFunctionData 𝕜 E₁ E₂ F}
     ContDiffAt 𝕜 n φ.implicitFunction.uncurry (φ.prodFun φ.pt) := by
   rw [implicitFunction_def, Function.uncurry_curry, ← HasStrictFDerivAt.localInverse_def]
   refine ContDiffAt.to_localInverse ?_ (φ.hasStrictFDerivAt.hasFDerivAt) pn
-  convert hl.prodMk hr <;> simp
+  convert! hl.prodMk hr <;> simp
 
 end ImplicitFunctionData
 
diff --git a/Mathlib/Analysis/Calculus/InverseFunctionTheorem/ApproximatesLinearOn.lean b/Mathlib/Analysis/Calculus/InverseFunctionTheorem/ApproximatesLinearOn.lean
index 11988c4b077cf6..12be69422c973e 100644
--- a/Mathlib/Analysis/Calculus/InverseFunctionTheorem/ApproximatesLinearOn.lean
+++ b/Mathlib/Analysis/Calculus/InverseFunctionTheorem/ApproximatesLinearOn.lean
@@ -233,7 +233,7 @@ theorem surjOn_closedBall_of_nonlinearRightInverse
                   · exact IH.2
         _ = f'symm.nnnorm * (1 - ((c : ℝ) * f'symm.nnnorm) ^ n.succ) /
               (1 - (c : ℝ) * f'symm.nnnorm) * dist (f b) y := by
-          replace Jcf' : (1 : ℝ) - f'symm.nnnorm * c ≠ 0 := by convert Jcf' using 1; ring
+          replace Jcf' : (1 : ℝ) - f'symm.nnnorm * c ≠ 0 := by convert! Jcf' using 1; ring
           simp [field, pow_succ, -mul_eq_mul_left_iff]
           ring
     refine ⟨?_, Ign⟩
@@ -313,7 +313,7 @@ protected theorem antilipschitz (hf : ApproximatesLinearOn f (f' : E →L[𝕜]
     (hc : Subsingleton E ∨ c < N⁻¹) : AntilipschitzWith (N⁻¹ - c)⁻¹ (s.restrict f) := by
   rcases hc with hE | hc
   · exact AntilipschitzWith.of_subsingleton
-  convert (f'.antilipschitz.restrict s).add_lipschitzWith hf.lipschitz_sub hc
+  convert! (f'.antilipschitz.restrict s).add_lipschitzWith hf.lipschitz_sub hc
   simp [restrict]
 
 protected theorem injective (hf : ApproximatesLinearOn f (f' : E →L[𝕜] F) s c)
diff --git a/Mathlib/Analysis/Calculus/InverseFunctionTheorem/ContDiff.lean b/Mathlib/Analysis/Calculus/InverseFunctionTheorem/ContDiff.lean
index 87303606543f11..add6679659423f 100644
--- a/Mathlib/Analysis/Calculus/InverseFunctionTheorem/ContDiff.lean
+++ b/Mathlib/Analysis/Calculus/InverseFunctionTheorem/ContDiff.lean
@@ -69,7 +69,7 @@ theorem to_localInverse (hf : ContDiffAt 𝕂 n f a)
   have := hf.localInverse_apply_image hf' hn
   apply (hf.toOpenPartialHomeomorph f hf' hn).contDiffAt_symm
     (image_mem_toOpenPartialHomeomorph_target hf hf' hn)
-  · convert hf'
-  · convert hf
+  · convert! hf'
+  · convert! hf
 
 end ContDiffAt
diff --git a/Mathlib/Analysis/Calculus/InverseFunctionTheorem/FiniteDimensional.lean b/Mathlib/Analysis/Calculus/InverseFunctionTheorem/FiniteDimensional.lean
index 7942a00615383a..786bee9c4324cb 100644
--- a/Mathlib/Analysis/Calculus/InverseFunctionTheorem/FiniteDimensional.lean
+++ b/Mathlib/Analysis/Calculus/InverseFunctionTheorem/FiniteDimensional.lean
@@ -44,7 +44,7 @@ theorem exists_homeomorph_extension {E : Type*} [NormedAddCommGroup E] [NormedSp
   have hg : ApproximatesLinearOn g (f' : E →L[ℝ] F) univ (lipschitzExtensionConstant F * c) := by
     apply LipschitzOnWith.approximatesLinearOn
     rw [lipschitzOnWith_univ]
-    convert hu
+    convert! hu
     ext x
     simp only [g, add_sub_cancel_left, ContinuousLinearEquiv.coe_coe, Pi.sub_apply]
   haveI : FiniteDimensional ℝ E := f'.symm.finiteDimensional
diff --git a/Mathlib/Analysis/Calculus/IteratedDeriv/Defs.lean b/Mathlib/Analysis/Calculus/IteratedDeriv/Defs.lean
index b74f3bc2dae41e..301c2076a2ee07 100644
--- a/Mathlib/Analysis/Calculus/IteratedDeriv/Defs.lean
+++ b/Mathlib/Analysis/Calculus/IteratedDeriv/Defs.lean
@@ -312,7 +312,7 @@ differentiation operation. -/
 theorem iteratedDeriv_eq_iterate : iteratedDeriv n f = deriv^[n] f := by
   ext x
   rw [← iteratedDerivWithin_univ]
-  convert iteratedDerivWithin_eq_iterate (F := F)
+  convert! iteratedDerivWithin_eq_iterate (F := F)
   simp [derivWithin_univ]
 
 theorem iteratedDerivWithin_of_isOpen (hs : IsOpen s) :
@@ -341,7 +341,7 @@ lemma AnalyticAt.hasFPowerSeriesAt {𝕜 : Type*} [NontriviallyNormedField 𝕜]
     HasFPowerSeriesAt f
       (FormalMultilinearSeries.ofScalars 𝕜 (fun n ↦ iteratedDeriv n f x / n.factorial)) x := by
   obtain ⟨p, hp⟩ := h
-  convert hp
+  convert! hp
   obtain ⟨r, hpr⟩ := hp
   ext n
   have h_fact_smul := hpr.factorial_smul 1
diff --git a/Mathlib/Analysis/Calculus/LagrangeMultipliers.lean b/Mathlib/Analysis/Calculus/LagrangeMultipliers.lean
index 1a2d30db0a7667..983f9829f75c8a 100644
--- a/Mathlib/Analysis/Calculus/LagrangeMultipliers.lean
+++ b/Mathlib/Analysis/Calculus/LagrangeMultipliers.lean
@@ -71,7 +71,9 @@ theorem IsLocalExtrOn.exists_linear_map_of_hasStrictFDerivAt
       (LinearMap.coprodEquiv ℝ)
   rcases e.surjective Λ' with ⟨⟨Λ, Λ₀⟩, rfl⟩
   refine ⟨Λ, Λ₀, e.map_ne_zero_iff.1 h0, fun x => ?_⟩
-  convert LinearMap.congr_fun (LinearMap.range_le_ker_iff.1 hΛ') x using 1
+  convert! LinearMap.congr_fun (LinearMap.range_le_ker_iff.1 hΛ') x using 1
+    -- squeezed `simp [mul_comm]` to speed up elaboration
+
   -- squeezed `simp [mul_comm]` to speed up elaboration
   simp only [e, smul_eq_mul, LinearEquiv.trans_apply, LinearEquiv.prodCongr_apply,
     LinearEquiv.refl_apply, LinearMap.ringLmapEquivSelf_symm_apply, LinearMap.coprodEquiv_apply,
diff --git a/Mathlib/Analysis/Calculus/LineDeriv/Basic.lean b/Mathlib/Analysis/Calculus/LineDeriv/Basic.lean
index fe86d614d1312f..26b5023a3eb74e 100644
--- a/Mathlib/Analysis/Calculus/LineDeriv/Basic.lean
+++ b/Mathlib/Analysis/Calculus/LineDeriv/Basic.lean
@@ -303,7 +303,7 @@ theorem hasLineDerivWithinAt_congr_set (h : s =ᶠ[𝓝 x] t) :
   apply hasDerivWithinAt_congr_set
   let F := fun (t : 𝕜) ↦ x + t • v
   have B : ContinuousAt F 0 := by apply Continuous.continuousAt; fun_prop
-  have : s =ᶠ[𝓝 (F 0)] t := by convert h; simp [F]
+  have : s =ᶠ[𝓝 (F 0)] t := by convert! h; simp [F]
   exact B.preimage_mem_nhds this
 
 theorem lineDifferentiableWithinAt_congr_set (h : s =ᶠ[𝓝 x] t) :
@@ -318,7 +318,7 @@ theorem lineDerivWithin_congr_set (h : s =ᶠ[𝓝 x] t) :
   apply derivWithin_congr_set
   let F := fun (t : 𝕜) ↦ x + t • v
   have B : ContinuousAt F 0 := by apply Continuous.continuousAt; fun_prop
-  have : s =ᶠ[𝓝 (F 0)] t := by convert h; simp [F]
+  have : s =ᶠ[𝓝 (F 0)] t := by convert! h; simp [F]
   exact B.preimage_mem_nhds this
 
 theorem Filter.EventuallyEq.hasLineDerivAt_iff (h : f₀ =ᶠ[𝓝 x] f₁) :
@@ -326,7 +326,7 @@ theorem Filter.EventuallyEq.hasLineDerivAt_iff (h : f₀ =ᶠ[𝓝 x] f₁) :
   apply hasDerivAt_iff
   let F := fun (t : 𝕜) ↦ x + t • v
   have B : ContinuousAt F 0 := by apply Continuous.continuousAt; fun_prop
-  have : f₀ =ᶠ[𝓝 (F 0)] f₁ := by convert h; simp [F]
+  have : f₀ =ᶠ[𝓝 (F 0)] f₁ := by convert! h; simp [F]
   exact B.preimage_mem_nhds this
 
 theorem Filter.EventuallyEq.lineDifferentiableAt_iff (h : f₀ =ᶠ[𝓝 x] f₁) :
@@ -503,7 +503,7 @@ theorem HasLineDerivWithinAt.smul (h : HasLineDerivWithinAt 𝕜 f f' s x v) (c
   have B : HasDerivWithinAt (fun t ↦ f (x + t • v)) f' s' (g 0) := by simpa [g] using h
   have Z := B.scomp (0 : 𝕜) A.hasDerivWithinAt (mapsTo_preimage g s')
   simp only [g, s', Function.comp_def, smul_eq_mul, mul_comm c, ← smul_smul] at Z
-  convert Z
+  convert! Z
   ext t
   simp [← smul_smul]
 
diff --git a/Mathlib/Analysis/Calculus/LineDeriv/IntegrationByParts.lean b/Mathlib/Analysis/Calculus/LineDeriv/IntegrationByParts.lean
index e17ed658c074d6..8340a614624533 100644
--- a/Mathlib/Analysis/Calculus/LineDeriv/IntegrationByParts.lean
+++ b/Mathlib/Analysis/Calculus/LineDeriv/IntegrationByParts.lean
@@ -72,13 +72,14 @@ lemma integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux1 [Sig
     · intro t ht
       have : (x, t) ∈ tsupport g :=
         tsupport_comp_subset_preimage (f := fun y ↦ (x, y)) g (by fun_prop) ht
-      convert (hf (x, t) this).scomp_of_eq t ((hasDerivAt_id t).add (hasDerivAt_const t (-t)))
+      convert! (hf (x, t) this).scomp_of_eq t ((hasDerivAt_id t).add (hasDerivAt_const t (-t)))
         (by simp) <;> simp
     · intro t ht
       have : (x, t) ∈ tsupport f :=
         tsupport_comp_subset_preimage (f := fun y ↦ (x, y)) f (by fun_prop) ht
-      convert (hg (x, t) this).scomp_of_eq t ((hasDerivAt_id t).add (hasDerivAt_const t (-t)))
-        (by simp) <;> simp
+      convert!
+        (hg (x, t) this).scomp_of_eq t ((hasDerivAt_id t).add (hasDerivAt_const t (-t)))
+          (by simp) <;> simp
   _ = - ∫ x, B (f' x) (g x) ∂(μ.prod volume) := by rw [integral_neg, integral_prod _ hf'g]
 
 variable [BorelSpace E]
@@ -158,7 +159,7 @@ theorem integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable
       (Set.ext_iff.mp (tsupport_comp_eq_preimage g L.symm.toHomeomorph) x).mp hx
     specialize hf (L.symm x) h2x
     rw [this] at hf
-    convert hf.of_comp using 1
+    convert! hf.of_comp using 1
     · simp
     · simp [← hL]
   · intro x hx
@@ -167,7 +168,7 @@ theorem integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable
       (Set.ext_iff.mp (tsupport_comp_eq_preimage f L.symm.toHomeomorph) x).mp hx
     specialize hg (L.symm x) h2x
     rw [this] at hg
-    convert hg.of_comp using 1
+    convert! hg.of_comp using 1
     · simp
     · simp [← hL]
 
diff --git a/Mathlib/Analysis/Calculus/LogDeriv.lean b/Mathlib/Analysis/Calculus/LogDeriv.lean
index b9fd883b3618cb..90db509ede78e6 100644
--- a/Mathlib/Analysis/Calculus/LogDeriv.lean
+++ b/Mathlib/Analysis/Calculus/LogDeriv.lean
@@ -150,6 +150,6 @@ theorem AnalyticAt.tendsto_mul_logDeriv_simple_zero [CompleteSpace 𝕜]
       (𝓝[≠] x) (𝓝 1) := by
   have h_slope := hasDerivAt_iff_tendsto_slope.mp hf.differentiableAt.hasDerivAt
   rw [← div_self hf']
-  convert hf.deriv.continuousAt.tendsto.mono_left nhdsWithin_le_nhds |>.div h_slope hf' using 2
+  convert! hf.deriv.continuousAt.tendsto.mono_left nhdsWithin_le_nhds |>.div h_slope hf' using 2
   simp [logDeriv, slope, hfx]
   field
diff --git a/Mathlib/Analysis/Calculus/MeanValue.lean b/Mathlib/Analysis/Calculus/MeanValue.lean
index 0b42a9bdeb31e3..807a954454a326 100644
--- a/Mathlib/Analysis/Calculus/MeanValue.lean
+++ b/Mathlib/Analysis/Calculus/MeanValue.lean
@@ -152,7 +152,7 @@ theorem image_le_of_liminf_slope_right_le_deriv_boundary {f : ℝ → ℝ} {a b
     exact hx
   intro x hx
   have : ContinuousWithinAt (fun r => B x + r * (x - a)) (Ioi 0) 0 := by fun_prop
-  convert continuousWithinAt_const.closure_le _ this (Hr x hx) using 1 <;> simp
+  convert! continuousWithinAt_const.closure_le _ this (Hr x hx) using 1 <;> simp
 
 /-- General fencing theorem for continuous functions with an estimate on the derivative.
 Let `f` and `B` be continuous functions on `[a, b]` such that
@@ -317,7 +317,7 @@ theorem norm_image_sub_le_of_norm_deriv_right_le_segment {f' : ℝ → E} {C : 
   have hB : ∀ x, HasDerivAt B C x := by
     intro x
     simpa using (hasDerivAt_const x C).mul ((hasDerivAt_id x).sub (hasDerivAt_const x a))
-  convert image_norm_le_of_norm_deriv_right_le_deriv_boundary hg hg' _ hB bound
+  convert! image_norm_le_of_norm_deriv_right_le_deriv_boundary hg hg' _ hB bound
   simp only [g, B]; rw [sub_self, norm_zero, sub_self, mul_zero]
 
 /-- A function on `[a, b]` with the norm of the derivative within `[a, b]`
@@ -662,9 +662,11 @@ lemma isLittleO_pow_succ {x₀ : E} {n : ℕ} (hs : Convex ℝ s) (hx₀s : x₀
     gcongr
     exact norm_sub_le_of_mem_segment hy
   filter_upwards [this] with x ⟨h_segment, h⟩
-  convert (convex_segment x₀ x).norm_image_sub_le_of_norm_hasFDerivWithin_le
-    (f := fun x ↦ f x - f x₀) (y := x) (x := x₀) (s := segment ℝ x₀ x) ?_ h
-    (left_mem_segment ℝ x₀ x) (right_mem_segment ℝ x₀ x) using 1
+  convert!
+    (convex_segment x₀ x).norm_image_sub_le_of_norm_hasFDerivWithin_le (f := fun x ↦ f x - f x₀)
+      (y := x) (x := x₀) (s := segment ℝ x₀ x) ?_ h
+      (left_mem_segment ℝ x₀ x)
+      (right_mem_segment ℝ x₀ x) using 1
   · simp
   · simp only [hasFDerivWithinAt_sub_const_iff]
     exact fun x hx ↦ (hff' x (h_segment hx)).mono h_segment
@@ -677,7 +679,7 @@ theorem isLittleO_pow_succ_real {f f' : ℝ → E} {x₀ : ℝ} {n : ℕ} {s : S
   · rw [Asymptotics.isLittleO_iff] at h ⊢
     simpa using h
   · rw [Asymptotics.isLittleO_iff] at hf' ⊢
-    convert hf' using 4 with c hc x
+    convert! hf' using 4 with c hc x
     simp
 
 end Convex
diff --git a/Mathlib/Analysis/Calculus/ParametricIntegral.lean b/Mathlib/Analysis/Calculus/ParametricIntegral.lean
index dcc712ca6c90fb..0e3ea6293533a6 100644
--- a/Mathlib/Analysis/Calculus/ParametricIntegral.lean
+++ b/Mathlib/Analysis/Calculus/ParametricIntegral.lean
@@ -111,7 +111,7 @@ theorem hasFDerivAt_integral_of_dominated_loc_of_lip' {F' : α → H →L[𝕜]
   by_cases hE : CompleteSpace E; swap
   · rcases subsingleton_or_nontrivial H with hH | hH
     · have : Subsingleton (H →L[𝕜] E) := inferInstance
-      convert hasFDerivAt_of_subsingleton _ x₀
+      convert! hasFDerivAt_of_subsingleton _ x₀
     · have : ¬(CompleteSpace (H →L[𝕜] E)) := by
         simpa [SeparatingDual.completeSpace_continuousLinearMap_iff] using hE
       simp only [integral, hE, ↓reduceDIte, this]
diff --git a/Mathlib/Analysis/Calculus/Rademacher.lean b/Mathlib/Analysis/Calculus/Rademacher.lean
index 14b3940d46e7f2..d582d301482c81 100644
--- a/Mathlib/Analysis/Calculus/Rademacher.lean
+++ b/Mathlib/Analysis/Calculus/Rademacher.lean
@@ -86,7 +86,7 @@ theorem ae_lineDifferentiableAt
   have h's : DifferentiableAt ℝ (fun t ↦ f (p + t • v)) (s + 0) := by simpa using hs
   have : DifferentiableAt ℝ (fun t ↦ s + t) 0 := differentiableAt_id.const_add _
   simp only [LineDifferentiableAt]
-  convert h's.comp 0 this with _ t
+  convert! h's.comp 0 this with _ t
   simp only [add_assoc, Function.comp_apply, add_smul]
 
 theorem locallyIntegrable_lineDeriv (hf : LipschitzWith C f) (v : E) :
@@ -257,7 +257,7 @@ theorem ae_exists_fderiv_of_countable
   let L : StrongDual ℝ E :=
     LinearMap.toContinuousLinearMap (B.constr ℝ (fun i ↦ lineDeriv ℝ f x (B i)))
   refine ⟨L, fun v hv ↦ ?_⟩
-  have J : L v = lineDeriv ℝ f x v := by convert (hx v hv).symm <;> simp [L, B.sum_repr v]
+  have J : L v = lineDeriv ℝ f x v := by convert! (hx v hv).symm <;> simp [L, B.sum_repr v]
   simpa [J] using (h'x v hv).hasLineDerivAt
 
 omit [MeasurableSpace E] in
diff --git a/Mathlib/Analysis/Calculus/SmoothSeries.lean b/Mathlib/Analysis/Calculus/SmoothSeries.lean
index 3a2018ee9f057a..a4e9ff00e3668c 100644
--- a/Mathlib/Analysis/Calculus/SmoothSeries.lean
+++ b/Mathlib/Analysis/Calculus/SmoothSeries.lean
@@ -92,7 +92,7 @@ theorem hasDerivAt_tsum_of_isPreconnected (hu : Summable u) (ht : IsOpen t)
     (hg' : ∀ n y, y ∈ t → ‖g' n y‖ ≤ u n) (hy₀ : y₀ ∈ t) (hg0 : Summable fun n => g n y₀)
     (hy : y ∈ t) : HasDerivAt (fun z => ∑' n, g n z) (∑' n, g' n y) y := by
   simp_rw [hasDerivAt_iff_hasFDerivAt] at hg ⊢
-  convert hasFDerivAt_tsum_of_isPreconnected hu ht h't hg ?_ hy₀ hg0 hy
+  convert! hasFDerivAt_tsum_of_isPreconnected hu ht h't hg ?_ hy₀ hg0 hy
   · exact (ContinuousLinearMap.smulRightL 𝕜 𝕜 F 1).map_tsum <|
       .of_norm_bounded hu fun n ↦ hg' n y hy
   · simpa
diff --git a/Mathlib/Analysis/Calculus/Taylor.lean b/Mathlib/Analysis/Calculus/Taylor.lean
index 90ac78008a641a..76825e8e75a768 100644
--- a/Mathlib/Analysis/Calculus/Taylor.lean
+++ b/Mathlib/Analysis/Calculus/Taylor.lean
@@ -140,7 +140,7 @@ theorem monomial_has_deriv_aux (t x : ℝ) (n : ℕ) :
     HasDerivAt (fun y => (x - y) ^ (n + 1)) (-(n + 1) * (x - t) ^ n) t := by
   simp_rw [sub_eq_neg_add]
   rw [← neg_one_mul, mul_comm (-1 : ℝ), mul_assoc, mul_comm (-1 : ℝ), ← mul_assoc]
-  convert ((hasDerivAt_id t).neg.add_const x).pow (n + 1)
+  convert! ((hasDerivAt_id t).neg.add_const x).pow (n + 1)
   simp only [Nat.cast_add, Nat.cast_one]
 
 theorem hasDerivWithinAt_taylor_coeff_within {f : ℝ → E} {x y : ℝ} {k : ℕ} {s t : Set ℝ}
@@ -152,7 +152,7 @@ theorem hasDerivWithinAt_taylor_coeff_within {f : ℝ → E} {x y : ℝ} {k : 
         ((k ! : ℝ)⁻¹ * (x - y) ^ k) • iteratedDerivWithin (k + 1) f s y) t y := by
   replace hf :
     HasDerivWithinAt (iteratedDerivWithin (k + 1) f s) (iteratedDerivWithin (k + 2) f s y) t y := by
-    convert (hf.mono_of_mem_nhdsWithin hs).hasDerivWithinAt using 1
+    convert! (hf.mono_of_mem_nhdsWithin hs).hasDerivWithinAt using 1
     rw [iteratedDerivWithin_succ]
     exact (derivWithin_of_mem_nhdsWithin hs ht hf).symm
   have : HasDerivWithinAt (fun t => ((k + 1 : ℝ) * k !)⁻¹ * (x - t) ^ (k + 1))
@@ -162,7 +162,7 @@ theorem hasDerivWithinAt_taylor_coeff_within {f : ℝ → E} {x y : ℝ} {k : 
       field
     rw [this]
     exact (monomial_has_deriv_aux y x _).hasDerivWithinAt.const_mul _
-  convert this.smul hf using 1
+  convert! this.smul hf using 1
   field_simp
   module
 
@@ -191,8 +191,10 @@ theorem hasDerivWithinAt_taylorWithinEval {f : ℝ → E} {x y : ℝ} {n : ℕ}
     have hdiff : DifferentiableOn ℝ (iteratedDerivWithin k f s) s' :=
       (hf.differentiableOn_iteratedDerivWithin (mod_cast coe_lt_succ) hs_unique).mono h
     specialize hk hf.of_succ ((hdiff y hy).mono_of_mem_nhdsWithin hs')
-    convert hk.add (hasDerivWithinAt_taylor_coeff_within hs'_unique
-      (nhdsWithin_mono _ h self_mem_nhdsWithin) hf') using 1
+    convert!
+      hk.add
+        (hasDerivWithinAt_taylor_coeff_within hs'_unique (nhdsWithin_mono _ h self_mem_nhdsWithin)
+          hf') using 1
     exact (add_sub_cancel _ _).symm
 
 /-- Calculate the derivative of the Taylor polynomial with respect to `x₀`.
@@ -250,8 +252,9 @@ theorem taylor_isLittleO {f : ℝ → E} {x₀ : ℝ} {n : ℕ} {s : Set ℝ}
     · simp
     replace hs' := uniqueDiffOn_convex hs (hs.nontrivial_iff_nonempty_interior.1 hs')
     simp only [Nat.cast_add, Nat.cast_one] at hf
-    convert Convex.isLittleO_pow_succ_real hs hx₀s ?_ (h (hf.derivWithin hs' le_rfl))
-      (f := fun x ↦ f x - taylorWithinEval f (n + 1) s x₀ x) using 1
+    convert!
+      Convex.isLittleO_pow_succ_real hs hx₀s ?_ (h (hf.derivWithin hs' le_rfl)) (f := fun x ↦
+        f x - taylorWithinEval f (n + 1) s x₀ x) using 1
     · simp
     · intro x hx
       refine HasDerivWithinAt.sub ?_ (hasDerivAt_taylorWithinEval_succ f n).hasDerivWithinAt
@@ -281,7 +284,7 @@ theorem Real.taylor_tendsto {f : ℝ → ℝ} {x₀ : ℝ} {n : ℕ} {s : Set 
     (hs : Convex ℝ s) (hx₀s : x₀ ∈ s) (hf : ContDiffOn ℝ n f s) :
     Filter.Tendsto (fun x ↦ (f x - taylorWithinEval f n s x₀ x) / (x - x₀) ^ n)
       (𝓝[s] x₀) (𝓝 0) := by
-  convert _root_.taylor_tendsto hs hx₀s hf using 2 with x
+  convert! _root_.taylor_tendsto hs hx₀s hf using 2 with x
   simp [div_eq_inv_mul]
 
 
@@ -479,7 +482,7 @@ theorem taylor_integral_remainder_aux [NormedAddCommGroup F] [NormedSpace ℝ F]
     rw [sub_add_eq_sub_sub, ih]
     simp only [Nat.factorial, Nat.succ_eq_add_one, Nat.cast_mul, Nat.cast_add, Nat.cast_one]
     have := hf (n + 1) (by rfl)
-    convert this.symm using 1
+    convert! this.symm using 1
     · simp only [sub_self, ne_eq, Nat.add_eq_zero_iff, one_ne_zero, and_false, not_false_eq_true,
         zero_pow, zero_div, zero_smul, zero_sub, deriv_div_const, Nat.factorial]
       apply fun (a b c d : F) (_ : b = c) (_ : a = -d) ↦ show a - b = -c - d by grind
diff --git a/Mathlib/Analysis/Calculus/UniformLimitsDeriv.lean b/Mathlib/Analysis/Calculus/UniformLimitsDeriv.lean
index 45e7bca2eba51a..2e008f60735e90 100644
--- a/Mathlib/Analysis/Calculus/UniformLimitsDeriv.lean
+++ b/Mathlib/Analysis/Calculus/UniformLimitsDeriv.lean
@@ -360,7 +360,7 @@ theorem hasFDerivAt_of_tendstoUniformlyOnFilter [NeBot l]
     apply ((this ε hε).filter_mono curry_le_prod).mono
     intro n hn
     rw [dist_eq_norm] at hn ⊢
-    convert hn using 2
+    convert! hn using 2
     module
   · -- (Almost) the definition of the derivatives
     rw [Metric.tendsto_nhds]
diff --git a/Mathlib/Analysis/Calculus/VectorField.lean b/Mathlib/Analysis/Calculus/VectorField.lean
index afaf566c25c560..2f0c18003f0756 100644
--- a/Mathlib/Analysis/Calculus/VectorField.lean
+++ b/Mathlib/Analysis/Calculus/VectorField.lean
@@ -562,7 +562,7 @@ lemma _root_.exists_continuousLinearEquiv_fderivWithin_symm_eq
   have hN' : ContDiffWithinAt 𝕜 1 (fun y ↦ ((N y).symm : F →L[𝕜] E)) s x := by
     have : ContDiffWithinAt 𝕜 1 (ContinuousLinearMap.inverse ∘ (fun y ↦ (N y : E →L[𝕜] F))) s x :=
       (contDiffAt_map_inverse (N x)).comp_contDiffWithinAt x hN
-    convert this with y
+    convert! this with y
     simp only [Function.comp_apply, ContinuousLinearMap.inverse_equiv]
   refine ⟨N, hN, hN', eN, fun v ↦ ?_⟩
   have A' y : ContinuousLinearMap.compL 𝕜 F E F (N y : E →L[𝕜] F) ((N y).symm : F →L[𝕜] E)
diff --git a/Mathlib/Analysis/Complex/AbelLimit.lean b/Mathlib/Analysis/Complex/AbelLimit.lean
index f83a7ed78aef25..e5c69cb9bf16d0 100644
--- a/Mathlib/Analysis/Complex/AbelLimit.lean
+++ b/Mathlib/Analysis/Complex/AbelLimit.lean
@@ -233,7 +233,7 @@ theorem tendsto_tsum_powerSeries_nhdsWithin_stolzSet
       _ = _ := by
         rw [← mul_rotate, mul_div_cancel_right₀ _ (by linarith only [zn]),
           div_mul_cancel₀ _ (by linarith only [hM])]
-  convert add_lt_add S₁ S₂ using 1
+  convert! add_lt_add S₁ S₂ using 1
   linarith only
 
 /-- **Abel's limit theorem**. Given a power series converging at 1, the corresponding function
@@ -270,7 +270,7 @@ theorem tendsto_tsum_powerSeries_nhdsWithin_lt
   replace h := Complex.tendsto_tsum_powerSeries_nhdsWithin_lt h
   rw [tendsto_map'_iff] at h
   rw [Metric.tendsto_nhdsWithin_nhds] at h ⊢
-  convert h
+  convert! h
   simp_rw [Function.comp_apply, dist_eq_norm]
   norm_cast
 
diff --git a/Mathlib/Analysis/Complex/Angle.lean b/Mathlib/Analysis/Complex/Angle.lean
index 4faa1bded52fe7..85128732d363be 100644
--- a/Mathlib/Analysis/Complex/Angle.lean
+++ b/Mathlib/Analysis/Complex/Angle.lean
@@ -104,7 +104,7 @@ lemma norm_sub_mem_Icc_angle (hx : ‖x‖ = 1) (hy : ‖y‖ = 1) :
         _ = 2 * (1 - θ.cos) := by linear_combination θ.cos_sq_add_sin_sq
         _ ≤ 2 * (1 - (1 - θ ^ 2 / 2)) := by gcongr; exact Real.one_sub_sq_div_two_le_cos
         _ = _ := by ring
-  · convert hθ
+  · convert! hθ
     ring
 
 /-- Chord-length is always less than arc-length. -/
diff --git a/Mathlib/Analysis/Complex/Basic.lean b/Mathlib/Analysis/Complex/Basic.lean
index aff044a00312c0..56eac1c32d7a6b 100644
--- a/Mathlib/Analysis/Complex/Basic.lean
+++ b/Mathlib/Analysis/Complex/Basic.lean
@@ -311,8 +311,9 @@ lemma _root_.Filter.Tendsto.ofReal {α : Type*} {l : Filter α} {f : α → ℝ}
 
 /-- The only continuous ring homomorphism from `ℝ` to `ℂ` is the identity. -/
 theorem ringHom_eq_ofReal_of_continuous {f : ℝ →+* ℂ} (h : Continuous f) : f = ofRealHom := by
-  convert congr_arg AlgHom.toRingHom <| Subsingleton.elim (AlgHom.mk' f <| map_real_smul f h)
-    (Algebra.ofId ℝ ℂ)
+  convert!
+    congr_arg AlgHom.toRingHom <|
+      Subsingleton.elim (AlgHom.mk' f <| map_real_smul f h) (Algebra.ofId ℝ ℂ)
 
 /-- Continuous linear map version of the canonical embedding of `ℝ` in `ℂ`. -/
 def ofRealCLM : ℝ →L[ℝ] ℂ :=
diff --git a/Mathlib/Analysis/Complex/BranchLogRoot.lean b/Mathlib/Analysis/Complex/BranchLogRoot.lean
index 78f13cb30db58e..2a00d8bd917320 100644
--- a/Mathlib/Analysis/Complex/BranchLogRoot.lean
+++ b/Mathlib/Analysis/Complex/BranchLogRoot.lean
@@ -51,7 +51,7 @@ theorem exists_continuousOn_eqOn_exp_comp (hUc : IsSimplyConnected U) (hUo : IsO
   refine ⟨g, ?hg_cont, ?hg_inv⟩
   case hg_cont =>
     rw [continuousOn_iff_continuous_restrict]
-    convert map_continuous f
+    convert! map_continuous f
     ext z
     exact hg z
   case hg_inv =>
diff --git a/Mathlib/Analysis/Complex/Convex.lean b/Mathlib/Analysis/Complex/Convex.lean
index 7e12a67c4ea9a5..66f002d230f6ba 100644
--- a/Mathlib/Analysis/Complex/Convex.lean
+++ b/Mathlib/Analysis/Complex/Convex.lean
@@ -98,11 +98,12 @@ lemma Convex.rectangle_subset {U : Set ℂ} (U_convex : Convex ℝ U) {z w : ℂ
 instance : PathConnectedSpace ℂˣ :=
   have : PathConnectedSpace { z : ℂ // z ≠ 0 } :=
     (isPathConnected_iff_pathConnectedSpace (F := {0}ᶜ)).mp (by
-      convert (((convex_halfSpace_im_gt 0).isPathConnected ⟨.I, by simp⟩).union
-        ((convex_halfSpace_re_gt 0).isPathConnected ⟨1, by simp⟩) ⟨1 + .I, by simp⟩).union
-        (((convex_halfSpace_im_lt 0).isPathConnected ⟨-.I, by simp⟩).union
-        ((convex_halfSpace_re_lt 0).isPathConnected ⟨-1, by simp⟩) ⟨-1 - .I, by simp⟩)
-        ⟨1 - .I, by simp⟩ using 1
+      convert!
+        (((convex_halfSpace_im_gt 0).isPathConnected ⟨.I, by simp⟩).union
+              ((convex_halfSpace_re_gt 0).isPathConnected ⟨1, by simp⟩) ⟨1 + .I, by simp⟩).union
+          (((convex_halfSpace_im_lt 0).isPathConnected ⟨-.I, by simp⟩).union
+            ((convex_halfSpace_re_lt 0).isPathConnected ⟨-1, by simp⟩) ⟨-1 - .I, by simp⟩)
+          ⟨1 - .I, by simp⟩ using 1
       ext x
       refine ⟨?_, by aesop⟩
       simp +contextual [Complex.ext_iff, -not_and, not_and_or, or_imp, ← ne_eq, ← lt_or_lt_iff_ne])
diff --git a/Mathlib/Analysis/Complex/CoveringMap.lean b/Mathlib/Analysis/Complex/CoveringMap.lean
index bc7060861e9749..3ea0da9b427166 100644
--- a/Mathlib/Analysis/Complex/CoveringMap.lean
+++ b/Mathlib/Analysis/Complex/CoveringMap.lean
@@ -62,7 +62,7 @@ theorem Polynomial.isCoveringMapOn_eval (p : 𝕜[X]) :
 
 theorem isCoveringMapOn_npow (n : ℕ) (hn : (n : 𝕜) ≠ 0) :
     IsCoveringMapOn (fun x : 𝕜 ↦ x ^ n) {0}ᶜ := by
-  convert (X ^ n).isCoveringMapOn_eval.mono fun x' h ↦ _ with x
+  convert! (X ^ n).isCoveringMapOn_eval.mono fun x' h ↦ _ with x
   · simp
   · assumption
   · simpa [derivative_X_pow, hn, show n ≠ 0 by aesop] using fun _ ↦ Ne.symm h
@@ -70,16 +70,17 @@ theorem isCoveringMapOn_npow (n : ℕ) (hn : (n : 𝕜) ≠ 0) :
 /-- `(· ^ n) : 𝕜 \ {0} → 𝕜 \ {0}` is a covering map (if `n ≠ 0` in `𝕜`). -/
 theorem isCoveringMap_npow (n : ℕ) (hn : (n : 𝕜) ≠ 0) :
     IsCoveringMap fun x : {x : 𝕜 // x ≠ 0} ↦ (⟨x ^ n, pow_ne_zero n x.2⟩ : {x : 𝕜 // x ≠ 0}) := by
-  convert (isCoveringMapOn_npow n hn).isCoveringMap_restrictPreimage.comp_homeomorph
-    (.setCongr (s := {x | x ≠ 0}) _) using 1
+  convert!
+    (isCoveringMapOn_npow n hn).isCoveringMap_restrictPreimage.comp_homeomorph
+      (.setCongr (s := {x | x ≠ 0}) _) using 1
   ext; simp [show n ≠ 0 by aesop]
 
 /-- `(· ^ n) : 𝕜 \ {0} → 𝕜 \ {0}` is a covering map (if `n ≠ 0` in `𝕜`). -/
 theorem isCoveringMap_zpow (n : ℤ) (hn : (n : 𝕜) ≠ 0) :
     IsCoveringMap fun x : {x : 𝕜 // x ≠ 0} ↦ (⟨x ^ n, zpow_ne_zero n x.2⟩ : {x : 𝕜 // x ≠ 0}) := by
   obtain ⟨n, rfl | rfl⟩ := n.eq_nat_or_neg
-  · convert isCoveringMap_npow n _ <;> aesop
-  · convert (isCoveringMap_npow n _).comp_homeomorph (.inv₀ 𝕜)
+  · convert! isCoveringMap_npow n _ <;> aesop
+  · convert! (isCoveringMap_npow n _).comp_homeomorph (.inv₀ 𝕜)
     · simp [Homeomorph.inv₀]
     · simpa using hn
 
@@ -87,9 +88,9 @@ theorem isCoveringMapOn_zpow (n : ℤ) (hn : (n : 𝕜) ≠ 0) :
     IsCoveringMapOn (fun x : 𝕜 ↦ x ^ n) {0}ᶜ := by
   have (x : 𝕜) : x ^ n = 0 ↔ x = 0 := zpow_eq_zero_iff (by aesop)
   refine .of_isCoveringMap_restrictPreimage _ (by simp) ?_ ?_
-  · convert isClosed_singleton (x := (0 : 𝕜)).isOpen_compl using 1
+  · convert! isClosed_singleton (x := (0 : 𝕜)).isOpen_compl using 1
     ext; simp [this]
-  · convert (isCoveringMap_zpow n hn).comp_homeomorph (.ofEqSubtypes _) using 1
+  · convert! (isCoveringMap_zpow n hn).comp_homeomorph (.ofEqSubtypes _) using 1
     ext; simpa using (this _).not
 
 attribute [-instance] Units.mulAction'
@@ -103,7 +104,7 @@ theorem isQuotientCoveringMap_npow (n : ℕ) (hn : (n : 𝕜) ≠ 0)
     (by fun_prop) (.restrictPreimage _ surj)
   have : IsQuotientMap fun x : 𝕜ˣ ↦ x ^ n := by
     let e := unitsHomeomorphNeZero (G₀ := 𝕜)
-    convert (e.symm.isQuotientMap.comp this).comp (e.trans (.ofEqSubtypes _)).isQuotientMap
+    convert! (e.symm.isQuotientMap.comp this).comp (e.trans (.ofEqSubtypes _)).isQuotientMap
     · exact (e.left_inv _).symm
     · ext; simp [NeZero.ne]
   refine this.isQuotientCoveringMap_of_subgroup _
@@ -120,8 +121,8 @@ theorem isQuotientCoveringMap_zpow (n : ℤ) (hn : (n : 𝕜) ≠ 0)
   obtain ⟨n, rfl | rfl⟩ := n.eq_nat_or_neg
   · exact isQuotientCoveringMap_npow n (by aesop) (by simpa using surj)
   rw [show (zpowGroupHom (α := 𝕜ˣ) (-n)).ker = (powMonoidHom n).ker by ext; simp]
-  convert (isQuotientCoveringMap_npow n (by aesop) _).homeomorph_comp (.inv 𝕜ˣ) using 1
+  convert! (isQuotientCoveringMap_npow n (by aesop) _).homeomorph_comp (.inv 𝕜ˣ) using 1
   · ext; simp
-  convert inv_involutive.surjective.comp surj; simp
+  convert! inv_involutive.surjective.comp surj; simp
 
 end
diff --git a/Mathlib/Analysis/Complex/Exponential.lean b/Mathlib/Analysis/Complex/Exponential.lean
index c6040e68c47939..fe589ea2143973 100644
--- a/Mathlib/Analysis/Complex/Exponential.lean
+++ b/Mathlib/Analysis/Complex/Exponential.lean
@@ -93,7 +93,7 @@ variable (x y : ℂ)
 theorem exp_zero : exp 0 = 1 := by
   rw [exp]
   refine lim_eq_of_equiv_const fun ε ε0 => ⟨1, fun j hj => ?_⟩
-  convert (config := .unfoldSameFun) ε0 -- ε0 : ε > 0 but goal is _ < ε
+  convert! (config := .unfoldSameFun) ε0 -- ε0 : ε > 0 but goal is _ < ε
   rcases j with - | j
   · exact absurd hj (not_le_of_gt zero_lt_one)
   · dsimp [exp']
@@ -475,7 +475,7 @@ lemma norm_exp_sub_sum_le_exp_norm_sub_sum (x : ℂ) (n : ℕ) :
     exact Real.sum_le_exp_of_nonneg (norm_nonneg _) _
 
 lemma norm_exp_le_exp_norm (x : ℂ) : ‖exp x‖ ≤ Real.exp ‖x‖ := by
-  convert norm_exp_sub_sum_le_exp_norm_sub_sum x 0 using 1 <;> simp
+  convert! norm_exp_sub_sum_le_exp_norm_sub_sum x 0 using 1 <;> simp
 
 lemma norm_exp_sub_sum_le_norm_mul_exp (x : ℂ) (n : ℕ) :
     ‖exp x - ∑ m ∈ range n, x ^ m / m.factorial‖ ≤ ‖x‖ ^ n * Real.exp ‖x‖ := by
@@ -528,7 +528,7 @@ open Complex Finset
 nonrec theorem exp_bound {x : ℝ} (hx : |x| ≤ 1) {n : ℕ} (hn : 0 < n) :
     |exp x - ∑ m ∈ range n, x ^ m / m.factorial| ≤ |x| ^ n * (n.succ / (n.factorial * n)) := by
   have hxc : ‖(x : ℂ)‖ ≤ 1 := mod_cast hx
-  convert exp_bound hxc hn using 2 <;>
+  convert! exp_bound hxc hn using 2 <;>
   norm_cast
 
 theorem exp_bound' {x : ℝ} (h1 : 0 ≤ x) (h2 : x ≤ 1) {n : ℕ} (hn : 0 < n) :
@@ -574,7 +574,7 @@ theorem expNear_sub (n x r₁ r₂) : expNear n x r₁ -
 theorem exp_approx_end (n m : ℕ) (x : ℝ) (e₁ : n + 1 = m) (h : |x| ≤ 1) :
     |exp x - expNear m x 0| ≤ |x| ^ m / m.factorial * ((m + 1) / m) := by
   simp only [expNear, mul_zero, add_zero]
-  convert exp_bound (n := m) h ?_ using 1
+  convert! exp_bound (n := m) h ?_ using 1
   · simp [field]
   · lia
 
@@ -584,8 +584,9 @@ theorem exp_approx_succ {n} {x a₁ b₁ : ℝ} (m : ℕ) (e₁ : n + 1 = m) (a
     |exp x - expNear n x a₁| ≤ |x| ^ n / n.factorial * b₁ := by
   grw [abs_sub_le, h]
   subst e₁; rw [expNear_succ, expNear_sub, abs_mul]
-  convert mul_le_mul_of_nonneg_left (a := |x| ^ n / ↑(Nat.factorial n))
-      (le_sub_iff_add_le'.1 e) ?_ using 1
+  convert!
+    mul_le_mul_of_nonneg_left (a := |x| ^ n / ↑(Nat.factorial n)) (le_sub_iff_add_le'.1 e) ?_
+      using 1
   · simp [mul_add, pow_succ', div_eq_mul_inv, abs_mul, abs_inv, Nat.factorial]
     ac_rfl
   · simp [div_nonneg, abs_nonneg]
diff --git a/Mathlib/Analysis/Complex/Hadamard.lean b/Mathlib/Analysis/Complex/Hadamard.lean
index 4e7bca3f74d0a5..95cbb65a5bc8f7 100644
--- a/Mathlib/Analysis/Complex/Hadamard.lean
+++ b/Mathlib/Analysis/Complex/Hadamard.lean
@@ -426,7 +426,7 @@ lemma norm_le_interpStrip_of_mem_verticalStrip_zero (z : ℂ)
   · simp only [tendsto_const_nhds_iff]
   -- Proof that we can let epsilon tend to zero.
   · rw [interpStrip_eq_of_mem_verticalStrip _ _ hz]
-    convert ContinuousWithinAt.tendsto _ using 2
+    convert! ContinuousWithinAt.tendsto _ using 2
     · simp only [ofReal_zero, zero_add]
     · simp_rw [← ofReal_add]
       have : ∀ x ∈ Ioi 0, (x + sSupNormIm f 0) ^ (1 - z.re) * (x + sSupNormIm f 1) ^ z.re
diff --git a/Mathlib/Analysis/Complex/HasPrimitives.lean b/Mathlib/Analysis/Complex/HasPrimitives.lean
index 39732041f120db..ce8389f6b12e97 100644
--- a/Mathlib/Analysis/Complex/HasPrimitives.lean
+++ b/Mathlib/Analysis/Complex/HasPrimitives.lean
@@ -70,12 +70,12 @@ private lemma mem_closedBall_aux (z_in_ball : z ∈ closedBall c r) (y_in_I : y
 
 private lemma mem_ball_of_map_re_aux {a₁ a₂ b : ℝ} (ha₁ : a₁ + b * I ∈ ball c r)
     (ha₂ : a₂ + b * I ∈ ball c r) : (fun (x : ℝ) ↦ x + b * I) '' [[a₁, a₂]] ⊆ ball c r := by
-  convert Convex.rectangle_subset (convex_ball c r) ha₁ ha₂ ?_ ?_ using 1 <;>
+  convert! Convex.rectangle_subset (convex_ball c r) ha₁ ha₂ ?_ ?_ using 1 <;>
   simp [horizontalSegment_eq a₁ a₂ b, ha₁, ha₂, Rectangle]
 
 private lemma mem_ball_of_map_im_aux₁ {a b₁ b₂ : ℝ} (hb₁ : a + b₁ * I ∈ ball c r)
     (hb₂ : a + b₂ * I ∈ ball c r) : (fun (y : ℝ) ↦ a + y * I) '' [[b₁, b₂]] ⊆ ball c r := by
-  convert Convex.rectangle_subset (convex_ball c r) hb₁ hb₂ ?_ ?_ using 1 <;>
+  convert! Convex.rectangle_subset (convex_ball c r) hb₁ hb₂ ?_ ?_ using 1 <;>
   simp [verticalSegment_eq a b₁ b₂, hb₁, hb₂, Rectangle]
 
 private lemma mem_ball_of_map_im_aux₂ {w : ℂ} (hw : w ∈ ball z (r - dist z c)) :
diff --git a/Mathlib/Analysis/Complex/Liouville.lean b/Mathlib/Analysis/Complex/Liouville.lean
index 9a89efdcaef4d2..e41f3c7a152acd 100644
--- a/Mathlib/Analysis/Complex/Liouville.lean
+++ b/Mathlib/Analysis/Complex/Liouville.lean
@@ -142,7 +142,7 @@ theorem eq_const_of_tendsto_cocompact [Nontrivial E] {f : E → F} (hf : Differe
       Set.univ = t ∪ tᶜ := t.union_compl_self.symm
       _        ⊆ t ∪ s  := by gcongr
   obtain ⟨c', hc'⟩ := hf.exists_eq_const_of_bounded h_bdd
-  convert hc'
+  convert! hc'
   exact tendsto_nhds_unique hb (by simpa [hc'] using tendsto_const_nhds)
 
 /-- A corollary of Liouville's theorem where the function tends to a finite value at infinity
diff --git a/Mathlib/Analysis/Complex/LocallyUniformLimit.lean b/Mathlib/Analysis/Complex/LocallyUniformLimit.lean
index 49a1a56ac5287d..e4b73ec97a8bfb 100644
--- a/Mathlib/Analysis/Complex/LocallyUniformLimit.lean
+++ b/Mathlib/Analysis/Complex/LocallyUniformLimit.lean
@@ -185,8 +185,10 @@ theorem hasSum_deriv_of_summable_norm {u : ι → ℝ} (hu : Summable u)
     HasSum (fun i : ι => deriv (F i) z) (deriv (fun w : ℂ => ∑' i : ι, F i w) z) := by
   rw [HasSum]
   have hc := (tendstoUniformlyOn_tsum hu hF_le).tendstoLocallyUniformlyOn
-  convert (hc.deriv (Eventually.of_forall fun s =>
-    DifferentiableOn.fun_sum fun i _ => hf i) hU).tendsto_at hz using 1
+  convert!
+    (hc.deriv (Eventually.of_forall fun s => DifferentiableOn.fun_sum fun i _ => hf i)
+          hU).tendsto_at
+      hz using 1
   ext1 s
   exact (deriv_fun_sum fun i _ => (hf i).differentiableAt (hU.mem_nhds hz)).symm
 
diff --git a/Mathlib/Analysis/Complex/OpenMapping.lean b/Mathlib/Analysis/Complex/OpenMapping.lean
index 470a5fbc65c825..8ce1b615c2303f 100644
--- a/Mathlib/Analysis/Complex/OpenMapping.lean
+++ b/Mathlib/Analysis/Complex/OpenMapping.lean
@@ -251,7 +251,7 @@ theorem Polynomial.isOpenQuotientMap_eval (p : Polynomial ℂ) (hp : p.natDegree
 namespace Complex
 
 theorem isOpenQuotientMap_pow (n : ℕ) [NeZero n] : IsOpenQuotientMap (· ^ n : ℂ → ℂ) := by
-  convert Polynomial.isOpenQuotientMap_eval (.X ^ n) _
+  convert! Polynomial.isOpenQuotientMap_eval (.X ^ n) _
   · simp
   · simpa using NeZero.ne n
 
@@ -271,7 +271,7 @@ theorem isOpenQuotientMap_zpow_compl_zero (n : ℤ) [NeZero n] :
   · have : NeZero n := ⟨Nat.cast_ne_zero.mp (NeZero.ne (n : ℤ))⟩
     exact isOpenQuotientMap_pow_compl_zero n
   · have : NeZero n := ⟨Nat.cast_ne_zero.mp <| neg_ne_zero.mp (NeZero.ne (-n : ℤ))⟩
-    convert (isOpenQuotientMap_pow_compl_zero n).comp (Homeomorph.inv₀ ℂ).isOpenQuotientMap
+    convert! (isOpenQuotientMap_pow_compl_zero n).comp (Homeomorph.inv₀ ℂ).isOpenQuotientMap
     simp [Homeomorph.inv₀]
 
 end Complex
diff --git a/Mathlib/Analysis/Complex/PhragmenLindelof.lean b/Mathlib/Analysis/Complex/PhragmenLindelof.lean
index a45986b5bd0738..914557a609c68b 100644
--- a/Mathlib/Analysis/Complex/PhragmenLindelof.lean
+++ b/Mathlib/Analysis/Complex/PhragmenLindelof.lean
@@ -204,8 +204,9 @@ theorem horizontal_strip (hfd : DiffContOnCl ℂ f (im ⁻¹' Ioo a b))
             ((differentiable_id.sub_const _).const_mul _).neg.cexp).const_mul _).cexp
   replace hd : DiffContOnCl ℂ (fun w => g ε w • f w) (Ioo (-R) R ×ℂ Ioo (a - b) (a + b)) :=
     (hgd.diffContOnCl.smul hfd).mono inter_subset_right
-  convert norm_le_of_forall_mem_frontier_norm_le ((isBounded_Ioo _ _).reProdIm (isBounded_Ioo _ _))
-    hd (fun w hw => _) _
+  convert!
+    norm_le_of_forall_mem_frontier_norm_le ((isBounded_Ioo _ _).reProdIm (isBounded_Ioo _ _)) hd
+      (fun w hw => _) _
   · rw [frontier_reProdIm, closure_Ioo (neg_lt_self hR₀).ne, frontier_Ioo hab, closure_Ioo hab.ne,
       frontier_Ioo (neg_lt_self hR₀)] at hw
     by_cases him : w.im = a - b ∨ w.im = a + b
diff --git a/Mathlib/Analysis/Complex/Poisson.lean b/Mathlib/Analysis/Complex/Poisson.lean
index d0d19b46dfc6cb..4a0d2429ef660a 100644
--- a/Mathlib/Analysis/Complex/Poisson.lean
+++ b/Mathlib/Analysis/Complex/Poisson.lean
@@ -85,7 +85,7 @@ private lemma re_herglotzRieszKernel_le_aux (φ θ r R : ℝ) (h₁ : 0 < r) (h
   have h_subst :
       (R ^ 2 - r ^ 2) / (R ^ 2 + r ^ 2 - 2 * R * r * Real.cos (θ - φ)) ≤ (R + r) / (R - r) := by
     rw [div_le_div_iff₀] <;> nlinarith [mul_pos h₁ (sub_pos.mpr h₂)]
-  convert h_subst using 1
+  convert! h_subst using 1
   rw [← div_eq_mul_inv, poissonKernel_eq_re_herglotzRieszKernel_aux]
   suffices (R * R * normSq (cexp (θ * I)) + r * r * normSq (cexp (φ * I)) -
       2 * (R * Real.cos θ * (r * Real.cos φ) + R * Real.sin θ * (r * Real.sin φ))) =
diff --git a/Mathlib/Analysis/Complex/Polynomial/Basic.lean b/Mathlib/Analysis/Complex/Polynomial/Basic.lean
index 9e325ce4b70220..0497165b9d3ba6 100644
--- a/Mathlib/Analysis/Complex/Polynomial/Basic.lean
+++ b/Mathlib/Analysis/Complex/Polynomial/Basic.lean
@@ -185,7 +185,7 @@ then `p` is divisible by a quadratic polynomial. -/
 lemma Polynomial.quadratic_dvd_of_aeval_eq_zero_im_ne_zero (p : ℝ[X]) {z : ℂ} (h0 : aeval z p = 0)
     (hz : z.im ≠ 0) : X ^ 2 - C (2 * z.re) * X + C (‖z‖ ^ 2) ∣ p := by
   rw [← map_dvd_map' (algebraMap ℝ ℂ)]
-  convert p.mul_star_dvd_of_aeval_eq_zero_im_ne_zero h0 hz
+  convert! p.mul_star_dvd_of_aeval_eq_zero_im_ne_zero h0 hz
   calc
     map (algebraMap ℝ ℂ) (X ^ 2 - C (2 * z.re) * X + C (‖z‖ ^ 2))
     _ = X ^ 2 - C (↑(2 * z.re) : ℂ) * X + C (‖z‖ ^ 2 : ℂ) := by simp
diff --git a/Mathlib/Analysis/Complex/Positivity.lean b/Mathlib/Analysis/Complex/Positivity.lean
index e040eb68fe472f..fa36ef97d7808a 100644
--- a/Mathlib/Analysis/Complex/Positivity.lean
+++ b/Mathlib/Analysis/Complex/Positivity.lean
@@ -75,8 +75,9 @@ set `c - ℝ≥0`. -/
 theorem apply_le_of_iteratedDeriv_alternating {f : ℂ → ℂ} {c : ℂ} (hf : Differentiable ℂ f)
     (h : ∀ n ≠ 0, 0 ≤ (-1) ^ n * iteratedDeriv n f c) ⦃z : ℂ⦄ (hz : z ≤ c) :
     f c ≤ f z := by
-  convert apply_le_of_iteratedDeriv_nonneg (f := fun z ↦ f (-z))
-    (hf.comp <| differentiable_neg) (fun n hn ↦ ?_) (neg_le_neg_iff.mpr hz) using 1
+  convert!
+    apply_le_of_iteratedDeriv_nonneg (f := fun z ↦ f (-z)) (hf.comp <| differentiable_neg)
+      (fun n hn ↦ ?_) (neg_le_neg_iff.mpr hz) using 1
   · simp only [neg_neg]
   · simp only [neg_neg]
   · simpa only [iteratedDeriv_comp_neg, neg_neg, smul_eq_mul] using h n hn
diff --git a/Mathlib/Analysis/Complex/TaylorSeries.lean b/Mathlib/Analysis/Complex/TaylorSeries.lean
index eb3f6db079961e..ab6844609a75e1 100644
--- a/Mathlib/Analysis/Complex/TaylorSeries.lean
+++ b/Mathlib/Analysis/Complex/TaylorSeries.lean
@@ -54,7 +54,7 @@ lemma hasSum_taylorSeries_on_ball :
   have H := (hf.mono <| Metric.closedBall_subset_ball hr').hasFPowerSeriesOnBall hr'₀
       |>.hasSum_iteratedFDeriv hz'
   simp only [add_sub_cancel] at H
-  convert H using 4 with n
+  convert! H using 4 with n
   simpa only [iteratedDeriv_eq_iteratedFDeriv, smul_eq_mul, mul_one, Finset.prod_const,
     Finset.card_fin]
     using ((iteratedFDeriv ℂ n f c).map_smul_univ (fun _ ↦ z - c) (fun _ ↦ 1)).symm
@@ -71,7 +71,7 @@ include hz in
 is given by evaluating its Taylor series at `c` on this open ball. -/
 lemma taylorSeries_eq_on_ball' {f : ℂ → ℂ} (hf : DifferentiableOn ℂ f (Metric.ball c r)) :
     ∑' n : ℕ, (n ! : ℂ)⁻¹ * iteratedDeriv n f c * (z - c) ^ n = f z := by
-  convert taylorSeries_eq_on_ball hf hz using 3 with n
+  convert! taylorSeries_eq_on_ball hf hz using 3 with n
   rw [mul_right_comm, smul_eq_mul, smul_eq_mul, mul_assoc]
 
 end ball
@@ -111,7 +111,7 @@ include hz in
 is given by evaluating its Taylor series at `c` on this open ball. -/
 lemma taylorSeries_eq_on_eball' {f : ℂ → ℂ} (hf : DifferentiableOn ℂ f (Metric.eball c r)) :
     ∑' n : ℕ, (n ! : ℂ)⁻¹ * iteratedDeriv n f c * (z - c) ^ n = f z := by
-  convert taylorSeries_eq_on_eball hf hz using 3 with n
+  convert! taylorSeries_eq_on_eball hf hz using 3 with n
   rw [mul_right_comm, smul_eq_mul, smul_eq_mul, mul_assoc]
 
 @[deprecated (since := "2026-01-24")]
@@ -142,7 +142,7 @@ lemma taylorSeries_eq_of_entire :
 its Taylor series at any point `c`. -/
 lemma taylorSeries_eq_of_entire' {f : ℂ → ℂ} (hf : Differentiable ℂ f) :
     ∑' n : ℕ, (n ! : ℂ)⁻¹ * iteratedDeriv n f c * (z - c) ^ n = f z := by
-  convert taylorSeries_eq_of_entire hf c z using 3 with n
+  convert! taylorSeries_eq_of_entire hf c z using 3 with n
   rw [mul_right_comm, smul_eq_mul, smul_eq_mul, mul_assoc]
 
 end entire
diff --git a/Mathlib/Analysis/Complex/Trigonometric.lean b/Mathlib/Analysis/Complex/Trigonometric.lean
index a8957cd0c6c181..22eeb80938f413 100644
--- a/Mathlib/Analysis/Complex/Trigonometric.lean
+++ b/Mathlib/Analysis/Complex/Trigonometric.lean
@@ -331,13 +331,13 @@ theorem sin_add_mul_I (x y : ℂ) : sin (x + y * I) = sin x * cosh y + cos x * s
   rw [sin_add, cos_mul_I, sin_mul_I, mul_assoc]
 
 theorem sin_eq (z : ℂ) : sin z = sin z.re * cosh z.im + cos z.re * sinh z.im * I := by
-  convert sin_add_mul_I z.re z.im; exact (re_add_im z).symm
+  convert! sin_add_mul_I z.re z.im; exact (re_add_im z).symm
 
 theorem cos_add_mul_I (x y : ℂ) : cos (x + y * I) = cos x * cosh y - sin x * sinh y * I := by
   rw [cos_add, cos_mul_I, sin_mul_I, mul_assoc]
 
 theorem cos_eq (z : ℂ) : cos z = cos z.re * cosh z.im - sin z.re * sinh z.im * I := by
-  convert cos_add_mul_I z.re z.im; exact (re_add_im z).symm
+  convert! cos_add_mul_I z.re z.im; exact (re_add_im z).symm
 
 theorem sin_sub_sin : sin x - sin y = 2 * sin ((x - y) / 2) * cos ((x + y) / 2) := by
   have s1 := sin_add ((x + y) / 2) ((x - y) / 2)
diff --git a/Mathlib/Analysis/Complex/UpperHalfPlane/Manifold.lean b/Mathlib/Analysis/Complex/UpperHalfPlane/Manifold.lean
index 48a4fc371d48c3..9ee16c35b35656 100644
--- a/Mathlib/Analysis/Complex/UpperHalfPlane/Manifold.lean
+++ b/Mathlib/Analysis/Complex/UpperHalfPlane/Manifold.lean
@@ -124,7 +124,7 @@ lemma eq_zero_of_frequently {f : ℍ → ℂ} (hf : MDiff f) {τ : ℍ} (hτ : 
   rw [mdifferentiable_iff] at hf
   have := hf.analyticOnNhd isOpen_upperHalfPlaneSet
   ext w
-  convert this.eqOn_zero_of_preconnected_of_frequently_eq_zero (z₀ := ↑τ) ?_ τ.2 ?_ w.im_pos
+  convert! this.eqOn_zero_of_preconnected_of_frequently_eq_zero (z₀ := ↑τ) ?_ τ.2 ?_ w.im_pos
   · rw [Function.comp_apply, ofComplex_apply]
   · exact (Complex.isConnected_of_upperHalfPlane subset_rfl (by grind)).isPreconnected
   · contrapose! hτ
@@ -162,8 +162,9 @@ lemma hasStrictDerivAt_smul {g : GL (Fin 2) ℝ} (hg : 0 < g.val.det) (τ : ℍ)
     refine this.congr_of_eventuallyEq ?_
     rw [← isOpenEmbedding_coe.map_nhds_eq, eventuallyEq_map]
     simp [Function.comp_def, coe_smul_of_det_pos hg]
-  convert ((hasStrictDerivAt_id (τ : ℂ)).const_mul _ |>.add_const _).div
-    ((hasStrictDerivAt_id (τ : ℂ)).const_mul _ |>.add_const _) _ using 2
+  convert!
+    ((hasStrictDerivAt_id (τ : ℂ)).const_mul _ |>.add_const _).div
+      ((hasStrictDerivAt_id (τ : ℂ)).const_mul _ |>.add_const _) _ using 2
   · simp [Matrix.det_fin_two]; ring
   · apply denom_ne_zero
 
@@ -231,7 +232,7 @@ lemma hasStrictFDerivAt_smul (g : GL (Fin 2) ℝ) (τ : ℍ) :
     HasStrictFDerivAt (fun z ↦ ↑(g • ofComplex z) : ℂ → ℂ) (smulFDeriv g τ) τ := by
   wlog hg : 0 < g.det.val generalizing g
   · replace hg := g.det.ne_zero.lt_or_gt.resolve_right hg
-    convert Complex.conjCLE.hasStrictFDerivAt.neg.comp _ (this (J * g) (by simpa))
+    convert! Complex.conjCLE.hasStrictFDerivAt.neg.comp _ (this (J * g) (by simpa))
     · simp [mul_smul, coe_J_smul]
     · ext
       simp
diff --git a/Mathlib/Analysis/Complex/UpperHalfPlane/Measure.lean b/Mathlib/Analysis/Complex/UpperHalfPlane/Measure.lean
index 340e7b286823bc..985c8b34f2a157 100644
--- a/Mathlib/Analysis/Complex/UpperHalfPlane/Measure.lean
+++ b/Mathlib/Analysis/Complex/UpperHalfPlane/Measure.lean
@@ -100,7 +100,7 @@ instance : SMulInvariantMeasure (GL (Fin 2) ℝ) ℍ volume := by
         (hasStrictFDerivAt_smul g _).hasFDerivAt.hasFDerivWithinAt)
       hinj
       (fun z ↦ ↑((1 / ‖z.im‖₊) ^ 2 : NNReal))
-  convert main using 1
+  convert! main using 1
   · simp [Set.image_image]
   · apply setLIntegral_congr_fun (measurableEmbedding_coe.measurableSet_image.mpr hs)
     rintro _ ⟨τ, -, rfl⟩
diff --git a/Mathlib/Analysis/Complex/UpperHalfPlane/ProperAction.lean b/Mathlib/Analysis/Complex/UpperHalfPlane/ProperAction.lean
index 73679d61ab0067..aa9604b24b4f2c 100644
--- a/Mathlib/Analysis/Complex/UpperHalfPlane/ProperAction.lean
+++ b/Mathlib/Analysis/Complex/UpperHalfPlane/ProperAction.lean
@@ -89,7 +89,7 @@ private lemma absq_le {K : Set ℍ} (hK : IsCompact K) :
   let S : SL(2, ℝ) := ⟨!![0, -1; 1, 0], by simp⟩
   obtain ⟨A, hA⟩ := cdsq_le (K := S • K) (hK.image <| continuous_const_smul S)
   refine ⟨A, fun g hg ↦ ?_⟩
-  convert hA (S * g) (by rwa [mul_smul, Set.smul_mem_smul_set_iff]) using 1
+  convert! hA (S * g) (by rwa [mul_smul, Set.smul_mem_smul_set_iff]) using 1
   rw [Matrix.SpecialLinearGroup.coe_mul, Matrix.eta_fin_two g.val, Matrix.mul_fin_two]
   simp
 
@@ -102,7 +102,7 @@ lemma isProperMap_smul_I : IsProperMap fun g : SL(2, ℝ) ↦ g • I := by
   let : SeminormedAddCommGroup (Matrix (Fin 2) (Fin 2) ℝ) := Matrix.seminormedAddCommGroup
   have : ProperSpace (Matrix (Fin 2) (Fin 2) ℝ) := pi_properSpace
   have : IsCompact {m : Matrix (Fin 2) (Fin 2) ℝ | ∀ i j, |m i j| ≤ max √A √A'} := by
-    convert ProperSpace.isCompact_closedBall (0 : Matrix (Fin 2) (Fin 2) ℝ) (max √A √A')
+    convert! ProperSpace.isCompact_closedBall (0 : Matrix (Fin 2) (Fin 2) ℝ) (max √A √A')
     simp only [le_sup_iff, Fin.forall_fin_two, Fin.isValue, Metric.closedBall, dist_zero_right,
       Matrix.norm_def, pi_norm_le_iff_of_nonempty, Real.norm_eq_abs]
     #adaptation_note /-- Before https://github.com/leanprover/lean4/pull/13166
diff --git a/Mathlib/Analysis/Complex/ValueDistribution/FirstMainTheorem.lean b/Mathlib/Analysis/Complex/ValueDistribution/FirstMainTheorem.lean
index 9e704089df90ab..a08119f5e7bbc6 100644
--- a/Mathlib/Analysis/Complex/ValueDistribution/FirstMainTheorem.lean
+++ b/Mathlib/Analysis/Complex/ValueDistribution/FirstMainTheorem.lean
@@ -147,7 +147,7 @@ theorem abs_characteristic_sub_characteristic_shift_le {r : ℝ} (h : Meromorphi
         using (posLog_norm_add_le (f θ - a₀) a₀)
     · simp only [abs_of_nonpos (le_of_not_ge h), neg_sub, tsub_le_iff_right,
         add_comm (log⁺ ‖a₀‖ + log 2), ← add_assoc]
-      convert posLog_norm_add_le (-f θ) (a₀) using 2
+      convert! posLog_norm_add_le (-f θ) (a₀) using 2
       · rw [← norm_neg]
         abel_nf
       · simp
diff --git a/Mathlib/Analysis/ConstantSpeed.lean b/Mathlib/Analysis/ConstantSpeed.lean
index d7ab627aaaba27..b01b287321c026 100644
--- a/Mathlib/Analysis/ConstantSpeed.lean
+++ b/Mathlib/Analysis/ConstantSpeed.lean
@@ -200,7 +200,7 @@ monotonically maps `s` onto `t`, then `φ` is just a translation (on `s`).
 theorem unique_unit_speed {φ : ℝ → ℝ} (φm : MonotoneOn φ s) (hfφ : HasUnitSpeedOn (f ∘ φ) s)
     (hf : HasUnitSpeedOn f (φ '' s)) ⦃x : ℝ⦄ (xs : x ∈ s) : EqOn φ (fun y => y - x + φ x) s := by
   dsimp only [HasUnitSpeedOn] at hf hfφ
-  convert HasConstantSpeedOnWith.ratio one_ne_zero φm hfφ hf xs using 3
+  convert! HasConstantSpeedOnWith.ratio one_ne_zero φm hfφ hf xs using 3
   simp
 
 /-- If both `f` and `f ∘ φ` have unit speed (on `Icc 0 t` and `Icc 0 s` respectively)
@@ -211,7 +211,7 @@ theorem unique_unit_speed_on_Icc_zero {s t : ℝ} (hs : 0 ≤ s) (ht : 0 ≤ t)
     (hfφ : HasUnitSpeedOn (f ∘ φ) (Icc 0 s)) (hf : HasUnitSpeedOn f (Icc 0 t)) :
     EqOn φ id (Icc 0 s) := by
   rw [← φst] at hf
-  convert unique_unit_speed φm hfφ hf ⟨le_rfl, hs⟩ using 1
+  convert! unique_unit_speed φm hfφ hf ⟨le_rfl, hs⟩ using 1
   have : φ 0 = 0 := by
     have hm : 0 ∈ φ '' Icc 0 s := by simp only [φst, ht, mem_Icc, le_refl, and_self]
     obtain ⟨x, xs, hx⟩ := hm
diff --git a/Mathlib/Analysis/Convex/Basic.lean b/Mathlib/Analysis/Convex/Basic.lean
index a1039fdb828d5a..de07cfd5c9ac2a 100644
--- a/Mathlib/Analysis/Convex/Basic.lean
+++ b/Mathlib/Analysis/Convex/Basic.lean
@@ -643,7 +643,7 @@ lemma convex_of_nonneg_surjective_algebraMap [FaithfulSMul R A] {s : Set M}
   intro u hu v hv a b ha hb hab
   obtain ⟨c, hc1, hc2⟩ := halg ha
   obtain ⟨d, hd1, hd2⟩ := halg hb
-  convert hs hu hv hc1 hd1 _ using 2
+  convert! hs hu hv hc1 hd1 _ using 2
   · rw [← hc2, algebraMap_smul]
   · rw [← hd2, algebraMap_smul]
   rw [← hc2, ← hd2, ← algebraMap.coe_add] at hab
diff --git a/Mathlib/Analysis/Convex/Between.lean b/Mathlib/Analysis/Convex/Between.lean
index 6d5dbd0f6dcccf..644e30e935d809 100644
--- a/Mathlib/Analysis/Convex/Between.lean
+++ b/Mathlib/Analysis/Convex/Between.lean
@@ -658,10 +658,10 @@ lemma closedInterior_face_eq_affineSegment {n : ℕ} (s : Simplex R P n) {i j :
       simp [max_eq_left hji.le, min_eq_right hji.le]
   rw [h', (s.face (Finset.card_pair h)).closedInterior_eq_affineSegment, face_points, face_points]
   congr 2
-  · convert Finset.orderEmbOfFin_zero _ _
+  · convert! Finset.orderEmbOfFin_zero _ _
     · exact (Finset.min'_pair i j).symm
     · lia
-  · convert Finset.orderEmbOfFin_last _ _
+  · convert! Finset.orderEmbOfFin_last _ _
     · exact (Finset.max'_pair i j).symm
     · lia
 
@@ -712,10 +712,10 @@ lemma mem_interior_face_iff_sbtw [IsDomain R] [IsTorsionFree R V] {n : ℕ}
       simp [max_eq_left hji.le, min_eq_right hji.le]
   rw [h', mem_interior_iff_sbtw, face_points, face_points]
   congr! 4
-  · convert Finset.orderEmbOfFin_zero _ _
+  · convert! Finset.orderEmbOfFin_zero _ _
     · exact (Finset.min'_pair i j).symm
     · lia
-  · convert Finset.orderEmbOfFin_last _ _
+  · convert! Finset.orderEmbOfFin_last _ _
     · exact (Finset.max'_pair i j).symm
     · lia
 
@@ -941,8 +941,10 @@ theorem wbtw_or_wbtw_smul_vadd_of_nonneg (x : P) (v : V) {r₁ r₂ : R} (hr₁
 
 theorem wbtw_smul_vadd_smul_vadd_of_nonpos_of_le (x : P) (v : V) {r₁ r₂ : R} (hr₁ : r₁ ≤ 0)
     (hr₂ : r₂ ≤ r₁) : Wbtw R x (r₁ • v +ᵥ x) (r₂ • v +ᵥ x) := by
-  convert wbtw_smul_vadd_smul_vadd_of_nonneg_of_le x (-v) (Left.nonneg_neg_iff.2 hr₁)
-      (neg_le_neg_iff.2 hr₂) using 1 <;>
+  convert!
+    wbtw_smul_vadd_smul_vadd_of_nonneg_of_le x (-v) (Left.nonneg_neg_iff.2 hr₁)
+      (neg_le_neg_iff.2 hr₂) using
+    1 <;>
     rw [neg_smul_neg]
 
 theorem wbtw_or_wbtw_smul_vadd_of_nonpos (x : P) (v : V) {r₁ r₂ : R} (hr₁ : r₁ ≤ 0) (hr₂ : r₂ ≤ 0) :
@@ -953,8 +955,10 @@ theorem wbtw_or_wbtw_smul_vadd_of_nonpos (x : P) (v : V) {r₁ r₂ : R} (hr₁
 
 theorem wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonneg (x : P) (v : V) {r₁ r₂ : R} (hr₁ : r₁ ≤ 0)
     (hr₂ : 0 ≤ r₂) : Wbtw R (r₁ • v +ᵥ x) x (r₂ • v +ᵥ x) := by
-  convert wbtw_smul_vadd_smul_vadd_of_nonneg_of_le (r₁ • v +ᵥ x) v (Left.nonneg_neg_iff.2 hr₁)
-      (neg_le_sub_iff_le_add.2 ((le_add_iff_nonneg_left r₁).2 hr₂)) using 1 <;>
+  convert!
+    wbtw_smul_vadd_smul_vadd_of_nonneg_of_le (r₁ • v +ᵥ x) v (Left.nonneg_neg_iff.2 hr₁)
+      (neg_le_sub_iff_le_add.2 ((le_add_iff_nonneg_left r₁).2 hr₂)) using
+    1 <;>
     simp [sub_smul, ← add_vadd]
 
 theorem wbtw_smul_vadd_smul_vadd_of_nonneg_of_nonpos (x : P) (v : V) {r₁ r₂ : R} (hr₁ : 0 ≤ r₁)
@@ -1101,12 +1105,12 @@ theorem sbtw_pointReflection_of_ne {x y : P} (h : x ≠ y) : Sbtw R y x (pointRe
   exact (pointReflection_involutive R x).injective.ne h
 
 theorem wbtw_midpoint (x y : P) : Wbtw R x (midpoint R x y) y := by
-  convert wbtw_pointReflection R (midpoint R x y) x
+  convert! wbtw_pointReflection R (midpoint R x y) x
   rw [pointReflection_midpoint_left]
 
 theorem sbtw_midpoint_of_ne {x y : P} (h : x ≠ y) : Sbtw R x (midpoint R x y) y := by
   have h : midpoint R x y ≠ x := by simp [h]
-  convert sbtw_pointReflection_of_ne R h
+  convert! sbtw_pointReflection_of_ne R h
   rw [pointReflection_midpoint_left]
 
 end LinearOrderedField
diff --git a/Mathlib/Analysis/Convex/Caratheodory.lean b/Mathlib/Analysis/Convex/Caratheodory.lean
index 7cd7dd08e02fe2..5e03e56b84c3ae 100644
--- a/Mathlib/Analysis/Convex/Caratheodory.lean
+++ b/Mathlib/Analysis/Convex/Caratheodory.lean
@@ -77,7 +77,7 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
         conv_rhs => rw [← insert_erase hi₀, sum_insert (notMem_erase i₀ t), hk, zero_add]
       _ = ∑ e ∈ t, (f e - f i₀ / g i₀ * g e) := rfl
       _ = 1 := by rw [sum_sub_distrib, fsum, ← mul_sum, gsum, mul_zero, sub_zero]
-  refine ⟨⟨i₀, hi₀⟩, k, ?_, by convert ksum, ?_⟩
+  refine ⟨⟨i₀, hi₀⟩, k, ?_, by convert! ksum, ?_⟩
   · simp only [k, and_imp, sub_nonneg, mem_erase, Ne]
     intro e _ het
     by_cases hes : e ∈ s
@@ -155,7 +155,7 @@ theorem convexHull_eq_union : convexHull 𝕜 s =
       Caratheodory.minCardFinsetOfMemConvexHull_subseteq hx,
       Caratheodory.affineIndependent_minCardFinsetOfMemConvexHull hx,
       Caratheodory.mem_minCardFinsetOfMemConvexHull hx⟩
-  · iterate 3 convert Set.iUnion_subset _; intro
+  · iterate 3 convert! Set.iUnion_subset _; intro
     exact convexHull_mono ‹_›
 
 /-- A more explicit version of `convexHull_eq_union`. -/
diff --git a/Mathlib/Analysis/Convex/Combination.lean b/Mathlib/Analysis/Convex/Combination.lean
index 48e48fcb09f569..ce97f12f200196 100644
--- a/Mathlib/Analysis/Convex/Combination.lean
+++ b/Mathlib/Analysis/Convex/Combination.lean
@@ -242,7 +242,7 @@ theorem convex_iff_sum_mem : Convex R s ↔ ∀ (t : Finset E) (w : E → R),
   by_cases h_cases : x = y
   · rw [h_cases, ← add_smul, hab, one_smul]
     exact hy
-  · convert h {x, y} (fun z => if z = y then b else a) _ _ _
+  · convert! h { x, y } (fun z => if z = y then b else a) _ _ _
     · simp only [sum_pair h_cases, if_neg h_cases, if_pos trivial]
     · grind
     · simp only [sum_pair h_cases, if_neg h_cases, if_pos trivial, hab]
diff --git a/Mathlib/Analysis/Convex/Cone/Extension.lean b/Mathlib/Analysis/Convex/Cone/Extension.lean
index ac70c5e315fdc3..b1b22e905185b1 100644
--- a/Mathlib/Analysis/Convex/Cone/Extension.lean
+++ b/Mathlib/Analysis/Convex/Cone/Extension.lean
@@ -125,7 +125,7 @@ theorem exists_top (p : E →ₗ.[ℝ] ℝ) (hp_nonneg : ∀ x : p.domain, (x :
       directedOn_image.2 (hcd.mono LinearPMap.domain_mono.monotone)
     rcases (mem_sSup_of_directed (cne.image _) hdir).1 hx with ⟨_, ⟨f, hfc, rfl⟩, hfx⟩
     have : f ≤ LinearPMap.sSup c hcd := LinearPMap.le_sSup _ hfc
-    convert ← hcs hfc ⟨x, hfx⟩ hxs using 1
+    convert! ← hcs hfc ⟨x, hfx⟩ hxs using 1
     exact this.2 rfl
   obtain ⟨q, hpq, hqs, hq⟩ := zorn_le_nonempty₀ S hSc p hp_nonneg
   refine ⟨q, hpq, ?_, hqs⟩
diff --git a/Mathlib/Analysis/Convex/Continuous.lean b/Mathlib/Analysis/Convex/Continuous.lean
index 60510a54c5e82e..a6aaec87944436 100644
--- a/Mathlib/Analysis/Convex/Continuous.lean
+++ b/Mathlib/Analysis/Convex/Continuous.lean
@@ -82,7 +82,7 @@ lemma ConvexOn.exists_lipschitzOnWith_of_isBounded (hf : ConvexOn ℝ (ball x₀
 
 lemma ConcaveOn.exists_lipschitzOnWith_of_isBounded (hf : ConcaveOn ℝ (ball x₀ r) f) (hr : r' < r)
     (hf' : IsBounded (f '' ball x₀ r)) : ∃ K, LipschitzOnWith K f (ball x₀ r') := by
-  replace hf' : IsBounded ((-f) '' ball x₀ r) := by convert hf'.neg; ext; simp [neg_eq_iff_eq_neg]
+  replace hf' : IsBounded ((-f) '' ball x₀ r) := by convert! hf'.neg; ext; simp [neg_eq_iff_eq_neg]
   simpa using hf.neg.exists_lipschitzOnWith_of_isBounded hr hf'
 
 lemma ConvexOn.isBoundedUnder_abs (hf : ConvexOn ℝ C f) {x₀ : E} (hC : C ∈ 𝓝 x₀) :
@@ -168,7 +168,7 @@ lemma ConcaveOn.continuousOn_tfae (hC : IsOpen C) (hC' : C.Nonempty) (hf : Conca
   have := hf.neg.continuousOn_tfae hC hC'
   simp only [locallyLipschitzOn_neg_iff, continuousOn_neg_iff, continuousAt_neg_iff, abs_neg]
     at this
-  convert this using 8 <;> exact (Equiv.neg ℝ).exists_congr (by simp)
+  convert! this using 8 <;> exact (Equiv.neg ℝ).exists_congr (by simp)
 
 lemma ConvexOn.locallyLipschitzOn_iff_continuousOn (hC : IsOpen C) (hf : ConvexOn ℝ C f) :
     LocallyLipschitzOn C f ↔ ContinuousOn f C := by
diff --git a/Mathlib/Analysis/Convex/Deriv.lean b/Mathlib/Analysis/Convex/Deriv.lean
index e019ff474af538..21c1d7869eacbb 100644
--- a/Mathlib/Analysis/Convex/Deriv.lean
+++ b/Mathlib/Analysis/Convex/Deriv.lean
@@ -238,7 +238,7 @@ lemma convexOn_of_hasDerivWithinAt2_nonneg {D : Set ℝ} (hD : Convex ℝ D) {f
   · rw [differentiableOn_congr this]
     exact fun x hx ↦ (hf'' _ hx).differentiableWithinAt
   · rintro x hx
-    convert hf''₀ _ hx using 1
+    convert! hf''₀ _ hx using 1
     dsimp
     rw [deriv_eqOn isOpen_interior (fun y hy ↦ ?_) hx]
     exact (hf'' _ hy).congr this <| by rw [this hy]
@@ -254,7 +254,7 @@ lemma concaveOn_of_hasDerivWithinAt2_nonpos {D : Set ℝ} (hD : Convex ℝ D) {f
   · rw [differentiableOn_congr this]
     exact fun x hx ↦ (hf'' _ hx).differentiableWithinAt
   · rintro x hx
-    convert hf''₀ _ hx using 1
+    convert! hf''₀ _ hx using 1
     dsimp
     rw [deriv_eqOn isOpen_interior (fun y hy ↦ ?_) hx]
     exact (hf'' _ hy).congr this <| by rw [this hy]
diff --git a/Mathlib/Analysis/Convex/Gauge.lean b/Mathlib/Analysis/Convex/Gauge.lean
index 9fb5689a4a7e0d..6e2eea7f3179a9 100644
--- a/Mathlib/Analysis/Convex/Gauge.lean
+++ b/Mathlib/Analysis/Convex/Gauge.lean
@@ -102,7 +102,7 @@ theorem gauge_zero' : gauge (0 : Set E) = 0 := by
   obtain rfl | hx := eq_or_ne x 0
   · simp only [csInf_Ioi, mem_zero, Pi.zero_apply, sep_true, smul_zero]
   · simp only [mem_zero, Pi.zero_apply, inv_eq_zero, smul_eq_zero]
-    convert Real.sInf_empty
+    convert! Real.sInf_empty
     exact eq_empty_iff_forall_notMem.2 fun r hr => hr.2.elim (ne_of_gt hr.1) hx
 
 @[simp]
@@ -203,7 +203,7 @@ theorem Convex.gauge_le (hs : Convex ℝ s) (h₀ : (0 : E) ∈ s) (absorbs : Ab
   by_cases ha : 0 ≤ a
   · rw [gauge_le_eq hs h₀ absorbs ha]
     exact convex_iInter fun i => convex_iInter fun _ => hs.smul _
-  · convert convex_empty (𝕜 := ℝ)
+  · convert! convex_empty (𝕜 := ℝ)
     exact eq_empty_iff_forall_notMem.2 fun x hx => ha <| (gauge_nonneg _).trans hx
 
 theorem Balanced.starConvex (hs : Balanced ℝ s) : StarConvex ℝ 0 s :=
@@ -360,7 +360,7 @@ theorem interior_subset_gauge_lt_one (s : Set E) : interior s ⊆ { x | gauge s
 theorem gauge_lt_one_eq_self_of_isOpen (hs₁ : Convex ℝ s) (hs₀ : (0 : E) ∈ s) (hs₂ : IsOpen s) :
     { x | gauge s x < 1 } = s := by
   refine (gauge_lt_one_subset_self hs₁ ‹_› <| absorbent_nhds_zero <| hs₂.mem_nhds hs₀).antisymm ?_
-  convert interior_subset_gauge_lt_one s
+  convert! interior_subset_gauge_lt_one s
   exact hs₂.interior_eq.symm
 
 theorem gauge_lt_one_of_mem_of_isOpen (hs₂ : IsOpen s) {x : E} (hx : x ∈ s) :
@@ -543,9 +543,9 @@ theorem gauge_closure_zero : gauge (closure (0 : Set E)) = 0 := funext fun x ↦
   simp only [← singleton_zero, gauge_def', mem_closure_zero_iff_norm, norm_smul, mul_eq_zero,
     norm_eq_zero, inv_eq_zero]
   rcases (norm_nonneg x).eq_or_lt' with hx | hx
-  · convert csInf_Ioi (a := (0 : ℝ))
+  · convert! csInf_Ioi (a := (0 : ℝ))
     exact Set.ext fun r ↦ and_iff_left (.inr hx)
-  · convert Real.sInf_empty
+  · convert! Real.sInf_empty
     exact eq_empty_of_forall_notMem fun r ⟨hr₀, hr⟩ ↦ hx.ne' <| hr.resolve_left hr₀.out.ne'
 
 @[simp]
diff --git a/Mathlib/Analysis/Convex/Independent.lean b/Mathlib/Analysis/Convex/Independent.lean
index a5e1b2e7559a1a..c7b9a8a152a995 100644
--- a/Mathlib/Analysis/Convex/Independent.lean
+++ b/Mathlib/Analysis/Convex/Independent.lean
@@ -93,7 +93,7 @@ protected theorem ConvexIndependent.range {p : ι → E} (hc : ConvexIndependent
   let f : Set.range p → ι := fun x => x.property.choose
   have hf : ∀ x, p (f x) = x := fun x => x.property.choose_spec
   let fe : Set.range p ↪ ι := ⟨f, fun x₁ x₂ he => Subtype.ext (hf x₁ ▸ hf x₂ ▸ he ▸ rfl)⟩
-  convert hc.comp_embedding fe
+  convert! hc.comp_embedding fe
   ext
   rw [Embedding.coeFn_mk, comp_apply, hf]
 
diff --git a/Mathlib/Analysis/Convex/Jensen.lean b/Mathlib/Analysis/Convex/Jensen.lean
index c5478929caf55e..ed073f079b1b25 100644
--- a/Mathlib/Analysis/Convex/Jensen.lean
+++ b/Mathlib/Analysis/Convex/Jensen.lean
@@ -54,7 +54,7 @@ theorem ConvexOn.map_centerMass_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t,
     f (t.centerMass w p) ≤ t.centerMass w (f ∘ p) := by
   have hmem' : ∀ i ∈ t, (p i, (f ∘ p) i) ∈ { p : E × β | p.1 ∈ s ∧ f p.1 ≤ p.2 } := fun i hi =>
     ⟨hmem i hi, le_rfl⟩
-  convert (hf.convex_epigraph.centerMass_mem h₀ h₁ hmem').2 <;>
+  convert! (hf.convex_epigraph.centerMass_mem h₀ h₁ hmem').2 <;>
     simp only [centerMass, Function.comp, Prod.smul_fst, Prod.fst_sum, Prod.smul_snd, Prod.snd_sum]
 
 /-- Concave **Jensen's inequality**, `Finset.centerMass` version. -/
diff --git a/Mathlib/Analysis/Convex/PathConnected.lean b/Mathlib/Analysis/Convex/PathConnected.lean
index 5275a4a3966a82..2daa2c26a7bec5 100644
--- a/Mathlib/Analysis/Convex/PathConnected.lean
+++ b/Mathlib/Analysis/Convex/PathConnected.lean
@@ -109,7 +109,7 @@ protected theorem IsTopologicalAddGroup.pathConnectedSpace : PathConnectedSpace
 is path connected in `p` then the complement of `q` is path connected in `E`. -/
 theorem isPathConnected_compl_of_isPathConnected_compl_zero {p q : Submodule ℝ E}
     (hpq : IsCompl p q) (hpc : IsPathConnected ({0}ᶜ : Set p)) : IsPathConnected (qᶜ : Set E) := by
-  convert (hpc.image continuous_subtype_val).add q.isPathConnected using 1
+  convert! (hpc.image continuous_subtype_val).add q.isPathConnected using 1
   trans Submodule.prodEquivOfIsCompl p q hpq '' ({0}ᶜ ×ˢ univ)
   · rw [prod_univ, LinearEquiv.image_eq_preimage_symm]
     ext
@@ -123,12 +123,12 @@ theorem segment_image_Ico {x y : ℝ} (h : x < y) : (Path.segment x y) '' Ico 0
   simp_rw [Path.segment_apply, ← image_image _ Subtype.val (Ico 0 1)]
   simp only [lineMap_apply, vsub_eq_sub, smul_eq_mul, vadd_eq_add, image_subtype_val_Ico,
     Icc.coe_zero, Icc.coe_one]
-  convert image_affine_Ico (sub_pos_of_lt h) x 0 1 using 2 <;> ring
+  convert! image_affine_Ico (sub_pos_of_lt h) x 0 1 using 2 <;> ring
 
 theorem segment_image_Ioc {x y : ℝ} (h : x < y) : (Path.segment x y) '' Ioc 0 1 = Ioc x y := by
   simp_rw [Path.segment_apply, ← image_image _ Subtype.val (Ioc 0 1)]
   simp only [lineMap_apply, vsub_eq_sub, smul_eq_mul, vadd_eq_add, image_subtype_val_Ioc,
     Icc.coe_zero, Icc.coe_one]
-  convert image_affine_Ioc (sub_pos_of_lt h) x 0 1 using 2 <;> ring
+  convert! image_affine_Ioc (sub_pos_of_lt h) x 0 1 using 2 <;> ring
 
 end Real
diff --git a/Mathlib/Analysis/Convex/Segment.lean b/Mathlib/Analysis/Convex/Segment.lean
index 753c068b626707..55af8816d0d3cd 100644
--- a/Mathlib/Analysis/Convex/Segment.lean
+++ b/Mathlib/Analysis/Convex/Segment.lean
@@ -206,24 +206,24 @@ theorem openSegment_eq_image (x y : E) :
 
 theorem segment_eq_image' (x y : E) :
     [x -[𝕜] y] = (fun θ : 𝕜 => x + θ • (y - x)) '' Icc (0 : 𝕜) 1 := by
-  convert segment_eq_image 𝕜 x y using 2
+  convert! segment_eq_image 𝕜 x y using 2
   simp only [smul_sub, sub_smul, one_smul]
   abel
 
 theorem openSegment_eq_image' (x y : E) :
     openSegment 𝕜 x y = (fun θ : 𝕜 => x + θ • (y - x)) '' Ioo (0 : 𝕜) 1 := by
-  convert openSegment_eq_image 𝕜 x y using 2
+  convert! openSegment_eq_image 𝕜 x y using 2
   simp only [smul_sub, sub_smul, one_smul]
   abel
 
 theorem segment_eq_image_lineMap (x y : E) : [x -[𝕜] y] =
     AffineMap.lineMap x y '' Icc (0 : 𝕜) 1 := by
-  convert segment_eq_image 𝕜 x y using 2
+  convert! segment_eq_image 𝕜 x y using 2
   exact AffineMap.lineMap_apply_module _ _ _
 
 theorem openSegment_eq_image_lineMap (x y : E) :
     openSegment 𝕜 x y = AffineMap.lineMap x y '' Ioo (0 : 𝕜) 1 := by
-  convert openSegment_eq_image 𝕜 x y using 2
+  convert! openSegment_eq_image 𝕜 x y using 2
   exact AffineMap.lineMap_apply_module _ _ _
 
 theorem lineMap_mem_openSegment (a b : E) {t : 𝕜} (ht : t ∈ Ioo 0 1) :
@@ -297,7 +297,7 @@ lemma segment_inter_subset_endpoint_of_linearIndependent_sub
   have Hy : y = (y - c) + c := by abel
   rw [Hx, Hy, smul_add, smul_add] at H
   have : c + q • (y - c) = c + p • (x - c) := by
-    convert H using 1 <;> simp [sub_smul]
+    convert! H using 1 <;> simp [sub_smul]
   obtain ⟨rfl, rfl⟩ : p = 0 ∧ q = 0 := h.eq_zero_of_pair' ((add_right_inj c).1 this).symm
   simp
 
@@ -324,7 +324,7 @@ lemma segment_inter_eq_endpoint_of_linearIndependent_of_ne
   apply segment_inter_eq_endpoint_of_linearIndependent_sub
   simp only [add_sub_add_left_eq_sub]
   suffices H : LinearIndependent 𝕜 ![(-1 : 𝕜) • x + t • y, (-1 : 𝕜) • x + s • y] by
-    convert H using 1; simp only [neg_smul, one_smul]; abel_nf
+    convert! H using 1; simp only [neg_smul, one_smul]; abel_nf
   nontriviality 𝕜
   rw [LinearIndependent.pair_add_smul_add_smul_iff]
   aesop
@@ -343,7 +343,7 @@ theorem midpoint_mem_segment [Invertible (2 : 𝕜)] (x y : E) : midpoint 𝕜 x
 
 theorem mem_openSegment_sub_add [Invertible (2 : 𝕜)] (x y : E) :
     x ∈ openSegment 𝕜 (x - y) (x + y) := by
-  convert midpoint_mem_openSegment (𝕜 := 𝕜) (x - y) (x + y)
+  convert! midpoint_mem_openSegment (𝕜 := 𝕜) (x - y) (x + y)
   rw [midpoint_sub_add]
 
 theorem mem_segment_sub_add [Invertible (2 : 𝕜)] (x y : E) : x ∈ [x - y -[𝕜] x + y] :=
@@ -351,7 +351,7 @@ theorem mem_segment_sub_add [Invertible (2 : 𝕜)] (x y : E) : x ∈ [x - y -[
 
 theorem mem_openSegment_add_sub [Invertible (2 : 𝕜)] (x y : E) :
     x ∈ openSegment 𝕜 (x + y) (x - y) := by
-  convert midpoint_mem_openSegment (𝕜 := 𝕜) (x + y) (x - y)
+  convert! midpoint_mem_openSegment (𝕜 := 𝕜) (x + y) (x - y)
   rw [midpoint_add_sub]
 
 theorem mem_segment_add_sub [Invertible (2 : 𝕜)] (x y : E) : x ∈ [x + y -[𝕜] x - y] :=
diff --git a/Mathlib/Analysis/Convex/Side.lean b/Mathlib/Analysis/Convex/Side.lean
index e96ba115ac515b..000cf596517e4f 100644
--- a/Mathlib/Analysis/Convex/Side.lean
+++ b/Mathlib/Analysis/Convex/Side.lean
@@ -748,7 +748,7 @@ theorem isConnected_setOf_wSameSide {s : AffineSubspace ℝ P} (x : P) (h : (s :
   · rw [setOf_wSameSide_eq_image2 hx hp, ← Set.image_prod]
     refine (isConnected_Ici.prod (isConnected_iff_connectedSpace.2 ?_)).image _
       ((continuous_fst.smul continuous_const).vadd continuous_snd).continuousOn
-    convert AddTorsor.connectedSpace s.direction s
+    convert! AddTorsor.connectedSpace s.direction s
 
 theorem isPreconnected_setOf_wSameSide (s : AffineSubspace ℝ P) (x : P) :
     IsPreconnected { y | s.WSameSide x y } := by
@@ -765,7 +765,7 @@ theorem isConnected_setOf_sSameSide {s : AffineSubspace ℝ P} {x : P} (hx : x 
   rw [setOf_sSameSide_eq_image2 hx hp, ← Set.image_prod]
   refine (isConnected_Ioi.prod (isConnected_iff_connectedSpace.2 ?_)).image _
     ((continuous_fst.smul continuous_const).vadd continuous_snd).continuousOn
-  convert AddTorsor.connectedSpace s.direction s
+  convert! AddTorsor.connectedSpace s.direction s
 
 theorem isPreconnected_setOf_sSameSide (s : AffineSubspace ℝ P) (x : P) :
     IsPreconnected { y | s.SSameSide x y } := by
@@ -789,7 +789,7 @@ theorem isConnected_setOf_wOppSide {s : AffineSubspace ℝ P} (x : P) (h : (s :
   · rw [setOf_wOppSide_eq_image2 hx hp, ← Set.image_prod]
     refine (isConnected_Iic.prod (isConnected_iff_connectedSpace.2 ?_)).image _
       ((continuous_fst.smul continuous_const).vadd continuous_snd).continuousOn
-    convert AddTorsor.connectedSpace s.direction s
+    convert! AddTorsor.connectedSpace s.direction s
 
 theorem isPreconnected_setOf_wOppSide (s : AffineSubspace ℝ P) (x : P) :
     IsPreconnected { y | s.WOppSide x y } := by
@@ -806,7 +806,7 @@ theorem isConnected_setOf_sOppSide {s : AffineSubspace ℝ P} {x : P} (hx : x 
   rw [setOf_sOppSide_eq_image2 hx hp, ← Set.image_prod]
   refine (isConnected_Iio.prod (isConnected_iff_connectedSpace.2 ?_)).image _
     ((continuous_fst.smul continuous_const).vadd continuous_snd).continuousOn
-  convert AddTorsor.connectedSpace s.direction s
+  convert! AddTorsor.connectedSpace s.direction s
 
 theorem isPreconnected_setOf_sOppSide (s : AffineSubspace ℝ P) (x : P) :
     IsPreconnected { y | s.SOppSide x y } := by
diff --git a/Mathlib/Analysis/Convex/SimplicialComplex/Basic.lean b/Mathlib/Analysis/Convex/SimplicialComplex/Basic.lean
index f3ac4cc75bc7ac..fb37553a12e151 100644
--- a/Mathlib/Analysis/Convex/SimplicialComplex/Basic.lean
+++ b/Mathlib/Analysis/Convex/SimplicialComplex/Basic.lean
@@ -82,7 +82,7 @@ theorem mem_space_iff : x ∈ K.space ↔ ∃ s ∈ K.faces, x ∈ convexHull 
   simp [space]
 
 theorem convexHull_subset_space (hs : s ∈ K.faces) : convexHull 𝕜 s ⊆ K.space := by
-  convert subset_biUnion_of_mem hs
+  convert! subset_biUnion_of_mem hs
   rfl
 
 protected theorem subset_space (hs : s ∈ K.faces) : (s : Set E) ⊆ K.space :=
diff --git a/Mathlib/Analysis/Convex/Slope.lean b/Mathlib/Analysis/Convex/Slope.lean
index 191b5a019bea56..9fc671d386ac95 100644
--- a/Mathlib/Analysis/Convex/Slope.lean
+++ b/Mathlib/Analysis/Convex/Slope.lean
@@ -206,8 +206,8 @@ theorem ConvexOn.secant_mono (hf : ConvexOn 𝕜 s f) {a x y : 𝕜} (ha : a ∈
   · simp
   rcases lt_or_gt_of_ne hxa with hxa | hxa
   · rcases lt_or_gt_of_ne hya with hya | hya
-    · convert hf.secant_mono_aux3 hx ha hxy hya using 1 <;> rw [← neg_div_neg_eq] <;> simp
-    · convert hf.slope_mono_adjacent hx hy hxa hya using 1
+    · convert! hf.secant_mono_aux3 hx ha hxy hya using 1 <;> rw [← neg_div_neg_eq] <;> simp
+    · convert! hf.slope_mono_adjacent hx hy hxa hya using 1
       rw [← neg_div_neg_eq]; simp
   · exact hf.secant_mono_aux2 ha hy hxa hxy
 
@@ -246,9 +246,9 @@ theorem StrictConvexOn.secant_strict_mono (hf : StrictConvexOn 𝕜 s f) {a x y
     (f x - f a) / (x - a) < (f y - f a) / (y - a) := by
   rcases lt_or_gt_of_ne hxa with hxa | hxa
   · rcases lt_or_gt_of_ne hya with hya | hya
-    · convert hf.secant_strict_mono_aux3 hx ha hxy hya using 1 <;> rw [← neg_div_neg_eq] <;>
+    · convert! hf.secant_strict_mono_aux3 hx ha hxy hya using 1 <;> rw [← neg_div_neg_eq] <;>
         simp
-    · convert hf.slope_strict_mono_adjacent hx hy hxa hya using 1
+    · convert! hf.slope_strict_mono_adjacent hx hy hxa hya using 1
       rw [← neg_div_neg_eq]; simp
   · exact hf.secant_strict_mono_aux2 ha hy hxa hxy
 
diff --git a/Mathlib/Analysis/Convex/SpecificFunctions/Basic.lean b/Mathlib/Analysis/Convex/SpecificFunctions/Basic.lean
index 94dfe931b0ba52..0784a2b67c997c 100644
--- a/Mathlib/Analysis/Convex/SpecificFunctions/Basic.lean
+++ b/Mathlib/Analysis/Convex/SpecificFunctions/Basic.lean
@@ -110,13 +110,13 @@ theorem one_add_mul_self_lt_rpow_one_add {s : ℝ} (hs : -1 ≤ s) (hs' : s ≠
   apply exp_strictMono
   rcases lt_or_gt_of_ne hs' with hs' | hs'
   · rw [← div_lt_iff₀ hp', ← div_lt_div_right_of_neg hs']
-    convert strictConcaveOn_log_Ioi.secant_strict_mono (zero_lt_one' ℝ) hs2 hs1 hs4 hs3 _ using 1
+    convert! strictConcaveOn_log_Ioi.secant_strict_mono (zero_lt_one' ℝ) hs2 hs1 hs4 hs3 _ using 1
     · rw [add_sub_cancel_left, log_one, sub_zero]
     · rw [add_sub_cancel_left, div_div, log_one, sub_zero]
     · gcongr
       exact mul_lt_of_one_lt_left hs' hp
   · rw [← div_lt_iff₀ hp', ← div_lt_div_iff_of_pos_right hs']
-    convert strictConcaveOn_log_Ioi.secant_strict_mono (zero_lt_one' ℝ) hs1 hs2 hs3 hs4 _ using 1
+    convert! strictConcaveOn_log_Ioi.secant_strict_mono (zero_lt_one' ℝ) hs1 hs2 hs3 hs4 _ using 1
     · rw [add_sub_cancel_left, div_div, log_one, sub_zero]
     · rw [add_sub_cancel_left, log_one, sub_zero]
     · gcongr
@@ -151,13 +151,13 @@ theorem rpow_one_add_lt_one_add_mul_self {s : ℝ} (hs : -1 ≤ s) (hs' : s ≠
   apply exp_strictMono
   rcases lt_or_gt_of_ne hs' with hs' | hs'
   · rw [← lt_div_iff₀ hp1, ← div_lt_div_right_of_neg hs']
-    convert strictConcaveOn_log_Ioi.secant_strict_mono (zero_lt_one' ℝ) hs1 hs2 hs3 hs4 _ using 1
+    convert! strictConcaveOn_log_Ioi.secant_strict_mono (zero_lt_one' ℝ) hs1 hs2 hs3 hs4 _ using 1
     · rw [add_sub_cancel_left, div_div, log_one, sub_zero]
     · rw [add_sub_cancel_left, log_one, sub_zero]
     · gcongr
       exact lt_mul_of_lt_one_left hs' hp2
   · rw [← lt_div_iff₀ hp1, ← div_lt_div_iff_of_pos_right hs']
-    convert strictConcaveOn_log_Ioi.secant_strict_mono (zero_lt_one' ℝ) hs2 hs1 hs4 hs3 _ using 1
+    convert! strictConcaveOn_log_Ioi.secant_strict_mono (zero_lt_one' ℝ) hs2 hs1 hs4 hs3 _ using 1
     · rw [add_sub_cancel_left, log_one, sub_zero]
     · rw [add_sub_cancel_left, div_div, log_one, sub_zero]
     · gcongr
@@ -210,7 +210,7 @@ theorem convexOn_rpow {p : ℝ} (hp : 1 ≤ p) : ConvexOn ℝ (Ici 0) fun x : 
   exact (strictConvexOn_rpow hp).convexOn
 
 theorem convexOn_rpow_left {b : ℝ} (hb : 0 < b) : ConvexOn ℝ Set.univ (fun (x : ℝ) => b ^ x) := by
-  convert convexOn_exp.comp_linearMap (LinearMap.mul ℝ ℝ (Real.log b)) using 1
+  convert! convexOn_exp.comp_linearMap (LinearMap.mul ℝ ℝ (Real.log b)) using 1
   ext x
   simp [Real.rpow_def_of_pos hb]
 
diff --git a/Mathlib/Analysis/Convex/SpecificFunctions/Deriv.lean b/Mathlib/Analysis/Convex/SpecificFunctions/Deriv.lean
index cc113fe23a219e..33d22c76e8fff5 100644
--- a/Mathlib/Analysis/Convex/SpecificFunctions/Deriv.lean
+++ b/Mathlib/Analysis/Convex/SpecificFunctions/Deriv.lean
@@ -83,8 +83,8 @@ theorem int_prod_range_nonneg (m : ℤ) (n : ℕ) (hn : Even n) :
     refine mul_nonneg ihn ?_; generalize (1 + 1) * n = k
     rcases le_or_gt m k with hmk | hmk
     · have : m ≤ k + 1 := hmk.trans (lt_add_one (k : ℤ)).le
-      convert mul_nonneg_of_nonpos_of_nonpos (sub_nonpos_of_le hmk) _
-      convert sub_nonpos_of_le this
+      convert! mul_nonneg_of_nonpos_of_nonpos (sub_nonpos_of_le hmk) _
+      convert! sub_nonpos_of_le this
     · exact mul_nonneg (sub_nonneg_of_le hmk.le) (sub_nonneg_of_le hmk)
 
 theorem int_prod_range_pos {m : ℤ} {n : ℕ} (hn : Even n) (hm : m ∉ Ico (0 : ℤ) n) :
@@ -114,7 +114,7 @@ section SqrtMulLog
 
 theorem hasDerivAt_sqrt_mul_log {x : ℝ} (hx : x ≠ 0) :
     HasDerivAt (fun x => √x * log x) ((2 + log x) / (2 * √x)) x := by
-  convert (hasDerivAt_sqrt hx).mul (hasDerivAt_log hx) using 1
+  convert! (hasDerivAt_sqrt hx).mul (hasDerivAt_log hx) using 1
   rw [add_div, div_mul_cancel_left₀ two_ne_zero, ← div_eq_mul_inv, sqrt_div_self', add_comm,
     one_div, one_div, ← div_eq_inv_mul]
 
@@ -140,8 +140,9 @@ theorem deriv2_sqrt_mul_log (x : ℝ) :
     refine (hasDerivWithinAt_const _ _ 0).congr_of_mem (fun x hx => ?_) hx
     rw [sqrt_eq_zero_of_nonpos hx, mul_zero, div_zero]
   · have h₀ : √x ≠ 0 := sqrt_ne_zero'.2 hx
-    convert (((hasDerivAt_log hx.ne').const_add 2).div ((hasDerivAt_sqrt hx.ne').const_mul 2) <|
-      mul_ne_zero two_ne_zero h₀).deriv using 1
+    convert!
+      (((hasDerivAt_log hx.ne').const_add 2).div ((hasDerivAt_sqrt hx.ne').const_mul 2) <|
+          mul_ne_zero two_ne_zero h₀).deriv using 1
     nth_rw 3 [← mul_self_sqrt hx.le]
     field
 
diff --git a/Mathlib/Analysis/Convex/Star.lean b/Mathlib/Analysis/Convex/Star.lean
index a375ccd0faeee6..1681d767da1ebe 100644
--- a/Mathlib/Analysis/Convex/Star.lean
+++ b/Mathlib/Analysis/Convex/Star.lean
@@ -156,7 +156,7 @@ variable [Module 𝕜 E] [Module 𝕜 F] {x y z : E} {s : Set E}
 
 theorem StarConvex.mem [ZeroLEOneClass 𝕜] (hs : StarConvex 𝕜 x s) (h : s.Nonempty) : x ∈ s := by
   obtain ⟨y, hy⟩ := h
-  convert hs hy zero_le_one le_rfl (add_zero 1)
+  convert! hs hy zero_le_one le_rfl (add_zero 1)
   rw [one_smul, zero_smul, add_zero]
 
 theorem starConvex_iff_forall_pos (hx : x ∈ s) : StarConvex 𝕜 x s ↔
diff --git a/Mathlib/Analysis/Convex/StdSimplex.lean b/Mathlib/Analysis/Convex/StdSimplex.lean
index 795c64bf9773fc..d66293dae57801 100644
--- a/Mathlib/Analysis/Convex/StdSimplex.lean
+++ b/Mathlib/Analysis/Convex/StdSimplex.lean
@@ -148,7 +148,7 @@ theorem convexHull_basis_eq_stdSimplex [DecidableEq ι] :
 /-- `stdSimplex 𝕜 ι` is the convex hull of the points `Pi.single i 1` for `i : ι`. -/
 theorem convexHull_rangle_single_eq_stdSimplex [DecidableEq ι] :
     convexHull R (range fun i : ι ↦ Pi.single i 1) = stdSimplex R ι := by
-  convert convexHull_basis_eq_stdSimplex R ι
+  convert! convexHull_basis_eq_stdSimplex R ι
   aesop
 
 variable {ι R}
diff --git a/Mathlib/Analysis/Convex/StoneSeparation.lean b/Mathlib/Analysis/Convex/StoneSeparation.lean
index 0aeefbef488dff..7926af5443eda2 100644
--- a/Mathlib/Analysis/Convex/StoneSeparation.lean
+++ b/Mathlib/Analysis/Convex/StoneSeparation.lean
@@ -65,8 +65,10 @@ theorem not_disjoint_segment_convexHull_triple {p q u v x y z : E} (hz : z ∈ s
       · simp [w, Fin.sum_univ_succ]
       linear_combination (au * bv - 1 * au) * habz + (-(1 * az * au) + au) * habv + az * av * habu
     have hz : ∀ i, z i ∈ ({p, q, az • x + bz • y} : Set E) := fun i => by fin_cases i <;> simp [z]
-    convert (Finset.centerMass_mem_convexHull (Finset.univ : Finset (Fin 3)) (fun i _ => hw₀ i)
-        (by rwa [hw]) fun i _ => hz i : Finset.univ.centerMass w z ∈ _)
+    convert!
+      (Finset.centerMass_mem_convexHull (Finset.univ : Finset (Fin 3)) (fun i _ => hw₀ i)
+          (by rwa [hw]) fun i _ => hz i :
+        Finset.univ.centerMass w z ∈ _)
     rw [Finset.centerMass, hw]
     trans (az * av + bz * au)⁻¹ •
       ((az * av * bu) • p + ((bz * au * bv) • q + (au * av) • (az • x + bz • y)))
diff --git a/Mathlib/Analysis/Convex/Strict.lean b/Mathlib/Analysis/Convex/Strict.lean
index 0fccb78045d6a9..2604263348abc9 100644
--- a/Mathlib/Analysis/Convex/Strict.lean
+++ b/Mathlib/Analysis/Convex/Strict.lean
@@ -361,7 +361,7 @@ theorem strictConvex_iff_div :
         ∀ ⦃a b : 𝕜⦄, 0 < a → 0 < b → (a / (a + b)) • x + (b / (a + b)) • y ∈ interior s :=
   ⟨fun h x hx y hy hxy a b ha hb ↦ h hx hy hxy (by positivity) (by positivity) (by field),
     fun h x hx y hy hxy a b ha hb hab ↦ by
-    convert h hx hy hxy ha hb <;> rw [hab, div_one]⟩
+    convert! h hx hy hxy ha hb <;> rw [hab, div_one]⟩
 
 theorem StrictConvex.mem_smul_of_zero_mem (hs : StrictConvex 𝕜 s) (zero_mem : (0 : E) ∈ s)
     (hx : x ∈ s) (hx₀ : x ≠ 0) {t : 𝕜} (ht : 1 < t) : x ∈ t • interior s := by
diff --git a/Mathlib/Analysis/Convex/Visible.lean b/Mathlib/Analysis/Convex/Visible.lean
index c22d2e245e0eb5..4edf4e41f7bf90 100644
--- a/Mathlib/Analysis/Convex/Visible.lean
+++ b/Mathlib/Analysis/Convex/Visible.lean
@@ -78,7 +78,7 @@ lemma IsVisible.of_convexHull_of_pos {ι : Type*} {t : Finset ι} {a : ι → V}
     (hi : i ∈ t) (hwi : 0 < w i) : IsVisible 𝕜 (convexHull 𝕜 s) x (a i) := by
   classical
   obtain hwi | hwi : w i = 1 ∨ w i < 1 := eq_or_lt_of_le <| (single_le_sum hw₀ hi).trans_eq hw₁
-  · convert hw
+  · convert! hw
     rw [← one_smul 𝕜 (a i), ← hwi, eq_comm]
     rw [← hwi, ← sub_eq_zero, ← sum_erase_eq_sub hi,
       sum_eq_zero_iff_of_nonneg fun j hj ↦ hw₀ _ <| erase_subset _ _ hj] at hw₁
diff --git a/Mathlib/Analysis/Convolution.lean b/Mathlib/Analysis/Convolution.lean
index 76e2530c5a9983..e11a45fc803e23 100644
--- a/Mathlib/Analysis/Convolution.lean
+++ b/Mathlib/Analysis/Convolution.lean
@@ -143,7 +143,7 @@ theorem _root_.HasCompactSupport.convolution_integrand_bound_left (hcf : HasComp
     (hf : Continuous f) {x t : G} {s : Set G} (hx : x ∈ s) :
     ‖L (f (x - t)) (g t)‖ ≤
       (-tsupport f + s).indicator (fun t => (‖L‖ * ⨆ i, ‖f i‖) * ‖g t‖) t := by
-  convert hcf.convolution_integrand_bound_right L.flip hf hx using 1
+  convert! hcf.convolution_integrand_bound_right L.flip hf hx using 1
   simp_rw [L.opNorm_flip, mul_right_comm]
 
 end NoMeasurability
@@ -307,9 +307,11 @@ theorem _root_.HasCompactSupport.convolutionExistsAt {x₀ : G}
       (μ.restrict (tsupport fun t : G => L (f t) (g (x₀ - t)))) := by
     apply (hg.comp v.continuous).continuousOn.aestronglyMeasurable_of_isCompact h
     exact (isClosed_tsupport _).measurableSet
-  convert ((v.continuous.measurable.measurePreserving
-      (μ.restrict (tsupport fun t => L (f t) (g (x₀ - t))))).aestronglyMeasurable_comp_iff
-    v.measurableEmbedding).1 A
+  convert!
+    ((v.continuous.measurable.measurePreserving
+              (μ.restrict (tsupport fun t => L (f t) (g (x₀ - t))))).aestronglyMeasurable_comp_iff
+          v.measurableEmbedding).1
+      A
   ext x
   simp only [v, Homeomorph.neg, sub_eq_add_neg, val_toAddUnits_apply, Homeomorph.trans_apply,
     Equiv.neg_apply, Homeomorph.homeomorph_mk_coe, Homeomorph.coe_addLeft]
@@ -368,7 +370,7 @@ theorem convolutionExistsAt_flip :
 
 theorem ConvolutionExistsAt.integrable_swap (h : ConvolutionExistsAt f g x L μ) :
     Integrable (fun t => L (f (x - t)) (g t)) μ := by
-  convert h.comp_sub_left x
+  convert! h.comp_sub_left x
   simp_rw [sub_sub_self]
 
 theorem convolutionExistsAt_iff_integrable_swap :
@@ -504,7 +506,7 @@ theorem support_convolution_subset_swap : support (f ⋆[L, μ] g) ⊆ support g
   apply h2x
   simp_rw [Set.mem_add, ← exists_and_left, not_exists, not_and_or, notMem_support] at hx
   rw [convolution_def]
-  convert integral_zero G F using 2
+  convert! integral_zero G F using 2
   ext t
   rcases hx (x - t) t with (h | h | h)
   · rw [h, (L _).map_zero]
@@ -770,7 +772,7 @@ theorem dist_convolution_le {f : G → ℝ} {x₀ : G} {R ε : ℝ} {z₀ : E'}
     (hmg : AEStronglyMeasurable g μ) (hg : ∀ x ∈ ball x₀ R, dist (g x) z₀ ≤ ε) :
     dist ((f ⋆[lsmul ℝ ℝ, μ] g : G → E') x₀) z₀ ≤ ε := by
   have hif : Integrable f μ := integrable_of_integral_eq_one hintf
-  convert (dist_convolution_le' (lsmul ℝ ℝ) hε hif hf hmg hg).trans _
+  convert! (dist_convolution_le' (lsmul ℝ ℝ) hε hif hf hmg hg).trans _
   · simp_rw [lsmul_apply, integral_smul_const, hintf, one_smul]
   · simp_rw [Real.norm_of_nonneg (hnf _), hintf, mul_one]
     exact (mul_le_mul_of_nonneg_right opNorm_lsmul_le hε).trans_eq (one_mul ε)
@@ -904,7 +906,7 @@ theorem convolution_assoc (hL : ∀ (x : E) (y : E') (z : E''), L₂ (L x y) z =
     (measurePreserving_sub_prod μ ν).map_eq
   suffices Integrable (uncurry fun x y => L₃ (f y) (L₄ (g x) (k (x₀ - y - x)))) (μ.prod ν) by
     rw [← h3] at this
-    convert this.comp_measurable (measurable_sub.prodMk measurable_snd)
+    convert! this.comp_measurable (measurable_sub.prodMk measurable_snd)
     ext ⟨x, y⟩
     simp +unfoldPartialApp only [uncurry, Function.comp_apply,
       sub_sub_sub_cancel_right]
@@ -964,7 +966,7 @@ theorem posConvolution_eq_convolution_indicator (f : ℝ → E) (g : ℝ → E')
           indicator_of_mem (mem_Ioi.mpr <| sub_pos.mpr ht.2)]
     · rw [indicator_of_notMem (notMem_Ioo_of_ge ht),
           indicator_of_notMem (notMem_Ioi.mpr (sub_nonpos_of_le ht)), map_zero]
-  · convert (integral_zero ℝ F).symm with t
+  · convert! (integral_zero ℝ F).symm with t
     by_cases ht : 0 < t
     · rw [indicator_of_notMem (_ : x - t ∉ Ioi 0), map_zero]
       rw [notMem_Ioi] at h ⊢
@@ -989,7 +991,7 @@ theorem integral_posConvolution [CompleteSpace E] [CompleteSpace E'] [CompleteSp
       L (∫ x : ℝ in Ioi 0, f x ∂ν) (∫ x : ℝ in Ioi 0, g x ∂μ) := by
   rw [← integrable_indicator_iff measurableSet_Ioi] at hf hg
   simp_rw [← integral_indicator measurableSet_Ioi]
-  convert integral_convolution L hf hg using 4 with x
+  convert! integral_convolution L hf hg using 4 with x
   apply posConvolution_eq_convolution_indicator
 
 end Nonneg
diff --git a/Mathlib/Analysis/Distribution/SchwartzSpace/Basic.lean b/Mathlib/Analysis/Distribution/SchwartzSpace/Basic.lean
index 26f811b264ed76..d72492b71f3b0c 100644
--- a/Mathlib/Analysis/Distribution/SchwartzSpace/Basic.lean
+++ b/Mathlib/Analysis/Distribution/SchwartzSpace/Basic.lean
@@ -779,7 +779,7 @@ theorem smulLeftCLM_compL_smulLeftCLM {g₁ g₂ : E → 𝕜} (hg₁ : g₁.Has
 theorem smulLeftCLM_smul {g : E → 𝕜} (hg : g.HasTemperateGrowth) (c : 𝕜) :
     smulLeftCLM F (c • g) = c • smulLeftCLM F g := by
   have : (fun (_ : E) ↦ c).HasTemperateGrowth := by fun_prop
-  convert (smulLeftCLM_compL_smulLeftCLM this hg).symm using 1
+  convert! (smulLeftCLM_compL_smulLeftCLM this hg).symm using 1
   simp
 
 theorem smulLeftCLM_add {g₁ g₂ : E → 𝕜} (hg₁ : g₁.HasTemperateGrowth)
@@ -1131,7 +1131,7 @@ lemma integrable_pow_mul_iteratedFDeriv
 variable (μ) in
 lemma integrable_pow_mul (f : 𝓢(D, V))
     (k : ℕ) : Integrable (fun x ↦ ‖x‖ ^ k * ‖f x‖) μ := by
-  convert integrable_pow_mul_iteratedFDeriv μ f k 0 with x
+  convert! integrable_pow_mul_iteratedFDeriv μ f k 0 with x
   simp
 
 @[fun_prop]
diff --git a/Mathlib/Analysis/Distribution/SchwartzSpace/Fourier.lean b/Mathlib/Analysis/Distribution/SchwartzSpace/Fourier.lean
index 539f3d7454f562..e3a8167086a257 100644
--- a/Mathlib/Analysis/Distribution/SchwartzSpace/Fourier.lean
+++ b/Mathlib/Analysis/Distribution/SchwartzSpace/Fourier.lean
@@ -259,7 +259,7 @@ theorem integral_fourier_mul_eq (f : 𝓢(V, ℂ)) (g : 𝓢(V, ℂ)) :
 Version where the multiplication is replaced by a general bilinear form `M`. -/
 theorem integral_bilin_fourierInv_eq (f : 𝓢(V, E)) (g : 𝓢(V, F)) (M : E →L[ℂ] F →L[ℂ] G) :
     ∫ ξ, M (𝓕⁻ f ξ) (g ξ) = ∫ x, M (f x) (𝓕⁻ g x) := by
-  convert (integral_bilin_fourier_eq (𝓕⁻ f) (𝓕⁻ g) M).symm
+  convert! (integral_bilin_fourier_eq (𝓕⁻ f) (𝓕⁻ g) M).symm
   · exact (FourierTransform.fourier_fourierInv_eq g).symm
   · exact (FourierTransform.fourier_fourierInv_eq f).symm
 
diff --git a/Mathlib/Analysis/Distribution/Sobolev.lean b/Mathlib/Analysis/Distribution/Sobolev.lean
index 2dee899f1db877..f92508dc030efc 100644
--- a/Mathlib/Analysis/Distribution/Sobolev.lean
+++ b/Mathlib/Analysis/Distribution/Sobolev.lean
@@ -252,7 +252,7 @@ theorem MemSobolev.fourier_memL1 {s : ℝ} (hs : Module.finrank ℝ E < 2 * s) {
         norm_cast
         simp_rw [ofReal_norm] at h
         simp_rw [← enorm_pow]
-        convert h using 4
+        convert! h using 4
         rw [← Real.rpow_mul_natCast (by positivity)]
         simp
       apply ((integrable_rpow_neg_one_add_norm_sq hs).congr _).lintegral_lt_top
@@ -264,7 +264,7 @@ theorem MemSobolev.fourier_memL1 {s : ℝ} (hs : Module.finrank ℝ E < 2 * s) {
   use this.toLp • u
   rw [MeasureTheory.Lp.toTemperedDistribution_smul_eq]
   · rw [← hu, smulLeftCLM_smulLeftCLM_apply (by fun_prop) (by fun_prop)]
-    convert (smulLeftCLM_const 1 (𝓕 f)).symm using 1
+    convert! (smulLeftCLM_const 1 (𝓕 f)).symm using 1
     · simp
     · congr
       ext x
diff --git a/Mathlib/Analysis/Distribution/TemperateGrowth.lean b/Mathlib/Analysis/Distribution/TemperateGrowth.lean
index 91e88fd68cc8ed..9ac74e75efeddc 100644
--- a/Mathlib/Analysis/Distribution/TemperateGrowth.lean
+++ b/Mathlib/Analysis/Distribution/TemperateGrowth.lean
@@ -208,7 +208,7 @@ theorem HasTemperateGrowth.add (hf : f.HasTemperateGrowth) (hg : g.HasTemperateG
 @[to_fun (attr := fun_prop)]
 theorem HasTemperateGrowth.sub (hf : f.HasTemperateGrowth) (hg : g.HasTemperateGrowth) :
     (f - g).HasTemperateGrowth := by
-  convert hf.add hg.neg using 1
+  convert! hf.add hg.neg using 1
   grind
 
 @[fun_prop]
@@ -326,7 +326,7 @@ variable (H) in
 theorem hasTemperateGrowth_norm_sq : (fun (x : H) ↦ ‖x‖ ^ 2).HasTemperateGrowth := by
   apply _root_.Function.HasTemperateGrowth.of_fderiv (C := 1) (k := 2)
   · rw [fderiv_norm_sq]
-    convert (2 • innerSL ℝ).hasTemperateGrowth
+    convert! (2 • innerSL ℝ).hasTemperateGrowth
   · exact .norm_sq ℝ differentiable_id
   · intro x
     rw [norm_pow, norm_norm, one_mul, add_pow_two]
diff --git a/Mathlib/Analysis/Fourier/AddCircle.lean b/Mathlib/Analysis/Fourier/AddCircle.lean
index 4a0e6ec25a7c13..a29469c3576dde 100644
--- a/Mathlib/Analysis/Fourier/AddCircle.lean
+++ b/Mathlib/Analysis/Fourier/AddCircle.lean
@@ -192,7 +192,7 @@ theorem fourier_add_half_inv_index {n : ℤ} (hn : n ≠ 0) (hT : 0 < T) (x : Ad
     Metric.unitSphere.coe_mul]
   have : (@toCircle T (n • (T / 2 / n) : ℝ) : ℂ) = -1 := by
     rw [zsmul_eq_mul, toCircle, Function.Periodic.lift_coe, Circle.coe_exp]
-    convert Complex.exp_pi_mul_I using 3
+    convert! Complex.exp_pi_mul_I using 3
     field_simp
   rw [this]; simp
 
@@ -259,7 +259,7 @@ theorem coeFn_fourierLp (p : ℝ≥0∞) [Fact (1 ≤ p)] (n : ℤ) :
 `Lp ℂ p haarAddCircle`. -/
 theorem span_fourierLp_closure_eq_top {p : ℝ≥0∞} [Fact (1 ≤ p)] (hp : p ≠ ∞) :
     (span ℂ (range (@fourierLp T _ p _))).topologicalClosure = ⊤ := by
-  convert
+  convert!
     (ContinuousMap.toLp_denseRange ℂ (@haarAddCircle T hT) ℂ hp).topologicalClosure_map_submodule
       span_fourier_closure_eq_top
   rw [map_span]
@@ -277,8 +277,9 @@ theorem orthonormal_fourier : Orthonormal ℂ (@fourierLp T _ 2 _) := by
   · simp [h]
   have hij : j + -i ≠ 0 := by
     exact sub_ne_zero.mpr (Ne.symm h)
-  convert integral_eq_zero_of_add_right_eq_neg (μ := haarAddCircle)
-    (fourier_add_half_inv_index hij hT.elim)
+  convert!
+    integral_eq_zero_of_add_right_eq_neg (μ := haarAddCircle)
+      (fourier_add_half_inv_index hij hT.elim)
 
 end Monomials
 
@@ -462,7 +463,7 @@ theorem hasSum_sq_fourierCoeffOn
   haveI := Fact.mk (by linarith : 0 < b - a)
   rw [← add_sub_cancel a b] at hL2
   have h := hL2.memLp_liftIoc.haarAddCircle
-  convert hasSum_sq_fourierCoeff h.toLp using 1
+  convert! hasSum_sq_fourierCoeff h.toLp using 1
   · simp [fourierCoeff_congr_ae h.coeFn_toLp, fourierCoeff_liftIoc_eq]
   · nth_rw 2 [← add_sub_cancel a b]
     rw [← AddCircle.integral_liftIoc_eq_intervalIntegral, ← Function.comp_def (f := (‖·‖ ^ 2))]
@@ -503,7 +504,7 @@ theorem hasSum_fourier_series_of_summable (h : Summable (fourierCoeff f)) :
 converges everywhere pointwise to `f`. -/
 theorem has_pointwise_sum_fourier_series_of_summable (h : Summable (fourierCoeff f))
     (x : AddCircle T) : HasSum (fun i => fourierCoeff f i • fourier i x) (f x) := by
-  convert (ContinuousMap.evalCLM ℂ x).hasSum (hasSum_fourier_series_of_summable h)
+  convert! (ContinuousMap.evalCLM ℂ x).hasSum (hasSum_fourier_series_of_summable h)
 
 end Convergence
 
@@ -537,7 +538,7 @@ theorem hasDerivAt_fourier (n : ℤ) (x : ℝ) :
   refine (?_ : HasDerivAt (fun y => exp (2 * π * I * n * y / T)) _ _).comp_ofReal
   rw [(fun α β => by ring : ∀ α β : ℂ, α * exp β = exp β * α)]
   refine (hasDerivAt_exp _).comp (x : ℂ) ?_
-  convert hasDerivAt_mul_const (2 * ↑π * I * ↑n / T) using 1
+  convert! hasDerivAt_mul_const (2 * ↑π * I * ↑n / T) using 1
   ext1 y; ring
 
 theorem hasDerivAt_fourier_neg (n : ℤ) (x : ℝ) :
@@ -550,7 +551,7 @@ variable {T}
 theorem has_antideriv_at_fourier_neg (hT : Fact (0 < T)) {n : ℤ} (hn : n ≠ 0) (x : ℝ) :
     HasDerivAt (fun y : ℝ => (T : ℂ) / (-2 * π * I * n) * fourier (-n) (y : AddCircle T))
       (fourier (-n) (x : AddCircle T)) x := by
-  convert (hasDerivAt_fourier_neg T n x).div_const (-2 * π * I * n / T) using 1
+  convert! (hasDerivAt_fourier_neg T n x).div_const (-2 * π * I * n / T) using 1
   · ext1 y; rw [div_div_eq_mul_div]; ring
   · simp [mul_div_cancel_left₀, hn, (Fact.out : 0 < T).ne', Real.pi_pos.ne']
 
diff --git a/Mathlib/Analysis/Fourier/AddCircleMulti.lean b/Mathlib/Analysis/Fourier/AddCircleMulti.lean
index cf36d3e4f5a05c..b2f003cf804611 100644
--- a/Mathlib/Analysis/Fourier/AddCircleMulti.lean
+++ b/Mathlib/Analysis/Fourier/AddCircleMulti.lean
@@ -178,17 +178,17 @@ lemma measurePreserving_equivPiIoc :
     measurable_subtype_coe (α := {x : d → ℝ // ∀ i, x i ∈ Ioc (a i) (a i + 1)})
   simp only [Function.comp_def] at this
   simp_rw [coe_symm_measurableEquivPiIoc, ← this]
-  convert (measurePreserving_pi _ _ (fun i => AddCircle.measurePreserving_mk 1 (a i))).map_eq.symm
+  convert! (measurePreserving_pi _ _ (fun i => AddCircle.measurePreserving_mk 1 (a i))).map_eq.symm
   · simp [volume, AddCircle.haarAddCircle]
-  · convert (map_comap_subtype_coe (MeasurableSet.univ_pi'
-      (fun i => measurableSet_Ioc (a := a i))) volume)
-    convert (Measure.restrict_pi_pi (fun i => volume) (fun i => Ioc (a i) (a i + 1))).symm
+  · convert!
+    (map_comap_subtype_coe (MeasurableSet.univ_pi' (fun i => measurableSet_Ioc (a := a i))) volume)
+    convert! (Measure.restrict_pi_pi (fun i => volume) (fun i => Ioc (a i) (a i + 1))).symm
     grind
 
 theorem lintegral_preimage (f : UnitAddTorus d → ℝ≥0∞) (a : d → ℝ) :
     ∫⁻ x : UnitAddTorus d, f x =
     ∫⁻ (x : d → ℝ) in {x : d → ℝ | ∀ i, x i ∈ Ioc (a i) (a i + 1)}, f (fun i => x i) := by
-  convert lintegral_map_equiv (μ := volume.comap Subtype.val) f (measurableEquivPiIoc a).symm
+  convert! lintegral_map_equiv (μ := volume.comap Subtype.val) f (measurableEquivPiIoc a).symm
   · exact (measurePreserving_equivPiIoc a).symm.map_eq.symm
   · rw [← lintegral_subtype_comap (MeasurableSet.univ_pi' (fun i => measurableSet_Ioc))]
     rfl
@@ -197,7 +197,7 @@ theorem integral_preimage {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]
     (f : UnitAddTorus d → E) (a : d → ℝ) :
     ∫ x : UnitAddTorus d, f x =
     ∫ (x : d → ℝ) in {x : d → ℝ | ∀ i, x i ∈ Ioc (a i) (a i + 1)}, f (fun i => x i) := by
-  convert integral_map_equiv (μ := volume.comap Subtype.val) (measurableEquivPiIoc a).symm f
+  convert! integral_map_equiv (μ := volume.comap Subtype.val) (measurableEquivPiIoc a).symm f
   · exact (measurePreserving_equivPiIoc a).symm.map_eq.symm
   · rw [← integral_subtype_comap (MeasurableSet.univ_pi' (fun i => measurableSet_Ioc))]
     rfl
diff --git a/Mathlib/Analysis/Fourier/Convolution.lean b/Mathlib/Analysis/Fourier/Convolution.lean
index 3ecf80926f6b94..7d6a45f64d377e 100644
--- a/Mathlib/Analysis/Fourier/Convolution.lean
+++ b/Mathlib/Analysis/Fourier/Convolution.lean
@@ -54,12 +54,12 @@ theorem integrable_prod_sub (B : F₁ →L[𝕜] F₂ →L[𝕜] F₃) {f₁ : E
   have : Integrable (fun x ↦ ((∫ y, ‖f₁ y‖) * ‖f₂ x‖)) := by
     apply hf₂.norm.bdd_mul (by fun_prop) (c := ‖(∫ y, ‖f₁ y‖)‖)
     filter_upwards with; rfl
-  convert this using 1
+  convert! this using 1
   ext x
   simp_rw [norm_mul, norm_norm]
   rw [integral_mul_const]
   congr 1
-  convert integral_sub_right_eq_self _ x (μ := volume)
+  convert! integral_sub_right_eq_self _ x (μ := volume)
   rfl
 
 open FourierTransform
@@ -89,7 +89,7 @@ theorem fourier_bilin_convolution_eq_integral (B : F₁ →L[𝕜] F₂ →L[
     congr
     ext y
     -- Linear change of variables
-    convert integral_sub_right_eq_self _ y (μ := volume)
+    convert! integral_sub_right_eq_self _ y (μ := volume)
     congr
     simp
 
@@ -215,7 +215,7 @@ theorem convolution_apply (B : F₁ →L[ℂ] F₂ →L[ℂ] F₃) (f : 𝓢(E,
       exact ⟨SchwartzMap.seminorm ℝ 0 0 g, fun x ⟨y, hy⟩ ↦ hy ▸ norm_le_seminorm ℝ g y⟩
     · exact f.integrable.integrable_convolution B g.integrable
     · have : Integrable (fun ξ ↦ B (𝓕 f ξ) (𝓕 g ξ)) volume := (pairing B (𝓕 f) (𝓕 g)).integrable
-      convert this
+      convert! this
       rw [← fourier_convolution_apply B f g, fourier_convolution, pairing_apply_apply]
 
 
diff --git a/Mathlib/Analysis/Fourier/FourierTransform.lean b/Mathlib/Analysis/Fourier/FourierTransform.lean
index 1ae41a8c269724..5b68556816ea00 100644
--- a/Mathlib/Analysis/Fourier/FourierTransform.lean
+++ b/Mathlib/Analysis/Fourier/FourierTransform.lean
@@ -206,7 +206,7 @@ theorem integral_fourierIntegral_swap
     apply hM.comp_aestronglyMeasurable A' -- `exact` works, but `apply` is 10x faster!
   · filter_upwards with ⟨ξ, x⟩
     simp only [Function.uncurry_apply_pair, norm_mul, norm_norm, ge_iff_le, ← mul_assoc]
-    convert M.le_opNorm₂ (g ξ) (e (-L x ξ) • f x) using 2
+    convert! M.le_opNorm₂ (g ξ) (e (-L x ξ) • f x) using 2
     simp
 
 variable [CompleteSpace E] [CompleteSpace F]
diff --git a/Mathlib/Analysis/Fourier/FourierTransformDeriv.lean b/Mathlib/Analysis/Fourier/FourierTransformDeriv.lean
index 4e230bf96e2d0d..82dad07434eedc 100644
--- a/Mathlib/Analysis/Fourier/FourierTransformDeriv.lean
+++ b/Mathlib/Analysis/Fourier/FourierTransformDeriv.lean
@@ -116,7 +116,7 @@ lemma hasFDerivAt_fourierChar_neg_bilinear_right (v : V) (w : W) :
     HasFDerivAt (fun w ↦ (𝐞 (-L v w) : ℂ))
       ((-2 * π * I * 𝐞 (-L v w)) • (ofRealCLM ∘L (L v))) w := by
   have ha : HasFDerivAt (fun w' : W ↦ L v w') (L v) w := ContinuousLinearMap.hasFDerivAt (L v)
-  convert (hasDerivAt_fourierChar (-L v w)).hasFDerivAt.comp w ha.neg using 1
+  convert! (hasDerivAt_fourierChar (-L v w)).hasFDerivAt.comp w ha.neg using 1
   ext y
   simp only [neg_mul, ContinuousLinearMap.coe_smul', ContinuousLinearMap.coe_comp', Pi.smul_apply,
     Function.comp_apply, ofRealCLM_apply, smul_eq_mul, ContinuousLinearMap.comp_neg,
@@ -172,7 +172,7 @@ set_option backward.isDefEq.respectTransparency false in
 lemma hasFDerivAt_fourierChar_smul (v : V) (w : W) :
     HasFDerivAt (fun w' ↦ 𝐞 (-L v w') • f v) (𝐞 (-L v w) • fourierSMulRight L f v) w := by
   have ha : HasFDerivAt (fun w' : W ↦ L v w') (L v) w := ContinuousLinearMap.hasFDerivAt (L v)
-  convert ((hasDerivAt_fourierChar (-L v w)).hasFDerivAt.comp w ha.neg).smul_const (f v)
+  convert! ((hasDerivAt_fourierChar (-L v w)).hasFDerivAt.comp w ha.neg).smul_const (f v)
   ext w' : 1
   simp_rw [fourierSMulRight, ContinuousLinearMap.smul_apply, ContinuousLinearMap.smulRight_apply]
   rw [ContinuousLinearMap.comp_apply, ContinuousLinearMap.neg_apply,
@@ -274,7 +274,7 @@ theorem fourierIntegral_fderiv [MeasurableSpace V] [BorelSpace V] [FiniteDimensi
   · simp only [A, neg_mul, neg_smul, neg_neg]
   · have : Integrable (fun x ↦ (-(2 * ↑π * I * ↑((L y) w)) • ((g x : ℂ) • f x))) μ :=
       ((fourierIntegral_convergent_iff' _ _).2 hf).smul _
-    convert this using 2 with x
+    convert! this using 2 with x
     simp only [A, neg_mul, neg_smul, smul_smul]
   · exact (fourierIntegral_convergent_iff' _ _).2 (hf'.apply_continuousLinearMap _)
   · exact (fourierIntegral_convergent_iff' _ _).2 hf
@@ -799,7 +799,7 @@ lemma hasDerivAt_fourier
     rw [ContinuousLinearMap.smulRight_apply, ContinuousLinearMap.flip_apply,
       ContinuousLinearMap.mul_apply', one_mul, map_smul]
     exact congr_arg (fun x ↦ v • x) (one_smul ℝ (f v)).symm
-  convert (VectorFourier.hasFDerivAt_fourierIntegral L hf hf'' w).hasDerivAt using 1
+  convert! (VectorFourier.hasFDerivAt_fourierIntegral L hf hf'' w).hasDerivAt using 1
   rw [fourierIntegral_continuousLinearMap_apply' h_int, VectorFourier.fourierIntegral,
     fourier_real_eq]
   simp [fourierSMulRight, L, ContinuousLinearMap.smul_apply,
@@ -842,7 +842,7 @@ theorem iteratedDeriv_fourier {f : ℝ → E} {N : ℕ∞} {n : ℕ}
     iteratedDeriv n (𝓕 f) = 𝓕 (fun x : ℝ ↦ (-2 * π * I * x) ^ n • f x) := by
   ext x : 1
   have A (n : ℕ) (hn : n ≤ N) : Integrable (fun v ↦ ‖v‖ ^ n * ‖f v‖) := by
-    convert (hf n hn).norm with x
+    convert! (hf n hn).norm with x
     simp [norm_smul]
   have B : AEStronglyMeasurable f := by simpa using (hf 0 zero_le).1
   rw [iteratedDeriv, iteratedFDeriv_fourier A B hn,
diff --git a/Mathlib/Analysis/Fourier/Inversion.lean b/Mathlib/Analysis/Fourier/Inversion.lean
index 18c273dcb241d1..1277a33325b9df 100644
--- a/Mathlib/Analysis/Fourier/Inversion.lean
+++ b/Mathlib/Analysis/Fourier/Inversion.lean
@@ -83,7 +83,7 @@ lemma tendsto_integral_gaussian_smul (hf : Integrable f) (h'f : Integrable (𝓕
       have B : Continuous fun p : V × V => (- innerₗ V) p.1 p.2 := continuous_inner.neg
       simpa using
         (VectorFourier.fourierIntegral_convergent_iff Real.continuous_fourierChar B v).2 h'f
-    convert tendsto_integral_cexp_sq_smul this using 4 with c w
+    convert! tendsto_integral_cexp_sq_smul this using 4 with c w
     · rw [Submonoid.smul_def, Real.fourierChar_apply, smul_smul, ← Complex.exp_add, real_inner_comm]
       congr 3
       simp only [ofReal_mul, ofReal_ofNat]
@@ -127,7 +127,7 @@ lemma tendsto_integral_gaussian_smul' (hf : Integrable f) {v : V} (h'f : Continu
       have B := tendsto_rpow_mul_exp_neg_mul_atTop_nhds_zero (finrank ℝ V / 2) 1
         zero_lt_one |>.comp A |>.const_mul (π ^ (-finrank ℝ V / 2 : ℝ))
       rw [mul_zero] at B
-      convert B using 2 with x
+      convert! B using 2 with x
       simp only [neg_mul, one_mul, Function.comp_apply, ← mul_assoc, ← rpow_natCast, φ]
       congr 1
       rw [mul_rpow (by positivity) (by positivity), ← rpow_mul pi_nonneg,
diff --git a/Mathlib/Analysis/Fourier/LpSpace.lean b/Mathlib/Analysis/Fourier/LpSpace.lean
index 7efc4420fe5ef5..702a38dd177a69 100644
--- a/Mathlib/Analysis/Fourier/LpSpace.lean
+++ b/Mathlib/Analysis/Fourier/LpSpace.lean
@@ -113,7 +113,7 @@ theorem SchwartzMap.toLp_fourierInv_eq (f : 𝓢(E, F)) : 𝓕⁻ (f.toLp 2) = (
   use 1
   intro f
   rw [one_mul]
-  convert (norm_fourier_toL2_eq (𝓕⁻ f)).symm.le
+  convert! (norm_fourier_toL2_eq (𝓕⁻ f)).symm.le
   simp
 
 @[deprecated (since := "2025-12-31")]
diff --git a/Mathlib/Analysis/Fourier/PoissonSummation.lean b/Mathlib/Analysis/Fourier/PoissonSummation.lean
index 4d507a1386050a..cc7e59172f12b9 100644
--- a/Mathlib/Analysis/Fourier/PoissonSummation.lean
+++ b/Mathlib/Analysis/Fourier/PoissonSummation.lean
@@ -76,7 +76,7 @@ theorem Real.fourierCoeff_tsum_comp_add {f : C(ℝ, ℂ)}
     -- Swap sum and integral.
     _ = ∑' n : ℤ, ∫ x in (0 : ℝ)..1, (e * f.comp (ContinuousMap.addRight n)) x := by
       refine (intervalIntegral.tsum_intervalIntegral_eq_of_summable_norm ?_).symm
-      convert hf ⟨uIcc 0 1, isCompact_uIcc⟩ using 1
+      convert! hf ⟨uIcc 0 1, isCompact_uIcc⟩ using 1
       exact funext fun n => neK _ _
     _ = ∑' n : ℤ, ∫ x in (0 : ℝ)..1, (e * f).comp (ContinuousMap.addRight n) x := by
       simp only [mul_comp] at eadd ⊢
@@ -85,7 +85,7 @@ theorem Real.fourierCoeff_tsum_comp_add {f : C(ℝ, ℂ)}
     _ = ∫ x, e x * f x := by
       suffices Integrable (e * f) from this.hasSum_intervalIntegral_comp_add_int.tsum_eq
       apply integrable_of_summable_norm_Icc
-      convert hf ⟨Icc 0 1, isCompact_Icc⟩ using 1
+      convert! hf ⟨Icc 0 1, isCompact_Icc⟩ using 1
       simp_rw [mul_comp] at eadd ⊢
       simp_rw [eadd]
       exact funext fun n => neK ⟨Icc 0 1, isCompact_Icc⟩ _
@@ -107,9 +107,9 @@ theorem Real.tsum_eq_tsum_fourier {f : C(ℝ, ℂ)}
   let F : C(UnitAddCircle, ℂ) :=
     ⟨(f.periodic_tsum_comp_add_zsmul 1).lift, continuous_coinduced_dom.mpr (map_continuous _)⟩
   have : Summable (fourierCoeff F) := by
-    convert h_sum
+    convert! h_sum
     exact Real.fourierCoeff_tsum_comp_add h_norm _
-  convert (has_pointwise_sum_fourier_series_of_summable this x).tsum_eq.symm using 1
+  convert! (has_pointwise_sum_fourier_series_of_summable this x).tsum_eq.symm using 1
   · simpa only [F, coe_mk, ← QuotientAddGroup.mk_zero, Periodic.lift_coe, zsmul_one, comp_apply,
       coe_addRight, zero_add]
        using (hasSum_apply (summable_of_locally_summable_norm h_norm).hasSum x).tsum_eq
@@ -148,7 +148,7 @@ theorem isBigO_norm_Icc_restrict_atTop {f : C(ℝ, E)} {b : ℝ} (hb : 0 < b)
   refine fun y => (hd y.1 (by linarith [hx.1, y.2.1])).trans ?_
   have A : ∀ x : ℝ, 0 ≤ |x| ^ (-b) := fun x => by positivity
   rw [mul_assoc, mul_le_mul_iff_right₀ hc, norm_of_nonneg (A _), norm_of_nonneg (A _)]
-  convert claim x (by linarith only [hx.1]) y.1 y.2.1
+  convert! claim x (by linarith only [hx.1]) y.1 y.2.1
   · apply abs_of_nonneg; linarith [y.2.1]
   · exact abs_of_pos hx'.1
 
@@ -156,7 +156,7 @@ theorem isBigO_norm_Icc_restrict_atBot {f : C(ℝ, E)} {b : ℝ} (hb : 0 < b)
     (hf : f =O[atBot] fun x : ℝ => |x| ^ (-b)) (R S : ℝ) :
     (fun x : ℝ => ‖f.restrict (Icc (x + R) (x + S))‖) =O[atBot] fun x : ℝ => |x| ^ (-b) := by
   have h1 : (f.comp (ContinuousMap.mk _ continuous_neg)) =O[atTop] fun x : ℝ => |x| ^ (-b) := by
-    convert hf.comp_tendsto tendsto_neg_atTop_atBot using 1
+    convert! hf.comp_tendsto tendsto_neg_atTop_atBot using 1
     ext1 x; simp only [Function.comp_apply, abs_neg]
   have h2 := (isBigO_norm_Icc_restrict_atTop hb h1 (-S) (-R)).comp_tendsto tendsto_neg_atBot_atTop
   have : (fun x : ℝ => |x| ^ (-b)) ∘ Neg.neg = fun x : ℝ => |x| ^ (-b) := by
diff --git a/Mathlib/Analysis/Fourier/RiemannLebesgueLemma.lean b/Mathlib/Analysis/Fourier/RiemannLebesgueLemma.lean
index 668dda39a82e3a..d45231572cf6f0 100644
--- a/Mathlib/Analysis/Fourier/RiemannLebesgueLemma.lean
+++ b/Mathlib/Analysis/Fourier/RiemannLebesgueLemma.lean
@@ -180,7 +180,7 @@ variable (f)
 theorem tendsto_integral_exp_inner_smul_cocompact :
     Tendsto (fun w : V => ∫ v, 𝐞 (-⟪v, w⟫) • f v) (cocompact V) (𝓝 0) := by
   by_cases hfi : Integrable f; swap
-  · convert tendsto_const_nhds (x := (0 : E)) with w
+  · convert! tendsto_const_nhds (x := (0 : E)) with w
     apply integral_undef
     rwa [Real.fourierIntegral_convergent_iff]
   refine Metric.tendsto_nhds.mpr fun ε hε => ?_
@@ -261,8 +261,10 @@ theorem tendsto_integral_exp_smul_cocompact (μ : Measure V) [μ.IsAddHaarMeasur
   -- isomorphism between duals derived from A
   let Adual : StrongDual ℝ V ≃L[ℝ] StrongDual ℝ V' := A.arrowCongrSL (.refl _ _)
   have : (μ.map Aₘ).IsAddHaarMeasure := A.isAddHaarMeasure_map _
-  convert (tendsto_integral_exp_smul_cocompact_of_inner_product (f ∘ A.symm) (μ.map Aₘ)).comp
-    Adual.toHomeomorph.toCocompactMap.cocompact_tendsto' with w
+  convert!
+    (tendsto_integral_exp_smul_cocompact_of_inner_product (f ∘ A.symm) (μ.map Aₘ)).comp
+      Adual.toHomeomorph.toCocompactMap.cocompact_tendsto' with
+    w
   suffices ∫ v, 𝐞 (-w v) • f v ∂μ = ∫ (x : V), 𝐞 (-w (A.symm (Aₘ x))) • f (A.symm (Aₘ x)) ∂μ by
     simpa [Function.comp_apply, integral_map_equiv, Adual]
   simp [Aₘ]
diff --git a/Mathlib/Analysis/FunctionalSpaces/SobolevInequality.lean b/Mathlib/Analysis/FunctionalSpaces/SobolevInequality.lean
index 7c6669e0607510..1793353fe9f39b 100644
--- a/Mathlib/Analysis/FunctionalSpaces/SobolevInequality.lean
+++ b/Mathlib/Analysis/FunctionalSpaces/SobolevInequality.lean
@@ -225,7 +225,7 @@ theorem T_lmarginal_antitone [Fintype ι] [∀ i, SigmaFinite (μ i)]
   rw [Finset.antitone_iff_forall_insert_le]
   intro s i hi
   -- apply the lemma designed to encapsulate the inductive step
-  convert T_insert_le_T_lmarginal_singleton μ hp₀ s ?_ i hi (hf.lmarginal μ) using 2
+  convert! T_insert_le_T_lmarginal_singleton μ hp₀ s ?_ i hi (hf.lmarginal μ) using 2
   · rw [← lmarginal_union μ f hf]
     · rw [← insert_compl_insert hi]
       rfl
@@ -285,7 +285,7 @@ theorem lintegral_prod_lintegral_pow_le [Fintype ι] [∀ i, SigmaFinite (μ i)]
   have h3 : (#ι - 1 : ℝ) * ((1 : ℝ) / (#ι - 1 : ℝ)) ≤ 1 := by field_simp; rfl
   have h4 : p = 1 + 1 / (↑#ι - 1) := by simp [field]; rw [mul_comm, hp.sub_one_mul_conj]
   rw [h4]
-  convert lintegral_mul_prod_lintegral_pow_le μ h2 h3 hf using 2
+  convert! lintegral_mul_prod_lintegral_pow_le μ h2 h3 hf using 2
   field_simp
   simp
 
@@ -338,7 +338,7 @@ theorem lintegral_pow_le_pow_lintegral_fderiv_aux [Fintype ι]
   calc ‖u x‖ₑ
     _ ≤ ∫⁻ xᵢ in Iic (x i), ‖deriv (u ∘ update x i) xᵢ‖ₑ := by
         apply le_trans (by simp) (HasCompactSupport.enorm_le_lintegral_Ici_deriv _ _ _)
-        · exact hu.comp (by convert contDiff_update 1 x i)
+        · exact hu.comp (by convert! contDiff_update 1 x i)
         · exact h2u.comp_isClosedEmbedding (isClosedEmbedding_update x i)
     _ ≤ ∫⁻ xᵢ, ‖fderiv ℝ u (update x i xᵢ)‖ₑ := ?_
   gcongr with y
@@ -493,7 +493,7 @@ theorem eLpNorm_le_eLpNorm_fderiv_of_eq_inner {u : E → F'}
   have hnp : (0 : ℝ) < n - p := by simp_rw [sub_pos]; exact h2p
   rcases hp.eq_or_lt with rfl | hp
   -- the case `p = 1`
-  · convert eLpNorm_le_eLpNorm_fderiv_one μ hu h2u hn using 2
+  · convert! eLpNorm_le_eLpNorm_fderiv_one μ hu h2u hn using 2
     · suffices (p' : ℝ) = n' by simpa using this
       rw [← inv_inj, hp']
       simp [field, n', NNReal.conjExponent, *]
@@ -556,8 +556,9 @@ theorem eLpNorm_le_eLpNorm_fderiv_of_eq_inner {u : E → F'}
     _ ≤ C * γ * ((∫⁻ x, ‖u x‖ₑ ^ (p' : ℝ) ∂μ) ^ (1 / q) *
         (∫⁻ x, ‖fderiv ℝ u x‖ₑ ^ (p : ℝ) ∂μ) ^ (1 / (p : ℝ))) := by
         gcongr
-        convert ENNReal.lintegral_mul_le_Lp_mul_Lq μ
-          (.symm <| .conjExponent <| show 1 < (p : ℝ) from hp) ?_ ?_ using 5
+        convert!
+          ENNReal.lintegral_mul_le_Lp_mul_Lq μ (.symm <| .conjExponent <| show 1 < (p : ℝ) from hp)
+            ?_ ?_ using 5
         · simp [γ, n, q, ← ENNReal.rpow_mul, ← h3γ]
         · borelize F'
           fun_prop
@@ -681,7 +682,7 @@ theorem eLpNorm_le_eLpNorm_fderiv_of_le [FiniteDimensional ℝ F]
   calc eLpNorm u q μ
       = eLpNorm u q (μ.restrict s) := by rw [eLpNorm_restrict_eq_of_support_subset h2u]
     _ ≤ eLpNorm u p' (μ.restrict s) * t := by
-        convert eLpNorm_le_eLpNorm_mul_rpow_measure_univ this hu.continuous.aestronglyMeasurable
+        convert! eLpNorm_le_eLpNorm_mul_rpow_measure_univ this hu.continuous.aestronglyMeasurable
         rw [ENNReal.coe_rpow_of_nonneg]
         · simp [ENNReal.coe_toNNReal hs.measure_lt_top.ne]
         · rw [one_div, one_div]
diff --git a/Mathlib/Analysis/InnerProductSpace/Basic.lean b/Mathlib/Analysis/InnerProductSpace/Basic.lean
index 0df3c135b15b5d..1e70260831746d 100644
--- a/Mathlib/Analysis/InnerProductSpace/Basic.lean
+++ b/Mathlib/Analysis/InnerProductSpace/Basic.lean
@@ -356,7 +356,7 @@ theorem linearIndependent_of_ne_zero_of_inner_eq_zero {ι : Type*} {v : ι → E
   have h' : g i * ⟪v i, v i⟫ = ⟪v i, ∑ j ∈ s, g j • v j⟫ := by
     rw [inner_sum]
     symm
-    convert Finset.sum_eq_single (M := 𝕜) i ?_ ?_
+    convert! Finset.sum_eq_single (M := 𝕜) i ?_ ?_
     · rw [inner_smul_right]
     · intro j _hj hji
       rw [inner_smul_right, ho hji.symm, mul_zero]
@@ -817,7 +817,7 @@ theorem real_inner_div_norm_mul_norm_eq_neg_one_iff (x y : F) :
 the equality case for Cauchy-Schwarz. -/
 theorem inner_eq_one_iff_of_norm_eq_one {x y : E} (hx : ‖x‖ = 1) (hy : ‖y‖ = 1) :
     ⟪x, y⟫ = 1 ↔ x = y := by
-  convert inner_eq_norm_mul_iff (𝕜 := 𝕜) (E := E) using 2 <;> simp [hx, hy]
+  convert! inner_eq_norm_mul_iff (𝕜 := 𝕜) (E := E) using 2 <;> simp [hx, hy]
 
 /-- If the inner product of two unit vectors is `-1`, then the two vectors are negations of each
 other. -/
@@ -852,7 +852,7 @@ theorem inner_lt_norm_mul_iff_real {x y : F} : ⟪x, y⟫_ℝ < ‖x‖ * ‖y
 /-- If the inner product of two unit vectors is strictly less than `1`, then the two vectors are
 distinct. One form of the equality case for Cauchy-Schwarz. -/
 theorem inner_lt_one_iff_real_of_norm_eq_one {x y : F} (hx : ‖x‖ = 1) (hy : ‖y‖ = 1) :
-    ⟪x, y⟫_ℝ < 1 ↔ x ≠ y := by convert inner_lt_norm_mul_iff_real (F := F) <;> simp [hx, hy]
+    ⟪x, y⟫_ℝ < 1 ↔ x ≠ y := by convert! inner_lt_norm_mul_iff_real (F := F) <;> simp [hx, hy]
 
 /-- The sphere of radius `r = ‖y‖` is tangent to the plane `⟪x, y⟫ = ‖y‖ ^ 2` at `x = y`. -/
 theorem eq_of_norm_le_re_inner_eq_norm_sq {x y : E} (hle : ‖x‖ ≤ ‖y‖) (h : re ⟪x, y⟫ = ‖y‖ ^ 2) :
diff --git a/Mathlib/Analysis/InnerProductSpace/Calculus.lean b/Mathlib/Analysis/InnerProductSpace/Calculus.lean
index efec86444df931..85393a4cd9d432 100644
--- a/Mathlib/Analysis/InnerProductSpace/Calculus.lean
+++ b/Mathlib/Analysis/InnerProductSpace/Calculus.lean
@@ -138,7 +138,7 @@ section
 include 𝕜
 
 theorem contDiff_norm_sq : ContDiff ℝ n fun x : E => ‖x‖ ^ 2 := by
-  convert (reCLM : 𝕜 →L[ℝ] ℝ).contDiff.comp ((contDiff_id (E := E)).inner 𝕜 (contDiff_id (E := E)))
+  convert! (reCLM : 𝕜 →L[ℝ] ℝ).contDiff.comp ((contDiff_id (E := E)).inner 𝕜 (contDiff_id (E := E)))
   exact (inner_self_eq_norm_sq _).symm
 
 theorem ContDiff.norm_sq (hf : ContDiff ℝ n f) : ContDiff ℝ n fun x => ‖f x‖ ^ 2 :=
@@ -197,7 +197,7 @@ open scoped RealInnerProductSpace
 theorem hasStrictFDerivAt_norm_sq (x : F) :
     HasStrictFDerivAt (fun x => ‖x‖ ^ 2) (2 • (innerSL ℝ x)) x := by
   simp only [sq, ← @inner_self_eq_norm_mul_norm ℝ]
-  convert (hasStrictFDerivAt_id x).inner ℝ (hasStrictFDerivAt_id x)
+  convert! (hasStrictFDerivAt_id x).inner ℝ (hasStrictFDerivAt_id x)
   ext y
   simp [two_smul, real_inner_comm]
 
diff --git a/Mathlib/Analysis/InnerProductSpace/Defs.lean b/Mathlib/Analysis/InnerProductSpace/Defs.lean
index 7048d51799729e..cc34ea1e8dda94 100644
--- a/Mathlib/Analysis/InnerProductSpace/Defs.lean
+++ b/Mathlib/Analysis/InnerProductSpace/Defs.lean
@@ -359,7 +359,7 @@ theorem inner_mul_inner_self_le (x y : F) : ‖⟪x, y⟫‖ * ‖⟪y, x⟫‖
     obtain ⟨hx, hy⟩ : (0 ≤ normSqF x ∧ 0 ≤ normSqF y) := ⟨inner_self_nonneg, inner_self_nonneg⟩
     positivity
   · have hzero' : ‖⟪x, y⟫‖ ≠ 0 := norm_ne_zero_iff.2 hzero
-    convert cauchy_schwarz_aux' (𝕜 := 𝕜) (⟪x, y⟫ • x) y (t / ‖⟪x, y⟫‖) using 3
+    convert! cauchy_schwarz_aux' (𝕜 := 𝕜) (⟪x, y⟫ • x) y (t / ‖⟪x, y⟫‖) using 3
     · field_simp
       rw [normSq, normSq, inner_smul_right, inner_smul_left, ← mul_assoc _ _ ⟪x, x⟫,
         mul_conj]
diff --git a/Mathlib/Analysis/InnerProductSpace/Dual.lean b/Mathlib/Analysis/InnerProductSpace/Dual.lean
index 193f1befcc71cb..1b5d9ae1b582e4 100644
--- a/Mathlib/Analysis/InnerProductSpace/Dual.lean
+++ b/Mathlib/Analysis/InnerProductSpace/Dual.lean
@@ -221,7 +221,7 @@ instance [NormedAddCommGroup E] [CompleteSpace E] [InnerProductSpace ℝ E] :
   continuous_uncurry := continuous_inner
   bijective_left := (toDual ℝ E).bijective
   bijective_right := by
-    convert (toDual ℝ E).bijective
+    convert! (toDual ℝ E).bijective
     ext y
     simp
 
diff --git a/Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean b/Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean
index 9c7c828dbc2281..321c82d092f333 100644
--- a/Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean
+++ b/Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean
@@ -117,7 +117,7 @@ theorem gramSchmidt_inv_triangular (v : ι → E) {i j : ι} (hij : i < j) :
   rw [gramSchmidt_def'' 𝕜 v]
   simp only [inner_add_right, inner_sum, inner_smul_right]
   set b : ι → E := gramSchmidt 𝕜 v
-  convert zero_add (0 : 𝕜)
+  convert! zero_add (0 : 𝕜)
   · exact gramSchmidt_orthogonal 𝕜 v hij.ne'
   apply Finset.sum_eq_zero
   rintro k hki'
@@ -371,7 +371,7 @@ theorem gramSchmidtOrthonormalBasis_inv_blockTriangular :
 theorem gramSchmidtOrthonormalBasis_det [DecidableEq ι] :
     (gramSchmidtOrthonormalBasis h f).toBasis.det f =
       ∏ i, ⟪gramSchmidtOrthonormalBasis h f i, f i⟫ := by
-  convert Matrix.det_of_upperTriangular (gramSchmidtOrthonormalBasis_inv_blockTriangular h f)
+  convert! Matrix.det_of_upperTriangular (gramSchmidtOrthonormalBasis_inv_blockTriangular h f)
   exact ((gramSchmidtOrthonormalBasis h f).repr_apply_apply (f _) _).symm
 
 end OrthonormalBasis
diff --git a/Mathlib/Analysis/InnerProductSpace/LinearPMap.lean b/Mathlib/Analysis/InnerProductSpace/LinearPMap.lean
index b0e8ab31277576..9cf3e7608ebd4c 100644
--- a/Mathlib/Analysis/InnerProductSpace/LinearPMap.lean
+++ b/Mathlib/Analysis/InnerProductSpace/LinearPMap.lean
@@ -166,7 +166,7 @@ theorem mem_adjoint_domain_of_exists (y : F) (h : ∃ w : E, ∀ x : T.domain, 
   obtain ⟨w, hw⟩ := h
   rw [T.mem_adjoint_domain_iff]
   have : Continuous ((innerSL 𝕜 w).comp T.domain.subtypeL) := by fun_prop
-  convert this using 1
+  convert! this using 1
   exact funext fun x => (hw x).symm
 
 theorem adjoint_apply_of_not_dense (hT : ¬Dense (T.domain : Set E)) (y : T†.domain) : T† y = 0 := by
diff --git a/Mathlib/Analysis/InnerProductSpace/NormPow.lean b/Mathlib/Analysis/InnerProductSpace/NormPow.lean
index 7151281c244162..31e04699fc7e43 100644
--- a/Mathlib/Analysis/InnerProductSpace/NormPow.lean
+++ b/Mathlib/Analysis/InnerProductSpace/NormPow.lean
@@ -43,12 +43,12 @@ theorem hasFDerivAt_norm_rpow (x : E) {p : ℝ} (hp : 1 < p) :
           ring_nf
       _ =o[𝓝 0] (fun x : E ↦ ‖x‖ * 1) := by
         refine (isBigO_refl _ _).mul_isLittleO <| (isLittleO_const_iff <| by simp).mpr ?_
-        convert continuousAt_id.norm.rpow_const (.inr h2p.le) |>.tendsto
+        convert! continuousAt_id.norm.rpow_const (.inr h2p.le) |>.tendsto
         simp [h2p.ne']
       _ =O[𝓝 0] (fun (x : E) ↦ x - 0) := by
         simp_rw [mul_one, isBigO_norm_left (f' := fun x ↦ x), sub_zero, isBigO_refl]
   · apply HasStrictFDerivAt.hasFDerivAt
-    convert (hasStrictFDerivAt_norm_sq x).rpow_const (p := p / 2) (by simp [hx]) using 0
+    convert! (hasStrictFDerivAt_norm_sq x).rpow_const (p := p / 2) (by simp [hx]) using 0
     simp_rw [← Real.rpow_natCast_mul (norm_nonneg _), ← Nat.cast_smul_eq_nsmul ℝ, smul_smul]
     ring_nf
 
@@ -58,7 +58,7 @@ theorem differentiable_norm_rpow {p : ℝ} (hp : 1 < p) :
 
 theorem hasDerivAt_norm_rpow (x : ℝ) {p : ℝ} (hp : 1 < p) :
     HasDerivAt (fun x : ℝ ↦ ‖x‖ ^ p) (p * ‖x‖ ^ (p - 2) * x) x := by
-  convert hasFDerivAt_norm_rpow x hp |>.hasDerivAt using 1; simp
+  convert! hasFDerivAt_norm_rpow x hp |>.hasDerivAt using 1; simp
 
 theorem hasDerivAt_abs_rpow (x : ℝ) {p : ℝ} (hp : 1 < p) :
     HasDerivAt (fun x : ℝ ↦ |x| ^ p) (p * |x| ^ (p - 2) * x) x := by
diff --git a/Mathlib/Analysis/InnerProductSpace/OfNorm.lean b/Mathlib/Analysis/InnerProductSpace/OfNorm.lean
index 1ac2adecaa0ea3..49ffd3cc9cd697 100644
--- a/Mathlib/Analysis/InnerProductSpace/OfNorm.lean
+++ b/Mathlib/Analysis/InnerProductSpace/OfNorm.lean
@@ -118,7 +118,7 @@ theorem inner_.norm_sq (x : E) : ‖x‖ ^ 2 = re (inner_ 𝕜 x x) := by
   simp only [inner_, normSq_apply, ofNat_re, ofNat_im, map_sub, map_add,
     ofReal_re, ofReal_im, mul_re, inv_re, mul_im, I_re, inv_im]
   have h₁ : ‖x - x‖ = 0 := by simp
-  have h₂ : ‖x + x‖ = 2 • ‖x‖ := by convert norm_nsmul 𝕜 2 x using 2; module
+  have h₂ : ‖x + x‖ = 2 • ‖x‖ := by convert! norm_nsmul 𝕜 2 x using 2; module
   rw [h₁, h₂]
   ring
 
@@ -132,10 +132,10 @@ theorem inner_.conj_symm (x y : E) : conj (inner_ 𝕜 y x) = inner_ 𝕜 x y :=
   have hI' := I_mul_I_of_nonzero hI
   have I_smul (v : E) : ‖(I : 𝕜) • v‖ = ‖v‖ := by rw [norm_smul, norm_I_of_ne_zero hI, one_mul]
   have h₁ : ‖(I : 𝕜) • y - x‖ = ‖(I : 𝕜) • x + y‖ := by
-    convert I_smul ((I : 𝕜) • x + y) using 2
+    convert! I_smul ((I : 𝕜) • x + y) using 2
     linear_combination (norm := module) -hI' • x
   have h₂ : ‖(I : 𝕜) • y + x‖ = ‖(I : 𝕜) • x - y‖ := by
-    convert (I_smul ((I : 𝕜) • y + x)).symm using 2
+    convert! (I_smul ((I : 𝕜) • y + x)).symm using 2
     linear_combination (norm := module) -hI' • y
   rw [h₁, h₂]
   ring
diff --git a/Mathlib/Analysis/InnerProductSpace/Orientation.lean b/Mathlib/Analysis/InnerProductSpace/Orientation.lean
index 48a770f98db49f..8837c31940f679 100644
--- a/Mathlib/Analysis/InnerProductSpace/Orientation.lean
+++ b/Mathlib/Analysis/InnerProductSpace/Orientation.lean
@@ -215,7 +215,7 @@ theorem volumeForm_robust_neg (b : OrthonormalBasis (Fin n) ℝ E) (hb : b.toBas
   let e : OrthonormalBasis (Fin n.succ) ℝ E := o.finOrthonormalBasis n.succ_pos Fact.out
   simp_rw [volumeForm]
   apply e.det_eq_neg_det_of_opposite_orientation b
-  convert hb.symm
+  convert! hb.symm
   exact o.finOrthonormalBasis_orientation _ _
 
 @[simp]
@@ -253,7 +253,7 @@ theorem abs_volumeForm_apply_le (v : Fin n → E) : |o.volumeForm v| ≤ ∏ i :
   · intro i _
     positivity
   intro i _
-  convert abs_real_inner_le_norm (b i) (v i)
+  convert! abs_real_inner_le_norm (b i) (v i)
   simp [b.orthonormal.1 i]
 
 theorem volumeForm_apply_le (v : Fin n → E) : o.volumeForm v ≤ ∏ i : Fin n, ‖v i‖ :=
@@ -311,7 +311,7 @@ theorem volumeForm_comp_linearIsometryEquiv (φ : E ≃ₗᵢ[ℝ] E)
   rcases n with - | n
   · refine o.eq_or_eq_neg_of_isEmpty.elim ?_ ?_ <;> rintro rfl <;> simp
   have : FiniteDimensional ℝ E := .of_fact_finrank_eq_succ n
-  convert o.volumeForm_map φ (φ ∘ x)
+  convert! o.volumeForm_map φ (φ ∘ x)
   · symm
     rwa [← o.map_eq_iff_det_pos φ.toLinearEquiv] at hφ
     rw [_i.out, Fintype.card_fin]
diff --git a/Mathlib/Analysis/InnerProductSpace/Orthogonal.lean b/Mathlib/Analysis/InnerProductSpace/Orthogonal.lean
index eb3dbd9461af9f..ff11ca04944a18 100644
--- a/Mathlib/Analysis/InnerProductSpace/Orthogonal.lean
+++ b/Mathlib/Analysis/InnerProductSpace/Orthogonal.lean
@@ -113,7 +113,7 @@ theorem orthogonal_eq_inter : Kᗮ = ⨅ v : K, (innerSL 𝕜 (v : E)).ker := by
 /-- The orthogonal complement of any submodule `K` is closed. -/
 theorem isClosed_orthogonal : IsClosed (Kᗮ : Set E) := by
   rw [orthogonal_eq_inter K]
-  convert isClosed_iInter <| fun v : K => ContinuousLinearMap.isClosed_ker (innerSL 𝕜 (v : E))
+  convert! isClosed_iInter <| fun v : K => ContinuousLinearMap.isClosed_ker (innerSL 𝕜 (v : E))
   simp
 
 /-- In a complete space, the orthogonal complement of any submodule `K` is complete. -/
@@ -372,7 +372,7 @@ theorem IsOrtho.map_iff (f : E ≃ₗᵢ[𝕜] F) {U V : Submodule 𝕜 E} :
 @[simp]
 theorem IsOrtho.comap_iff (f : E ≃ₗᵢ[𝕜] F) {U V : Submodule 𝕜 F} :
     U.comap (f : E →ₗ[𝕜] F) ⟂ V.comap (f : E →ₗ[𝕜] F) ↔ U ⟂ V := by
-  convert IsOrtho.map_iff f.symm using 2 <;>
+  convert! IsOrtho.map_iff f.symm using 2 <;>
     exact Submodule.comap_equiv_eq_map_symm (f : E ≃ₗ[𝕜] F) _
 
 end Submodule
diff --git a/Mathlib/Analysis/InnerProductSpace/Orthonormal.lean b/Mathlib/Analysis/InnerProductSpace/Orthonormal.lean
index aa2f444b27f6d6..d70a9099f6a927 100644
--- a/Mathlib/Analysis/InnerProductSpace/Orthonormal.lean
+++ b/Mathlib/Analysis/InnerProductSpace/Orthonormal.lean
@@ -193,7 +193,7 @@ theorem Orthonormal.comp {ι' : Type*} {v : ι → E} (hv : Orthonormal 𝕜 v)
   classical
   rw [orthonormal_iff_ite] at hv ⊢
   intro i j
-  convert hv (f i) (f j) using 1
+  convert! hv (f i) (f j) using 1
   simp [hf.eq_iff]
 
 /-- An injective family `v : ι → E` is orthonormal if and only if `Subtype.val : (range v) → E` is
diff --git a/Mathlib/Analysis/InnerProductSpace/PiL2.lean b/Mathlib/Analysis/InnerProductSpace/PiL2.lean
index 78f09a00c16529..39460e363ca116 100644
--- a/Mathlib/Analysis/InnerProductSpace/PiL2.lean
+++ b/Mathlib/Analysis/InnerProductSpace/PiL2.lean
@@ -198,7 +198,7 @@ variable [Fintype ι]
 @[simp]
 theorem finrank_euclideanSpace :
     Module.finrank 𝕜 (EuclideanSpace 𝕜 ι) = Fintype.card ι := by
-  convert (WithLp.linearEquiv 2 𝕜 (ι → 𝕜)).finrank_eq
+  convert! (WithLp.linearEquiv 2 𝕜 (ι → 𝕜)).finrank_eq
   simp
 
 theorem finrank_euclideanSpace_fin {n : ℕ} :
@@ -248,7 +248,7 @@ def DirectSum.IsInternal.isometryL2OfOrthogonalFamily [DecidableEq ι] {V : ι 
   suffices ∀ (v w : PiLp 2 fun i => V i), ⟪v, w⟫ = ⟪e₂ (e₁.symm v), e₂ (e₁.symm w)⟫ by
     intro v₀ w₀
     simp only [LinearEquiv.trans_apply]
-    convert this (toLp 2 (e₁ (e₂.symm v₀))) (toLp 2 (e₁ (e₂.symm w₀))) <;> simp
+    convert! this (toLp 2 (e₁ (e₂.symm v₀))) (toLp 2 (e₁ (e₂.symm w₀))) <;> simp
   intro v w
   trans ⟪∑ i, (V i).subtypeₗᵢ (v i), ∑ i, (V i).subtypeₗᵢ (w i)⟫
   · simp only [sum_inner, hV'.inner_right_fintype, PiLp.inner_apply]
@@ -505,7 +505,7 @@ protected theorem sum_inner_mul_inner (b : OrthonormalBasis ι 𝕜 E) (x y : E)
     ∑ i, ⟪x, b i⟫ * ⟪b i, y⟫ = ⟪x, y⟫ := by
   have := congr_arg (innerSL 𝕜 x) (b.sum_repr y)
   rw [map_sum] at this
-  convert this
+  convert! this
   rw [map_smul, b.repr_apply_apply, mul_comm]
   simp
 
@@ -519,7 +519,7 @@ lemma sum_sq_norm_inner_right (b : OrthonormalBasis ι 𝕜 E) (x : E) :
 
 lemma sum_sq_norm_inner_left (b : OrthonormalBasis ι 𝕜 E) (x : E) :
     ∑ i, ‖⟪x, b i⟫‖ ^ 2 = ‖x‖ ^ 2 := by
-  convert sum_sq_norm_inner_right b x using 2 with i -
+  convert! sum_sq_norm_inner_right b x using 2 with i -
   rw [← inner_conj_symm, RCLike.norm_conj]
 
 open scoped RealInnerProductSpace in
@@ -599,7 +599,7 @@ def _root_.Module.Basis.toOrthonormalBasis (v : Basis ι 𝕜 E) (hv : Orthonorm
         let q : EuclideanSpace 𝕜 ι := toLp 2 (v.equivFun y)
         have key : ⟪p, q⟫ = ⟪∑ i, p i • v i, ∑ i, q i • v i⟫ := by
           simp [inner_sum, inner_smul_right, hv.inner_left_fintype, PiLp.inner_apply]
-        convert key
+        convert! key
         · rw [← v.equivFun.symm_apply_apply x, v.equivFun_symm_apply]
         · rw [← v.equivFun.symm_apply_apply y, v.equivFun_symm_apply])
 
@@ -718,7 +718,7 @@ protected def span [DecidableEq E] {v' : ι' → E} (h : Orthonormal 𝕜 v') (s
   let e₀ : OrthonormalBasis s 𝕜 _ :=
     OrthonormalBasis.mk
       (by
-        convert orthonormal_span (h.comp ((↑) : s → ι') Subtype.val_injective)
+        convert! orthonormal_span (h.comp ((↑) : s → ι') Subtype.val_injective)
         simp [e₀', Basis.span_apply])
       e₀'.span_eq.ge
   let φ : span 𝕜 (s.image v' : Set E) ≃ₗᵢ[𝕜] span 𝕜 (range (v' ∘ ((↑) : s → ι'))) :=
@@ -931,7 +931,7 @@ theorem OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self [Finty
     (a : OrthonormalBasis ι' 𝕜 E) (b : OrthonormalBasis ι 𝕜 E) :
     (a.toBasis.toMatrix b)ᴴ * a.toBasis.toMatrix b = 1 := by
   ext i j
-  convert a.repr.inner_map_map (b i) (b j)
+  convert! a.repr.inner_map_map (b i) (b j)
   · simp only [Matrix.mul_apply, Matrix.conjTranspose_apply, star_def, PiLp.inner_apply,
       inner_apply']
     congr
diff --git a/Mathlib/Analysis/InnerProductSpace/Positive.lean b/Mathlib/Analysis/InnerProductSpace/Positive.lean
index 38b2fcbbe3fda1..f09b2d61f4f04e 100644
--- a/Mathlib/Analysis/InnerProductSpace/Positive.lean
+++ b/Mathlib/Analysis/InnerProductSpace/Positive.lean
@@ -214,7 +214,7 @@ theorem isPositive_linearIsometryEquiv_conj_iff {T : E →ₗ[𝕜] E} (f : E 
     {A : E →ₗ[𝕜] E} (b : OrthonormalBasis ι 𝕜 E) :
     (A.toMatrix b.toBasis b.toBasis).PosSemidef ↔ A.IsPositive := by
   rw [← Matrix.isPositive_toEuclideanLin_iff]
-  convert isPositive_linearIsometryEquiv_conj_iff b.repr
+  convert! isPositive_linearIsometryEquiv_conj_iff b.repr
   ext
   simp [LinearMap.toMatrix]
 
@@ -365,7 +365,7 @@ theorem isPositive_self_comp_adjoint [CompleteSpace E] [CompleteSpace F] (S : E
 @[aesop safe apply]
 theorem IsPositive.adjoint_conj [CompleteSpace E] [CompleteSpace F] {T : E →L[𝕜] E}
     (hT : T.IsPositive) (S : F →L[𝕜] E) : (S† ∘L T ∘L S).IsPositive := by
-  convert hT.conj_adjoint (S†)
+  convert! hT.conj_adjoint (S†)
   rw [adjoint_adjoint]
 
 theorem isPositive_adjoint_comp_self [CompleteSpace E] [CompleteSpace F] (S : E →L[𝕜] F) :
@@ -390,7 +390,7 @@ theorem _root_.LinearMap.isPositive_self_comp_adjoint (S : E →ₗ[𝕜] F) :
 @[aesop safe apply]
 theorem _root_.LinearMap.IsPositive.adjoint_conj {T : E →ₗ[𝕜] E}
     (hT : T.IsPositive) (S : F →ₗ[𝕜] E) : (S.adjoint ∘ₗ T ∘ₗ S).IsPositive := by
-  convert hT.conj_adjoint S.adjoint
+  convert! hT.conj_adjoint S.adjoint
   rw [LinearMap.adjoint_adjoint]
 
 theorem _root_.LinearMap.isPositive_adjoint_comp_self (S : E →ₗ[𝕜] F) :
diff --git a/Mathlib/Analysis/InnerProductSpace/Projection/Basic.lean b/Mathlib/Analysis/InnerProductSpace/Projection/Basic.lean
index 3cae48ca82f6c4..676ab7984e189e 100644
--- a/Mathlib/Analysis/InnerProductSpace/Projection/Basic.lean
+++ b/Mathlib/Analysis/InnerProductSpace/Projection/Basic.lean
@@ -137,7 +137,7 @@ theorem orthogonalProjectionFn_norm_sq (v : E) :
   set p := K.orthogonalProjectionFn v
   have h' : ⟪v - p, p⟫ = 0 :=
     orthogonalProjectionFn_inner_eq_zero _ _ (orthogonalProjectionFn_mem v)
-  convert norm_add_sq_eq_norm_sq_add_norm_sq_of_inner_eq_zero (v - p) p h' using 2 <;> simp
+  convert! norm_add_sq_eq_norm_sq_add_norm_sq_of_inner_eq_zero (v - p) p h' using 2 <;> simp
 
 /-- The orthogonal projection onto a complete subspace. -/
 def orthogonalProjection : E →L[𝕜] K :=
@@ -411,7 +411,7 @@ theorem starProjection_singleton {v : E} (w : E) :
     (((‖v‖ ^ 2 : ℝ) : 𝕜)⁻¹ * ((‖v‖ ^ 2 : ℝ) : 𝕜)) • (𝕜 ∙ v).starProjection w =
       (((‖v‖ ^ 2 : ℝ) : 𝕜)⁻¹ * ⟪v, w⟫) • v := by
     simp [mul_smul, smul_starProjection_singleton 𝕜 w, -map_pow]
-  convert key using 1 <;> match_scalars <;> field_simp [hv']
+  convert! key using 1 <;> match_scalars <;> field_simp [hv']
 
 /-- Formula for orthogonal projection onto a single unit vector. -/
 theorem starProjection_unit_singleton {v : E} (hv : ‖v‖ = 1) (w : E) :
@@ -450,7 +450,7 @@ theorem IsOrtho.starProjection_comp_starProjection {U V : Submodule 𝕜 E}
 theorem orthogonalProjection_comp_subtypeL_eq_zero_iff {U V : Submodule 𝕜 E}
     [U.HasOrthogonalProjection] : U.orthogonalProjection ∘L V.subtypeL = 0 ↔ U ⟂ V :=
   ⟨fun h u hu v hv => by
-    convert starProjection_inner_eq_zero v u hu using 2
+    convert! starProjection_inner_eq_zero v u hu using 2
     have : U.orthogonalProjection v = 0 := DFunLike.congr_fun h (⟨_, hv⟩ : V)
     rw [starProjection_apply, this, Submodule.coe_zero, sub_zero],
     Submodule.IsOrtho.orthogonalProjection_comp_subtypeL⟩
diff --git a/Mathlib/Analysis/InnerProductSpace/Projection/FiniteDimensional.lean b/Mathlib/Analysis/InnerProductSpace/Projection/FiniteDimensional.lean
index 4859a3e25751cb..8808764b35d86b 100644
--- a/Mathlib/Analysis/InnerProductSpace/Projection/FiniteDimensional.lean
+++ b/Mathlib/Analysis/InnerProductSpace/Projection/FiniteDimensional.lean
@@ -111,7 +111,7 @@ theorem finrank_add_inf_finrank_orthogonal' {K₁ K₂ : Submodule 𝕜 E}
 that of `E`. -/
 theorem finrank_add_finrank_orthogonal [FiniteDimensional 𝕜 E] (K : Submodule 𝕜 E) :
     finrank 𝕜 K + finrank 𝕜 Kᗮ = finrank 𝕜 E := by
-  convert Submodule.finrank_add_inf_finrank_orthogonal (le_top : K ≤ ⊤) using 1
+  convert! Submodule.finrank_add_inf_finrank_orthogonal (le_top : K ≤ ⊤) using 1
   · rw [inf_top_eq]
   · simp
 
@@ -402,7 +402,7 @@ theorem maximal_orthonormal_iff_basis_of_finiteDimensional (hv : Orthonormal 
   have hv_coe : range ((↑) : v → E) = v := by simp
   constructor
   · refine fun h => ⟨Basis.mk hv.linearIndependent _, Basis.coe_mk _ ?_⟩
-    convert h.ge
+    convert! h.ge
   · rintro ⟨h, coe_h⟩
     rw [← h.span_eq, coe_h, hv_coe]
 
diff --git a/Mathlib/Analysis/InnerProductSpace/Projection/Minimal.lean b/Mathlib/Analysis/InnerProductSpace/Projection/Minimal.lean
index 6ae2a163f50db1..6e1e5fbdfe7621 100644
--- a/Mathlib/Analysis/InnerProductSpace/Projection/Minimal.lean
+++ b/Mathlib/Analysis/InnerProductSpace/Projection/Minimal.lean
@@ -51,7 +51,7 @@ theorem exists_norm_eq_iInf_of_complete_convex {K : Set F} (ne : K.Nonempty) (h
   have norm_tendsto : Tendsto (fun n => ‖u - w n‖) atTop (𝓝 δ) := by
     have h : Tendsto (fun _ : ℕ => δ) atTop (𝓝 δ) := tendsto_const_nhds
     have h' : Tendsto (fun n : ℕ => δ + 1 / (n + 1)) atTop (𝓝 δ) := by
-      convert h.add tendsto_one_div_add_atTop_nhds_zero_nat
+      convert! h.add tendsto_one_div_add_atTop_nhds_zero_nat
       simp only [add_zero]
     exact tendsto_of_tendsto_of_tendsto_of_le_of_le h h' (fun x => δ_le _) fun x => le_of_lt (hw _)
   -- Step 2: Prove that the sequence `w : ℕ → K` is a Cauchy sequence
@@ -130,7 +130,7 @@ theorem exists_norm_eq_iInf_of_complete_convex {K : Set F} (ne : K.Nonempty) (h
   use v, hv
   have h_cont : Continuous fun v => ‖u - v‖ := by fun_prop
   have : Tendsto (fun n => ‖u - w n‖) atTop (𝓝 ‖u - v‖) := by
-    convert Tendsto.comp h_cont.continuousAt w_tendsto
+    convert! Tendsto.comp h_cont.continuousAt w_tendsto
   exact tendsto_nhds_unique this norm_tendsto
 
 /-- Characterization of minimizers for the projection on a convex set in a real inner product
diff --git a/Mathlib/Analysis/InnerProductSpace/Projection/Reflection.lean b/Mathlib/Analysis/InnerProductSpace/Projection/Reflection.lean
index 60a5da6f20eaaf..4d8a0b48016da6 100644
--- a/Mathlib/Analysis/InnerProductSpace/Projection/Reflection.lean
+++ b/Mathlib/Analysis/InnerProductSpace/Projection/Reflection.lean
@@ -51,7 +51,7 @@ def reflection : E ≃ₗᵢ[𝕜] E :=
       let w : K := K.orthogonalProjection x
       let v := x - w
       have : ⟪v, w⟫ = 0 := starProjection_inner_eq_zero x w w.2
-      convert norm_sub_eq_norm_add this using 2
+      convert! norm_sub_eq_norm_add this using 2
       · dsimp [reflectionLinearEquiv, v, w]
         abel
       · simp only [v, add_sub_cancel] }
@@ -160,7 +160,7 @@ theorem reflection_sub {v w : F} (h : ‖v‖ = ‖w‖) : reflection (ℝ ∙ (
     rw [Submodule.mem_orthogonal_singleton_iff_inner_left]
     rw [real_inner_add_sub_eq_zero_iff]
     exact h
-  convert congr_arg₂ (· + ·) h₂ h₁ using 1
+  convert! congr_arg₂ (· + ·) h₂ h₁ using 1
   · simp
   · abel
 
diff --git a/Mathlib/Analysis/InnerProductSpace/Projection/Submodule.lean b/Mathlib/Analysis/InnerProductSpace/Projection/Submodule.lean
index 22dd5d909dbab5..b28b4b28e06839 100644
--- a/Mathlib/Analysis/InnerProductSpace/Projection/Submodule.lean
+++ b/Mathlib/Analysis/InnerProductSpace/Projection/Submodule.lean
@@ -47,7 +47,7 @@ theorem sup_orthogonal_inf_of_hasOrthogonalProjection {K₁ K₂ : Submodule 
 variable {K} in
 /-- If `K` admits an orthogonal projection, then `K` and `Kᗮ` span the whole space. -/
 theorem sup_orthogonal_of_hasOrthogonalProjection [K.HasOrthogonalProjection] : K ⊔ Kᗮ = ⊤ := by
-  convert Submodule.sup_orthogonal_inf_of_hasOrthogonalProjection (le_top : K ≤ ⊤) using 2
+  convert! Submodule.sup_orthogonal_inf_of_hasOrthogonalProjection (le_top : K ≤ ⊤) using 2
   simp
 
 /-- If `K` admits an orthogonal projection, then the orthogonal complement of its orthogonal
@@ -87,7 +87,7 @@ of all elements equal to zero. Then `Kᗮ = ⊥`, `Kᗮᗮ = ⊤`. -/
 theorem orthogonal_orthogonal_eq_closure [CompleteSpace E] :
     Kᗮᗮ = K.topologicalClosure := by
   refine le_antisymm ?_ ?_
-  · convert Submodule.orthogonal_orthogonal_monotone K.le_topologicalClosure using 1
+  · convert! Submodule.orthogonal_orthogonal_monotone K.le_topologicalClosure using 1
     rw [K.topologicalClosure.orthogonal_orthogonal]
   · exact K.topologicalClosure_minimal K.le_orthogonal_orthogonal Kᗮ.isClosed_orthogonal
 
@@ -150,7 +150,7 @@ theorem starProjection_tendsto_self {ι : Type*} [Preorder ι]
   have : (⨆ i, U i).topologicalClosure.HasOrthogonalProjection := by
     rw [top_unique hU']
     infer_instance
-  convert starProjection_tendsto_closure_iSup U hU x
+  convert! starProjection_tendsto_closure_iSup U hU x
   rw [eq_comm, starProjection_eq_self_iff, top_unique hU']
   trivial
 
diff --git a/Mathlib/Analysis/InnerProductSpace/Rayleigh.lean b/Mathlib/Analysis/InnerProductSpace/Rayleigh.lean
index 75aa1e71cd5cca..a6d1ebadaf3ce1 100644
--- a/Mathlib/Analysis/InnerProductSpace/Rayleigh.lean
+++ b/Mathlib/Analysis/InnerProductSpace/Rayleigh.lean
@@ -201,7 +201,7 @@ variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℝ F]
 theorem _root_.LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf {T : F →L[ℝ] F}
     (hT : (T : F →ₗ[ℝ] F).IsSymmetric) (x₀ : F) :
     HasStrictFDerivAt T.reApplyInnerSelf (2 • (innerSL ℝ (T x₀))) x₀ := by
-  convert T.hasStrictFDerivAt.inner ℝ (hasStrictFDerivAt_id x₀) using 1
+  convert! T.hasStrictFDerivAt.inner ℝ (hasStrictFDerivAt_id x₀) using 1
   ext y
   rw [ContinuousLinearMap.smul_apply, ContinuousLinearMap.comp_apply, fderivInnerCLM_apply,
     ContinuousLinearMap.prod_apply, innerSL_apply_apply, id, ContinuousLinearMap.id_apply,
@@ -213,7 +213,7 @@ theorem linearly_dependent_of_isLocalExtrOn (hT : IsSelfAdjoint T) {x₀ : F}
     (hextr : IsLocalExtrOn T.reApplyInnerSelf (sphere (0 : F) ‖x₀‖) x₀) :
     ∃ a b : ℝ, (a, b) ≠ 0 ∧ a • x₀ + b • T x₀ = 0 := by
   have H : IsLocalExtrOn T.reApplyInnerSelf {x : F | ‖x‖ ^ 2 = ‖x₀‖ ^ 2} x₀ := by
-    convert hextr
+    convert! hextr
     ext x
     simp
   -- find Lagrange multipliers for the function `T.re_apply_inner_self` and the
@@ -245,7 +245,7 @@ theorem eq_smul_self_of_isLocalExtrOn_real (hT : IsSelfAdjoint T) {x₀ : F}
   have hc : T x₀ = (-b⁻¹ * a) • x₀ := by
     linear_combination (norm := match_scalars <;> field) b⁻¹ • h₂
   set c : ℝ := -b⁻¹ * a
-  convert hc
+  convert! hc
   simpa [field, inner_smul_left, mul_comm a] using congr_arg (fun x => ⟪x, x₀⟫_ℝ) hc
 
 end Real
@@ -276,7 +276,7 @@ quotient. -/
 theorem hasEigenvector_of_isMaxOn (hT : IsSelfAdjoint T) {x₀ : E} (hx₀ : x₀ ≠ 0)
     (hextr : IsMaxOn T.reApplyInnerSelf (sphere (0 : E) ‖x₀‖) x₀) :
     HasEigenvector (T : E →ₗ[𝕜] E) (⨆ x : { x : E // x ≠ 0 }, T.rayleighQuotient x : ℝ) x₀ := by
-  convert hT.hasEigenvector_of_isLocalExtrOn hx₀ (Or.inr hextr.localize)
+  convert! hT.hasEigenvector_of_isLocalExtrOn hx₀ (Or.inr hextr.localize)
   have hx₀' : 0 < ‖x₀‖ := by simp [hx₀]
   have hx₀'' : x₀ ∈ sphere (0 : E) ‖x₀‖ := by simp
   rw [T.iSup_rayleigh_eq_iSup_rayleigh_sphere hx₀']
@@ -295,7 +295,7 @@ quotient. -/
 theorem hasEigenvector_of_isMinOn (hT : IsSelfAdjoint T) {x₀ : E} (hx₀ : x₀ ≠ 0)
     (hextr : IsMinOn T.reApplyInnerSelf (sphere (0 : E) ‖x₀‖) x₀) :
     HasEigenvector (T : E →ₗ[𝕜] E) (⨅ x : { x : E // x ≠ 0 }, T.rayleighQuotient x : ℝ) x₀ := by
-  convert hT.hasEigenvector_of_isLocalExtrOn hx₀ (Or.inl hextr.localize)
+  convert! hT.hasEigenvector_of_isLocalExtrOn hx₀ (Or.inl hextr.localize)
   have hx₀' : 0 < ‖x₀‖ := by simp [hx₀]
   have hx₀'' : x₀ ∈ sphere (0 : E) ‖x₀‖ := by simp
   rw [T.iInf_rayleigh_eq_iInf_rayleigh_sphere hx₀']
diff --git a/Mathlib/Analysis/InnerProductSpace/Reproducing.lean b/Mathlib/Analysis/InnerProductSpace/Reproducing.lean
index e5afb58cb220c8..7fe97d9977d220 100644
--- a/Mathlib/Analysis/InnerProductSpace/Reproducing.lean
+++ b/Mathlib/Analysis/InnerProductSpace/Reproducing.lean
@@ -197,8 +197,7 @@ theorem posSemidef_tfae : List.TFAE [K.PosSemidef, K.IsHermitian ∧ ∀ (f : X
   obtain ⟨v, hv⟩ := exists_ne (0 : V)
   tfae_have 1 → 2 := fun h ff ↦ by
     rw [Finsupp.sum_comm]
-    convert h (ff.sum fun xv z ↦ .single xv.1
-      ((z / ‖v‖ ^ 2) • (innerSL 𝕜 v).smulRight xv.2)) v
+    convert! h (ff.sum fun xv z ↦ .single xv.1 ((z / ‖v‖ ^ 2) • (innerSL 𝕜 v).smulRight xv.2)) v
     simp [Finsupp.sum_sum_index, inner_add_right, inner_add_left, ← smul_assoc, hv]
     simp [inner_smul_left, inner_smul_right, ← mul_assoc, mul_comm]
   tfae_have 2 → 3 := fun h vv ↦ by
diff --git a/Mathlib/Analysis/InnerProductSpace/SingularValues.lean b/Mathlib/Analysis/InnerProductSpace/SingularValues.lean
index 29e365fda845fc..fe226adee921b1 100644
--- a/Mathlib/Analysis/InnerProductSpace/SingularValues.lean
+++ b/Mathlib/Analysis/InnerProductSpace/SingularValues.lean
@@ -134,7 +134,7 @@ theorem sq_singularValues_of_lt {n : ℕ} (hn : finrank 𝕜 E = n) {i : ℕ} (h
 
 theorem hasEigenvalue_adjoint_comp_self_sq_singularValues {n : ℕ} (hn : n < finrank 𝕜 E) :
     End.HasEigenvalue (adjoint T ∘ₗ T) (T.singularValues n ^ 2) := by
-  convert T.isSymmetric_adjoint_comp_self.hasEigenvalue_eigenvalues rfl ⟨n, hn⟩ using 1
+  convert! T.isSymmetric_adjoint_comp_self.hasEigenvalue_eigenvalues rfl ⟨n, hn⟩ using 1
   simp [← T.sq_singularValues_fin]
 
 theorem singularValues_antitone : Antitone T.singularValues := by
@@ -162,7 +162,7 @@ theorem injective_iff_forall_lt_finrank_singularValues_pos :
     use i, i.isLt
     simp [RCLike.ofReal_eq_zero.mp hi, T.singularValues_fin rfl]
   · intro ⟨i, h, hz⟩
-    convert T.isSymmetric_adjoint_comp_self.hasEigenvalue_eigenvalues rfl ⟨i, h⟩
+    convert! T.isSymmetric_adjoint_comp_self.hasEigenvalue_eigenvalues rfl ⟨i, h⟩
     rw [← sq_singularValues_of_lt, le_antisymm hz (T.singularValues_nonneg i)]
     simp
 
diff --git a/Mathlib/Analysis/InnerProductSpace/Spectrum.lean b/Mathlib/Analysis/InnerProductSpace/Spectrum.lean
index 40db395b63cfff..3a764c774eaaf8 100644
--- a/Mathlib/Analysis/InnerProductSpace/Spectrum.lean
+++ b/Mathlib/Analysis/InnerProductSpace/Spectrum.lean
@@ -234,8 +234,9 @@ private theorem card_filter_unsortedEigenvalues_eq (hT : T.IsSymmetric)
     (hn : Module.finrank 𝕜 E = n) (μ : 𝕜) :
     Finset.card {i | hT.unsortedEigenvalues hn i = μ} = Module.finrank 𝕜 (eigenspace T μ) := by
   by_cases hμ : HasEigenvalue T μ
-  · convert hT.direct_sum_isInternal.card_filter_subordinateOrthonormalBasisIndex_eq hn
-      hT.orthogonalFamily_eigenspaces' ⟨μ, hμ⟩ with i
+  · convert!
+      hT.direct_sum_isInternal.card_filter_subordinateOrthonormalBasisIndex_eq hn
+        hT.orthogonalFamily_eigenspaces' ⟨μ, hμ⟩ with i
     unfold unsortedEigenvalues
     let ⟨x, hx⟩ := hT.direct_sum_isInternal.subordinateOrthonormalBasisIndex hn i
       hT.orthogonalFamily_eigenspaces'
@@ -370,9 +371,9 @@ theorem sort_roots_charpoly_eq_eigenvalues (hT : T.IsSymmetric) (hn : Module.fin
   simp_rw [hT.roots_charpoly_eq_eigenvalues, Fin.univ_val_map, Multiset.map_coe, List.map_ofFn,
     Function.comp_def, RCLike.ofReal_re, Multiset.coe_sort]
   have := hn.symm
-  convert List.mergeSort_of_pairwise ?_
+  convert! List.mergeSort_of_pairwise ?_
   simp_rw [decide_eq_true_eq, ← List.sortedGE_iff_pairwise]
-  convert (hT.eigenvalues_antitone hn).sortedGE_ofFn
+  convert! (hT.eigenvalues_antitone hn).sortedGE_ofFn
 
 theorem eigenvalues_eq_eigenvalues_iff {E' : Type*} [NormedAddCommGroup E'] [InnerProductSpace 𝕜 E']
     [FiniteDimensional 𝕜 E'] {T' : E' →ₗ[𝕜] E'} (hT : T.IsSymmetric) (hn : Module.finrank 𝕜 E = n)
diff --git a/Mathlib/Analysis/InnerProductSpace/Subspace.lean b/Mathlib/Analysis/InnerProductSpace/Subspace.lean
index 7c4ad95e590b1e..f94e9483b448c3 100644
--- a/Mathlib/Analysis/InnerProductSpace/Subspace.lean
+++ b/Mathlib/Analysis/InnerProductSpace/Subspace.lean
@@ -181,7 +181,7 @@ theorem OrthogonalFamily.norm_sq_diff_sum [DecidableEq ι] (f : ∀ i, G i) (s
       (∑ i ∈ s₁ \ s₂, ‖F i‖ ^ 2) + ∑ i ∈ s₂ \ s₁, ‖F i‖ ^ 2 := by
     have hs : Disjoint (s₁ \ s₂) (s₂ \ s₁) := disjoint_sdiff_sdiff
     simpa only [Finset.sum_union hs] using hV.norm_sum F (s₁ \ s₂ ∪ s₂ \ s₁)
-  convert this using 4
+  convert! this using 4
   · refine Finset.sum_congr rfl fun i hi => ?_
     simp only [hF₁ i hi]
   · refine Finset.sum_congr rfl fun i hi => ?_
@@ -220,13 +220,13 @@ theorem OrthogonalFamily.summable_iff_norm_sq_summable [CompleteSpace E] (f : 
       have has : a ≤ s₁ ⊓ s₂ := le_inf hs₁ hs₂
       rw [hV.norm_sq_diff_sum]
       have Hs₁ : ∑ x ∈ s₁ \ s₂, ‖f x‖ ^ 2 < ε ^ 2 / 2 := by
-        convert H _ hs₁ _ has
+        convert! H _ hs₁ _ has
         have : s₁ ⊓ s₂ ⊆ s₁ := Finset.inter_subset_left
         rw [← Finset.sum_sdiff this, add_tsub_cancel_right, Finset.abs_sum_of_nonneg']
         · simp
         · exact fun i => sq_nonneg _
       have Hs₂ : ∑ x ∈ s₂ \ s₁, ‖f x‖ ^ 2 < ε ^ 2 / 2 := by
-        convert H _ hs₂ _ has
+        convert! H _ hs₂ _ has
         have : s₁ ⊓ s₂ ⊆ s₂ := Finset.inter_subset_right
         rw [← Finset.sum_sdiff this, add_tsub_cancel_right, Finset.abs_sum_of_nonneg']
         · simp
diff --git a/Mathlib/Analysis/InnerProductSpace/TensorProduct.lean b/Mathlib/Analysis/InnerProductSpace/TensorProduct.lean
index 00acc51790a69b..b6845890790c9e 100644
--- a/Mathlib/Analysis/InnerProductSpace/TensorProduct.lean
+++ b/Mathlib/Analysis/InnerProductSpace/TensorProduct.lean
@@ -469,7 +469,7 @@ theorem Orthonormal.tmul
 theorem Orthonormal.basisTensorProduct
     {b₁ : Basis ι₁ 𝕜 E} {b₂ : Basis ι₂ 𝕜 F} (hb₁ : Orthonormal 𝕜 b₁) (hb₂ : Orthonormal 𝕜 b₂) :
     Orthonormal 𝕜 (b₁.tensorProduct b₂) := by
-  convert hb₁.tmul hb₂
+  convert! hb₁.tmul hb₂
   exact b₁.tensorProduct_apply' b₂ _
 
 namespace OrthonormalBasis
diff --git a/Mathlib/Analysis/InnerProductSpace/TwoDim.lean b/Mathlib/Analysis/InnerProductSpace/TwoDim.lean
index d8018b1a19152a..9e6e5d472f877b 100644
--- a/Mathlib/Analysis/InnerProductSpace/TwoDim.lean
+++ b/Mathlib/Analysis/InnerProductSpace/TwoDim.lean
@@ -108,7 +108,7 @@ theorem areaForm_apply_self (x : E) : ω x x = 0 := by
 
 theorem areaForm_swap (x y : E) : ω x y = -ω y x := by
   simp only [areaForm_to_volumeForm]
-  convert o.volumeForm.map_swap ![y, x] (_ : (0 : Fin 2) ≠ 1)
+  convert! o.volumeForm.map_swap ![y, x] (_ : (0 : Fin 2) ≠ 1)
   · ext i
     fin_cases i <;> rfl
   · simp
@@ -157,7 +157,7 @@ theorem areaForm_map {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℝ F
 theorem areaForm_comp_linearIsometryEquiv (φ : E ≃ₗᵢ[ℝ] E)
     (hφ : 0 < LinearMap.det (φ.toLinearEquiv : E →ₗ[ℝ] E)) (x y : E) :
     o.areaForm (φ x) (φ y) = o.areaForm x y := by
-  convert o.areaForm_map φ (φ x) (φ y)
+  convert! o.areaForm_map φ (φ x) (φ y)
   · symm
     rwa [← o.map_eq_iff_det_pos φ.toLinearEquiv] at hφ
     rw [@Fact.out (finrank ℝ E = 2), Fintype.card_fin]
@@ -308,7 +308,7 @@ theorem rightAngleRotation_map {F : Type*} [NormedAddCommGroup F] [InnerProductS
 /-- `J` commutes with any positively-oriented isometric automorphism. -/
 theorem linearIsometryEquiv_comp_rightAngleRotation (φ : E ≃ₗᵢ[ℝ] E)
     (hφ : 0 < LinearMap.det (φ.toLinearEquiv : E →ₗ[ℝ] E)) (x : E) : φ (J x) = J (φ x) := by
-  convert (o.rightAngleRotation_map φ (φ x)).symm
+  convert! (o.rightAngleRotation_map φ (φ x)).symm
   · simp
   · symm
     rwa [← o.map_eq_iff_det_pos φ.toLinearEquiv] at hφ
diff --git a/Mathlib/Analysis/InnerProductSpace/l2Space.lean b/Mathlib/Analysis/InnerProductSpace/l2Space.lean
index 0f7e1b57659a11..347b70bc4b4e0a 100644
--- a/Mathlib/Analysis/InnerProductSpace/l2Space.lean
+++ b/Mathlib/Analysis/InnerProductSpace/l2Space.lean
@@ -154,7 +154,7 @@ theorem inner_single_left [DecidableEq ι] (i : ι) (a : G i) (f : lp G 2) :
     ⟪lp.single 2 i a, f⟫ = ⟪a, f i⟫ := by
   refine (hasSum_inner (lp.single 2 i a) f).unique ?_
   simp_rw [lp.coeFn_single]
-  convert hasSum_ite_eq i ⟪a, f i⟫ using 1
+  convert! hasSum_ite_eq i ⟪a, f i⟫ using 1
   ext j
   split_ifs with h
   · subst h; rw [Pi.single_eq_same]
@@ -177,7 +177,7 @@ include hV
 protected theorem summable_of_lp (f : lp G 2) :
     Summable fun i => V i (f i) := by
   rw [hV.summable_iff_norm_sq_summable]
-  convert (lp.memℓp f).summable _
+  convert! (lp.memℓp f).summable _
   · norm_cast
   · norm_num
 
@@ -198,7 +198,7 @@ protected def linearIsometry (hV : OrthogonalFamily 𝕜 G V) : lp G 2 →ₗᵢ
       suffices ‖∑' i : ι, V i (f i)‖ ^ (2 : ℝ≥0∞).toReal = ‖f‖ ^ (2 : ℝ≥0∞).toReal by
         exact Real.rpow_left_injOn H.ne' (norm_nonneg _) (norm_nonneg _) this
       refine tendsto_nhds_unique ?_ (lp.hasSum_norm H f)
-      convert (hV.summable_of_lp f).hasSum.norm.rpow_const (Or.inr H.le) using 1
+      convert! (hV.summable_of_lp f).hasSum.norm.rpow_const (Or.inr H.le) using 1
       ext s
       exact mod_cast (hV.norm_sum f s).symm
 
@@ -344,7 +344,7 @@ theorem Orthonormal.isHilbertSum {v : ι → E} (hv : Orthonormal 𝕜 v)
     (hsp : ⊤ ≤ (span 𝕜 (Set.range v)).topologicalClosure) :
     IsHilbertSum 𝕜 (fun _ : ι => 𝕜) fun i => LinearIsometry.toSpanSingleton 𝕜 E (hv.1 i) :=
   IsHilbertSum.mk hv.orthogonalFamily (by
-    convert hsp
+    convert! hsp
     simp [← LinearMap.span_singleton_eq_range, ← Submodule.span_iUnion])
 
 theorem Submodule.isHilbertSumOrthogonal (K : Submodule 𝕜 E) [hK : CompleteSpace K] :
@@ -398,7 +398,7 @@ instance instFunLike : FunLike (HilbertBasis ι 𝕜 E) ι E where
 protected theorem repr_symm_single [DecidableEq ι] (b : HilbertBasis ι 𝕜 E) (i : ι) :
     b.repr.symm (lp.single 2 i (1 : 𝕜)) = b i := by
   dsimp +instances [instFunLike]
-  convert rfl
+  convert! rfl
 
 
 protected theorem repr_self [DecidableEq ι] (b : HilbertBasis ι 𝕜 E) (i : ι) :
@@ -456,7 +456,7 @@ protected theorem dense_span (b : HilbertBasis ι 𝕜 E) :
 
 protected theorem hasSum_inner_mul_inner (b : HilbertBasis ι 𝕜 E) (x y : E) :
     HasSum (fun i => ⟪x, b i⟫ * ⟪b i, y⟫) ⟪x, y⟫ := by
-  convert (b.hasSum_repr y).mapL (innerSL 𝕜 x) using 1
+  convert! (b.hasSum_repr y).mapL (innerSL 𝕜 x) using 1
   ext i
   rw [innerSL_apply_apply, b.repr_apply_apply, inner_smul_right, mul_comm]
 
diff --git a/Mathlib/Analysis/LocallyConvex/AbsConvexOpen.lean b/Mathlib/Analysis/LocallyConvex/AbsConvexOpen.lean
index 79624fc127d040..812c09cfba3a10 100644
--- a/Mathlib/Analysis/LocallyConvex/AbsConvexOpen.lean
+++ b/Mathlib/Analysis/LocallyConvex/AbsConvexOpen.lean
@@ -110,7 +110,7 @@ theorem with_gaugeSeminormFamily : WithSeminorms (gaugeSeminormFamily 𝕜 E) :=
   refine SeminormFamily.withSeminorms_of_hasBasis _ ?_
   refine (nhds_hasBasis_absConvex_open 𝕜 E).to_hasBasis (fun s hs => ?_) fun s hs => ?_
   · refine ⟨s, ⟨?_, rfl.subset⟩⟩
-    convert (gaugeSeminormFamily _ _).basisSets_singleton_mem ⟨s, hs⟩ one_pos
+    convert! (gaugeSeminormFamily _ _).basisSets_singleton_mem ⟨s, hs⟩ one_pos
     rw [gaugeSeminormFamily_ball, Subtype.coe_mk]
   refine ⟨s, ⟨?_, rfl.subset⟩⟩
   rw [SeminormFamily.basisSets_iff] at hs
diff --git a/Mathlib/Analysis/LocallyConvex/Barrelled.lean b/Mathlib/Analysis/LocallyConvex/Barrelled.lean
index 3d60f65543520b..415a5456bcaa8f 100644
--- a/Mathlib/Analysis/LocallyConvex/Barrelled.lean
+++ b/Mathlib/Analysis/LocallyConvex/Barrelled.lean
@@ -105,7 +105,7 @@ theorem Seminorm.continuous_iSup
   refine Seminorm.continuous_of_lowerSemicontinuous _ ?_
   rw [Seminorm.coe_iSup_eq bdd]
   rw [Seminorm.bddAbove_range_iff] at bdd
-  convert lowerSemicontinuous_ciSup (f := fun i x ↦ p i x) bdd (fun i ↦ (hp i).lowerSemicontinuous)
+  convert! lowerSemicontinuous_ciSup (f := fun i x ↦ p i x) bdd (fun i ↦ (hp i).lowerSemicontinuous)
   exact iSup_apply
 
 end defs
@@ -138,7 +138,7 @@ instance BaireSpace.instBarrelledSpace [TopologicalSpace E] [IsTopologicalAddGro
     -- radius `2*n` is a neighborhood of zero.
     refine Seminorm.continuous' (r := n + n) ?_
     rw [p.closedBall_zero_eq] at hxn ⊢
-    have hxn' : p x ≤ n := by convert interior_subset hxn
+    have hxn' : p x ≤ n := by convert! interior_subset hxn
     -- By definition, we have `p x' ≤ n` for `x'` sufficiently close to `x`.
     -- In other words, `p (x + y) ≤ n` for `y` sufficiently close to `0`.
     rw [mem_interior_iff_mem_nhds, ← map_add_left_nhds_zero] at hxn
diff --git a/Mathlib/Analysis/LocallyConvex/WithSeminorms.lean b/Mathlib/Analysis/LocallyConvex/WithSeminorms.lean
index b9dceb24d859fd..46fa0bc06a98bf 100644
--- a/Mathlib/Analysis/LocallyConvex/WithSeminorms.lean
+++ b/Mathlib/Analysis/LocallyConvex/WithSeminorms.lean
@@ -330,7 +330,7 @@ theorem WithSeminorms.hasBasis_ball (hp : WithSeminorms p) {x : E} :
     (fun sr : Finset ι × ℝ => 0 < sr.2) fun sr => (sr.1.sup p).ball x sr.2 := by
   have : IsTopologicalAddGroup E := hp.topologicalAddGroup
   rw [← map_add_left_nhds_zero]
-  convert hp.hasBasis_zero_ball.map (x + ·) using 1
+  convert! hp.hasBasis_zero_ball.map (x + ·) using 1
   ext sr : 1
   -- Porting note: extra type ascriptions needed on `0`
   have : (sr.fst.sup p).ball (x +ᵥ (0 : E)) sr.snd = x +ᵥ (sr.fst.sup p).ball 0 sr.snd :=
@@ -545,7 +545,7 @@ theorem WithSeminorms.isVonNBounded_iff_seminorm_bounded {s : Set E} (hp : WithS
   rw [hp.isVonNBounded_iff_finset_seminorm_bounded]
   constructor
   · intro hI i
-    convert hI {i}
+    convert! hI { i }
     rw [Finset.sup_singleton]
   intro hi I
   by_cases! hI : I.Nonempty
@@ -654,7 +654,7 @@ theorem continuous_of_continuous_comp {q : SeminormFamily 𝕝₂ F ι'} [Topolo
   simp_rw [ContinuousAt, f.map_zero, q.withSeminorms_iff_nhds_eq_iInf.mp hq, Filter.tendsto_iInf,
     Filter.tendsto_comap_iff]
   intro i
-  convert (hf i).continuousAt.tendsto
+  convert! (hf i).continuousAt.tendsto
   exact (map_zero _).symm
 
 @[deprecated (since := "2026-03-09")]
diff --git a/Mathlib/Analysis/MeanInequalities.lean b/Mathlib/Analysis/MeanInequalities.lean
index 3bc7e6ec8dbaaf..a94e89345a6651 100644
--- a/Mathlib/Analysis/MeanInequalities.lean
+++ b/Mathlib/Analysis/MeanInequalities.lean
@@ -141,7 +141,7 @@ theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ) (hw : ∀ i ∈ s, 0
   -- for `exp` and numbers `log (z i)` with weights `w i`.
   · have := convexOn_exp.map_sum_le hw hw' fun i _ => Set.mem_univ <| log (z i)
     simp only [exp_sum, smul_eq_mul, mul_comm (w _) (log _)] at this
-    convert this using 1 <;> [apply prod_congr rfl; apply sum_congr rfl] <;> intro i hi
+    convert! this using 1 <;> [apply prod_congr rfl; apply sum_congr rfl] <;> intro i hi
     · rcases eq_or_lt_of_le (hz i hi) with hz | hz
       · simp [A i hi hz.symm]
       · exact rpow_def_of_pos hz _
@@ -153,7 +153,7 @@ theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ) (hw : ∀ i ∈ s, 0
 theorem geom_mean_le_arith_mean {ι : Type*} (s : Finset ι) (w : ι → ℝ) (z : ι → ℝ)
     (hw : ∀ i ∈ s, 0 ≤ w i) (hw' : 0 < ∑ i ∈ s, w i) (hz : ∀ i ∈ s, 0 ≤ z i) :
     (∏ i ∈ s, z i ^ w i) ^ (∑ i ∈ s, w i)⁻¹ ≤ (∑ i ∈ s, w i * z i) / (∑ i ∈ s, w i) := by
-  convert geom_mean_le_arith_mean_weighted s (fun i => (w i) / ∑ i ∈ s, w i) z ?_ ?_ hz using 2
+  convert! geom_mean_le_arith_mean_weighted s (fun i => (w i) / ∑ i ∈ s, w i) z ?_ ?_ hz using 2
   · rw [← finsetProd_rpow _ _ (fun i hi => rpow_nonneg (hz _ hi) _) _]
     refine Finset.prod_congr rfl (fun _ ih => ?_)
     rw [div_eq_mul_inv, rpow_mul (hz _ ih)]
@@ -211,14 +211,14 @@ theorem geom_mean_eq_arith_mean_weighted_iff' (w z : ι → ℝ) (hw : ∀ i ∈
         apply (sum_eq_zero_iff_of_nonneg ?_).mp h.symm j hj
         exact fun i hi => (mul_nonneg_iff_of_pos_left (hw i hi)).mpr (hz i hi)
       · intro h
-        convert h i his
+        convert! h i his
         exact hzi.symm
     · rw [hzi]
       exact zero_rpow hwi
   · have hz' := fun i h => lt_of_le_of_ne (hz i h) (fun a => (ne_of_gt (hw i h)) (A i h a.symm))
     have := strictConvexOn_exp.map_sum_eq_iff hw hw' fun i _ => Set.mem_univ <| log (z i)
     simp only [exp_sum, smul_eq_mul, mul_comm (w _) (log _)] at this
-    convert this using 1
+    convert! this using 1
     · apply Eq.congr <;>
       [apply prod_congr rfl; apply sum_congr rfl] <;>
       intro i hi <;>
@@ -369,7 +369,7 @@ theorem harm_mean_le_geom_mean {ι : Type*} (s : Finset ι) (hs : s.Nonempty) (w
     set n := ∑ i ∈ s, w i
     nth_rw 1 [div_eq_mul_inv, (show n = (n⁻¹)⁻¹ by simp), ← mul_inv, Finset.mul_sum _ _ n⁻¹]
     simp_rw [inv_mul_eq_div n ((w _) / (z _)), div_right_comm _ _ n]
-    convert this
+    convert! this
     rw [← Real.finsetProd_rpow s _ (fun i hi ↦ by positivity [hz i hi])]
     refine Finset.prod_congr rfl (fun i hi => ?_)
     rw [← Real.rpow_mul (le_of_lt <| hz i hi) (w _) n⁻¹, div_eq_mul_inv (w _) n]
@@ -512,8 +512,9 @@ product of their `L^p` and `L^q` norms when `p`, `q`, and `r` form a `Real.Holde
 theorem Lr_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q r : ℝ} (hpqr : p.HolderTriple q r) :
     (∑ i ∈ s, (f i * g i) ^ r) ^ (1 / r) ≤
       (∑ i ∈ s, f i ^ p) ^ (1 / p) * (∑ i ∈ s, g i ^ q) ^ (1 / q) := by
-  convert rpow_le_rpow_iff (inv_eq_one_div r ▸ inv_pos.mpr hpqr.pos' : 0 < 1 / r) |>.mpr <|
-    Lr_rpow_le_Lp_mul_Lq s f g hpqr using 1
+  convert!
+    rpow_le_rpow_iff (inv_eq_one_div r ▸ inv_pos.mpr hpqr.pos' : 0 < 1 / r) |>.mpr <|
+      Lr_rpow_le_Lp_mul_Lq s f g hpqr using 1
   have hr := hpqr.pos'.ne'
   simp only [← rpow_mul, mul_rpow]
   field_simp
@@ -588,8 +589,9 @@ theorem Lr_rpow_le_Lp_mul_Lq_tsum {f g : ι → ℝ≥0} {p q r : ℝ} (hpqr : p
 theorem Lr_le_Lp_mul_Lq_tsum {f g : ι → ℝ≥0} {p q r : ℝ} (hpqr : p.HolderTriple q r)
     (hf : Summable fun i => f i ^ p) (hg : Summable fun i => g i ^ q) :
     (∑' i, (f i * g i) ^ r) ^ (1 / r) ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) := by
-  convert rpow_le_rpow_iff (inv_eq_one_div r ▸ inv_pos.mpr hpqr.pos') |>.mpr <|
-    Lr_rpow_le_Lp_mul_Lq_tsum hpqr hf hg
+  convert!
+    rpow_le_rpow_iff (inv_eq_one_div r ▸ inv_pos.mpr hpqr.pos') |>.mpr <|
+      Lr_rpow_le_Lp_mul_Lq_tsum hpqr hf hg
   have hr := hpqr.pos'.ne'
   simp only [← rpow_mul, mul_rpow]
   field_simp
@@ -776,7 +778,7 @@ with real-valued nonnegative functions. -/
 theorem inner_le_Lp_mul_Lq_of_nonneg (hpq : HolderConjugate p q) (hf : ∀ i ∈ s, 0 ≤ f i)
     (hg : ∀ i ∈ s, 0 ≤ g i) :
     ∑ i ∈ s, f i * g i ≤ (∑ i ∈ s, f i ^ p) ^ (1 / p) * (∑ i ∈ s, g i ^ q) ^ (1 / q) := by
-  convert inner_le_Lp_mul_Lq s f g hpq using 3 <;> apply sum_congr rfl <;> intro i hi <;>
+  convert! inner_le_Lp_mul_Lq s f g hpq using 3 <;> apply sum_congr rfl <;> intro i hi <;>
     simp only [abs_of_nonneg, hf i hi, hg i hi]
 
 /-- **Hölder inequality**: the sum of (the `r`-power of) the product of two functions is bounded
@@ -785,7 +787,7 @@ by (the `r`-power of) the product of their `L^p` and `L^q` norms, when `p`, `q`,
 theorem Lr_rpow_le_Lp_mul_Lq_of_nonneg {ι : Type*} (s : Finset ι) {f g : ι → ℝ} {p q r : ℝ}
     (hpqr : p.HolderTriple q r) (hf : ∀ i ∈ s, 0 ≤ f i) (hg : ∀ i ∈ s, 0 ≤ g i) :
     ∑ i ∈ s, (f i * g i) ^ r ≤ (∑ i ∈ s, f i ^ p) ^ (r / p) * (∑ i ∈ s, g i ^ q) ^ (r / q) := by
-  convert Lr_rpow_le_Lp_mul_Lq s f g hpqr using 3 with i hi
+  convert! Lr_rpow_le_Lp_mul_Lq s f g hpqr using 3 with i hi
   · rw [abs_of_nonneg (mul_nonneg (hf i hi) (hg i hi))]
   all_goals
     congr! with i hi
@@ -861,9 +863,10 @@ theorem Lr_le_Lp_mul_Lq_tsum_of_nonneg (hpqr : p.HolderTriple q r) (hf : ∀ i,
   have hf' : 0 ≤ ∑' i, f i ^ p := tsum_nonneg fun i ↦ rpow_nonneg (hf i) p
   have hg' : 0 ≤ ∑' i, g i ^ q := tsum_nonneg fun i ↦ rpow_nonneg (hg i) q
   have hr := hpqr.pos'
-  convert rpow_le_rpow_iff (tsum_nonneg fun i ↦ by positivity [hf i, hg i]) (by positivity)
-    (inv_eq_one_div r ▸ inv_pos.mpr hr) |>.mpr <|
-    Lr_rpow_le_Lp_mul_Lq_tsum_of_nonneg hpqr hf hg hf_sum hg_sum using 1
+  convert!
+    rpow_le_rpow_iff (tsum_nonneg fun i ↦ by positivity [hf i, hg i]) (by positivity)
+          (inv_eq_one_div r ▸ inv_pos.mpr hr) |>.mpr <|
+      Lr_rpow_le_Lp_mul_Lq_tsum_of_nonneg hpqr hf hg hf_sum hg_sum using 1
   rw [mul_rpow (rpow_nonneg hf' _) (rpow_nonneg hg' _), ← Real.rpow_mul hg', ← Real.rpow_mul hf']
   field_simp
 
@@ -899,7 +902,7 @@ sum of the `p`-th powers of `f i`. Version for sums over finite sets, with nonne
 functions. -/
 theorem rpow_sum_le_const_mul_sum_rpow_of_nonneg (hp : 1 ≤ p) (hf : ∀ i ∈ s, 0 ≤ f i) :
     (∑ i ∈ s, f i) ^ p ≤ (#s : ℝ) ^ (p - 1) * ∑ i ∈ s, f i ^ p := by
-  convert rpow_sum_le_const_mul_sum_rpow s f hp using 2 <;> apply sum_congr rfl <;> intro i hi <;>
+  convert! rpow_sum_le_const_mul_sum_rpow s f hp using 2 <;> apply sum_congr rfl <;> intro i hi <;>
     simp only [abs_of_nonneg, hf i hi]
 
 /-- **Minkowski inequality**: the `L_p` seminorm of the sum of two vectors is less than or equal
@@ -908,7 +911,7 @@ functions. -/
 theorem Lp_add_le_of_nonneg (hp : 1 ≤ p) (hf : ∀ i ∈ s, 0 ≤ f i) (hg : ∀ i ∈ s, 0 ≤ g i) :
     (∑ i ∈ s, (f i + g i) ^ p) ^ (1 / p) ≤
       (∑ i ∈ s, f i ^ p) ^ (1 / p) + (∑ i ∈ s, g i ^ p) ^ (1 / p) := by
-  convert Lp_add_le s f g hp using 2 <;> [skip; congr 1; congr 1] <;> apply sum_congr rfl <;>
+  convert! Lp_add_le s f g hp using 2 <;> [skip; congr 1; congr 1] <;> apply sum_congr rfl <;>
       intro i hi <;>
     simp only [abs_of_nonneg, hf i hi, hg i hi, add_nonneg]
 
@@ -987,7 +990,7 @@ theorem inner_le_Lp_mul_Lq (hpq : p.HolderConjugate q) :
   have := ENNReal.coe_le_coe.2 (@NNReal.inner_le_Lp_mul_Lq _ s (fun i => ENNReal.toNNReal (f i))
     (fun i => ENNReal.toNNReal (g i)) _ _ hpq)
   simp [ENNReal.coe_rpow_of_nonneg, hpq.pos.le, hpq.symm.pos.le] at this
-  convert this using 1 <;> [skip; congr 2] <;> [skip; skip; simp; skip; simp] <;>
+  convert! this using 1 <;> [skip; congr 2] <;> [skip; skip; simp; skip; simp] <;>
     · refine Finset.sum_congr rfl fun i hi => ?_
       simp [H'.1 i hi, H'.2 i hi, -WithZero.coe_mul]
 
@@ -1013,12 +1016,12 @@ lemma inner_le_weight_mul_Lp_of_nonneg (s : Finset ι) {p : ℝ} (hp : 1 ≤ p)
   simp_rw [coe_rpow_of_nonneg _ <| inv_nonneg.2 hp₀.le, coe_finsetSum, ← ENNReal.toNNReal_rpow,
     ← ENNReal.toNNReal_mul, sum_congr rfl fun i hi ↦ coe_toNNReal (H'.2 i hi)] at this
   simp only [toNNReal_mul, coe_mul, sub_nonneg, hp₁.le, coe_rpow_of_nonneg, coe_finsetSum] at this
-  convert this using 2 with i hi
+  convert! this using 2 with i hi
   · obtain hw | hw := eq_or_ne (w i) 0
     · simp [hw]
     rw [coe_toNNReal (H'.1 _ hi), coe_toNNReal]
     simpa [mul_eq_top, hw, hp₀, hp₀.not_gt, H'.1 _ hi] using H'.2 _ hi
-  · convert rfl with i hi
+  · convert! rfl with i hi
     exact coe_toNNReal (H'.1 _ hi)
 
 /-- For `1 ≤ p`, the `p`-th power of the sum of `f i` is bounded above by a constant times the
diff --git a/Mathlib/Analysis/MeanInequalitiesPow.lean b/Mathlib/Analysis/MeanInequalitiesPow.lean
index c11351d9785525..e07ad45e6921b3 100644
--- a/Mathlib/Analysis/MeanInequalitiesPow.lean
+++ b/Mathlib/Analysis/MeanInequalitiesPow.lean
@@ -118,8 +118,8 @@ theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0) {p : ℝ} (hp : 1 
     (z₁ + z₂) ^ p ≤ (2 : ℝ≥0) ^ (p - 1) * (z₁ ^ p + z₂ ^ p) := by
   rcases eq_or_lt_of_le hp with (rfl | h'p)
   · simp only [rpow_one, sub_self, rpow_zero, one_mul]; rfl
-  convert rpow_arith_mean_le_arith_mean2_rpow (1 / 2) (1 / 2) (2 * z₁) (2 * z₂) (add_halves 1) hp
-    using 1
+  convert!
+    rpow_arith_mean_le_arith_mean2_rpow (1 / 2) (1 / 2) (2 * z₁) (2 * z₂) (add_halves 1) hp using 1
   · simp only [one_div, inv_mul_cancel_left₀, Ne, two_ne_zero,
       not_false_iff]
   · have A : p - 1 ≠ 0 := ne_of_gt (sub_pos.2 h'p)
@@ -271,8 +271,9 @@ theorem rpow_arith_mean_le_arith_mean2_rpow (w₁ w₂ z₁ z₂ : ℝ≥0∞) (
 /-- Unweighted mean inequality, version for two elements of `ℝ≥0∞` and real exponents. -/
 theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0∞) {p : ℝ} (hp : 1 ≤ p) :
     (z₁ + z₂) ^ p ≤ (2 : ℝ≥0∞) ^ (p - 1) * (z₁ ^ p + z₂ ^ p) := by
-  convert rpow_arith_mean_le_arith_mean2_rpow (1 / 2) (1 / 2) (2 * z₁) (2 * z₂)
-      (ENNReal.add_halves 1) hp using 1
+  convert!
+    rpow_arith_mean_le_arith_mean2_rpow (1 / 2) (1 / 2) (2 * z₁) (2 * z₂) (ENNReal.add_halves 1) hp
+      using 1
   · simp [← mul_assoc, ENNReal.inv_mul_cancel two_ne_zero ofNat_ne_top]
   · simp only [mul_rpow_of_nonneg _ _ (zero_le_one.trans hp), rpow_sub _ _ two_ne_zero ofNat_ne_top,
       ENNReal.div_eq_inv_mul, rpow_one, mul_one]
@@ -365,7 +366,7 @@ theorem rpow_add_le_mul_rpow_add_rpow'' (z₁ z₂ : ℝ≥0∞) {p : ℝ≥0∞
       LpAddConst p * (z₁ ^ p.toReal⁻¹ + z₂ ^ p.toReal⁻¹) := by
   by_cases p_zero : p = 0
   · simp [p_zero, LpAddConst_zero]
-  convert rpow_add_le_mul_rpow_add_rpow' z₁ z₂ (p := p.toReal⁻¹) (by positivity) using 1
+  convert! rpow_add_le_mul_rpow_add_rpow' z₁ z₂ (p := p.toReal⁻¹) (by positivity) using 1
   rw [← ENNReal.toReal_inv, ENNReal.ofReal_toReal (by simpa), inv_inv]
 
 end ENNReal
diff --git a/Mathlib/Analysis/MellinTransform.lean b/Mathlib/Analysis/MellinTransform.lean
index aaf94516e55c1e..ec65cf9baa8f92 100644
--- a/Mathlib/Analysis/MellinTransform.lean
+++ b/Mathlib/Analysis/MellinTransform.lean
@@ -390,7 +390,7 @@ theorem mellin_hasDerivAt_of_isBigO_rpow [NormedSpace ℂ E] {a b : ℝ}
     refine (ae_restrict_mem measurableSet_Ioi).mono fun t ht y _ => ?_
     have ht' : (t : ℂ) ≠ 0 := ofReal_ne_zero.mpr (ne_of_gt ht)
     have u1 : HasDerivAt (fun z : ℂ => (t : ℂ) ^ (z - 1)) (t ^ (y - 1) * log t) y := by
-      convert ((hasDerivAt_id' y).sub_const 1).const_cpow (Or.inl ht') using 1
+      convert! ((hasDerivAt_id' y).sub_const 1).const_cpow (Or.inl ht') using 1
       rw [ofReal_log (le_of_lt ht)]
       ring
     exact u1.smul_const (f t)
diff --git a/Mathlib/Analysis/Meromorphic/Basic.lean b/Mathlib/Analysis/Meromorphic/Basic.lean
index 49c044035dba9c..2a85d8fa4af22c 100644
--- a/Mathlib/Analysis/Meromorphic/Basic.lean
+++ b/Mathlib/Analysis/Meromorphic/Basic.lean
@@ -90,7 +90,7 @@ lemma smul {f : 𝕜 → 𝕜} {g : 𝕜 → E} (hf : MeromorphicAt f x) (hg : M
   rcases hf with ⟨m, hf⟩
   rcases hg with ⟨n, hg⟩
   refine ⟨m + n, ?_⟩
-  convert hf.smul hg using 2 with z
+  convert! hf.smul hg using 2 with z
   simp
   module
 
@@ -100,7 +100,7 @@ lemma mul {f g : 𝕜 → 𝕜'} (hf : MeromorphicAt f x) (hg : MeromorphicAt g
   rcases hf with ⟨m, hf⟩
   rcases hg with ⟨n, hg⟩
   refine ⟨m + n, ?_⟩
-  convert hf.mul hg using 2 with z
+  convert! hf.mul hg using 2 with z
   simp
   module
 
@@ -122,7 +122,7 @@ theorem prod (hf : ∀ σ ∈ s, MeromorphicAt (F σ) x) :
 @[fun_prop]
 theorem fun_prod (h : ∀ σ ∈ s, MeromorphicAt (F σ) x) :
     MeromorphicAt (fun z ↦ ∏ n ∈ s, F n z) x := by
-  convert prod h (s := s)
+  convert! prod h (s := s)
   simp
 
 /-- Finprods of meromorphic functions are meromorphic. -/
@@ -151,7 +151,7 @@ theorem sum (h : ∀ σ ∈ s, MeromorphicAt (G σ) x) :
 @[fun_prop]
 theorem fun_sum (h : ∀ σ ∈ s, MeromorphicAt (G σ) x) :
     MeromorphicAt (fun z ↦ ∑ n ∈ s, G n z) x := by
-  convert sum h (s := s)
+  convert! sum h (s := s)
   simp
 
 /-- Finsums of meromorphic functions are meromorphic. -/
@@ -164,7 +164,7 @@ theorem finsum (hF : ∀ i, MeromorphicAt (F i) x) :
 
 @[to_fun (attr := fun_prop)]
 lemma neg {f : 𝕜 → E} (hf : MeromorphicAt f x) : MeromorphicAt (-f) x := by
-  convert (MeromorphicAt.const (-1 : 𝕜) x).smul hf using 1
+  convert! (MeromorphicAt.const (-1 : 𝕜) x).smul hf using 1
   ext1 z
   simp only [Pi.neg_apply, Pi.smul_apply', neg_smul, one_smul]
 
@@ -176,7 +176,7 @@ lemma neg_iff {f : 𝕜 → E} :
 @[to_fun (attr := fun_prop)]
 lemma sub {f g : 𝕜 → E} (hf : MeromorphicAt f x) (hg : MeromorphicAt g x) :
     MeromorphicAt (f - g) x := by
-  convert hf.add hg.neg using 1
+  convert! hf.add hg.neg using 1
   ext1 z
   simp_rw [Pi.sub_apply, Pi.add_apply, Pi.neg_apply, sub_eq_add_neg]
 
diff --git a/Mathlib/Analysis/Meromorphic/Divisor.lean b/Mathlib/Analysis/Meromorphic/Divisor.lean
index d11d81dd6dd08f..f012314865d5ab 100644
--- a/Mathlib/Analysis/Meromorphic/Divisor.lean
+++ b/Mathlib/Analysis/Meromorphic/Divisor.lean
@@ -180,7 +180,7 @@ The divisor of a constant function is `0`.
 -/
 @[simp] theorem divisor_ofNat (n : ℕ) :
     divisor (ofNat(n) : 𝕜 → 𝕜) U = 0 := by
-  convert divisor_const (n : 𝕜)
+  convert! divisor_const (n : 𝕜)
   simp [Semiring.toGrindSemiring_ofNat 𝕜 n]
 
 /-!
@@ -318,7 +318,7 @@ theorem divisor_fun_prod {ι : Type*} {s : Finset ι} {f : ι → 𝕜 → 𝕜}
     (h₁f : ∀ i ∈ s, MeromorphicOn (f i) U)
     (h₂f : ∀ i ∈ s, ∀ z ∈ U, meromorphicOrderAt (f i) z ≠ ⊤) :
     divisor (fun x ↦ ∏ i ∈ s, f i x) U = ∑ i ∈ s, divisor (f i) U := by
-  convert divisor_prod h₁f h₂f
+  convert! divisor_prod h₁f h₂f
   exact (Finset.prod_apply _ s f).symm
 
 /-- The divisor of the inverse is the negative of the divisor. -/
diff --git a/Mathlib/Analysis/Meromorphic/NormalForm.lean b/Mathlib/Analysis/Meromorphic/NormalForm.lean
index c740a4f9fff20e..75c430a7f71f17 100644
--- a/Mathlib/Analysis/Meromorphic/NormalForm.lean
+++ b/Mathlib/Analysis/Meromorphic/NormalForm.lean
@@ -297,7 +297,7 @@ theorem meromorphicNFAt_fun_prod {x : 𝕜} {ι : Type*} {s : Finset ι} {f : ι
     (h₁f : ∀ i ∈ s, MeromorphicNFAt (f i) x)
     (h₂f : Set.Subsingleton {σ ∈ s | f σ x = 0}) :
     MeromorphicNFAt (fun a ↦ ∏ i ∈ s, f i a) x := by
-  convert meromorphicNFAt_prod h₁f h₂f
+  convert! meromorphicNFAt_prod h₁f h₂f
   exact (Finset.prod_apply _ s f).symm
 
 /--
@@ -610,7 +610,7 @@ theorem meromorphicNFOn_fun_prod {ι : Type*} {s : Finset ι} {f : ι → 𝕜 
     (h₁f : ∀ i ∈ s, MeromorphicNFOn (f i) U)
     (h₂f : ∀ x ∈ U, Set.Subsingleton {σ ∈ s | f σ x = 0}) :
     MeromorphicNFOn (fun x ↦ ∏ i ∈ s, f i x) U := by
-  convert meromorphicNFOn_prod h₁f h₂f
+  convert! meromorphicNFOn_prod h₁f h₂f
   exact (Finset.prod_apply _ s f).symm
 
 /--
diff --git a/Mathlib/Analysis/Meromorphic/Order.lean b/Mathlib/Analysis/Meromorphic/Order.lean
index 00c76cd85b7062..6b1d596151a53e 100644
--- a/Mathlib/Analysis/Meromorphic/Order.lean
+++ b/Mathlib/Analysis/Meromorphic/Order.lean
@@ -358,7 +358,7 @@ The order of a constant function is `⊤` if the constant is zero and `0` otherw
 -/
 @[simp] theorem meromorphicOrderAt_const_ofNat (z₀ : 𝕜) (n : ℕ) [Decidable ((n : 𝕜) = 0)] :
     meromorphicOrderAt (ofNat(n) : 𝕜 → 𝕜) z₀ = if (n : 𝕜) = 0 then ⊤ else (0 : WithTop ℤ) := by
-  convert meromorphicOrderAt_const z₀ (n : 𝕜)
+  convert! meromorphicOrderAt_const z₀ (n : 𝕜)
   simp [Semiring.toGrindSemiring_ofNat 𝕜 n]
 
 /-- The order of `(· - x) ^ n` at `x` is `n`. -/
@@ -370,7 +370,7 @@ The order of a constant function is `⊤` if the constant is zero and `0` otherw
 /-- The order of `(· - x) ^ n` at `x` is `n`. -/
 @[simp, to_fun] theorem meromorphicOrderAt_pow_id_sub_const {n : ℕ} :
     meromorphicOrderAt ((· - x) ^ n) x = n := by
-  convert meromorphicOrderAt_zpow_id_sub_const
+  convert! meromorphicOrderAt_zpow_id_sub_const
   simp only [zpow_natCast]
 
 /-- The order of `· - x` at `x` is `1`. -/
@@ -456,7 +456,7 @@ The order is additive in products of meromorphic functions.
 theorem meromorphicOrderAt_fun_prod {x : 𝕜} {ι : Type*} {s : Finset ι} {f : ι → 𝕜 → 𝕜}
     (hf : ∀ i ∈ s, MeromorphicAt (f i) x) :
     meromorphicOrderAt (fun a ↦ ∏ i ∈ s, f i a) x = ∑ i ∈ s, meromorphicOrderAt (f i) x := by
-  convert meromorphicOrderAt_prod hf
+  convert! meromorphicOrderAt_prod hf
   exact (Finset.prod_apply _ s f).symm
 
 /-- The order multiplies by `n` when taking a meromorphic function to its `n`th power. -/
@@ -792,8 +792,9 @@ function has zero or infinite order is codiscrete within its domain of meromorph
 theorem codiscreteWithin_setOf_meromorphicOrderAt_eq_zero_or_top (h₁f : MeromorphicOn f U)
     (h₂f : ∀ u ∈ U, meromorphicOrderAt f u ≠ ⊤) :
     {u ∈ U | meromorphicOrderAt f u = 0 ∨ meromorphicOrderAt f u = ⊤} ∈ codiscreteWithin U := by
-  convert mem_codiscrete_subtype_iff_mem_codiscreteWithin.1
-    h₁f.codiscrete_setOf_meromorphicOrderAt_eq_zero_or_top
+  convert!
+    mem_codiscrete_subtype_iff_mem_codiscreteWithin.1
+      h₁f.codiscrete_setOf_meromorphicOrderAt_eq_zero_or_top
   aesop
 
 end MeromorphicOn
diff --git a/Mathlib/Analysis/Meromorphic/TrailingCoefficient.lean b/Mathlib/Analysis/Meromorphic/TrailingCoefficient.lean
index 459e144ce25152..7a830cde3f2de0 100644
--- a/Mathlib/Analysis/Meromorphic/TrailingCoefficient.lean
+++ b/Mathlib/Analysis/Meromorphic/TrailingCoefficient.lean
@@ -432,7 +432,7 @@ theorem meromorphicTrailingCoeffAt_fun_prod {ι : Type*} {s : Finset ι} {f : ι
     {x : 𝕜} (h : ∀ σ ∈ s, MeromorphicAt (f σ) x) :
     meromorphicTrailingCoeffAt (fun z ↦ ∏ n ∈ s, f n z) x
       = ∏ n ∈ s, meromorphicTrailingCoeffAt (f n) x := by
-  convert meromorphicTrailingCoeffAt_prod h
+  convert! meromorphicTrailingCoeffAt_prod h
   simp
 
 /--
@@ -495,7 +495,7 @@ The trailing coefficient of the power of a function is the power of the trailing
 lemma MeromorphicAt.meromorphicTrailingCoeffAt_pow {n : ℕ} {f : 𝕜 → 𝕜}
     (h₁ : MeromorphicAt f x) :
     meromorphicTrailingCoeffAt (f ^ n) x = (meromorphicTrailingCoeffAt f x) ^ n := by
-  convert h₁.meromorphicTrailingCoeffAt_zpow (n := n) <;> simp
+  convert! h₁.meromorphicTrailingCoeffAt_zpow (n := n) <;> simp
 
 /--
 The trailing coefficient of the power of a function is the power of the trailing coefficient.
diff --git a/Mathlib/Analysis/Normed/Affine/Isometry.lean b/Mathlib/Analysis/Normed/Affine/Isometry.lean
index ec549fa8c0989e..4c7b87b6630837 100644
--- a/Mathlib/Analysis/Normed/Affine/Isometry.lean
+++ b/Mathlib/Analysis/Normed/Affine/Isometry.lean
@@ -745,7 +745,7 @@ include 𝕜 in
 is an isometry if `f` is one. -/
 theorem vadd_vsub {f : P → P₂} (hf : Isometry f) {p : P} {g : V → V₂}
     (hg : ∀ v, g v = f (v +ᵥ p) -ᵥ f p) : Isometry g := by
-  convert (vaddConst 𝕜 (f p)).symm.isometry.comp (hf.comp (vaddConst 𝕜 p).isometry)
+  convert! (vaddConst 𝕜 (f p)).symm.isometry.comp (hf.comp (vaddConst 𝕜 p).isometry)
   exact funext hg
 
 variable (𝕜) in
diff --git a/Mathlib/Analysis/Normed/Affine/Simplex.lean b/Mathlib/Analysis/Normed/Affine/Simplex.lean
index ad3c73ffb4f6bd..ea42a187843e1d 100644
--- a/Mathlib/Analysis/Normed/Affine/Simplex.lean
+++ b/Mathlib/Analysis/Normed/Affine/Simplex.lean
@@ -70,7 +70,7 @@ lemma Scalene.dist_ne {s : Simplex R P n} (hs : s.Scalene) {i₁ i₂ i₃ i₄
      by grind,
      by grind⟩
   simp_rw [Scalene]
-  convert (Injective.of_comp_iff' _ (Equiv.bijective f)).symm
+  convert! (Injective.of_comp_iff' _ (Equiv.bijective f)).symm
   #adaptation_note /-- Before https://github.com/leanprover/lean4/pull/13166
   (replacing grind's canonicalizer with a type-directed normalizer), `grind` closed this goal.
   It is not yet clear whether this is due to defeq abuse in Mathlib or a problem in the new
@@ -92,8 +92,8 @@ lemma Equilateral.dist_eq {s : Simplex R P n} (he : s.Equilateral) {i₁ i₂ i
 @[simp] lemma equilateral_reindex_iff {s : Simplex R P m} (e : Fin (m + 1) ≃ Fin (n + 1)) :
     (s.reindex e).Equilateral ↔ s.Equilateral := by
   refine ⟨fun ⟨r, hr⟩ ↦ ⟨r, fun i j hij ↦ ?_⟩, fun ⟨r, hr⟩ ↦ ⟨r, fun i j hij ↦ ?_⟩⟩
-  · convert hr (e i) (e j) (e.injective.ne hij) using 2 <;> simp
-  · convert hr (e.symm i) (e.symm j) (e.symm.injective.ne hij) using 2
+  · convert! hr (e i) (e j) (e.injective.ne hij) using 2 <;> simp
+  · convert! hr (e.symm i) (e.symm j) (e.symm.injective.ne hij) using 2
 
 /-- A simplex is regular if it is equivalent under an isometry to any reindexing. -/
 def Regular (s : Simplex R P n) : Prop :=
@@ -120,13 +120,13 @@ lemma Regular.equilateral {s : Simplex R P n} (hr : s.Regular) : s.Equilateral :
     nth_rw 2 [← x.dist_eq]
     simp_rw [← Function.comp_apply (f := x), ← hx]
     simp only [comp_apply, Equiv.swap_apply_left]
-    convert rfl
+    convert! rfl
     rw [Equiv.swap_apply_of_ne_of_ne (by simp [hn]) (by lia)]
   · rcases hr ((Equiv.swap 0 i).trans (Equiv.swap 1 j)) with ⟨x, hx⟩
     nth_rw 2 [← x.dist_eq]
     simp_rw [← Function.comp_apply (f := x), ← hx]
     simp only [Equiv.coe_trans, comp_apply, Equiv.swap_apply_left]
-    convert rfl
+    convert! rfl
     · exact Equiv.swap_apply_of_ne_of_ne hi hij
     · rw [Equiv.swap_apply_of_ne_of_ne (by simp [hn]) (Ne.symm hi)]
       simp
diff --git a/Mathlib/Analysis/Normed/Algebra/Exponential.lean b/Mathlib/Analysis/Normed/Algebra/Exponential.lean
index 9bd381749db9eb..68a0c3a11a0f61 100644
--- a/Mathlib/Analysis/Normed/Algebra/Exponential.lean
+++ b/Mathlib/Analysis/Normed/Algebra/Exponential.lean
@@ -377,7 +377,7 @@ theorem isUnit_exp_of_mem_ball [CharZero 𝕂] {x : 𝔸}
 theorem invOf_exp_of_mem_ball [CharZero 𝕂] {x : 𝔸}
     (hx : x ∈ Metric.eball (0 : 𝔸) (expSeries 𝕂 𝔸).radius) [Invertible (exp x)] :
     ⅟(exp x) = exp (-x) := by
-  letI := invertibleExpOfMemBall hx; convert (rfl : ⅟(exp x) = _)
+  letI := invertibleExpOfMemBall hx; convert! (rfl : ⅟(exp x) = _)
 
 /-- Any continuous ring homomorphism commutes with `NormedSpace.exp`. -/
 theorem map_exp_of_mem_ball [Algebra 𝕂 𝔹] [CharZero 𝕂] {F} [FunLike F 𝔸 𝔹] [RingHomClass F 𝔸 𝔹]
diff --git a/Mathlib/Analysis/Normed/Algebra/GelfandFormula.lean b/Mathlib/Analysis/Normed/Algebra/GelfandFormula.lean
index 4fb3b14ff21579..f0fa1372fb78e5 100644
--- a/Mathlib/Analysis/Normed/Algebra/GelfandFormula.lean
+++ b/Mathlib/Analysis/Normed/Algebra/GelfandFormula.lean
@@ -75,7 +75,7 @@ end NonTriviallyNormedField
 theorem hasDerivAt_resolvent_const_right [NontriviallyNormedField 𝕜] [NontriviallyNormedField A]
     [NormedAlgebra 𝕜 A] [CompleteSpace A] {a : A} {k : 𝕜} (hk : k ∈ resolventSet 𝕜 a) :
     HasDerivAt (resolvent · k) (resolvent a k ^ 2) a := by
-  convert hasFDerivAt_resolvent (𝕜 := A) hk |>.hasDerivAt
+  convert! hasFDerivAt_resolvent (𝕜 := A) hk |>.hasDerivAt
   simp [resolvent, pow_two]
 
 open ENNReal in
@@ -107,7 +107,7 @@ theorem limsup_pow_nnnorm_pow_one_div_le_spectralRadius (a : A) :
   let p : FormalMultilinearSeries ℂ ℂ A := fun n =>
     ContinuousMultilinearMap.mkPiRing ℂ (Fin n) (a ^ n)
   suffices h : (r : ℝ≥0∞) ≤ p.radius by
-    convert h
+    convert! h
     simp only [p, p.radius_eq_liminf, ← norm_toNNReal, norm_mkPiRing]
     congr
     ext n
@@ -133,7 +133,7 @@ instead of `nnnorm`. -/
 theorem pow_norm_pow_one_div_tendsto_nhds_spectralRadius (a : A) :
     Tendsto (fun n : ℕ => ENNReal.ofReal (‖a ^ n‖ ^ (1 / n : ℝ))) atTop
       (𝓝 (spectralRadius ℂ a)) := by
-  convert pow_nnnorm_pow_one_div_tendsto_nhds_spectralRadius a using 1
+  convert! pow_nnnorm_pow_one_div_tendsto_nhds_spectralRadius a using 1
   ext1
   rw [← ofReal_rpow_of_nonneg (norm_nonneg _) _, ← coe_nnnorm, coe_nnreal_eq]
   simp
diff --git a/Mathlib/Analysis/Normed/Algebra/GelfandMazur.lean b/Mathlib/Analysis/Normed/Algebra/GelfandMazur.lean
index 62ccf26cb8650f..a01ba8752906a8 100644
--- a/Mathlib/Analysis/Normed/Algebra/GelfandMazur.lean
+++ b/Mathlib/Analysis/Normed/Algebra/GelfandMazur.lean
@@ -394,7 +394,7 @@ lemma exists_isMonicOfDegree_two_and_aeval_eq_zero (x : F) :
   have h' (r : ℝ) : √M ≤ ‖x - algebraMap ℝ F r‖ := by
     rw [← sq_le_sq₀ M.sqrt_nonneg (norm_nonneg _), Real.sq_sqrt (norm_nonneg _), ← norm_pow,
       Commute.sub_sq <| algebraMap_eq_smul_one (A := F) r ▸ commute_algebraMap_right r x]
-    convert isMinOn_univ_iff.mp h (2 * r, r ^ 2) using 4 <;>
+    convert! isMinOn_univ_iff.mp h (2 * r, r ^ 2) using 4 <;>
       simp [two_mul, add_mul, ← commutes, smul_def, mul_add]
   have := tendsto_norm_atTop_iff_cobounded.mpr <| tendsto_φ_cobounded (by positivity) h'
   simp only [norm_φ_eq_norm_φ_of_isMinOn h (norm_ne_zero_iff.mpr H)] at this
diff --git a/Mathlib/Analysis/Normed/Algebra/QuaternionExponential.lean b/Mathlib/Analysis/Normed/Algebra/QuaternionExponential.lean
index e2c6cc5a027e3e..a9da2d7116e7fc 100644
--- a/Mathlib/Analysis/Normed/Algebra/QuaternionExponential.lean
+++ b/Mathlib/Analysis/Normed/Algebra/QuaternionExponential.lean
@@ -87,10 +87,10 @@ theorem hasSum_expSeries_of_imaginary {q : Quaternion ℝ} (hq : q.re = 0) {c s
   replace hc := hasSum_coe.mpr hc
   replace hs := (hs.div_const ‖q‖).smul_const q
   refine HasSum.even_add_odd ?_ ?_
-  · convert hc using 1
+  · convert! hc using 1
     ext n : 1
     rw [expSeries_even_of_imaginary hq]
-  · convert hs using 1
+  · convert! hs using 1
     ext n : 1
     rw [expSeries_odd_of_imaginary hq]
 
diff --git a/Mathlib/Analysis/Normed/Algebra/Spectrum.lean b/Mathlib/Analysis/Normed/Algebra/Spectrum.lean
index 7092d45ca1c739..2dfce7ecbc61eb 100644
--- a/Mathlib/Analysis/Normed/Algebra/Spectrum.lean
+++ b/Mathlib/Analysis/Normed/Algebra/Spectrum.lean
@@ -254,7 +254,7 @@ theorem spectralRadius_le_pow_nnnorm_pow_one_div (a : A) (n : ℕ) :
       ENNReal.coe_mul] using coe_mono (Real.toNNReal_mono (norm_le_norm_mul_of_mem pow_mem))
   -- take (n + 1)ᵗʰ roots and clean up the left-hand side
   have hn : 0 < ((n + 1 : ℕ) : ℝ) := mod_cast Nat.succ_pos'
-  convert monotone_rpow_of_nonneg (one_div_pos.mpr hn).le nnnorm_pow_le using 1
+  convert! monotone_rpow_of_nonneg (one_div_pos.mpr hn).le nnnorm_pow_le using 1
   all_goals dsimp
   · rw [one_div, pow_rpow_inv_natCast]
     positivity
@@ -389,7 +389,7 @@ theorem exp_mem_exp [RCLike 𝕜] [NormedRing A] [NormedAlgebra 𝕜 A] [Complet
     simpa only [pow_succ, Algebra.smul_mul_assoc] using hb.tsum_mul_right (a - ↑ₐ z)
   have h₃ : exp (a - ↑ₐ z) = 1 + (a - ↑ₐ z) * b := by
     rw [exp_eq_tsum 𝕜]
-    convert (expSeries_summable' (𝕂 := 𝕜) (a - ↑ₐ z)).tsum_eq_zero_add
+    convert! (expSeries_summable' (𝕂 := 𝕜) (a - ↑ₐ z)).tsum_eq_zero_add
     · simp only [Nat.factorial_zero, Nat.cast_one, inv_one, pow_zero, one_smul]
     · exact h₀.symm
   rw [spectrum.mem_iff, IsUnit.sub_iff, ← one_mul (↑ₐ (exp z)), hexpmul, ← _root_.sub_mul,
@@ -658,7 +658,7 @@ lemma _root_.NNReal.spectralRadius_mem_spectrum {A : Type*} [NormedRing A] [Norm
   obtain ⟨x, hx₁, hx₂⟩ := spectrum.exists_nnnorm_eq_spectralRadius_of_nonempty ha
   rw [← hx₂, ENNReal.toNNReal_coe, ← spectrum.algebraMap_mem_iff ℝ, NNReal.algebraMap_eq_coe]
   have : 0 ≤ x := ha'.rightInvOn hx₁ ▸ NNReal.zero_le_coe
-  convert hx₁
+  convert! hx₁
   simpa
 
 lemma _root_.Real.spectralRadius_mem_spectrum {A : Type*} [NormedRing A] [NormedAlgebra ℝ A]
@@ -733,8 +733,9 @@ theorem upperHemicontinuous_quasispectrum [NontriviallyNormedField 𝕜] [Proper
     [NonUnitalNormedRing A] [NormedSpace 𝕜 A] [SMulCommClass 𝕜 A A] [IsScalarTower 𝕜 A A]
     [CompleteSpace A] :
     UpperHemicontinuous (quasispectrum 𝕜 : A → Set 𝕜) := by
-  convert upperHemicontinuous_spectrum 𝕜 (WithLp 1 (Unitization 𝕜 A)) |>.comp
-    unitization_isometry_inr.continuous
+  convert!
+    upperHemicontinuous_spectrum 𝕜 (WithLp 1 (Unitization 𝕜 A)) |>.comp
+      unitization_isometry_inr.continuous
   ext1 a
   rw [Unitization.quasispectrum_eq_spectrum_inr,
     ← AlgEquiv.spectrum_eq (unitizationAlgEquiv 𝕜 (𝕜 := 𝕜) (A := A) |>.symm)]
diff --git a/Mathlib/Analysis/Normed/Field/Approximation.lean b/Mathlib/Analysis/Normed/Field/Approximation.lean
index 97598f2c22f3aa..45800411ce9a60 100644
--- a/Mathlib/Analysis/Normed/Field/Approximation.lean
+++ b/Mathlib/Analysis/Normed/Field/Approximation.lean
@@ -78,7 +78,7 @@ theorem exists_roots_norm_sub_lt_of_norm_coeff_sub_lt (hε : 0 < ε) {a : K} (ha
     congr
     rw [hg.eval_eq_prod_roots_of_monic hgm]
   _ ≤ ‖g.eval a - f.eval a‖ + ‖f.eval a‖ := by
-    convert norm_add_le (g.eval a - f.eval a) (f.eval a)
+    convert! norm_add_le (g.eval a - f.eval a) (f.eval a)
     simp
   _ = ‖(∑ i ∈ Finset.range (g.natDegree + 1), C (g.coeff i - f.coeff i) * X ^ i).eval a‖ := by
     rw [← eval_sub]
@@ -96,7 +96,8 @@ theorem exists_roots_norm_sub_lt_of_norm_coeff_sub_lt (hε : 0 < ε) {a : K} (ha
     --     (fun i ↦ (C (g.coeff i - f.coeff i) * X ^ i).eval a)
   _ < _ := by
     rw [hdeg]
-    convert Finset.sum_lt_sum_of_nonempty (g := fun i ↦ ε * (‖a‖ ⊔ 1) ^ ↑f.natDegree)
+    convert!
+      Finset.sum_lt_sum_of_nonempty (g := fun i ↦ ε * (‖a‖ ⊔ 1) ^ ↑f.natDegree)
         (Finset.nonempty_range_add_one) ?_
     · simp [mul_assoc]
     · simp only [Finset.mem_range, norm_mul, norm_pow]
diff --git a/Mathlib/Analysis/Normed/Field/ProperSpace.lean b/Mathlib/Analysis/Normed/Field/ProperSpace.lean
index ae5e6929671483..22555e6cc03fcc 100644
--- a/Mathlib/Analysis/Normed/Field/ProperSpace.lean
+++ b/Mathlib/Analysis/Normed/Field/ProperSpace.lean
@@ -41,7 +41,7 @@ lemma ProperSpace.of_nontriviallyNormedField_of_weaklyLocallyCompactSpace
   rcases NormedField.exists_one_lt_norm 𝕜 with ⟨c, hc⟩
   have hC n : IsCompact (closedBall (0 : 𝕜) (‖c‖ ^ n * r)) := by
     have : c ^ n ≠ 0 := pow_ne_zero _ <| fun h ↦ by simp [h, zero_le_one.not_gt] at hc
-    convert hr.smul (c ^ n)
+    convert! hr.smul (c ^ n)
     ext
     simp only [mem_closedBall, dist_zero_right, Set.mem_smul_set_iff_inv_smul_mem₀ this,
       smul_eq_mul, norm_mul, norm_inv, norm_pow,
diff --git a/Mathlib/Analysis/Normed/Field/UnitBall.lean b/Mathlib/Analysis/Normed/Field/UnitBall.lean
index eb78b31718b9ce..99252ea7420fb0 100644
--- a/Mathlib/Analysis/Normed/Field/UnitBall.lean
+++ b/Mathlib/Analysis/Normed/Field/UnitBall.lean
@@ -248,7 +248,7 @@ theorem unitSphereToUnits_apply_coe [NormedDivisionRing 𝕜] (x : sphere (0 : 
 
 theorem unitSphereToUnits_injective [NormedDivisionRing 𝕜] :
     Function.Injective (unitSphereToUnits 𝕜) := fun x y h =>
-  Subtype.ext <| by convert congr_arg Units.val h
+  Subtype.ext <| by convert! congr_arg Units.val h
 
 instance Metric.unitSphere.instGroup [NormedDivisionRing 𝕜] : Group (sphere (0 : 𝕜) 1) :=
   fast_instance% unitSphereToUnits_injective.group (unitSphereToUnits 𝕜) (Units.ext rfl)
diff --git a/Mathlib/Analysis/Normed/Group/Basic.lean b/Mathlib/Analysis/Normed/Group/Basic.lean
index a84822245f2c57..d5944a5ed57882 100644
--- a/Mathlib/Analysis/Normed/Group/Basic.lean
+++ b/Mathlib/Analysis/Normed/Group/Basic.lean
@@ -352,7 +352,7 @@ theorem NormedGroup.nhds_basis_norm_lt (x : E) :
 @[to_additive]
 theorem NormedGroup.nhds_one_basis_norm_lt :
     (𝓝 (1 : E)).HasBasis (fun ε : ℝ => 0 < ε) fun ε => { y | ‖y‖ < ε } := by
-  convert NormedGroup.nhds_basis_norm_lt (1 : E) using 1
+  convert! NormedGroup.nhds_basis_norm_lt (1 : E) using 1
   simp
 
 @[deprecated (since := "2026-02-17")]
@@ -364,7 +364,7 @@ alias NormedAddCommGroup.nhds_zero_basis_norm_lt := NormedAddGroup.nhds_zero_bas
 @[to_additive]
 theorem NormedGroup.uniformity_basis_dist :
     (𝓤 E).HasBasis (fun ε : ℝ => 0 < ε) fun ε => { p : E × E | ‖p.fst⁻¹ * p.snd‖ < ε } := by
-  convert Metric.uniformity_basis_dist (α := E) using 1
+  convert! Metric.uniformity_basis_dist (α := E) using 1
   simp [dist_eq_norm_inv_mul]
 
 open Finset
diff --git a/Mathlib/Analysis/Normed/Group/Defs.lean b/Mathlib/Analysis/Normed/Group/Defs.lean
index 6e2caaeb22d910..986529b3cc34e4 100644
--- a/Mathlib/Analysis/Normed/Group/Defs.lean
+++ b/Mathlib/Analysis/Normed/Group/Defs.lean
@@ -410,8 +410,8 @@ abbrev GroupSeminorm.toSeminormedGroup [Group E] (f : GroupSeminorm E) : Seminor
   norm := f
   dist_eq _ _ := rfl
   dist_self x := by simp only [inv_mul_cancel, map_one_eq_zero]
-  dist_triangle x y z := by convert map_mul_le_add f (x⁻¹ * y) (y⁻¹ * z) using 2; group
-  dist_comm x y := by convert map_inv_eq_map f (y⁻¹ * x) using 2; group
+  dist_triangle x y z := by convert! map_mul_le_add f (x⁻¹ * y) (y⁻¹ * z) using 2; group
+  dist_comm x y := by convert! map_inv_eq_map f (y⁻¹ * x) using 2; group
 
 -- See note [reducible non-instances]
 /-- Construct a seminormed group from a seminorm, i.e., registering the pseudodistance and the
diff --git a/Mathlib/Analysis/Normed/Group/Pointwise.lean b/Mathlib/Analysis/Normed/Group/Pointwise.lean
index 3df8055aeac512..2bcb46700978cd 100644
--- a/Mathlib/Analysis/Normed/Group/Pointwise.lean
+++ b/Mathlib/Analysis/Normed/Group/Pointwise.lean
@@ -179,7 +179,7 @@ theorem smul_closedBall_one : x • closedBall (1 : E) δ = closedBall x δ := b
 @[to_additive]
 theorem mul_ball_one : s * ball 1 δ = thickening δ s := by
   rw [thickening_eq_biUnion_ball]
-  convert iUnion₂_mul (fun x (_ : x ∈ s) => {x}) (ball (1 : E) δ)
+  convert! iUnion₂_mul (fun x (_ : x ∈ s) => { x }) (ball (1 : E) δ)
   · exact s.biUnion_of_singleton.symm
   ext x
   simp_rw [singleton_mul_ball, mul_one]
diff --git a/Mathlib/Analysis/Normed/Group/SemiNormedGrp/Kernels.lean b/Mathlib/Analysis/Normed/Group/SemiNormedGrp/Kernels.lean
index c51708fdf40500..4366f50ec0c35c 100644
--- a/Mathlib/Analysis/Normed/Group/SemiNormedGrp/Kernels.lean
+++ b/Mathlib/Analysis/Normed/Group/SemiNormedGrp/Kernels.lean
@@ -193,7 +193,7 @@ set_option backward.isDefEq.respectTransparency false in
 @[reassoc (attr := simp)]
 theorem comp_explicitCokernelπ {X Y : SemiNormedGrp.{u}} (f : X ⟶ Y) :
     f ≫ explicitCokernelπ f = 0 := by
-  convert (cokernelCocone f).w WalkingParallelPairHom.left
+  convert! (cokernelCocone f).w WalkingParallelPairHom.left
   simp
 
 @[simp]
@@ -216,7 +216,7 @@ theorem explicitCokernelDesc_unique {X Y Z : SemiNormedGrp.{u}} {f : X ⟶ Y} {g
     e = explicitCokernelDesc w := by
   apply (isColimitCokernelCocone f).uniq (Cofork.ofπ g (by simp [w]))
   rintro (_ | _)
-  · convert w.symm
+  · convert! w.symm
     simp
   · exact he
 
diff --git a/Mathlib/Analysis/Normed/Group/Ultra.lean b/Mathlib/Analysis/Normed/Group/Ultra.lean
index 69447066f6860d..ce6c8c8133b2cc 100644
--- a/Mathlib/Analysis/Normed/Group/Ultra.lean
+++ b/Mathlib/Analysis/Normed/Group/Ultra.lean
@@ -61,7 +61,7 @@ lemma isUltrametricDist_of_isNonarchimedean_norm {S' : Type*} [SeminormedAddGrou
 lemma isNonarchimedean_norm {R} [SeminormedAddCommGroup R] [IsUltrametricDist R] :
     IsNonarchimedean (‖·‖ : R → ℝ) := by
   intro x y
-  convert dist_triangle_max 0 x (x + y) using 1
+  convert! dist_triangle_max 0 x (x + y) using 1
   · simp
   · congr <;> simp [SeminormedAddGroup.dist_eq]
 
diff --git a/Mathlib/Analysis/Normed/Lp/ProdLp.lean b/Mathlib/Analysis/Normed/Lp/ProdLp.lean
index c7940af3390717..42446607269ab1 100644
--- a/Mathlib/Analysis/Normed/Lp/ProdLp.lean
+++ b/Mathlib/Analysis/Normed/Lp/ProdLp.lean
@@ -184,7 +184,7 @@ variable {p α β}
 theorem prod_edist_eq_card (f g : WithLp 0 (α × β)) :
     edist f g =
       (if edist f.fst g.fst = 0 then 0 else 1) + (if edist f.snd g.snd = 0 then 0 else 1) := by
-  convert if_pos rfl
+  convert! if_pos rfl
 
 theorem prod_edist_eq_add (hp : 0 < p.toReal) (f g : WithLp p (α × β)) :
     edist f g = (edist f.fst g.fst ^ p.toReal + edist f.snd g.snd ^ p.toReal) ^ (1 / p.toReal) :=
@@ -251,7 +251,7 @@ variable {p α β}
 
 theorem prod_dist_eq_card (f g : WithLp 0 (α × β)) : dist f g =
     (if dist f.fst g.fst = 0 then 0 else 1) + (if dist f.snd g.snd = 0 then 0 else 1) := by
-  convert if_pos rfl
+  convert! if_pos rfl
 
 theorem prod_dist_eq_add (hp : 0 < p.toReal) (f g : WithLp p (α × β)) :
     dist f g = (dist f.fst g.fst ^ p.toReal + dist f.snd g.snd ^ p.toReal) ^ (1 / p.toReal) :=
@@ -288,7 +288,7 @@ variable {p α β}
 @[simp]
 theorem prod_norm_eq_card (f : WithLp 0 (α × β)) :
     ‖f‖ = (if ‖f.fst‖ = 0 then 0 else 1) + (if ‖f.snd‖ = 0 then 0 else 1) := by
-  convert if_pos rfl
+  convert! if_pos rfl
 
 theorem prod_norm_eq_sup (f : WithLp ∞ (α × β)) : ‖f‖ = ‖f.fst‖ ⊔ ‖f.snd‖ := rfl
 
diff --git a/Mathlib/Analysis/Normed/Lp/SmoothApprox.lean b/Mathlib/Analysis/Normed/Lp/SmoothApprox.lean
index 2fb2ad44aaaf50..aea9b538161c8f 100644
--- a/Mathlib/Analysis/Normed/Lp/SmoothApprox.lean
+++ b/Mathlib/Analysis/Normed/Lp/SmoothApprox.lean
@@ -105,7 +105,7 @@ theorem _root_.MeasureTheory.Lp.dense_hasCompactSupport_contDiff {p : ℝ≥0∞
   use ⟨g, hg₄.coeFn_toLp, hg₁, hg₂⟩
   rw [Metric.mem_closedBall, dist_comm, Lp.dist_def,
     ← le_ofReal_iff_toReal_le ((Lp.memLp f).sub (Lp.memLp hg₄.toLp)).eLpNorm_ne_top hε.le]
-  convert hg₃ using 1
+  convert! hg₃ using 1
   apply eLpNorm_congr_ae
   gcongr
   exact hg₄.coeFn_toLp
diff --git a/Mathlib/Analysis/Normed/Lp/lpSpace.lean b/Mathlib/Analysis/Normed/Lp/lpSpace.lean
index b3c6728b62dee5..515909235bb8db 100644
--- a/Mathlib/Analysis/Normed/Lp/lpSpace.lean
+++ b/Mathlib/Analysis/Normed/Lp/lpSpace.lean
@@ -587,7 +587,7 @@ theorem norm_apply_le_norm (hp : p ≠ 0) (f : lp E p) (i : α) : ‖f i‖ ≤
   have hp'' : 0 < p.toReal := ENNReal.toReal_pos hp hp'
   have : ∀ i, 0 ≤ ‖f i‖ ^ p.toReal := fun i ↦ by positivity
   rw [← Real.rpow_le_rpow_iff (norm_nonneg _) (norm_nonneg' _) hp'']
-  convert le_hasSum (hasSum_norm hp'' f) i fun i _ => this i
+  convert! le_hasSum (hasSum_norm hp'' f) i fun i _ => this i
 
 lemma lipschitzWith_one_eval (p : ℝ≥0∞) [Fact (1 ≤ p)] (i : α) :
     LipschitzWith 1 (fun x : lp E p ↦ x i) :=
diff --git a/Mathlib/Analysis/Normed/Module/Alternating/Basic.lean b/Mathlib/Analysis/Normed/Module/Alternating/Basic.lean
index 363541833fd6b1..b66cdf9d425823 100644
--- a/Mathlib/Analysis/Normed/Module/Alternating/Basic.lean
+++ b/Mathlib/Analysis/Normed/Module/Alternating/Basic.lean
@@ -470,7 +470,7 @@ def fderivCompContinuousLinearMap (f : F [⋀^ι]→L[𝕜] G) (g : E →L[𝕜]
     trans ∑ i, f fun j ↦ Function.update (fun _ ↦ g) i dg j (v j)
     · simp
     · rw [← Finset.sum_add_sum_compl {a, b}, Finset.sum_pair hne, Finset.sum_eq_zero, add_zero]
-      · convert f.map_add_swap _ hne with i
+      · convert! f.map_add_swap _ hne with i
         rcases eq_or_ne i a with rfl | hia
         · simp [heq, hne, hne.symm]
         · rcases eq_or_ne i b with rfl | hib
diff --git a/Mathlib/Analysis/Normed/Module/Connected.lean b/Mathlib/Analysis/Normed/Module/Connected.lean
index 85ed8cf12cd5e9..d6856e77058738 100644
--- a/Mathlib/Analysis/Normed/Module/Connected.lean
+++ b/Mathlib/Analysis/Normed/Module/Connected.lean
@@ -91,7 +91,7 @@ theorem Set.Countable.isPathConnected_compl_of_one_lt_rank
     rw [sub_eq_add_neg _ x]
     apply Eq.subset
     apply segment_inter_eq_endpoint_of_linearIndependent_of_ne _ htt'.symm
-    convert hy.units_smul ![-1, 1]
+    convert! hy.units_smul ![-1, 1]
     simp [← List.ofFn_inj]
   obtain ⟨t, ht⟩ : Set.Nonempty ({t : ℝ | ([c + x -[ℝ] c + t • y] ∩ s).Nonempty}
       ∪ {t : ℝ | ([c - x -[ℝ] c + t • y] ∩ s).Nonempty})ᶜ := ((A.union B).dense_compl ℝ).nonempty
@@ -101,12 +101,12 @@ theorem Set.Countable.isPathConnected_compl_of_one_lt_rank
   have JA : JoinedIn sᶜ a z := by
     apply JoinedIn.of_segment_subset
     rw [subset_compl_iff_disjoint_right, disjoint_iff_inter_eq_empty]
-    convert ht.2
+    convert! ht.2
     exact Ia.symm
   have JB : JoinedIn sᶜ b z := by
     apply JoinedIn.of_segment_subset
     rw [subset_compl_iff_disjoint_right, disjoint_iff_inter_eq_empty]
-    convert ht.1
+    convert! ht.1
     exact Ib.symm
   exact JA.trans JB.symm
 
diff --git a/Mathlib/Analysis/Normed/Module/FiniteDimension.lean b/Mathlib/Analysis/Normed/Module/FiniteDimension.lean
index 70ba4db566859a..0d54ddcd0b9400 100644
--- a/Mathlib/Analysis/Normed/Module/FiniteDimension.lean
+++ b/Mathlib/Analysis/Normed/Module/FiniteDimension.lean
@@ -644,8 +644,10 @@ theorem summable_norm_mul_geometric_of_norm_lt_one' {F : Type*} [NormedRing F]
       simpa [Nat.cast_pow] using
       (isBigO_norm_left.mpr (isBigO_norm_right.mpr hu)).mul (isBigO_refl (fun n ↦ (‖r‖ ^ n)) atTop)
   _ =O[atTop] fun n ↦ ‖r' ^ n‖ := by
-      convert isBigO_norm_right.mpr (isBigO_norm_left.mpr
-        (isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt k hrr').isBigO)
+      convert!
+        isBigO_norm_right.mpr
+          (isBigO_norm_left.mpr
+            (isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt k hrr').isBigO)
       simp only [norm_pow, norm_mul]
 
 theorem summable_of_isEquivalent {ι E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]
diff --git a/Mathlib/Analysis/Normed/Module/MStructure.lean b/Mathlib/Analysis/Normed/Module/MStructure.lean
index a07d3c7f5337d2..7550374313cde0 100644
--- a/Mathlib/Analysis/Normed/Module/MStructure.lean
+++ b/Mathlib/Analysis/Normed/Module/MStructure.lean
@@ -155,7 +155,7 @@ theorem mul [FaithfulSMul M X] {P Q : M} (h₁ : IsLprojection X P) (h₂ : IsLp
 
 theorem join [FaithfulSMul M X] {P Q : M} (h₁ : IsLprojection X P) (h₂ : IsLprojection X Q) :
     IsLprojection X (P + Q - P * Q) := by
-  convert (Lcomplement_iff _).mp (h₁.Lcomplement.mul h₂.Lcomplement) using 1
+  convert! (Lcomplement_iff _).mp (h₁.Lcomplement.mul h₂.Lcomplement) using 1
   noncomm_ring
 
 instance Subtype.instCompl : Compl { f : M // IsLprojection X f } :=
@@ -196,7 +196,7 @@ instance Subtype.partialOrder [FaithfulSMul M X] :
   le_trans P Q R h₁ h₂ := by
     simp only [coe_inf] at h₁ h₂ ⊢
     rw [h₁, mul_assoc, ← h₂]
-  le_antisymm P Q h₁ h₂ := Subtype.ext (by convert (P.prop.commute Q.prop).eq)
+  le_antisymm P Q h₁ h₂ := Subtype.ext (by convert! (P.prop.commute Q.prop).eq)
 
 theorem le_def [FaithfulSMul M X] (P Q : { P : M // IsLprojection X P }) :
     P ≤ Q ↔ (P : M) = ↑(P ⊓ Q) :=
diff --git a/Mathlib/Analysis/Normed/Module/Multilinear/Basic.lean b/Mathlib/Analysis/Normed/Module/Multilinear/Basic.lean
index d9d2341dcdbd71..d4eeb3d24b5df3 100644
--- a/Mathlib/Analysis/Normed/Module/Multilinear/Basic.lean
+++ b/Mathlib/Analysis/Normed/Module/Multilinear/Basic.lean
@@ -240,7 +240,7 @@ theorem norm_image_sub_le_of_bound' [DecidableEq ι] (f : MultilinearMap 𝕜 E
           (add_le_add Hrec I)
         _ = C * ∑ i ∈ insert i s, ∏ j, if j = i then ‖m₁ i - m₂ i‖ else max ‖m₁ j‖ ‖m₂ j‖ := by
           simp [his, add_comm, left_distrib]
-  convert A univ
+  convert! A univ
   simp
 
 /-- If `f` satisfies a boundedness property around `0`, one can deduce a bound on `f m₁ - f m₂`
@@ -313,11 +313,11 @@ theorem restr_norm_le {k n : ℕ} (f : MultilinearMap 𝕜 (fun _ : Fin n => G)
     (s : Finset (Fin n)) (hk : #s = k) (z : G) {C : ℝ} (H : ∀ m, ‖f m‖ ≤ C * ∏ i, ‖m i‖)
     (v : Fin k → G) : ‖f.restr s hk z v‖ ≤ C * ‖z‖ ^ (n - k) * ∏ i, ‖v i‖ := by
   rw [mul_right_comm, mul_assoc]
-  convert H _ using 2
+  convert! H _ using 2
   simp only [apply_dite norm, Fintype.prod_dite, prod_const ‖z‖, Finset.card_univ,
     Fintype.card_of_subtype sᶜ fun _ => mem_compl, card_compl, Fintype.card_fin, hk, ←
     (s.orderIsoOfFin hk).symm.bijective.prod_comp fun x => ‖v x‖]
-  convert rfl
+  convert! rfl
 
 end MultilinearMap
 
@@ -718,7 +718,7 @@ theorem norm_mkPiAlgebra_of_empty [IsEmpty ι] :
     ‖ContinuousMultilinearMap.mkPiAlgebra 𝕜 ι A‖ = ‖(1 : A)‖ := by
   apply le_antisymm
   · apply opNorm_le_bound <;> simp
-  · convert ratio_le_opNorm (ContinuousMultilinearMap.mkPiAlgebra 𝕜 ι A) fun _ => 1
+  · convert! ratio_le_opNorm (ContinuousMultilinearMap.mkPiAlgebra 𝕜 ι A) fun _ => 1
     simp
 
 @[simp]
@@ -726,7 +726,7 @@ theorem norm_mkPiAlgebra [NormOneClass A] : ‖ContinuousMultilinearMap.mkPiAlge
   cases isEmpty_or_nonempty ι
   · simp [norm_mkPiAlgebra_of_empty]
   · refine le_antisymm norm_mkPiAlgebra_le ?_
-    convert ratio_le_opNorm (ContinuousMultilinearMap.mkPiAlgebra 𝕜 ι A) fun _ => 1
+    convert! ratio_le_opNorm (ContinuousMultilinearMap.mkPiAlgebra 𝕜 ι A) fun _ => 1
     simp
 
 end
@@ -753,7 +753,7 @@ theorem norm_mkPiAlgebraFin_zero : ‖ContinuousMultilinearMap.mkPiAlgebraFin 
   refine le_antisymm ?_ ?_
   · refine opNorm_le_bound (norm_nonneg (1 : A)) ?_
     simp
-  · convert ratio_le_opNorm (ContinuousMultilinearMap.mkPiAlgebraFin 𝕜 0 A) fun _ => (1 : A)
+  · convert! ratio_le_opNorm (ContinuousMultilinearMap.mkPiAlgebraFin 𝕜 0 A) fun _ => (1 : A)
     simp
 
 theorem norm_mkPiAlgebraFin_le :
@@ -1072,13 +1072,13 @@ def compContinuousLinearMapLRight (g : ContinuousMultilinearMap 𝕜 E₁ G) :
         intro h f i f₁ f₂
         ext x
         simp only [compContinuousLinearMap_apply, add_apply]
-        convert g.map_update_add (fun j ↦ f j (x j)) i (f₁ (x i)) (f₂ (x i)) <;>
+        convert! g.map_update_add (fun j ↦ f j (x j)) i (f₁ (x i)) (f₂ (x i)) <;>
           exact apply_update (fun (i : ι) (f : E i →L[𝕜] E₁ i) ↦ f (x i)) f i _ _
       map_update_smul' := by
         intro h f i a f₀
         ext x
         simp only [compContinuousLinearMap_apply, smul_apply]
-        convert g.map_update_smul (fun j ↦ f j (x j)) i a (f₀ (x i)) <;>
+        convert! g.map_update_smul (fun j ↦ f j (x j)) i a (f₀ (x i)) <;>
           exact apply_update (fun (i : ι) (f : E i →L[𝕜] E₁ i) ↦ f (x i)) f i _ _ }
     (‖g‖) (fun f ↦ by simp [norm_compContinuousLinearMap_le])
 
@@ -1107,12 +1107,12 @@ noncomputable def compContinuousLinearMapMultilinear :
     ext g x
     change (g fun j ↦ update f i (f₁ + f₂) j <| x j) =
         (g fun j ↦ update f i f₁ j <| x j) + g fun j ↦ update f i f₂ j (x j)
-    convert g.map_update_add (fun j ↦ f j (x j)) i (f₁ (x i)) (f₂ (x i)) <;>
+    convert! g.map_update_add (fun j ↦ f j (x j)) i (f₁ (x i)) (f₂ (x i)) <;>
       exact apply_update (fun (i : ι) (f : E i →L[𝕜] E₁ i) ↦ f (x i)) f i _ _
   map_update_smul' f i a f₀ := by
     ext g x
     change (g fun j ↦ update f i (a • f₀) j <| x j) = a • g fun j ↦ update f i f₀ j (x j)
-    convert g.map_update_smul (fun j ↦ f j (x j)) i a (f₀ (x i)) <;>
+    convert! g.map_update_smul (fun j ↦ f j (x j)) i a (f₀ (x i)) <;>
       exact apply_update (fun (i : ι) (f : E i →L[𝕜] E₁ i) ↦ f (x i)) f i _ _
 
 /-- If `f` is a collection of continuous linear maps, then the construction
diff --git a/Mathlib/Analysis/Normed/Module/MultipliableUniformlyOn.lean b/Mathlib/Analysis/Normed/Module/MultipliableUniformlyOn.lean
index 2151c22bcd0467..2f96bba86fc9c1 100644
--- a/Mathlib/Analysis/Normed/Module/MultipliableUniformlyOn.lean
+++ b/Mathlib/Analysis/Normed/Module/MultipliableUniformlyOn.lean
@@ -99,7 +99,7 @@ lemma hasProdUniformlyOn_one_add (hK : IsCompact K) (hu : Summable u)
       filter_upwards [h] with i hi using fun x ↦ hi x x.2
     have hM : Multipliable fun i ↦ 1 + f' i :=
       multipliable_one_add_of_summable (hu.of_norm_bounded_eventually (by simpa using hf'_bd))
-    convert ContinuousMap.tendsto_iff_tendstoUniformly.mp hM.hasProd
+    convert! ContinuousMap.tendsto_iff_tendstoUniformly.mp hM.hasProd
     · simp [f']
     · exact funext fun k ↦ ContinuousMap.tprod_apply hM k
 
diff --git a/Mathlib/Analysis/Normed/Module/PiTensorProduct/ProjectiveSeminorm.lean b/Mathlib/Analysis/Normed/Module/PiTensorProduct/ProjectiveSeminorm.lean
index 08275090fd53ad..b2319ec8628f80 100644
--- a/Mathlib/Analysis/Normed/Module/PiTensorProduct/ProjectiveSeminorm.lean
+++ b/Mathlib/Analysis/Normed/Module/PiTensorProduct/ProjectiveSeminorm.lean
@@ -114,7 +114,7 @@ theorem projectiveSeminorm_apply (x : ⨂[𝕜] i, E i) :
 
 theorem projectiveSeminorm_tprod_le (m : Π i, E i) :
     projectiveSeminorm (⨂ₜ[𝕜] i, m i) ≤ ∏ i, ‖m i‖ := by
-  convert ciInf_le (bddBelow_projectiveSemiNormAux _) ⟨FreeAddMonoid.of ((1 : 𝕜), m), ?_⟩
+  convert! ciInf_le (bddBelow_projectiveSemiNormAux _) ⟨FreeAddMonoid.of ((1 : 𝕜), m), ?_⟩
   · simp [projectiveSeminormAux]
   · simp [mem_lifts_iff]
 
diff --git a/Mathlib/Analysis/Normed/Module/RCLike/Real.lean b/Mathlib/Analysis/Normed/Module/RCLike/Real.lean
index 3009146f78351a..e09623c37462a6 100644
--- a/Mathlib/Analysis/Normed/Module/RCLike/Real.lean
+++ b/Mathlib/Analysis/Normed/Module/RCLike/Real.lean
@@ -59,7 +59,7 @@ theorem dist_smul_add_one_sub_smul_le {r : ℝ} {x y : E} (h : r ∈ Icc 0 1) :
 theorem closure_ball (x : E) {r : ℝ} (hr : r ≠ 0) : closure (ball x r) = closedBall x r := by
   refine Subset.antisymm closure_ball_subset_closedBall fun y hy => ?_
   have : ContinuousWithinAt (fun c : ℝ => c • (y - x) + x) (Ico 0 1) 1 := by fun_prop
-  convert this.mem_closure _ _
+  convert! this.mem_closure _ _
   · rw [one_smul, sub_add_cancel]
   · simp [closure_Ico zero_ne_one, zero_le_one]
   · rintro c ⟨hc0, hc1⟩
diff --git a/Mathlib/Analysis/Normed/Module/WeakDual.lean b/Mathlib/Analysis/Normed/Module/WeakDual.lean
index e87a1ab65cb66b..857a24373b9937 100644
--- a/Mathlib/Analysis/Normed/Module/WeakDual.lean
+++ b/Mathlib/Analysis/Normed/Module/WeakDual.lean
@@ -172,7 +172,7 @@ def continuousLinearMapToWeakDual : StrongDual 𝕜 E →L[𝕜] WeakDual 𝕜 E
 theorem dual_norm_topology_le_weak_dual_topology :
     (UniformSpace.toTopologicalSpace : TopologicalSpace (StrongDual 𝕜 E)) ≤
       (instTopologicalSpaceWeakDual .. : TopologicalSpace (WeakDual 𝕜 E)) := by
-  convert (@toWeakDual_continuous _ _ _ _ (by assumption)).le_induced
+  convert! (@toWeakDual_continuous _ _ _ _ (by assumption)).le_induced
   exact induced_id.symm
 
 end Dual
diff --git a/Mathlib/Analysis/Normed/Operator/Banach.lean b/Mathlib/Analysis/Normed/Operator/Banach.lean
index 9af071be0edbf7..c8246b741c8091 100644
--- a/Mathlib/Analysis/Normed/Operator/Banach.lean
+++ b/Mathlib/Analysis/Normed/Operator/Banach.lean
@@ -414,7 +414,7 @@ noncomputable def leftInverse_of_injective_of_isClosed_range
     rintro ⟨y, x, rfl⟩
     have aux := hfK.le_mul_dist x 0
     simp only [dist_zero_right, map_zero] at aux
-    convert aux
+    convert! aux
     exact f.rangeRestrict.leftInverse_apply_of_inj
       (by rw [ker_codRestrict]; exact LinearMap.ker_eq_bot.mpr hf) x)
 
diff --git a/Mathlib/Analysis/Normed/Operator/BoundedLinearMaps.lean b/Mathlib/Analysis/Normed/Operator/BoundedLinearMaps.lean
index a44502c3cae6be..7607b3481dc65f 100644
--- a/Mathlib/Analysis/Normed/Operator/BoundedLinearMaps.lean
+++ b/Mathlib/Analysis/Normed/Operator/BoundedLinearMaps.lean
@@ -542,7 +542,7 @@ protected theorem isOpen [CompleteSpace E] : IsOpen (range ((↑) : (E ≃L[𝕜
   refine fun e => IsOpen.mem_nhds ?_ (mem_range_self _)
   let O : (E →L[𝕜] F) → E →L[𝕜] E := fun f => (e.symm : F →L[𝕜] E).comp f
   have h_O : Continuous O := (isBoundedBilinearMap_comp (𝕜 := 𝕜) (F := F) (G := E)).continuous_right
-  convert show IsOpen (O ⁻¹' { x | IsUnit x }) from Units.isOpen.preimage h_O using 1
+  convert! show IsOpen (O ⁻¹' {x | IsUnit x}) from Units.isOpen.preimage h_O using 1
   ext f'
   constructor
   · rintro ⟨e', rfl⟩
diff --git a/Mathlib/Analysis/Normed/Operator/Compact/Basic.lean b/Mathlib/Analysis/Normed/Operator/Compact/Basic.lean
index 3b752e92f3ca67..5d56fbdd627983 100644
--- a/Mathlib/Analysis/Normed/Operator/Compact/Basic.lean
+++ b/Mathlib/Analysis/Normed/Operator/Compact/Basic.lean
@@ -445,7 +445,7 @@ theorem isClosed_setOf_isCompactOperator {𝕜₁ 𝕜₂ : Type*} [Nontrivially
   rcases hTv with ⟨t, ht, htx⟩
   refine ⟨t, ht, ?_⟩
   rw [mem_preimage, mem_vadd_set_iff_neg_vadd_mem, vadd_eq_add, neg_add_eq_sub] at htx ⊢
-  convert hVU _ htx _ (huv x hx) using 1
+  convert! hVU _ htx _ (huv x hx) using 1
   rw [ContinuousLinearMap.sub_apply]
   abel
 
diff --git a/Mathlib/Analysis/Normed/Operator/Compact/FredholmAlternative.lean b/Mathlib/Analysis/Normed/Operator/Compact/FredholmAlternative.lean
index 20d58f09b39d7f..6f8d04b6f65c5b 100644
--- a/Mathlib/Analysis/Normed/Operator/Compact/FredholmAlternative.lean
+++ b/Mathlib/Analysis/Normed/Operator/Compact/FredholmAlternative.lean
@@ -173,7 +173,7 @@ theorem hasEigenvalue_or_mem_resolventSet (hT : IsCompactOperator T) (hμ : μ 
   replace h₂ : ¬ (S : X → X).Bijective := by
     rw [spectrum.mem_resolventSet_iff, ← IsUnit.neg_iff,
       ContinuousLinearMap.isUnit_iff_bijective] at h₂
-    convert h₂
+    convert! h₂
     ext x
     simp [S]
   replace h₂ : ¬ (S : X → X).Surjective := by grind [Function.Bijective, hK.injective]
diff --git a/Mathlib/Analysis/Normed/Operator/Extend.lean b/Mathlib/Analysis/Normed/Operator/Extend.lean
index 80fc7a52ef3152..e44677a95ff1ab 100644
--- a/Mathlib/Analysis/Normed/Operator/Extend.lean
+++ b/Mathlib/Analysis/Normed/Operator/Extend.lean
@@ -195,7 +195,7 @@ theorem extendOfNorm_eq (h_dense : DenseRange e) (h_norm : ∃ C, ∀ x, ‖f x
     (x : E) : f.extendOfNorm e (e x) = f x := by
   have := (f.compLeftInverse e).extend_eq (e := (LinearMap.range e).subtypeL)
     (by simpa using h_dense) isUniformEmbedding_subtype_val.isUniformInducing
-  convert this ⟨e x, LinearMap.mem_range_self e x⟩
+  convert! this ⟨e x, LinearMap.mem_range_self e x⟩
   exact (compLeftInverse_apply_of_bdd _ _ h_norm _ _ rfl).symm
 
 theorem norm_extendOfNorm_apply_le (h_dense : DenseRange e) (C : ℝ)
@@ -327,7 +327,7 @@ def extendOfIsometry (h_dense₁ : DenseRange e₁) (h_dense₂ : DenseRange e
       refine h_dense₁.induction ?_ (isClosed_eq (by
         simp only [ContinuousLinearEquiv.coe_toLinearEquiv]; fun_prop) continuous_norm)
       rintro x ⟨y, rfl⟩
-      convert h_norm y
+      convert! h_norm y
       apply LinearMap.extendOfNorm_eq h_dense₁ (by use 1; simp [h_norm]) }
 
 theorem extendOfIsometry_apply (h_dense₁ : DenseRange e₁) (h_dense₂ : DenseRange e₂)
diff --git a/Mathlib/Analysis/Normed/Operator/Mul.lean b/Mathlib/Analysis/Normed/Operator/Mul.lean
index 34bda47df590c5..faae470656da15 100644
--- a/Mathlib/Analysis/Normed/Operator/Mul.lean
+++ b/Mathlib/Analysis/Normed/Operator/Mul.lean
@@ -112,7 +112,7 @@ instance _root_.NormedAlgebra.instRegularNormedAlgebra {𝕜 R : Type*} [Nontriv
     [SeminormedRing R] [NormedAlgebra 𝕜 R] [NormOneClass R] : RegularNormedAlgebra 𝕜 R where
   isometry_mul' := AddMonoidHomClass.isometry_of_norm (mul 𝕜 R) <|
     fun x => le_antisymm (opNorm_mul_apply_le _ _ _) <| by
-      convert ratio_le_opNorm ((mul 𝕜 R) x) (1 : R)
+      convert! ratio_le_opNorm ((mul 𝕜 R) x) (1 : R)
       simp [norm_one]
 
 variable [RegularNormedAlgebra 𝕜 R]
diff --git a/Mathlib/Analysis/Normed/Operator/NormedSpace.lean b/Mathlib/Analysis/Normed/Operator/NormedSpace.lean
index 560ac9585c1feb..0178cf84c0ddcf 100644
--- a/Mathlib/Analysis/Normed/Operator/NormedSpace.lean
+++ b/Mathlib/Analysis/Normed/Operator/NormedSpace.lean
@@ -200,10 +200,11 @@ theorem opNorm_comp_linearIsometryEquiv (f : F →SL[σ₂₃] G) (g : F' ≃ₛ
   · haveI := g.symm.toLinearEquiv.toEquiv.subsingleton
     simp
   refine le_antisymm ?_ ?_
-  · convert f.opNorm_comp_le g.toLinearIsometry.toContinuousLinearMap
+  · convert! f.opNorm_comp_le g.toLinearIsometry.toContinuousLinearMap
     simp [g.toLinearIsometry.norm_toContinuousLinearMap]
-  · convert (f.comp g.toLinearIsometry.toContinuousLinearMap).opNorm_comp_le
-        g.symm.toLinearIsometry.toContinuousLinearMap
+  · convert!
+    (f.comp g.toLinearIsometry.toContinuousLinearMap).opNorm_comp_le
+      g.symm.toLinearIsometry.toContinuousLinearMap
     · ext
       simp
     haveI := g.symm.surjective.nontrivial
@@ -244,7 +245,7 @@ protected theorem antilipschitz (e : E ≃SL[σ₁₂] F) :
 theorem one_le_norm_mul_norm_symm [RingHomIsometric σ₁₂] [Nontrivial E] (e : E ≃SL[σ₁₂] F) :
     1 ≤ ‖(e : E →SL[σ₁₂] F)‖ * ‖(e.symm : F →SL[σ₂₁] E)‖ := by
   rw [mul_comm]
-  convert (e.symm : F →SL[σ₂₁] E).opNorm_comp_le (e : E →SL[σ₁₂] F)
+  convert! (e.symm : F →SL[σ₂₁] E).opNorm_comp_le (e : E →SL[σ₁₂] F)
   rw [e.coe_symm_comp_coe, ContinuousLinearMap.norm_id]
 
 theorem norm_pos [RingHomIsometric σ₁₂] [Nontrivial E] (e : E ≃SL[σ₁₂] F) :
diff --git a/Mathlib/Analysis/Normed/Order/Hom/Basic.lean b/Mathlib/Analysis/Normed/Order/Hom/Basic.lean
index bb65587d1cc24c..b965dfda85e085 100644
--- a/Mathlib/Analysis/Normed/Order/Hom/Basic.lean
+++ b/Mathlib/Analysis/Normed/Order/Hom/Basic.lean
@@ -33,7 +33,7 @@ abbrev GroupSeminormClass.toSeminormedGroup [Group α] [GroupSeminormClass F α
   dist_eq _ _ := rfl
   dist_self _ := by simp
   dist_comm x y := by simp [← map_inv_eq_map f (x⁻¹ * y)]
-  dist_triangle x y z := by convert map_mul_le_add f (x⁻¹ * y) (y⁻¹ * z) using 2; group
+  dist_triangle x y z := by convert! map_mul_le_add f (x⁻¹ * y) (y⁻¹ * z) using 2; group
 
 @[to_additive]
 lemma GroupSeminormClass.toSeminormedGroup_norm_eq [Group α] [GroupSeminormClass F α ℝ]
diff --git a/Mathlib/Analysis/Normed/Order/Hom/Ultra.lean b/Mathlib/Analysis/Normed/Order/Hom/Ultra.lean
index 4ee73fd2852c50..f6901611ecbf11 100644
--- a/Mathlib/Analysis/Normed/Order/Hom/Ultra.lean
+++ b/Mathlib/Analysis/Normed/Order/Hom/Ultra.lean
@@ -35,5 +35,5 @@ lemma AddGroupSeminormClass.isUltrametricDist [AddGroup α] [AddGroupSeminormCla
   ⟨fun x y z ↦ by
     simp +instances only [hd, dist_eq_norm_neg_add,
       AddGroupSeminormClass.toSeminormedAddGroup_norm_eq]
-    convert hna (-x + y) (-y + z) using 2
+    convert! hna (-x + y) (-y + z) using 2
     rw [add_assoc, ← add_assoc y, add_neg_cancel, zero_add]⟩
diff --git a/Mathlib/Analysis/Normed/Order/Lattice.lean b/Mathlib/Analysis/Normed/Order/Lattice.lean
index 89fe7a06c04dad..402142c6b44f90 100644
--- a/Mathlib/Analysis/Normed/Order/Lattice.lean
+++ b/Mathlib/Analysis/Normed/Order/Lattice.lean
@@ -132,8 +132,9 @@ instance (priority := 100) HasSolidNorm.continuousInf : ContinuousInf α := by
   have : ∀ p : α × α, ‖p.1 ⊓ p.2 - q.1 ⊓ q.2‖ ≤ ‖p.1 - q.1‖ + ‖p.2 - q.2‖ := fun _ =>
     norm_inf_sub_inf_le_add_norm _ _ _ _
   refine squeeze_zero (fun e => norm_nonneg _) this ?_
-  convert ((continuous_fst.tendsto q).sub <| tendsto_const_nhds).norm.add
-    ((continuous_snd.tendsto q).sub <| tendsto_const_nhds).norm
+  convert!
+    ((continuous_fst.tendsto q).sub <| tendsto_const_nhds).norm.add
+      ((continuous_snd.tendsto q).sub <| tendsto_const_nhds).norm
   simp
 
 set_option backward.isDefEq.respectTransparency false in
diff --git a/Mathlib/Analysis/Normed/Ring/InfiniteSum.lean b/Mathlib/Analysis/Normed/Ring/InfiniteSum.lean
index bbe3dfd5ee6869..42db3ae793bb65 100644
--- a/Mathlib/Analysis/Normed/Ring/InfiniteSum.lean
+++ b/Mathlib/Analysis/Normed/Ring/InfiniteSum.lean
@@ -58,8 +58,10 @@ theorem summable_mul_of_summable_norm' {f : ι → R} {g : ι' → R}
   rw [← prod_atTop_atTop_eq]
   have := Tendsto.prodMap h'f.hasSum h'g.hasSum
   rw [← nhds_prod_eq] at this
-  convert ((continuous_mul (M := R)).continuousAt
-      (x := (∑' (i : ι), f i, ∑' (j : ι'), g j))).tendsto.comp this with p
+  convert!
+    ((continuous_mul (M := R)).continuousAt (x := (∑' (i : ι), f i, ∑' (j : ι'), g j))).tendsto.comp
+      this with
+    p
   simp [sum_product, ← mul_sum, ← sum_mul]
 
 /-- Product of two infinite sums indexed by arbitrary types.
@@ -150,7 +152,7 @@ theorem tsum_mul_tsum_eq_tsum_sum_range_of_summable_norm [CompleteSpace R] {f g
 theorem hasSum_sum_range_mul_of_summable_norm [CompleteSpace R] {f g : ℕ → R}
     (hf : Summable fun x => ‖f x‖) (hg : Summable fun x => ‖g x‖) :
     HasSum (fun n ↦ ∑ k ∈ range (n + 1), f k * g (n - k)) ((∑' n, f n) * ∑' n, g n) := by
-  convert (summable_norm_sum_mul_range_of_summable_norm hf hg).of_norm.hasSum
+  convert! (summable_norm_sum_mul_range_of_summable_norm hf hg).of_norm.hasSum
   exact tsum_mul_tsum_eq_tsum_sum_range_of_summable_norm hf hg
 
 theorem tsum_mul_tsum_eq_tsum_sum_range_of_summable_norm' {f g : ℕ → R}
@@ -164,7 +166,7 @@ theorem hasSum_sum_range_mul_of_summable_norm' {f g : ℕ → R}
     (hf : Summable fun x => ‖f x‖) (h'f : Summable f)
     (hg : Summable fun x => ‖g x‖) (h'g : Summable g) :
     HasSum (fun n ↦ ∑ k ∈ range (n + 1), f k * g (n - k)) ((∑' n, f n) * ∑' n, g n) := by
-  convert (summable_sum_mul_range_of_summable_norm' hf h'f hg h'g).hasSum
+  convert! (summable_sum_mul_range_of_summable_norm' hf h'f hg h'g).hasSum
   exact tsum_mul_tsum_eq_tsum_sum_range_of_summable_norm' hf h'f hg h'g
 
 end Nat
diff --git a/Mathlib/Analysis/Normed/Ring/Lemmas.lean b/Mathlib/Analysis/Normed/Ring/Lemmas.lean
index ad9dc11b8dc775..08751154c27ac6 100644
--- a/Mathlib/Analysis/Normed/Ring/Lemmas.lean
+++ b/Mathlib/Analysis/Normed/Ring/Lemmas.lean
@@ -168,7 +168,7 @@ instance (priority := 100) NonUnitalSeminormedRing.toContinuousMul [NonUnitalSem
             _ ≤ ‖e.1‖ * ‖e.2 - x.2‖ + ‖e.1 - x.1‖ * ‖x.2‖ :=
               norm_add_le_of_le (norm_mul_le _ _) (norm_mul_le _ _)
         refine squeeze_zero (fun e => norm_nonneg _) this ?_
-        convert
+        convert!
           ((continuous_fst.tendsto x).norm.mul
                 ((continuous_snd.tendsto x).sub tendsto_const_nhds).norm).add
             (((continuous_fst.tendsto x).sub tendsto_const_nhds).norm.mul tendsto_const_nhds)
@@ -213,8 +213,10 @@ lemma lipschitzWith_sub : LipschitzWith 2 (fun (p : ℝ≥0 × ℝ≥0) ↦ p.1
   rw [← NNReal.isometry_coe.lipschitzWith_iff]
   have : Isometry (Prod.map ((↑) : ℝ≥0 → ℝ) ((↑) : ℝ≥0 → ℝ)) :=
     NNReal.isometry_coe.prodMap NNReal.isometry_coe
-  convert (((LipschitzWith.prod_fst.comp this.lipschitz).sub
-    (LipschitzWith.prod_snd.comp this.lipschitz)).max_const 0)
+  convert!
+    (((LipschitzWith.prod_fst.comp this.lipschitz).sub
+          (LipschitzWith.prod_snd.comp this.lipschitz)).max_const
+      0)
   norm_num
 
 end NNReal
diff --git a/Mathlib/Analysis/Normed/Ring/Units.lean b/Mathlib/Analysis/Normed/Ring/Units.lean
index e9e308a0eb2bbc..0992672add03a7 100644
--- a/Mathlib/Analysis/Normed/Ring/Units.lean
+++ b/Mathlib/Analysis/Normed/Ring/Units.lean
@@ -176,7 +176,7 @@ theorem inverse_add_norm_diff_first_order (x : Rˣ) :
 /-- The function `fun t ↦ Ring.inverse (x + t) - x⁻¹ + x⁻¹ * t * x⁻¹` is `O(t ^ 2)` as `t → 0`. -/
 theorem inverse_add_norm_diff_second_order (x : Rˣ) :
     (fun t : R => (↑x + t)⁻¹ʳ - ↑x⁻¹ + ↑x⁻¹ * t * ↑x⁻¹) =O[𝓝 0] fun t => ‖t‖ ^ 2 := by
-  convert inverse_add_norm_diff_nth_order x 2 using 2
+  convert! inverse_add_norm_diff_nth_order x 2 using 2
   simp only [sum_range_succ, sum_range_zero, zero_add, pow_zero, pow_one, add_mul, one_mul,
     ← sub_sub, neg_mul, sub_neg_eq_add]
 
diff --git a/Mathlib/Analysis/Normed/Unbundled/SeminormFromBounded.lean b/Mathlib/Analysis/Normed/Unbundled/SeminormFromBounded.lean
index 93fd45b5db61ff..f9928117449d40 100644
--- a/Mathlib/Analysis/Normed/Unbundled/SeminormFromBounded.lean
+++ b/Mathlib/Analysis/Normed/Unbundled/SeminormFromBounded.lean
@@ -317,7 +317,7 @@ theorem seminormFromBounded_of_mul_le (f_nonneg : 0 ≤ f) {x : R}
       · rw [← mul_one (f x), ← div_self hy0, ← mul_div_assoc,
           div_le_iff₀ (lt_of_le_of_ne' (f_nonneg _) hy0), mul_div_assoc, div_self hy0, mul_one]
         exact hx y
-    convert le_ciSup h_bdd (1 : R)
+    convert! le_ciSup h_bdd (1 : R)
     by_cases h0 : f x = 0
     · rw [mul_one, h0, zero_div]
     · have heq : f 1 = 1 := by
diff --git a/Mathlib/Analysis/Normed/Unbundled/SeminormFromConst.lean b/Mathlib/Analysis/Normed/Unbundled/SeminormFromConst.lean
index 8131a0a5890ab7..d3ea0bf1ac6bde 100644
--- a/Mathlib/Analysis/Normed/Unbundled/SeminormFromConst.lean
+++ b/Mathlib/Analysis/Normed/Unbundled/SeminormFromConst.lean
@@ -190,7 +190,7 @@ theorem seminormFromConst_isPowMul : IsPowMul (seminormFromConst' c f) := fun x
       (tendsto_atTop_atTop_of_monotone (fun _ _ hnk ↦ mul_le_mul_right hnk m) _)
     rintro n; use n; exact le_mul_of_one_le_left' hm
   apply tendsto_nhds_unique hlim
-  convert (tendsto_seminormFromConst_seq_atTop hf1 hc hpm x).pow m using 1
+  convert! (tendsto_seminormFromConst_seq_atTop hf1 hc hpm x).pow m using 1
   ext n
   simp only [seminormFromConst_seq, div_pow, ← hpm _ hm, ← pow_mul, mul_pow, mul_comm m n]
 
diff --git a/Mathlib/Analysis/Normed/Unbundled/SmoothingSeminorm.lean b/Mathlib/Analysis/Normed/Unbundled/SmoothingSeminorm.lean
index 526d185ba6de8c..c738a8c586bd57 100644
--- a/Mathlib/Analysis/Normed/Unbundled/SmoothingSeminorm.lean
+++ b/Mathlib/Analysis/Normed/Unbundled/SmoothingSeminorm.lean
@@ -330,7 +330,7 @@ private theorem μ_bddAbove (hμ1 : μ 1 ≤ 1) {s : ℕ → ℕ} (hs : ∀ n :
 private theorem μ_bddAbove' (hμ1 : μ 1 ≤ 1) {s : ℕ → ℕ} (hs : ∀ n : ℕ, s n ≤ n) (x : R)
     (ψ : ℕ → ℕ) : BddAbove ((fun n : ℕ => μ (x ^ s (ψ n)) ^ (1 / (ψ n : ℝ))) '' Set.univ) := by
   rw [Set.image_eq_range]
-  convert μ_bddAbove μ hμ1 hs x ψ
+  convert! μ_bddAbove μ hμ1 hs x ψ
   ext
   simp [one_div, Set.mem_range, Subtype.exists, Set.mem_univ, exists_const]
 
@@ -366,7 +366,8 @@ private theorem μ_limsup_le_one {s : ℕ → ℕ} (hs_le : ∀ n : ℕ, s n ≤
           (mul_nonneg (cast_nonneg _) (one_div_nonneg.mpr (cast_nonneg _)))
     · have hμ_lim : Tendsto (fun n : ℕ => μ x ^ (↑(s (ψ n)) * (1 / (ψ n : ℝ)))) atTop (𝓝 1) := by
         nth_rw 1 [← rpow_zero (μ x)]
-        convert Tendsto.rpow tendsto_const_nhds hψ_lim
+        convert!
+          Tendsto.rpow tendsto_const_nhds hψ_lim
             (Or.inl (ne_of_gt (lt_of_lt_of_le zero_lt_one (not_lt.mp hμx))))
         · simp only [rpow_zero, mul_one_div, Function.comp_apply]
         · rw [rpow_zero]
diff --git a/Mathlib/Analysis/Normed/Unbundled/SpectralNorm.lean b/Mathlib/Analysis/Normed/Unbundled/SpectralNorm.lean
index e20a5106256907..d37f6500061b51 100644
--- a/Mathlib/Analysis/Normed/Unbundled/SpectralNorm.lean
+++ b/Mathlib/Analysis/Normed/Unbundled/SpectralNorm.lean
@@ -162,7 +162,7 @@ theorem spectralValue_X_pow (n : ℕ) : spectralValue (X ^ n : R[X]) = 0 := by
   rw [spectralValue]
   unfold spectralValueTerms
   simp_rw [coeff_X_pow n, natDegree_X_pow]
-  convert ciSup_const using 2
+  convert! ciSup_const using 2
   · ext m
     by_cases hmn : m < n
     · rw [if_pos hmn, rpow_eq_zero_iff_of_nonneg (norm_nonneg _), if_neg (_root_.ne_of_lt hmn),
diff --git a/Mathlib/Analysis/ODE/Gronwall.lean b/Mathlib/Analysis/ODE/Gronwall.lean
index e982b8cccf1f50..03ebd3aaf1fb0f 100644
--- a/Mathlib/Analysis/ODE/Gronwall.lean
+++ b/Mathlib/Analysis/ODE/Gronwall.lean
@@ -55,17 +55,18 @@ theorem hasDerivAt_gronwallBound (δ K ε x : ℝ) :
   by_cases hK : K = 0
   · subst K
     simp only [gronwallBound_K0, zero_mul, zero_add]
-    convert ((hasDerivAt_id x).const_mul ε).const_add δ
+    convert! ((hasDerivAt_id x).const_mul ε).const_add δ
     rw [mul_one]
   · simp only [gronwallBound_of_K_ne_0 hK]
-    convert (((hasDerivAt_id x).const_mul K).exp.const_mul δ).add
-      ((((hasDerivAt_id x).const_mul K).exp.sub_const 1).const_mul (ε / K)) using 1
+    convert!
+      (((hasDerivAt_id x).const_mul K).exp.const_mul δ).add
+        ((((hasDerivAt_id x).const_mul K).exp.sub_const 1).const_mul (ε / K)) using 1
     simp only [id]
     field
 
 theorem hasDerivAt_gronwallBound_shift (δ K ε x a : ℝ) :
     HasDerivAt (fun y => gronwallBound δ K ε (y - a)) (K * gronwallBound δ K ε (x - a) + ε) x := by
-  convert (hasDerivAt_gronwallBound δ K ε _).comp x ((hasDerivAt_id x).sub_const a) using 1
+  convert! (hasDerivAt_gronwallBound δ K ε _).comp x ((hasDerivAt_id x).sub_const a) using 1
   rw [id, mul_one]
 
 theorem gronwallBound_x0 (δ K ε : ℝ) : gronwallBound δ K ε 0 = δ := by
@@ -122,7 +123,7 @@ theorem le_gronwallBound_of_liminf_deriv_right_le {f f' : ℝ → ℝ} {δ K ε
     · exact hx
   intro x hx
   change f x ≤ (fun ε' => gronwallBound δ K ε' (x - a)) ε
-  convert continuousWithinAt_const.closure_le _ _ (H x hx)
+  convert! continuousWithinAt_const.closure_le _ _ (H x hx)
   · simp only [closure_Ioi, self_mem_Ici]
   exact (gronwallBound_continuous_ε δ K (x - a)).continuousWithinAt
 
@@ -281,18 +282,20 @@ theorem ODE_solution_unique_of_mem_Icc_left
     fun _ ht' ↦ mem_Iic.mpr <| neg_le_neg ht'
   suffices EqOn (f ∘ Neg.neg) (g ∘ Neg.neg) (Icc (-b) (-a)) by
     rw [eqOn_comp_right_iff] at this
-    convert this
+    convert! this
     simp
   apply ODE_solution_unique_of_mem_Icc_right hv'
     (hf.comp continuousOn_neg hmt1) _ (fun _ ht ↦ hfs _ (hmt2 ht))
     (hg.comp continuousOn_neg hmt1) _ (fun _ ht ↦ hgs _ (hmt2 ht)) (by simp [hb])
   · intro t ht
-    convert HasFDerivWithinAt.comp_hasDerivWithinAt t (hf' (-t) (hmt2 ht))
-      (hasDerivAt_neg t).hasDerivWithinAt (hmt3 t)
+    convert!
+      HasFDerivWithinAt.comp_hasDerivWithinAt t (hf' (-t) (hmt2 ht))
+        (hasDerivAt_neg t).hasDerivWithinAt (hmt3 t)
     simp
   · intro t ht
-    convert HasFDerivWithinAt.comp_hasDerivWithinAt t (hg' (-t) (hmt2 ht))
-      (hasDerivAt_neg t).hasDerivWithinAt (hmt3 t)
+    convert!
+      HasFDerivWithinAt.comp_hasDerivWithinAt t (hg' (-t) (hmt2 ht))
+        (hasDerivAt_neg t).hasDerivWithinAt (hmt3 t)
     simp
 
 /-- A version of `ODE_solution_unique_of_mem_Icc_right` for uniqueness in a closed interval whose
diff --git a/Mathlib/Analysis/ODE/PicardLindelof.lean b/Mathlib/Analysis/ODE/PicardLindelof.lean
index 5d11f3514a1220..edfe54041d89bb 100644
--- a/Mathlib/Analysis/ODE/PicardLindelof.lean
+++ b/Mathlib/Analysis/ODE/PicardLindelof.lean
@@ -468,7 +468,7 @@ lemma exists_forall_closedBall_funSpace_dist_le_mul [CompleteSpace E]
   · nth_rw 1 [← hα, dist_next_next]
     apply Filter.Tendsto.mul_const
     apply Filter.Tendsto.const_mul
-    convert hasSum_geometric_of_lt_one C.2 (h y hy).1 |>.tendsto_sum_nat
+    convert! hasSum_geometric_of_lt_one C.2 (h y hy).1 |>.tendsto_sum_nat
     simp [NNReal.coe_sub <| le_of_lt (h y hy).1, NNReal.coe_one]
 
 end
diff --git a/Mathlib/Analysis/ODE/Transform.lean b/Mathlib/Analysis/ODE/Transform.lean
index f3d13a15c1822e..34159766ddc293 100644
--- a/Mathlib/Analysis/ODE/Transform.lean
+++ b/Mathlib/Analysis/ODE/Transform.lean
@@ -45,7 +45,7 @@ lemma IsIntegralCurveOn.comp_add (hγ : IsIntegralCurveOn γ v s) (dt : ℝ) :
 lemma isIntegralCurveOn_comp_add {dt : ℝ} :
     IsIntegralCurveOn (γ ∘ (· + dt)) (v ∘ (· + dt)) (-dt +ᵥ s) ↔ IsIntegralCurveOn γ v s := by
   refine ⟨fun hγ ↦ ?_, fun hγ ↦ hγ.comp_add _⟩
-  convert hγ.comp_add (-dt)
+  convert! hγ.comp_add (-dt)
   · ext t
     simp only [comp_apply, neg_add_cancel_right]
   · ext t
@@ -64,7 +64,7 @@ lemma isIntegralCurveAt_comp_add {dt : ℝ} :
     IsIntegralCurveAt (γ ∘ (· + dt)) (v ∘ (· + dt)) (t₀ - dt) ↔ IsIntegralCurveAt γ v t₀ := by
   simp_rw [isIntegralCurveAt_iff_exists_pos]
   congrm ∃ ε > 0, ?_
-  convert isIntegralCurveOn_comp_add
+  convert! isIntegralCurveOn_comp_add
   simp [neg_add_eq_sub]
 
 lemma IsIntegralCurveAt.comp_add (hγ : IsIntegralCurveAt γ v t₀) (dt : ℝ) :
@@ -87,7 +87,7 @@ lemma IsIntegralCurve.comp_add (hγ : IsIntegralCurve γ v) (dt : ℝ) :
 lemma isIntegralCurve_comp_add {dt : ℝ} :
     IsIntegralCurve (γ ∘ (· + dt)) (v ∘ (· + dt)) ↔ IsIntegralCurve γ v := by
   simp_rw [← isIntegralCurveOn_univ]
-  convert isIntegralCurveOn_comp_add
+  convert! isIntegralCurveOn_comp_add
   simp
 
 lemma isIntegralCurve_comp_sub {dt : ℝ} :
@@ -117,7 +117,7 @@ lemma isIntegralCurveOn_comp_mul_ne_zero {a : ℝ} (ha : a ≠ 0) :
     rw [mem_inv_smul_set_iff₀ ha, smul_eq_mul, mul_comm]
     rfl
   refine ⟨fun hγ ↦ ?_, heq ▸ fun hγ ↦ hγ.comp_mul a⟩
-  convert hγ.comp_mul a⁻¹
+  convert! hγ.comp_mul a⁻¹
   · ext t
     simp only [comp_apply, mul_assoc, inv_mul_eq_div, div_self ha, mul_one]
   · ext t
@@ -131,7 +131,7 @@ lemma IsIntegralCurveAt.comp_mul_ne_zero (hγ : IsIntegralCurveAt γ v t₀) {a
   rw [isIntegralCurveAt_iff_exists_pos] at *
   obtain ⟨ε, hε, h⟩ := hγ
   refine ⟨ε / |a|, by positivity, ?_⟩
-  convert h.comp_mul a
+  convert! h.comp_mul a
   ext t
   rw [mem_setOf_eq, Metric.mem_ball, Metric.mem_ball, Real.dist_eq, Real.dist_eq,
     lt_div_iff₀ (abs_pos.mpr ha), ← abs_mul, sub_mul, div_mul_cancel₀ _ ha]
@@ -139,7 +139,7 @@ lemma IsIntegralCurveAt.comp_mul_ne_zero (hγ : IsIntegralCurveAt γ v t₀) {a
 lemma isIntegralCurveAt_comp_mul_ne_zero {a : ℝ} (ha : a ≠ 0) :
     IsIntegralCurveAt (γ ∘ (· * a)) (a • v ∘ (· * a)) (t₀ / a) ↔ IsIntegralCurveAt γ v t₀ := by
   refine ⟨fun hγ ↦ ?_, fun hγ ↦ hγ.comp_mul_ne_zero ha⟩
-  convert hγ.comp_mul_ne_zero (inv_ne_zero ha)
+  convert! hγ.comp_mul_ne_zero (inv_ne_zero ha)
   · ext t
     simp only [comp_apply, mul_assoc, inv_mul_eq_div, div_self ha, mul_one]
   · ext t
@@ -155,7 +155,7 @@ lemma IsIntegralCurve.comp_mul (hγ : IsIntegralCurve γ v) (a : ℝ) :
 lemma isIntegralCurve_comp_mul_ne_zero {a : ℝ} (ha : a ≠ 0) :
     IsIntegralCurve (γ ∘ (· * a)) (a • v ∘ (· * a)) ↔ IsIntegralCurve γ v := by
   refine ⟨fun hγ ↦ ?_, fun hγ ↦ hγ.comp_mul _⟩
-  convert hγ.comp_mul a⁻¹
+  convert! hγ.comp_mul a⁻¹
   · ext t
     simp only [comp_apply, mul_assoc, inv_mul_eq_div, div_self ha, mul_one]
   · ext t
diff --git a/Mathlib/Analysis/Oscillation.lean b/Mathlib/Analysis/Oscillation.lean
index 044eafdbcc6e3d..724add9e759f04 100644
--- a/Mathlib/Analysis/Oscillation.lean
+++ b/Mathlib/Analysis/Oscillation.lean
@@ -157,7 +157,7 @@ theorem uniform_oscillation {K : Set E} (comp : IsCompact K)
     {f : E → F} {ε : ENNReal} (hK : ∀ x ∈ K, oscillation f x < ε) :
     ∃ δ > 0, ∀ x ∈ K, ediam (f '' (eball x (ENNReal.ofReal δ))) ≤ ε := by
   simp only [← oscillationWithin_univ_eq_oscillation] at hK
-  convert ← comp.uniform_oscillationWithin hK
+  convert! ← comp.uniform_oscillationWithin hK
   exact inter_univ _
 
 end IsCompact
diff --git a/Mathlib/Analysis/PSeries.lean b/Mathlib/Analysis/PSeries.lean
index ffdf8264c6785e..f6f5ab73d3b059 100644
--- a/Mathlib/Analysis/PSeries.lean
+++ b/Mathlib/Analysis/PSeries.lean
@@ -62,13 +62,14 @@ theorem le_sum_schlomilch' (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f
       exacts [hu n.zero_le, hu n.le_succ]
     have : ∀ k ∈ Ico (u n) (u (n + 1)), f k ≤ f (u n) := fun k hk =>
       hf (Nat.succ_le_of_lt (h_pos n)) (mem_Ico.mp hk).1
-    convert sum_le_sum this
+    convert! sum_le_sum this
     simp
 
 theorem le_sum_condensed' (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
     (∑ k ∈ Ico 1 (2 ^ n), f k) ≤ ∑ k ∈ range n, 2 ^ k • f (2 ^ k) := by
-  convert le_sum_schlomilch' hf (fun n => pow_pos zero_lt_two n)
-    (fun m n hm => pow_right_mono₀ one_le_two hm) n using 2
+  convert!
+    le_sum_schlomilch' hf (fun n => pow_pos zero_lt_two n)
+      (fun m n hm => pow_right_mono₀ one_le_two hm) n using 2
   simp [pow_succ, mul_two]
 
 theorem le_sum_schlomilch (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) (h_pos : ∀ n, 0 < u n)
@@ -96,13 +97,14 @@ theorem sum_schlomilch_le' (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f
     have : ∀ k ∈ Ico (u n + 1) (u (n + 1) + 1), f (u (n + 1)) ≤ f k := fun k hk =>
       hf (Nat.lt_of_le_of_lt (Nat.succ_le_of_lt (h_pos n)) <| (Nat.lt_succ_of_le le_rfl).trans_le
         (mem_Ico.mp hk).1) (Nat.le_of_lt_succ <| (mem_Ico.mp hk).2)
-    convert sum_le_sum this
+    convert! sum_le_sum this
     simp
 
 theorem sum_condensed_le' (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
     (∑ k ∈ range n, 2 ^ k • f (2 ^ (k + 1))) ≤ ∑ k ∈ Ico 2 (2 ^ n + 1), f k := by
-  convert sum_schlomilch_le' hf (fun n => pow_pos zero_lt_two n)
-    (fun m n hm => pow_right_mono₀ one_le_two hm) n using 2
+  convert!
+    sum_schlomilch_le' hf (fun n => pow_pos zero_lt_two n)
+      (fun m n hm => pow_right_mono₀ one_le_two hm) n using 2
   simp [pow_succ, mul_two]
 
 theorem sum_schlomilch_le {C : ℕ} (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m) (h_pos : ∀ n, 0 < u n)
@@ -122,7 +124,7 @@ theorem sum_schlomilch_le {C : ℕ} (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f
     gcongr
     · exact h_nonneg (u (k + 1))
     exact mod_cast h_succ_diff k
-  convert sum_le_sum this
+  convert! sum_le_sum this
   simp [smul_sum]
 
 theorem sum_condensed_le (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
@@ -204,8 +206,9 @@ theorem summable_condensed_iff {f : ℕ → ℝ≥0} (hf : ∀ ⦃m n⦄, 0 < m
   have h_succ_diff : SuccDiffBounded 2 (2 ^ ·) := by
     intro n
     simp [pow_succ, mul_two, two_mul]
-  convert summable_schlomilch_iff hf (pow_pos zero_lt_two) (pow_right_strictMono₀ _root_.one_lt_two)
-    two_ne_zero h_succ_diff
+  convert!
+    summable_schlomilch_iff hf (pow_pos zero_lt_two) (pow_right_strictMono₀ _root_.one_lt_two)
+      two_ne_zero h_succ_diff
   simp [pow_succ, mul_two]
 
 end NNReal
@@ -231,8 +234,9 @@ theorem summable_condensed_iff_of_nonneg {f : ℕ → ℝ} (h_nonneg : ∀ n, 0
   have h_succ_diff : SuccDiffBounded 2 (2 ^ ·) := by
     intro n
     simp [pow_succ, mul_two, two_mul]
-  convert summable_schlomilch_iff_of_nonneg h_nonneg h_mono (pow_pos zero_lt_two)
-    (pow_right_strictMono₀ one_lt_two) two_ne_zero h_succ_diff
+  convert!
+    summable_schlomilch_iff_of_nonneg h_nonneg h_mono (pow_pos zero_lt_two)
+      (pow_right_strictMono₀ one_lt_two) two_ne_zero h_succ_diff
   simp [pow_succ, mul_two]
 
 /-- Cauchy condensation test for eventually antitone and nonnegative series of real numbers. -/
@@ -243,7 +247,7 @@ theorem summable_condensed_iff_of_eventually_nonneg {f : ℕ → ℝ} (h_nonneg
   rw [Filter.eventually_atTop] at h_mono
   rcases h_nonneg with ⟨n, hn⟩
   rcases h_mono with ⟨m, hm⟩
-  convert summable_condensed_iff_of_nonneg (f := fun k ↦ f (max k (n + m))) _ _ using 1
+  convert! summable_condensed_iff_of_nonneg (f := fun k ↦ f (max k (n + m))) _ _ using 1
   · rw [summable_congr_atTop]
     have h_pow := tendsto_pow_atTop_atTop_of_one_lt (r := 2) (by simp)
     filter_upwards [h_pow.eventually_ge_atTop (n + m)] with _ hk using by simp [max_eq_left hk]
diff --git a/Mathlib/Analysis/Polynomial/Basic.lean b/Mathlib/Analysis/Polynomial/Basic.lean
index 813621521feaf9..480ca8bcb02df2 100644
--- a/Mathlib/Analysis/Polynomial/Basic.lean
+++ b/Mathlib/Analysis/Polynomial/Basic.lean
@@ -121,13 +121,13 @@ end PolynomialAtTop
 section PolynomialAtBot
 
 theorem isEquivalent_atBot_lead : P.eval ~[atBot] (P.leadingCoeff * · ^ P.natDegree) := by
-  convert (P.comp (-X)).isEquivalent_atTop_lead.comp_tendsto tendsto_neg_atBot_atTop using 2
+  convert! (P.comp (-X)).isEquivalent_atTop_lead.comp_tendsto tendsto_neg_atBot_atTop using 2
   · simp
   · rw [Function.comp_apply, comp_neg_X_leadingCoeff_eq, ← mul_rotate]
     simp [natDegree_comp, ← mul_pow, mul_comm]
 
 theorem abs_tendsto_atBot (hdeg : 0 < P.degree) : Tendsto (|P.eval ·|) atBot atTop := by
-  convert ((P.comp (-X)).abs_tendsto_atTop (by simp [hdeg])).comp tendsto_neg_atBot_atTop using 2
+  convert! ((P.comp (-X)).abs_tendsto_atTop (by simp [hdeg])).comp tendsto_neg_atBot_atTop using 2
   simp
 
 theorem isBoundedUnder_abs_atBot_iff :
@@ -269,7 +269,7 @@ theorem isEquivalent_atBot_div :
 theorem div_tendsto_atBot_zero_of_degree_lt (hdeg : P.degree < Q.degree) :
     Tendsto (fun x ↦ eval x P / eval x Q) atBot (𝓝 0) := by
   rw [← P.degree_comp_neg_X, ← Q.degree_comp_neg_X] at hdeg
-  convert (div_tendsto_atTop_zero_of_degree_lt _ _ hdeg).comp tendsto_neg_atBot_atTop using 2
+  convert! (div_tendsto_atTop_zero_of_degree_lt _ _ hdeg).comp tendsto_neg_atBot_atTop using 2
   simp
 
 theorem div_tendsto_atBot_zero_iff_degree_lt (hQ : Q ≠ 0) :
@@ -280,7 +280,7 @@ theorem div_tendsto_atBot_zero_iff_degree_lt (hQ : Q ≠ 0) :
     rw [Ne, comp_eq_zero_iff]
     simp [hQ]
   rw [← div_tendsto_atTop_zero_iff_degree_lt _ _ hQ]
-  convert h.comp tendsto_neg_atTop_atBot using 2
+  convert! h.comp tendsto_neg_atTop_atBot using 2
   simp
 
 theorem div_tendsto_atBot_leadingCoeff_div_of_degree_eq (hdeg : P.degree = Q.degree) :
@@ -294,8 +294,8 @@ theorem abs_div_tendsto_atBot_atTop_of_degree_gt (hdeg : Q.degree < P.degree) (h
   replace hQ : Q.comp (-X) ≠ 0 := by
     rw [Ne, comp_eq_zero_iff]
     simp [hQ]
-  convert (abs_div_tendsto_atTop_atTop_of_degree_gt _ _ hdeg hQ).comp
-    tendsto_neg_atBot_atTop using 2
+  convert! (abs_div_tendsto_atTop_atTop_of_degree_gt _ _ hdeg hQ).comp tendsto_neg_atBot_atTop
+    using 2
   simp
 
 end PolynomialDivAtBot
@@ -310,7 +310,7 @@ theorem isLittleO_atTop_of_degree_lt (h : P.degree < Q.degree) : P.eval =o[atTop
 
 theorem isLittleO_atBot_of_degree_lt (h : P.degree < Q.degree) : P.eval =o[atBot] Q.eval := by
   rw [← P.degree_comp_neg_X, ← Q.degree_comp_neg_X] at h
-  convert (isLittleO_atTop_of_degree_lt _ _ h).comp_tendsto tendsto_neg_atBot_atTop using 2
+  convert! (isLittleO_atTop_of_degree_lt _ _ h).comp_tendsto tendsto_neg_atBot_atTop using 2
   all_goals simp
 
 theorem isBigO_atTop_of_degree_le (h : P.degree ≤ Q.degree) : P.eval =O[atTop] Q.eval := by
@@ -325,7 +325,7 @@ theorem isBigO_atTop_of_degree_le (h : P.degree ≤ Q.degree) : P.eval =O[atTop]
 
 theorem isBigO_atBot_of_degree_le (h : P.degree ≤ Q.degree) : P.eval =O[atBot] Q.eval := by
   rw [← P.degree_comp_neg_X, ← Q.degree_comp_neg_X] at h
-  convert (isBigO_atTop_of_degree_le _ _ h).comp_tendsto tendsto_neg_atBot_atTop using 2
+  convert! (isBigO_atTop_of_degree_le _ _ h).comp_tendsto tendsto_neg_atBot_atTop using 2
   all_goals simp
 
 @[deprecated (since := "2026-02-05")] alias isBigO_of_degree_le := isBigO_atTop_of_degree_le
diff --git a/Mathlib/Analysis/RCLike/Basic.lean b/Mathlib/Analysis/RCLike/Basic.lean
index d96e13a97e3ae7..8cd7f91d861bd8 100644
--- a/Mathlib/Analysis/RCLike/Basic.lean
+++ b/Mathlib/Analysis/RCLike/Basic.lean
@@ -1230,7 +1230,7 @@ lemma norm_le_im_iff_eq_I_mul_norm {z : K} :
   · simp [h, im_eq_zero]
   · have : (I : K) ≠ 0 := fun _ ↦ by simp_all
     rw [← mul_right_inj' (neg_ne_zero.mpr this)]
-    convert norm_le_re_iff_eq_norm (z := -I * z) using 2
+    convert! norm_le_re_iff_eq_norm (z := -I * z) using 2
     all_goals simp [neg_mul, ← mul_assoc, I_mul_I_of_nonzero this, norm_I_of_ne_zero this]
 
 lemma im_le_neg_norm_iff_eq_neg_I_mul_norm {z : K} :
diff --git a/Mathlib/Analysis/RCLike/Lemmas.lean b/Mathlib/Analysis/RCLike/Lemmas.lean
index 713e8292513c9b..354fa7cf92ac53 100644
--- a/Mathlib/Analysis/RCLike/Lemmas.lean
+++ b/Mathlib/Analysis/RCLike/Lemmas.lean
@@ -89,7 +89,7 @@ namespace RCLike
 @[simp, rclike_simps]
 theorem reCLM_norm : ‖(reCLM : StrongDual ℝ K)‖ = 1 := by
   apply le_antisymm (LinearMap.mkContinuous_norm_le _ zero_le_one _)
-  convert ContinuousLinearMap.ratio_le_opNorm (reCLM : StrongDual ℝ K) (1 : K)
+  convert! ContinuousLinearMap.ratio_le_opNorm (reCLM : StrongDual ℝ K) (1 : K)
   simp
 
 @[simp, rclike_simps]
diff --git a/Mathlib/Analysis/Real/Cardinality.lean b/Mathlib/Analysis/Real/Cardinality.lean
index bc81900ac79a29..ff769aca889f04 100644
--- a/Mathlib/Analysis/Real/Cardinality.lean
+++ b/Mathlib/Analysis/Real/Cardinality.lean
@@ -136,10 +136,10 @@ theorem increasing_cantorFunction (h1 : 0 < c) (h2 : c < 1 / 2) {n : ℕ} {f g :
     refine lt_of_lt_of_le ?_ (cantorFunction_le (le_of_lt h1) h3 hg_min)
     have : c / (1 - c) < 1 := by
       rw [div_lt_one, lt_sub_iff_add_lt]
-      · convert _root_.add_lt_add h2 h2
+      · convert! _root_.add_lt_add h2 h2
         norm_num
       rwa [sub_pos]
-    convert this
+    convert! this
     · rw [cantorFunction_succ _ (le_of_lt h1) h3, div_eq_mul_inv, ←
         tsum_geometric_of_lt_one (le_of_lt h1) h3]
       apply zero_add
@@ -188,7 +188,7 @@ theorem mk_real : #ℝ = 𝔠 := by
     apply mk_quotient_le.trans
     apply (mk_subtype_le _).trans_eq
     rw [← power_def, mk_nat, mkRat, aleph0_power_aleph0]
-  · convert mk_le_of_injective (cantorFunction_injective _ _)
+  · convert! mk_le_of_injective (cantorFunction_injective _ _)
     · rw [← power_def, mk_bool, mk_nat, two_power_aleph0]
     · exact 1 / 3
     · simp
@@ -212,12 +212,12 @@ theorem mk_Ioi_real (a : ℝ) : #(Ioi a) = 𝔠 := by
   intro h
   refine _root_.ne_of_lt ?_ mk_univ_real
   have hu : Iio a ∪ {a} ∪ Ioi a = Set.univ := by
-    convert @Iic_union_Ioi ℝ _ _
+    convert! @Iic_union_Ioi ℝ _ _
     exact Iio_union_right
   rw [← hu]
   grw [mk_union_le, mk_union_le]
   have h2 : (fun x => a + a - x) '' Ioi a = Iio a := by
-    convert @image_const_sub_Ioi ℝ _ _ _
+    convert! @image_const_sub_Ioi ℝ _ _ _
     simp
   rw [← h2]
   refine add_lt_of_lt (cantor _).le ?_ h
diff --git a/Mathlib/Analysis/Real/Hyperreal.lean b/Mathlib/Analysis/Real/Hyperreal.lean
index 35e64c6c0f343c..801634559d96f3 100644
--- a/Mathlib/Analysis/Real/Hyperreal.lean
+++ b/Mathlib/Analysis/Real/Hyperreal.lean
@@ -785,7 +785,7 @@ theorem infinitePos_add_not_infiniteNeg {x y : ℝ*} :
     InfinitePos x → ¬InfiniteNeg y → InfinitePos (x + y) := by
   intro hip hnin r
   obtain ⟨r₂, hr₂⟩ := not_forall.mp hnin
-  convert add_lt_add_of_lt_of_le (hip (r + -r₂)) (not_lt.mp hr₂) using 1
+  convert! add_lt_add_of_lt_of_le (hip (r + -r₂)) (not_lt.mp hr₂) using 1
   simp
 
 set_option linter.deprecated false in
diff --git a/Mathlib/Analysis/Real/OfDigits.lean b/Mathlib/Analysis/Real/OfDigits.lean
index 9a2c55b4899209..7617135d820ea8 100644
--- a/Mathlib/Analysis/Real/OfDigits.lean
+++ b/Mathlib/Analysis/Real/OfDigits.lean
@@ -74,7 +74,7 @@ theorem ofDigits_le_one {b : ℕ} (digits : ℕ → Fin b) : ofDigits digits ≤
   obtain rfl | hb := (Nat.one_le_of_lt (b_pos digits)).eq_or_lt
   · simp [ofDigits, ofDigitsTerm]
   rify at hb
-  convert Summable.tsum_mono summable_ofDigitsTerm _ (fun _ ↦ ofDigitsTerm_le)
+  convert! Summable.tsum_mono summable_ofDigitsTerm _ (fun _ ↦ ofDigitsTerm_le)
   · simp_rw [pow_succ', mul_inv, ← inv_pow, ← mul_assoc]
     rw [tsum_mul_left, tsum_geometric_of_lt_one (by positivity) (by simp [inv_lt_one_iff₀, hb])]
     have := sub_pos.mpr hb
@@ -102,8 +102,9 @@ theorem abs_ofDigits_sub_ofDigits_le {b : ℕ} {x y : ℕ → Fin b} {n : ℕ}
     Finset.sum_congr rfl fun i hi ↦ by simp [ofDigitsTerm, hxy i (Finset.mem_range.mp hi)]
   rw [this, add_sub_add_left_eq_sub, ← mul_sub, abs_mul, abs_of_nonneg (by positivity)]
   apply mul_le_of_le_one_right (by positivity)
-  convert abs_sub_le_of_le_of_le (ofDigits_nonneg _) (ofDigits_le_one _)
-    (ofDigits_nonneg _) (ofDigits_le_one _)
+  convert!
+    abs_sub_le_of_le_of_le (ofDigits_nonneg _) (ofDigits_le_one _) (ofDigits_nonneg _)
+      (ofDigits_le_one _)
   simp
 
 /-- Converts a real number `x` from the interval `[0, 1)` into sequence of
@@ -149,7 +150,7 @@ theorem hasSum_ofDigitsTerm_digits (x : ℝ) {b : ℕ} [NeZero b] (hb : 1 < b) (
   rw [hasSum_iff_tendsto_nat_of_summable_norm (by exact summable_ofDigitsTerm.abs)]
   refine tendsto_of_tendsto_of_tendsto_of_le_of_le ?_ tendsto_const_nhds
     (le_sum_ofDigitsTerm_digits hx) (sum_ofDigitsTerm_digits_le hx)
-  convert tendsto_const_nhds.sub (tendsto_pow_atTop_nhds_zero_of_abs_lt_one _)
+  convert! tendsto_const_nhds.sub (tendsto_pow_atTop_nhds_zero_of_abs_lt_one _)
   · simp
   · simp [abs_of_nonneg, inv_lt_one_iff₀, hb]
 
@@ -179,7 +180,7 @@ theorem ofDigits_const_last_eq_one (b : ℕ) [NeZero b] :
 /-- A generalization of the identity `0.(9) = 1` to arbitrary positional numeral systems. -/
 theorem ofDigits_const_last_eq_one' {b : ℕ} (hb : 1 < b) :
     ofDigits (fun _ ↦ (⟨b - 1, Nat.sub_one_lt_of_lt hb⟩ : Fin b)) = 1 := by
-  convert ofDigits_const_last_eq_one (b - 1)
+  convert! ofDigits_const_last_eq_one (b - 1)
   · grind
   · constructor
     grind
diff --git a/Mathlib/Analysis/Real/Pi/Irrational.lean b/Mathlib/Analysis/Real/Pi/Irrational.lean
index 3ce4808cca74a2..1651c973d025d5 100644
--- a/Mathlib/Analysis/Real/Pi/Irrational.lean
+++ b/Mathlib/Analysis/Real/Pi/Irrational.lean
@@ -82,15 +82,15 @@ private lemma recursion' (n : ℕ) :
   have hu₁_eval_neg_one : u₁ (-1) = 0 := by simp only [u₁, f]; simp
   have t : u₂ 1 * v₂ 1 - u₂ (-1) * v₂ (-1) = 2 * (0 ^ n * cos θ) := by simp [u₂, v₂, f, ← two_mul]
   have hf (x) : HasDerivAt f (- 2 * x) x := by
-    convert (hasDerivAt_pow 2 x).const_sub 1 using 1
+    convert! (hasDerivAt_pow 2 x).const_sub 1 using 1
     simp
   have hu₁ (x) : HasDerivAt u₁ (u₁' x) x := by
-    convert (hf x).pow _ using 1
+    convert! (hf x).pow _ using 1
     simp only [Nat.add_succ_sub_one, u₁', Nat.cast_add_one]
     ring
   have hv₁ (x) : HasDerivAt v₁ (v₁' x) x := (hasDerivAt_mul_const θ).sin
   have hu₂ (x) : HasDerivAt u₂ (u₂' x) x := by
-    convert (hasDerivAt_id' x).fun_mul ((hf x).fun_pow _) using 1
+    convert! (hasDerivAt_id' x).fun_mul ((hf x).fun_pow _) using 1
     simp only [u₂']
     ring
   have hv₂ (x) : HasDerivAt v₂ (v₂' x) x := (hasDerivAt_mul_const θ).cos
diff --git a/Mathlib/Analysis/Real/Pi/Wallis.lean b/Mathlib/Analysis/Real/Pi/Wallis.lean
index b55c4a8e3d704a..ec14dbd01d3e8f 100644
--- a/Mathlib/Analysis/Real/Pi/Wallis.lean
+++ b/Mathlib/Analysis/Real/Pi/Wallis.lean
@@ -87,7 +87,7 @@ theorem W_le (k : ℕ) : W k ≤ π / 2 := by
 theorem le_W (k : ℕ) : ((2 : ℝ) * k + 1) / (2 * k + 2) * (π / 2) ≤ W k := by
   rw [← le_div_iff₀ pi_div_two_pos, div_eq_inv_mul (W k) _]
   rw [W_eq_integral_sin_pow_div_integral_sin_pow, le_div_iff₀ (integral_sin_pow_pos _)]
-  convert integral_sin_pow_succ_le (2 * k + 1)
+  convert! integral_sin_pow_succ_le (2 * k + 1)
   rw [integral_sin_pow (2 * k)]
   simp
 
diff --git a/Mathlib/Analysis/Seminorm.lean b/Mathlib/Analysis/Seminorm.lean
index 925181a5acb12c..5b85fdc6f4f9dd 100644
--- a/Mathlib/Analysis/Seminorm.lean
+++ b/Mathlib/Analysis/Seminorm.lean
@@ -93,7 +93,7 @@ def Seminorm.ofSMulLE [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] (f : E
     rw [inv_mul_cancel_left₀ (norm_ne_zero_iff.mpr h)]
     specialize smul_le r⁻¹ (r • x)
     rw [norm_inv] at smul_le
-    convert smul_le
+    convert! smul_le
     simp [h]
 
 end Of
@@ -1015,7 +1015,7 @@ variable [Module ℝ E] [IsScalarTower ℝ 𝕜 E] (p : Seminorm 𝕜 E) (x : E)
 
 /-- Seminorm-balls are convex. -/
 theorem convex_ball : Convex ℝ (ball p x r) := by
-  convert (p.convexOn.translate_left (-x)).convex_lt r
+  convert! (p.convexOn.translate_left (-x)).convex_lt r
   ext y
   rw [preimage_univ, sep_univ, p.mem_ball, sub_eq_add_neg]
   rfl
diff --git a/Mathlib/Analysis/SpecialFunctions/ArithmeticGeometricMean.lean b/Mathlib/Analysis/SpecialFunctions/ArithmeticGeometricMean.lean
index 19faece604b370..491d320e82f600 100644
--- a/Mathlib/Analysis/SpecialFunctions/ArithmeticGeometricMean.lean
+++ b/Mathlib/Analysis/SpecialFunctions/ArithmeticGeometricMean.lean
@@ -243,7 +243,7 @@ lemma agm_eq_agm_agmSequences_fst_agmSequences_snd (n : ℕ) :
   refine tendsto_nhds_unique ?_ tendsto_agmSequences_snd_agm
   have key := @tendsto_agmSequences_snd_agm x y
   rw [← tendsto_add_atTop_iff_nat (n + 1)] at key
-  convert key using 2 with m
+  convert! key using 2 with m
   simp_rw [agmSequences, Prod.mk.eta, ← iterate_add_apply, add_right_comm]
 
 lemma agm_eq_agm_gm_am : agm x y = agm (sqrt (x * y)) ((x + y) / 2) := by
diff --git a/Mathlib/Analysis/SpecialFunctions/Arsinh.lean b/Mathlib/Analysis/SpecialFunctions/Arsinh.lean
index a8f3ac3f434ce4..69b898bf6ee3fc 100644
--- a/Mathlib/Analysis/SpecialFunctions/Arsinh.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Arsinh.lean
@@ -158,8 +158,9 @@ theorem arsinh_neg_iff : arsinh x < 0 ↔ x < 0 :=
   lt_iff_lt_of_le_iff_le arsinh_nonneg_iff
 
 theorem hasStrictDerivAt_arsinh (x : ℝ) : HasStrictDerivAt arsinh (√(1 + x ^ 2))⁻¹ x := by
-  convert sinhHomeomorph.toOpenPartialHomeomorph.hasStrictDerivAt_symm (mem_univ x) (cosh_pos _).ne'
-    (hasStrictDerivAt_sinh _) using 2
+  convert!
+    sinhHomeomorph.toOpenPartialHomeomorph.hasStrictDerivAt_symm (mem_univ x) (cosh_pos _).ne'
+      (hasStrictDerivAt_sinh _) using 2
   exact (cosh_arsinh _).symm
 
 theorem hasDerivAt_arsinh (x : ℝ) : HasDerivAt arsinh (√(1 + x ^ 2))⁻¹ x :=
diff --git a/Mathlib/Analysis/SpecialFunctions/Bernstein.lean b/Mathlib/Analysis/SpecialFunctions/Bernstein.lean
index 9dda84b3391df9..30d5dbaae35c12 100644
--- a/Mathlib/Analysis/SpecialFunctions/Bernstein.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Bernstein.lean
@@ -112,7 +112,7 @@ theorem probability (n : ℕ) (x : I) : (∑ k : Fin (n + 1), bernstein n k x) =
 
 theorem variance {n : ℕ} (hn : n ≠ 0) (x : I) :
     (∑ k : Fin (n + 1), (x - k/ₙ : ℝ) ^ 2 * bernstein n k x) = (x : ℝ) * (1 - x) / n := by
-  convert congr(Polynomial.aeval (x : ℝ) $(bernsteinPolynomial.variance ℝ n) / n ^ 2) using 1
+  convert! congr(Polynomial.aeval (x : ℝ) $(bernsteinPolynomial.variance ℝ n) / n ^ 2) using 1
   · simp only [z, bernstein_apply, nsmul_eq_mul, bernsteinPolynomial, Finset.sum_range, map_sum,
       Polynomial.coe_aeval_eq_eval, Polynomial.eval_mul, Polynomial.eval_pow, Polynomial.eval_sub,
       Polynomial.eval_natCast, Polynomial.eval_X, Polynomial.eval_one]
diff --git a/Mathlib/Analysis/SpecialFunctions/BinaryEntropy.lean b/Mathlib/Analysis/SpecialFunctions/BinaryEntropy.lean
index 0cd279e890e3a8..5a54ece56f0992 100644
--- a/Mathlib/Analysis/SpecialFunctions/BinaryEntropy.lean
+++ b/Mathlib/Analysis/SpecialFunctions/BinaryEntropy.lean
@@ -282,7 +282,7 @@ private lemma tendsto_log_one_sub_sub_log_nhdsLT_one_atBot :
     have : MapsTo ((1 : ℝ) - ·) (Iio 1) (Ioi 0) := by
       intro p hx
       simp_all only [mem_Iio, mem_Ioi, sub_pos]
-    convert ContinuousWithinAt.tendsto_nhdsWithin (x := (1 : ℝ)) contF.continuousWithinAt this
+    convert! ContinuousWithinAt.tendsto_nhdsWithin (x := (1 : ℝ)) contF.continuousWithinAt this
     exact Eq.symm (sub_eq_zero_of_eq rfl)
   · have h₁ : (1 : ℝ) - (2 : ℝ)⁻¹ < 1 := by norm_num
     filter_upwards [Ico_mem_nhdsLT h₁] with p hx
@@ -384,7 +384,7 @@ lemma qaryEntropy_strictMonoOn (qLe2 : 2 ≤ q) :
       · simp_all only [mem_Ioi, mul_pos_iff_of_pos_left, show 0 < (q : ℝ) - 1 by linarith]
       · have qpos : 0 < (q : ℝ) := by positivity
         have : q * p < q - 1 := by
-          convert mul_lt_mul_of_pos_left hp.2 qpos using 1
+          convert! mul_lt_mul_of_pos_left hp.2 qpos using 1
           simp only [mul_sub, mul_one, isUnit_iff_ne_zero, ne_eq, ne_of_gt qpos, not_false_eq_true,
             IsUnit.mul_inv_cancel]
         linarith
@@ -426,7 +426,7 @@ lemma binEntropy_strictMonoOn : StrictMonoOn binEntropy (Icc 0 2⁻¹) := by
 /-- Binary entropy is strictly decreasing in interval [1/2, 1]. -/
 lemma binEntropy_strictAntiOn : StrictAntiOn binEntropy (Icc 2⁻¹ 1) := by
   rw [show (Icc (2⁻¹ : ℝ) 1) = Icc (1 / 2) 1 by norm_num, ← qaryEntropy_two]
-  convert qaryEntropy_strictAntiOn (by rfl) using 1
+  convert! qaryEntropy_strictAntiOn (by rfl) using 1
   norm_num
 
 /-! ### Strict concavity of entropy -/
diff --git a/Mathlib/Analysis/SpecialFunctions/Complex/Arctan.lean b/Mathlib/Analysis/SpecialFunctions/Complex/Arctan.lean
index 8087dc3e00f567..c21a3ec5615687 100644
--- a/Mathlib/Analysis/SpecialFunctions/Complex/Arctan.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Complex/Arctan.lean
@@ -128,7 +128,7 @@ theorem hasSum_arctan {z : ℂ} (hz : ‖z‖ < 1) :
   simp_rw [← mul_comm 2 _] at this
   refine this.prod_fiberwise fun k => ?_
   dsimp only
-  convert hasSum_fintype (_ : Fin 2 → ℂ) using 1
+  convert! hasSum_fintype (_ : Fin 2 → ℂ) using 1
   rw [Fin.sum_univ_two, Fin.val_zero, Fin.val_one, Odd.neg_one_pow (n := 2 * k + 0 + 1) (by simp),
     neg_add_cancel, zero_mul, zero_div, mul_zero, zero_add,
     show 2 * k + 1 + 1 = 2 * (k + 1) by ring, Even.neg_one_pow (n := 2 * (k + 1)) (by simp),
diff --git a/Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean b/Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean
index 4ac8e9707dacdb..f1e483709208a3 100644
--- a/Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean
@@ -111,12 +111,13 @@ theorem arg_cos_add_sin_mul_I {θ : ℝ} (hθ : θ ∈ Set.Ioc (-π) π) : arg (
   rw [← one_mul (_ + _), ← ofReal_one, arg_mul_cos_add_sin_mul_I zero_lt_one hθ]
 
 theorem arg_exp (z : ℂ) : arg (exp z) = toIocMod Real.two_pi_pos (-π) z.im := by
-  convert arg_mul_cos_add_sin_mul_I (Real.exp_pos z.re)
-    (θ := toIocMod Real.two_pi_pos (-π) z.im) _ using 1
+  convert!
+    arg_mul_cos_add_sin_mul_I (Real.exp_pos z.re) (θ := toIocMod Real.two_pi_pos (-π) z.im) _
+    using 1
   · rw [← exp_mul_I, ofReal_exp, toIocMod]
     push_cast
     rw [exp_mul_I_periodic.sub_zsmul_eq, ← exp_add, re_add_im]
-  · convert toIocMod_mem_Ioc ..
+  · convert! toIocMod_mem_Ioc ..
     ring
 
 lemma arg_exp_mul_I (θ : ℝ) :
@@ -335,7 +336,7 @@ lemma norm_eq_one_iff' : ‖x‖ = 1 ↔ ∃ θ ∈ Set.Ioc (-π) π, exp (θ *
   constructor
   · rintro ⟨θ, rfl⟩
     refine ⟨toIocMod (mul_pos two_pos Real.pi_pos) (-π) θ, ?_, ?_⟩
-    · convert toIocMod_mem_Ioc _ _ _
+    · convert! toIocMod_mem_Ioc _ _ _
       ring
     · rw [eq_sub_of_add_eq <| toIocMod_add_toIocDiv_zsmul _ _ θ, ofReal_sub,
       ofReal_zsmul, ofReal_mul, ofReal_ofNat, exp_mul_I_periodic.sub_zsmul_eq]
@@ -486,7 +487,8 @@ theorem arg_cos_add_sin_mul_I_coe_angle (θ : Real.Angle) :
 
 theorem arg_mul_coe_angle {x y : ℂ} (hx : x ≠ 0) (hy : y ≠ 0) :
     (arg (x * y) : Real.Angle) = arg x + arg y := by
-  convert arg_mul_cos_add_sin_mul_I_coe_angle (mul_pos (norm_pos_iff.mpr hx) (norm_pos_iff.mpr hy))
+  convert!
+    arg_mul_cos_add_sin_mul_I_coe_angle (mul_pos (norm_pos_iff.mpr hx) (norm_pos_iff.mpr hy))
       (arg x + arg y : Real.Angle) using 3
   simp_rw [← Real.Angle.coe_add, Real.Angle.sin_coe, Real.Angle.cos_coe, ofReal_cos, ofReal_sin,
     cos_add_sin_I, ofReal_add, add_mul, exp_add, ofReal_mul]
@@ -602,9 +604,11 @@ theorem tendsto_arg_nhdsWithin_im_neg_of_re_neg_of_im_zero {z : ℂ} (hre : z.re
     have : ∀ᶠ x : ℂ in 𝓝 z, x.re < 0 := continuous_re.tendsto z (gt_mem_nhds hre)
     filter_upwards [self_mem_nhdsWithin, mem_nhdsWithin_of_mem_nhds this] with _ him hre
     rw [arg, if_neg hre.not_ge, if_neg him.not_ge]
-  convert (Real.continuousAt_arcsin.comp_continuousWithinAt
-    ((continuous_im.continuousAt.comp_continuousWithinAt continuousWithinAt_neg).div
-      continuous_norm.continuousWithinAt _)).sub_const π using 1
+  convert!
+    (Real.continuousAt_arcsin.comp_continuousWithinAt
+          ((continuous_im.continuousAt.comp_continuousWithinAt continuousWithinAt_neg).div
+            continuous_norm.continuousWithinAt _)).sub_const
+      π using 1
   · simp [him]
   · lift z to ℝ using him
     simpa using hre.ne
diff --git a/Mathlib/Analysis/SpecialFunctions/Complex/Circle.lean b/Mathlib/Analysis/SpecialFunctions/Complex/Circle.lean
index 0d08a7c0d9ab8a..6bca65ccb25844 100644
--- a/Mathlib/Analysis/SpecialFunctions/Complex/Circle.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Complex/Circle.lean
@@ -394,7 +394,7 @@ open AddCircle
 
 theorem Circle.isAddQuotientCoveringMap_exp :
     IsAddQuotientCoveringMap exp (AddSubgroup.zmultiples (2 * π)) := by
-  convert (isAddQuotientCoveringMap_coe _).homeomorph_comp (homeomorphCircle _)
+  convert! (isAddQuotientCoveringMap_coe _).homeomorph_comp (homeomorphCircle _)
   on_goal 2 => simp
   ext; simp [homeomorphCircle_apply, toCircle]
 
@@ -414,10 +414,12 @@ theorem Circle.isQuotientCoveringMap_zpow (n : ℤ) [NeZero n] :
   refine Topology.IsQuotientMap.isQuotientCoveringMap_of_isDiscrete_ker_monoidHom
     (f := zpowGroupHom (α := Circle) n) ?_ (Set.Finite.isDiscrete <| .of_preimage ?_ e.surjective)
   · refine .of_comp e.continuous (continuous_zpow n) ?_
-    convert e.isQuotientMap.comp <| IsUnit.isQuotientMap_zsmul (M := ℝ)
-      (QuotientAddGroup.mk' (AddSubgroup.zmultiples (1 : ℝ))) isQuotientMap_quotient_mk' n hn
+    convert!
+      e.isQuotientMap.comp <|
+        IsUnit.isQuotientMap_zsmul (M := ℝ) (QuotientAddGroup.mk' (AddSubgroup.zmultiples (1 : ℝ)))
+          isQuotientMap_quotient_mk' n hn
     ext; simp [zpowGroupHom, e, homeomorphCircle_apply, toCircle_zsmul]
-  · convert finite_torsion_of_isSMulRegular_int (1 : ℝ) n fun _ ↦ by simp [NeZero.ne]
+  · convert! finite_torsion_of_isSMulRegular_int (1 : ℝ) n fun _ ↦ by simp [NeZero.ne]
     ext
     simp [e, homeomorphCircle_apply, ← toCircle_zsmul, ← (injective_toCircle one_ne_zero).eq_iff]
 
diff --git a/Mathlib/Analysis/SpecialFunctions/Complex/Log.lean b/Mathlib/Analysis/SpecialFunctions/Complex/Log.lean
index 3073de182943f4..4e8f07b53d9af8 100644
--- a/Mathlib/Analysis/SpecialFunctions/Complex/Log.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Complex/Log.lean
@@ -200,9 +200,9 @@ alias ⟨_, _root_.Set.Countable.preimage_cexp⟩ := countable_preimage_exp
 
 theorem tendsto_log_nhdsWithin_im_neg_of_re_neg_of_im_zero {z : ℂ} (hre : z.re < 0)
     (him : z.im = 0) : Tendsto log (𝓝[{ z : ℂ | z.im < 0 }] z) (𝓝 <| Real.log ‖z‖ - π * I) := by
-  convert
+  convert!
     (continuous_ofReal.continuousAt.comp_continuousWithinAt
-            (continuous_norm.continuousWithinAt.log _)).tendsto.add
+          (continuous_norm.continuousWithinAt.log _)).tendsto.add
       (((continuous_ofReal.tendsto _).comp <|
             tendsto_arg_nhdsWithin_im_neg_of_re_neg_of_im_zero hre him).mul
         tendsto_const_nhds) using 1
@@ -212,9 +212,9 @@ theorem tendsto_log_nhdsWithin_im_neg_of_re_neg_of_im_zero {z : ℂ} (hre : z.re
 
 theorem continuousWithinAt_log_of_re_neg_of_im_zero {z : ℂ} (hre : z.re < 0) (him : z.im = 0) :
     ContinuousWithinAt log { z : ℂ | 0 ≤ z.im } z := by
-  convert
+  convert!
     (continuous_ofReal.continuousAt.comp_continuousWithinAt
-            (continuous_norm.continuousWithinAt.log _)).tendsto.add
+          (continuous_norm.continuousWithinAt.log _)).tendsto.add
       ((continuous_ofReal.continuousAt.comp_continuousWithinAt <|
             continuousWithinAt_arg_of_re_neg_of_im_zero hre him).mul
         tendsto_const_nhds) using 1
diff --git a/Mathlib/Analysis/SpecialFunctions/Complex/LogBounds.lean b/Mathlib/Analysis/SpecialFunctions/Complex/LogBounds.lean
index 44a13b9e764a5d..6e8b5e3d37582d 100644
--- a/Mathlib/Analysis/SpecialFunctions/Complex/LogBounds.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Complex/LogBounds.lean
@@ -44,9 +44,11 @@ open intervalIntegral in
 /-- Represent `log (1 + z)` as an integral over the unit interval -/
 lemma log_eq_integral {z : ℂ} (hz : 1 + z ∈ slitPlane) :
     log (1 + z) = z * ∫ (t : ℝ) in (0 : ℝ)..1, (1 + t • z)⁻¹ := by
-  convert (integral_unitInterval_deriv_eq_sub (continuousOn_one_add_mul_inv hz)
-    (fun _ ht ↦ hasDerivAt_log <|
-      StarConvex.add_smul_mem starConvex_one_slitPlane hz ht.1 ht.2)).symm using 1
+  convert!
+    (integral_unitInterval_deriv_eq_sub (continuousOn_one_add_mul_inv hz)
+        (fun _ ht ↦
+          hasDerivAt_log <|
+            StarConvex.add_smul_mem starConvex_one_slitPlane hz ht.1 ht.2)).symm using 1
   simp only [log_one, sub_zero]
 
 /-- Represent `log (1 - z)⁻¹` as an integral over the unit interval -/
@@ -54,7 +56,7 @@ lemma log_inv_eq_integral {z : ℂ} (hz : 1 - z ∈ slitPlane) :
     log (1 - z)⁻¹ = z * ∫ (t : ℝ) in (0 : ℝ)..1, (1 - t • z)⁻¹ := by
   rw [sub_eq_add_neg 1 z] at hz ⊢
   rw [log_inv _ <| slitPlane_arg_ne_pi hz, neg_eq_iff_eq_neg, ← neg_mul]
-  convert log_eq_integral hz using 5
+  convert! log_eq_integral hz using 5
   rw [sub_eq_add_neg, smul_neg]
 
 /-!
@@ -92,9 +94,9 @@ lemma hasDerivAt_logTaylor (n : ℕ) (z : ℂ) :
     simp only [mul_div_assoc]
     have : HasDerivAt (fun x : ℂ ↦ (x ^ (n + 1) / (n + 1))) (z ^ n) z := by
       simp_rw [div_eq_mul_inv]
-      convert HasDerivAt.mul_const (hasDerivAt_pow (n + 1) z) (((n : ℂ) + 1)⁻¹) using 1
+      convert! HasDerivAt.mul_const (hasDerivAt_pow (n + 1) z) (((n : ℂ) + 1)⁻¹) using 1
       simp [field]
-    convert HasDerivAt.const_mul _ this using 2
+    convert! HasDerivAt.const_mul _ this using 2
     ring
 
 /-!
@@ -103,7 +105,7 @@ lemma hasDerivAt_logTaylor (n : ℕ) (z : ℂ) :
 
 lemma hasDerivAt_log_sub_logTaylor (n : ℕ) {z : ℂ} (hz : 1 + z ∈ slitPlane) :
     HasDerivAt (fun z : ℂ ↦ log (1 + z) - logTaylor (n + 1) z) ((-z) ^ n * (1 + z)⁻¹) z := by
-  convert ((hasDerivAt_log hz).comp_const_add 1 z).sub (hasDerivAt_logTaylor n z) using 1
+  convert! ((hasDerivAt_log hz).comp_const_add 1 z).sub (hasDerivAt_logTaylor n z) using 1
   have hz' : -z ≠ 1 := by
     intro H
     rw [neg_eq_iff_eq_neg] at H
@@ -125,7 +127,7 @@ lemma norm_one_add_mul_inv_le {t : ℝ} (ht : t ∈ Set.Icc 0 1) {z : ℂ} (hz :
       rw [norm_mul, Complex.norm_of_nonneg ht.1]
     _ ≤ ‖1 + t * z‖ := by
       rw [← norm_neg (t * z), ← sub_neg_eq_add]
-      convert norm_sub_norm_le 1 (-(t * z))
+      convert! norm_sub_norm_le 1 (-(t * z))
       exact norm_one.symm
 
 lemma integrable_pow_mul_norm_one_add_mul_inv (n : ℕ) {z : ℂ} (hz : ‖z‖ < 1) :
@@ -153,7 +155,7 @@ lemma norm_log_sub_logTaylor_le (n : ℕ) {z : ℂ} (hz : ‖z‖ < 1) :
     exact (Continuous.continuousOn (by fun_prop)).mul <|
       continuousOn_one_add_mul_inv <| mem_slitPlane_of_norm_lt_one hz
   have H : f z = z * ∫ t in (0 : ℝ)..1, (-(t * z)) ^ n * (1 + t * z)⁻¹ := by
-    convert (integral_unitInterval_deriv_eq_sub hcont hderiv).symm using 1
+    convert! (integral_unitInterval_deriv_eq_sub hcont hderiv).symm using 1
     · simp only [f, zero_add, add_zero, log_one, logTaylor_at_zero, sub_self, sub_zero]
     · simp only [f', real_smul, zero_add,
         smul_eq_mul]
@@ -177,7 +179,7 @@ lemma norm_log_sub_logTaylor_le (n : ℕ) {z : ℂ} (hz : ‖z‖ < 1) :
 /-- The difference `log (1+z) - z` is bounded by `‖z‖^2/(2*(1-‖z‖))` when `‖z‖ < 1`. -/
 lemma norm_log_one_add_sub_self_le {z : ℂ} (hz : ‖z‖ < 1) :
     ‖log (1 + z) - z‖ ≤ ‖z‖ ^ 2 * (1 - ‖z‖)⁻¹ / 2 := by
-  convert norm_log_sub_logTaylor_le 1 hz using 2
+  convert! norm_log_sub_logTaylor_le 1 hz using 2
   · simp [logTaylor_succ, logTaylor_zero, sub_eq_add_neg]
   · norm_num
 
@@ -199,7 +201,7 @@ lemma log_sub_logTaylor_isBigO (n : ℕ) :
 open scoped Topology in
 lemma log_sub_self_isBigO :
     (fun z ↦ log (1 + z) - z) =O[𝓝 0] fun z ↦ z ^ 2 := by
-  convert log_sub_logTaylor_isBigO 1
+  convert! log_sub_logTaylor_isBigO 1
   simp [logTaylor_succ, logTaylor_zero]
 
 lemma norm_log_one_add_le {z : ℂ} (hz : ‖z‖ < 1) :
@@ -231,12 +233,12 @@ lemma norm_log_one_sub_inv_add_logTaylor_neg_le (n : ℕ) {z : ℂ} (hz : ‖z
   rw [sub_eq_add_neg,
     log_inv _ <| slitPlane_arg_ne_pi <| mem_slitPlane_of_norm_lt_one <| (norm_neg z).symm ▸ hz,
     ← sub_neg_eq_add, ← neg_sub', norm_neg]
-  convert norm_log_sub_logTaylor_le n <| (norm_neg z).symm ▸ hz using 4 <;> rw [norm_neg]
+  convert! norm_log_sub_logTaylor_le n <| (norm_neg z).symm ▸ hz using 4 <;> rw [norm_neg]
 
 /-- The difference `log (1-z)⁻¹ - z` is bounded by `‖z‖^2/(2*(1-‖z‖))` when `‖z‖ < 1`. -/
 lemma norm_log_one_sub_inv_sub_self_le {z : ℂ} (hz : ‖z‖ < 1) :
     ‖log (1 - z)⁻¹ - z‖ ≤ ‖z‖ ^ 2 * (1 - ‖z‖)⁻¹ / 2 := by
-  convert norm_log_one_sub_inv_add_logTaylor_neg_le 1 hz using 2
+  convert! norm_log_one_sub_inv_add_logTaylor_neg_le 1 hz using 2
   · simp [logTaylor_succ, logTaylor_zero, sub_eq_add_neg]
   · norm_num
 
@@ -272,7 +274,7 @@ lemma hasSum_taylorSeries_log {z : ℂ} (hz : ‖z‖ < 1) :
             · linarith
       exact (isBigOWith_of_le' atTop this).isBigO
     refine IsBigO.trans_isLittleO H ?_
-    convert isLittleO_pow_pow_of_lt_left (norm_nonneg z) hz
+    convert! isLittleO_pow_pow_of_lt_left (norm_nonneg z) hz
     exact (one_pow _).symm
 
 /-- The series `∑ z^n/n` converges to `-log (1-z)` on the open unit disk. -/
@@ -280,7 +282,7 @@ lemma hasSum_taylorSeries_neg_log {z : ℂ} (hz : ‖z‖ < 1) :
     HasSum (fun n : ℕ ↦ z ^ n / n) (-log (1 - z)) := by
   conv => enter [1, n]; rw [← neg_neg (z ^ n / n)]
   refine HasSum.neg ?_
-  convert hasSum_taylorSeries_log (z := -z) (norm_neg z ▸ hz) using 2 with n
+  convert! hasSum_taylorSeries_log (z := -z) (norm_neg z ▸ hz) using 2 with n
   rcases n.eq_zero_or_pos with rfl | hn
   · simp
   simp [field, pow_add, ← mul_pow]
@@ -367,7 +369,7 @@ lemma tendsto_pow_exp_of_isLittleO_sub_add_div {f : ℕ → ℂ} (t : ℂ)
     Tendsto (fun n ↦ f n ^ n) atTop (𝓝 (exp t)) := by
   rw [show (fun n ↦ f n ^ n) = (fun n ↦ (1 + (f n - 1)) ^ n) by ext; simp]
   refine tendsto_one_add_pow_exp_of_tendsto (tendsto_sub_nhds_zero_iff.1 ?_)
-  convert hf.tendsto_inv_smul_nhds_zero.congr' ?_
+  convert! hf.tendsto_inv_smul_nhds_zero.congr' ?_
   filter_upwards [eventually_ne_atTop 0] with n h0
   simp
   field_simp [n.cast_ne_zero.2 h0]
diff --git a/Mathlib/Analysis/SpecialFunctions/Elliptic/Weierstrass.lean b/Mathlib/Analysis/SpecialFunctions/Elliptic/Weierstrass.lean
index 28058fe0e8c107..4a0abb1a736926 100644
--- a/Mathlib/Analysis/SpecialFunctions/Elliptic/Weierstrass.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Elliptic/Weierstrass.lean
@@ -126,9 +126,9 @@ lemma isClosed_lattice : IsClosed (X := ℂ) L.lattice :=
     (inferInstanceAs (DiscreteTopology L.lattice))
 
 lemma isClosed_of_subset_lattice {s : Set ℂ} (hs : s ⊆ L.lattice) : IsClosed s := by
-  convert L.isClosed_lattice.isClosedMap_subtype_val _
-    (isClosed_discrete (α := L.lattice) ((↑) ⁻¹' s))
-  convert Set.image_preimage_eq_inter_range.symm using 1
+  convert!
+    L.isClosed_lattice.isClosedMap_subtype_val _ (isClosed_discrete (α := L.lattice) ((↑) ⁻¹' s))
+  convert! Set.image_preimage_eq_inter_range.symm using 1
   simpa
 
 lemma isOpen_compl_lattice_diff {s : Set ℂ} : IsOpen (L.lattice \ s)ᶜ :=
@@ -287,7 +287,7 @@ lemma weierstrassPExcept_of_notMem (l₀ : ℂ) (hl : l₀ ∉ L.lattice) :
 
 lemma hasSumLocallyUniformly_weierstrassP :
     HasSumLocallyUniformly (fun (l : L.lattice) (z : ℂ) ↦ 1 / (z - ↑l) ^ 2 - 1 / l ^ 2) ℘[L] := by
-  convert L.hasSumLocallyUniformly_weierstrassPExcept (L.ω₁ / 2) using 3 with l
+  convert! L.hasSumLocallyUniformly_weierstrassPExcept (L.ω₁ / 2) using 3 with l
   · rw [if_neg]; exact fun e ↦ L.ω₁_div_two_notMem_lattice (e ▸ l.2)
   · rw [L.weierstrassPExcept_of_notMem _ L.ω₁_div_two_notMem_lattice]
 
@@ -298,7 +298,7 @@ lemma hasSum_weierstrassP (z : ℂ) :
 lemma differentiableOn_weierstrassP :
     DifferentiableOn ℂ ℘[L] L.latticeᶜ := by
   rw [← L.weierstrassPExcept_of_notMem _ L.ω₁_div_two_notMem_lattice]
-  convert L.differentiableOn_weierstrassPExcept _
+  convert! L.differentiableOn_weierstrassPExcept _
   simp [L.ω₁_div_two_notMem_lattice]
 
 @[simp]
@@ -538,7 +538,7 @@ lemma derivWeierstrassPExcept_of_notMem (l₀ : ℂ) (hl : l₀ ∉ L.lattice) :
 
 lemma hasSumLocallyUniformly_derivWeierstrassP :
     HasSumLocallyUniformly (fun (l : L.lattice) (z : ℂ) ↦ - 2 / (z - l) ^ 3) ℘'[L] := by
-  convert L.hasSumLocallyUniformly_derivWeierstrassPExcept (L.ω₁ / 2) using 3 with l z
+  convert! L.hasSumLocallyUniformly_derivWeierstrassPExcept (L.ω₁ / 2) using 3 with l z
   · rw [if_neg, neg_div]; exact fun e ↦ L.ω₁_div_two_notMem_lattice (e ▸ l.2)
   · rw [L.derivWeierstrassPExcept_of_notMem _ L.ω₁_div_two_notMem_lattice]
 
@@ -549,7 +549,7 @@ lemma hasSum_derivWeierstrassP (z : ℂ) :
 lemma differentiableOn_derivWeierstrassP :
     DifferentiableOn ℂ ℘'[L] L.latticeᶜ := by
   rw [← L.derivWeierstrassPExcept_of_notMem _ L.ω₁_div_two_notMem_lattice]
-  convert L.differentiableOn_derivWeierstrassPExcept _
+  convert! L.differentiableOn_derivWeierstrassPExcept _
   simp [L.ω₁_div_two_notMem_lattice]
 
 @[simp]
@@ -734,8 +734,10 @@ lemma hasFPowerSeriesOnBall_weierstrassPExcept (l₀ x : ℂ) (r : NNReal) (hr0
     HasFPowerSeriesOnBall ℘[L - l₀] (L.weierstrassPExceptSeries l₀ x) x r := by
   constructor
   · apply FormalMultilinearSeries.le_radius_of_tendsto (l := 0)
-    convert tendsto_norm.comp (L.weierstrassPExceptSeries_hasSum l₀ (x + r) x
-      ?_).summable.tendsto_atTop_zero using 2 with i
+    convert!
+      tendsto_norm.comp
+        (L.weierstrassPExceptSeries_hasSum l₀ (x + r) x ?_).summable.tendsto_atTop_zero using
+      2 with i
     · simp
     · simp
     · intro l hl
@@ -749,7 +751,7 @@ lemma hasFPowerSeriesOnBall_weierstrassPExcept (l₀ x : ℂ) (r : NNReal) (hr0
     have A (l : ↥L.lattice) (hl : ↑l ≠ l₀) : r < ‖↑l - x‖ := by
       simpa [-Metric.mem_closedBall, mem_closedBall_iff_norm] using
         Set.subset_compl_comm.mp hr ⟨l.2, hl⟩
-    convert this (fun l hl ↦ hz.trans (A l hl)) with i
+    convert! this (fun l hl ↦ hz.trans (A l hl)) with i
     rw [weierstrassPExceptSeries, FormalMultilinearSeries.ofScalars_apply_eq,
       FormalMultilinearSeries.coeff_ofScalars, smul_eq_mul]
 
@@ -797,7 +799,7 @@ lemma hasFPowerSeriesOnBall_derivWeierstrassPExcept (l₀ x : ℂ) (r : NNReal)
   refine .congr ?_
     ((L.eqOn_deriv_weierstrassPExcept_derivWeierstrassPExcept l₀).mono (.trans ?_ hr))
   · have := (L.hasFPowerSeriesOnBall_weierstrassPExcept l₀ x r hr0 hr).fderiv
-    convert (ContinuousLinearMap.apply ℂ ℂ (1 : ℂ)).comp_hasFPowerSeriesOnBall this
+    convert! (ContinuousLinearMap.apply ℂ ℂ (1 : ℂ)).comp_hasFPowerSeriesOnBall this
     ext n
     simp [weierstrassPExceptSeries, derivWeierstrassPExceptSeries]
     ring
@@ -1045,7 +1047,7 @@ private lemma analyticAt_relation (x : ℂ) : AnalyticAt ℂ L.relation x := by
   · lift x to L.lattice using hx
     have := L.analyticAt_relation_zero
     rw [← sub_self x.1] at this
-    convert this.comp (f := (· - x.1)) (by fun_prop)
+    convert! this.comp (f := (· - x.1)) (by fun_prop)
     ext a
     simp
   · have : AnalyticAt ℂ (fun z ↦ ℘'[L] z ^ 2 - 4 * ℘[L] z ^ 3 + L.g₂ * ℘[L] z + L.g₃) x := by
diff --git a/Mathlib/Analysis/SpecialFunctions/Exp.lean b/Mathlib/Analysis/SpecialFunctions/Exp.lean
index 23fe81ee128f93..26a805eee4d867 100644
--- a/Mathlib/Analysis/SpecialFunctions/Exp.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Exp.lean
@@ -81,7 +81,7 @@ lemma exp_sub_sum_range_isBigO_pow (n : ℕ) :
   · refine .of_bound (n.succ / (n ! * n)) ?_
     rw [NormedAddGroup.nhds_zero_basis_norm_lt.eventually_iff]
     refine ⟨1, one_pos, fun x hx ↦ ?_⟩
-    convert exp_bound hx.out.le hn using 1
+    convert! exp_bound hx.out.le hn using 1
     simp [field]
 
 lemma exp_sub_sum_range_succ_isLittleO_pow (n : ℕ) :
@@ -224,7 +224,7 @@ theorem tendsto_exp_neg_atTop_nhds_zero : Tendsto (fun x => exp (-x)) atTop (
 
 /-- The real exponential function tends to `1` at `0`. -/
 theorem tendsto_exp_nhds_zero_nhds_one : Tendsto exp (𝓝 0) (𝓝 1) := by
-  convert continuous_exp.tendsto 0
+  convert! continuous_exp.tendsto 0
   simp
 
 theorem tendsto_exp_atBot : Tendsto exp atBot (𝓝 0) :=
@@ -288,12 +288,12 @@ theorem tendsto_div_pow_mul_exp_add_atTop (b c : ℝ) (n : ℕ) (hb : 0 ≠ b) :
     Tendsto (fun x => x ^ n / (b * exp x + c)) atTop (𝓝 0) := by
   have H : ∀ d e, 0 < d → Tendsto (fun x : ℝ => x ^ n / (d * exp x + e)) atTop (𝓝 0) := by
     intro b' c' h
-    convert (tendsto_mul_exp_add_div_pow_atTop b' c' n h).inv_tendsto_atTop using 1
+    convert! (tendsto_mul_exp_add_div_pow_atTop b' c' n h).inv_tendsto_atTop using 1
     ext x
     simp
   rcases lt_or_gt_of_ne hb with h | h
   · exact H b c h
-  · convert (H (-b) (-c) (neg_pos.mpr h)).neg using 1
+  · convert! (H (-b) (-c) (neg_pos.mpr h)).neg using 1
     · ext x
       field_simp
       rw [← neg_add (b * exp x) c, div_neg, neg_neg]
diff --git a/Mathlib/Analysis/SpecialFunctions/Exponential.lean b/Mathlib/Analysis/SpecialFunctions/Exponential.lean
index 7df936a7bdfcd1..4032b7535520ec 100644
--- a/Mathlib/Analysis/SpecialFunctions/Exponential.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Exponential.lean
@@ -71,7 +71,7 @@ variable {𝕂 𝔸 : Type*} [NontriviallyNormedField 𝕂] [NormedRing 𝔸] [C
 `1 : 𝔸 →L[𝕂] 𝔸` at zero, as long as it converges on a neighborhood of zero. -/
 theorem hasStrictFDerivAt_exp_zero_of_radius_pos (h : 0 < (expSeries 𝕂 𝔸).radius) :
     HasStrictFDerivAt exp (1 : 𝔸 →L[𝕂] 𝔸) 0 := by
-  convert (hasFPowerSeriesAt_exp_zero_of_radius_pos h).hasStrictFDerivAt
+  convert! (hasFPowerSeriesAt_exp_zero_of_radius_pos h).hasStrictFDerivAt
   ext x
   change x = expSeries 𝕂 𝔸 1 fun _ => x
   simp [expSeries_apply_eq, Nat.factorial]
@@ -286,7 +286,7 @@ theorem hasFDerivAt_exp_smul_const_of_mem_ball' (x : 𝔸) (t : 𝕊)
     (htx : t • x ∈ Metric.eball (0 : 𝔸) (expSeries 𝕂 𝔸).radius) :
     HasFDerivAt (fun u : 𝕊 => exp (u • x))
       (((1 : 𝕊 →L[𝕂] 𝕊).smulRight x).smulRight (exp (t • x))) t := by
-  convert hasFDerivAt_exp_smul_const_of_mem_ball 𝕂 _ _ htx using 1
+  convert! hasFDerivAt_exp_smul_const_of_mem_ball 𝕂 _ _ htx using 1
   ext t'
   change Commute (t' • x) (exp (t • x))
   exact (((Commute.refl x).smul_left t').smul_right t).exp_right
@@ -307,7 +307,7 @@ theorem hasStrictFDerivAt_exp_smul_const_of_mem_ball' (x : 𝔸) (t : 𝕊)
     HasStrictFDerivAt (fun u : 𝕊 => exp (u • x))
       (((1 : 𝕊 →L[𝕂] 𝕊).smulRight x).smulRight (exp (t • x))) t := by
   let ⟨_, _⟩ := analyticAt_exp_of_mem_ball (t • x) htx
-  convert hasStrictFDerivAt_exp_smul_const_of_mem_ball 𝕂 _ _ htx using 1
+  convert! hasStrictFDerivAt_exp_smul_const_of_mem_ball 𝕂 _ _ htx using 1
   ext t'
   change Commute (t' • x) (exp (t • x))
   exact (((Commute.refl x).smul_left t').smul_right t).exp_right
diff --git a/Mathlib/Analysis/SpecialFunctions/Gamma/Basic.lean b/Mathlib/Analysis/SpecialFunctions/Gamma/Basic.lean
index 913835f73bcfbb..bf6ca286384c5b 100644
--- a/Mathlib/Analysis/SpecialFunctions/Gamma/Basic.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Gamma/Basic.lean
@@ -158,7 +158,7 @@ private theorem Gamma_integrand_intervalIntegrable (s : ℂ) {X : ℝ} (hs : 0 <
 
 private theorem Gamma_integrand_deriv_integrable_A {s : ℂ} (hs : 0 < s.re) {X : ℝ} (hX : 0 ≤ X) :
     IntervalIntegrable (fun x => -((-x).exp * x ^ s) : ℝ → ℂ) volume 0 X := by
-  convert (Gamma_integrand_intervalIntegrable (s + 1) _ hX).neg
+  convert! (Gamma_integrand_intervalIntegrable (s + 1) _ hX).neg
   · simp only [ofReal_exp, ofReal_neg, add_sub_cancel_right]; rfl
   · simp only [add_re, one_re]; linarith
 
@@ -300,7 +300,7 @@ private theorem Gamma_eq_GammaAux (s : ℂ) (n : ℕ) (h1 : -s.re < ↑n) : Gamm
       simp only [sub_sub_cancel_left] at i0
       refine lt_add_of_lt_of_nonneg i0 ?_
       rw [← Nat.cast_zero, Nat.cast_le]; exact Nat.zero_le k
-  convert (u <| n - ⌊1 - s.re⌋₊).symm; rw [Nat.add_sub_of_le]
+  convert! (u <| n - ⌊1 - s.re⌋₊).symm; rw [Nat.add_sub_of_le]
   by_cases h : 0 ≤ 1 - s.re
   · apply Nat.le_of_lt_succ
     exact_mod_cast lt_of_le_of_lt (Nat.floor_le h) (by linarith : 1 - s.re < n + 1)
@@ -465,7 +465,7 @@ in terms of the Gamma function. -/
 lemma integral_rpow_mul_exp_neg_mul_Ioi {a r : ℝ} (ha : 0 < a) (hr : 0 < r) :
     ∫ t : ℝ in Ioi 0, t ^ (a - 1) * exp (-(r * t)) = (1 / r) ^ a * Gamma a := by
   rw [← ofReal_inj, ofReal_mul, ← Gamma_ofReal, ofReal_cpow (by positivity), ofReal_div]
-  convert integral_cpow_mul_exp_neg_mul_Ioi (by rwa [ofReal_re] : 0 < (a : ℂ).re) hr
+  convert! integral_cpow_mul_exp_neg_mul_Ioi (by rwa [ofReal_re] : 0 < (a : ℂ).re) hr
   refine integral_ofReal.symm.trans <| setIntegral_congr_fun measurableSet_Ioi (fun t ht ↦ ?_)
   norm_cast
   simp_rw [← ofReal_cpow ht.le, RCLike.ofReal_mul, coe_algebraMap]
diff --git a/Mathlib/Analysis/SpecialFunctions/Gamma/Beta.lean b/Mathlib/Analysis/SpecialFunctions/Gamma/Beta.lean
index c621c3abf18fd8..fe2b591e75040d 100644
--- a/Mathlib/Analysis/SpecialFunctions/Gamma/Beta.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Gamma/Beta.lean
@@ -80,7 +80,7 @@ theorem betaIntegral_convergent {u v : ℂ} (hu : 0 < re u) (hv : 0 < re v) :
       (x : ℂ) ^ (u - 1) * (1 - (x : ℂ)) ^ (v - 1) : ℝ → ℂ) volume 0 1 := by
   refine (betaIntegral_convergent_left hu v).trans ?_
   rw [IntervalIntegrable.iff_comp_neg]
-  convert ((betaIntegral_convergent_left hv u).comp_add_right 1).symm using 1
+  convert! ((betaIntegral_convergent_left hv u).comp_add_right 1).symm using 1
   · ext1 x
     conv_lhs => rw [mul_comm]
     congr 2 <;> · push_cast; ring
@@ -170,9 +170,9 @@ theorem betaIntegral_recurrence {u v : ℂ} (hu : 0 < re u) (hv : 0 < re v) :
       simp_rw [id] at A
       have B : HasDerivAt (fun y : ℂ => 1 - y) (-1) ↑x := by
         apply HasDerivAt.const_sub; apply hasDerivAt_id
-      convert HasDerivAt.comp (↑x) A B using 1
+      convert! HasDerivAt.comp (↑x) A B using 1
       ring
-    convert (U.mul V).comp_ofReal using 1
+    convert! (U.mul V).comp_ofReal using 1
     ring
   have h_int := ((betaIntegral_convergent hu hv').const_mul u).sub
     ((betaIntegral_convergent hu' hv).const_mul v)
@@ -189,11 +189,11 @@ theorem betaIntegral_recurrence {u v : ℂ} (hu : 0 < re u) (hv : 0 < re v) :
   rw [hF0, hF1, sub_zero, intervalIntegral.integral_sub, intervalIntegral.integral_const_mul,
     intervalIntegral.integral_const_mul] at int_ev
   · rw [betaIntegral, betaIntegral, ← sub_eq_zero]
-    convert int_ev <;> ring
+    convert! int_ev <;> ring
   · apply IntervalIntegrable.const_mul
-    convert betaIntegral_convergent hu hv'; ring
+    convert! betaIntegral_convergent hu hv'; ring
   · apply IntervalIntegrable.const_mul
-    convert betaIntegral_convergent hu' hv; ring
+    convert! betaIntegral_convergent hu' hv; ring
 
 /-- Explicit formula for the Beta function when second argument is a positive integer. -/
 theorem betaIntegral_eval_nat_add_one_right {u : ℂ} (hu : 0 < re u) (n : ℕ) :
@@ -302,13 +302,16 @@ theorem approx_Gamma_integral_tendsto_Gamma_integral {s : ℂ} (hs : 0 < re s) :
       exact ⟨hx, hn⟩
     · simp_rw [mul_comm]
       refine (Tendsto.comp (continuous_ofReal.tendsto _) ?_).const_mul _
-      convert Real.tendsto_one_add_div_pow_exp (-x) using 1
+      convert! Real.tendsto_one_add_div_pow_exp (-x) using 1
       ext1 n
       rw [neg_div, ← sub_eq_add_neg]
   -- let `convert` identify the remaining goals
-  convert tendsto_integral_of_dominated_convergence _ (fun n => (f_ible n).1)
-    (Real.GammaIntegral_convergent hs) _
-    ((ae_restrict_iff' measurableSet_Ioi).mpr (ae_of_all _ f_tends)) using 1
+  convert!
+    tendsto_integral_of_dominated_convergence _ (fun n => (f_ible n).1)
+      (Real.GammaIntegral_convergent hs) _
+      ((ae_restrict_iff' measurableSet_Ioi).mpr (ae_of_all _ f_tends)) using 1
+    -- limit of f is the integrand we want
+
   -- limit of f is the integrand we want
   · ext1 n
     rw [MeasureTheory.integral_indicator (measurableSet_Ioc : MeasurableSet (Ioc (_ : ℝ) _)),
@@ -409,13 +412,15 @@ theorem Gamma_mul_Gamma_one_sub (z : ℂ) : Gamma z * Gamma (1 - z) = π / sin (
         Complex.Gamma_neg_nat_eq_zero, mul_zero]
   refine tendsto_nhds_unique ((GammaSeq_tendsto_Gamma z).mul (GammaSeq_tendsto_Gamma <| 1 - z)) ?_
   have : ↑π / sin (↑π * z) = 1 * (π / sin (π * z)) := by rw [one_mul]
-  convert Tendsto.congr' ((eventually_ne_atTop 0).mp (Eventually.of_forall fun n hn =>
-    (GammaSeq_mul z hn).symm)) (Tendsto.mul _ _)
-  · convert tendsto_natCast_div_add_atTop (1 - z) using 1; ext1 n; rw [add_sub_assoc]
+  convert!
+    Tendsto.congr'
+      ((eventually_ne_atTop 0).mp (Eventually.of_forall fun n hn => (GammaSeq_mul z hn).symm))
+      (Tendsto.mul _ _)
+  · convert! tendsto_natCast_div_add_atTop (1 - z) using 1; ext1 n; rw [add_sub_assoc]
   · have : ↑π / sin (↑π * z) = 1 / (sin (π * z) / π) := by simp
-    convert tendsto_const_nhds.div _ (div_ne_zero hs pi_ne)
+    convert! tendsto_const_nhds.div _ (div_ne_zero hs pi_ne)
     rw [← tendsto_mul_iff_of_ne_zero tendsto_const_nhds pi_ne, div_mul_cancel₀ _ pi_ne]
-    convert tendsto_euler_sin_prod z using 1
+    convert! tendsto_euler_sin_prod z using 1
     ext1 n; rw [mul_comm, ← mul_assoc]
 
 /-- The Gamma function does not vanish on `ℂ` (except at non-positive integers, where the function
@@ -464,7 +469,7 @@ noncomputable def GammaSeq (s : ℝ) (n : ℕ) :=
 theorem GammaSeq_tendsto_Gamma (s : ℝ) : Tendsto (GammaSeq s) atTop (𝓝 <| Gamma s) := by
   suffices Tendsto ((↑) ∘ GammaSeq s : ℕ → ℂ) atTop (𝓝 <| Complex.Gamma s) by
     exact (Complex.continuous_re.tendsto (Complex.Gamma ↑s)).comp this
-  convert Complex.GammaSeq_tendsto_Gamma s
+  convert! Complex.GammaSeq_tendsto_Gamma s
   ext1 n
   dsimp only [GammaSeq, Function.comp_apply, Complex.GammaSeq]
   push_cast
@@ -543,7 +548,7 @@ theorem Gamma_mul_Gamma_add_half (s : ℂ) :
     Gamma s * Gamma (s + 1 / 2) = Gamma (2 * s) * (2 : ℂ) ^ (1 - 2 * s) * ↑(√π) := by
   suffices (fun z => (Gamma z)⁻¹ * (Gamma (z + 1 / 2))⁻¹) = fun z =>
       (Gamma (2 * z))⁻¹ * (2 : ℂ) ^ (2 * z - 1) / ↑(√π) by
-    convert congr_arg Inv.inv (congr_fun this s) using 1
+    convert! congr_arg Inv.inv (congr_fun this s) using 1
     · rw [mul_inv, inv_inv, inv_inv]
     · rw [div_eq_mul_inv, mul_inv, mul_inv, inv_inv, inv_inv, ← cpow_neg, neg_sub]
   have h1 : AnalyticOnNhd ℂ (fun z : ℂ => (Gamma z)⁻¹ * (Gamma (z + 1 / 2))⁻¹) univ := by
diff --git a/Mathlib/Analysis/SpecialFunctions/Gamma/BohrMollerup.lean b/Mathlib/Analysis/SpecialFunctions/Gamma/BohrMollerup.lean
index 53ea0ff4d7ae44..9ecdefb2fc89f5 100644
--- a/Mathlib/Analysis/SpecialFunctions/Gamma/BohrMollerup.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Gamma/BohrMollerup.lean
@@ -96,10 +96,9 @@ theorem Gamma_mul_add_mul_le_rpow_Gamma_mul_rpow_Gamma {s t a b : ℝ} (hs : 0 <
       exact continuousAt_rpow_const _ _ (Or.inl (mem_Ioi.mp hx).ne')
   -- now apply Hölder:
   rw [Gamma_eq_integral hs, Gamma_eq_integral ht, Gamma_eq_integral hst]
-  convert
+  convert!
     MeasureTheory.integral_mul_le_Lp_mul_Lq_of_nonneg e (posf' a s) (posf' b t) (f_mem_Lp ha hs)
-      (f_mem_Lp hb ht) using
-    1
+      (f_mem_Lp hb ht) using 1
   · refine setIntegral_congr_fun measurableSet_Ioi fun x hx => ?_
     dsimp only
     have A : exp (-x) = exp (-a * x) * exp (-b * x) := by
@@ -235,7 +234,7 @@ theorem tendsto_logGammaSeq_of_le_one (hf_conv : ConvexOn ℝ (Ioi 0) f)
     exact Tendsto.sub tendsto_const_nhds (tendsto_log_nat_add_one_sub_log.const_mul _)
   · filter_upwards with n
     rw [sub_le_iff_le_add', sub_le_iff_le_add']
-    convert le_logGammaSeq hf_conv (@hf_feq) hx hx' n using 1
+    convert! le_logGammaSeq hf_conv (@hf_feq) hx hx' n using 1
     ring
   · change ∀ᶠ n : ℕ in atTop, logGammaSeq x n ≤ f x - f 1
     filter_upwards [eventually_ne_atTop 0] with n hn using
@@ -248,7 +247,7 @@ theorem tendsto_logGammaSeq (hf_conv : ConvexOn ℝ (Ioi 0) f)
     refine this ⌈x - 1⌉₊ ?_ ?_
     · rcases lt_or_ge x 1 with ⟨⟩
       · rwa [Nat.ceil_eq_zero.mpr (by linarith : x - 1 ≤ 0), Nat.cast_zero]
-      · convert Nat.ceil_lt_add_one (by linarith : 0 ≤ x - 1)
+      · convert! Nat.ceil_lt_add_one (by linarith : 0 ≤ x - 1)
         abel
     · rw [← sub_le_iff_le_add]; exact Nat.le_ceil _
   intro m
@@ -286,7 +285,7 @@ theorem tendsto_logGammaSeq (hf_conv : ConvexOn ℝ (Ioi 0) f)
       dsimp only [Function.comp_apply]
       rw [sub_add_cancel, Nat.add_sub_cancel]
     rw [this] at hm
-    convert hm.sub (tendsto_log_nat_add_one_sub_log.const_mul x) using 2
+    convert! hm.sub (tendsto_log_nat_add_one_sub_log.const_mul x) using 2
     · ring
     · have := hf_feq ((Nat.cast_nonneg m).trans_lt hy)
       rw [sub_add_cancel] at this
@@ -354,9 +353,9 @@ theorem Gamma_strictAntiOn_Ioc : StrictAntiOn Gamma (Ioc 0 1) :=
     Gamma_one.symm ▸ Gamma_three_div_two_lt_one
 
 theorem Gamma_strictMonoOn_Ici : StrictMonoOn Gamma (Ici 2) := by
-  convert
-    convexOn_Gamma.strictMonoOn (by simp : (0 : ℝ) < 3 / 2)
-      (by norm_num : (3 / 2 : ℝ) < 2) (Gamma_two.symm ▸ Gamma_three_div_two_lt_one)
+  convert!
+    convexOn_Gamma.strictMonoOn (by simp : (0 : ℝ) < 3 / 2) (by norm_num : (3 / 2 : ℝ) < 2)
+      (Gamma_two.symm ▸ Gamma_three_div_two_lt_one)
   symm
   rw [inter_eq_right]
   exact fun x hx => two_pos.trans_le <| mem_Ici.mp hx
@@ -416,15 +415,14 @@ theorem log_doublingGamma_eq :
 
 theorem doublingGamma_log_convex_Ioi : ConvexOn ℝ (Ioi (0 : ℝ)) (log ∘ doublingGamma) := by
   refine (((ConvexOn.add ?_ ?_).add ?_).add_const _).congr log_doublingGamma_eq.symm
-  · convert
-      convexOn_log_Gamma.comp_affineMap (DistribSMul.toLinearMap ℝ ℝ (1 / 2 : ℝ)).toAffineMap
-      using 1
+  · convert!
+    convexOn_log_Gamma.comp_affineMap (DistribSMul.toLinearMap ℝ ℝ (1 / 2 : ℝ)).toAffineMap using 1
     · simpa only [zero_div] using (preimage_const_mul_Ioi₀ (0 : ℝ) one_half_pos).symm
     · ext1 x
       simp only [LinearMap.coe_toAffineMap, Function.comp_apply, DistribSMul.toLinearMap_apply]
       rw [smul_eq_mul, mul_comm, mul_one_div]
   · refine ConvexOn.subset ?_ (Ioi_subset_Ioi <| neg_one_lt_zero.le) (convex_Ioi _)
-    convert
+    convert!
       convexOn_log_Gamma.comp_affineMap
         ((DistribSMul.toLinearMap ℝ ℝ (1 / 2 : ℝ)).toAffineMap +
           AffineMap.const ℝ ℝ (1 / 2 : ℝ)) using 1
diff --git a/Mathlib/Analysis/SpecialFunctions/Gamma/Deligne.lean b/Mathlib/Analysis/SpecialFunctions/Gamma/Deligne.lean
index b098d210c928d5..fa8d2a794a3389 100644
--- a/Mathlib/Analysis/SpecialFunctions/Gamma/Deligne.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Gamma/Deligne.lean
@@ -103,7 +103,7 @@ lemma Gammaℝ_residue_zero : Tendsto (fun s ↦ s * Gammaℝ s) (𝓝[≠] 0) (
     refine Tendsto.mono_left (ContinuousAt.tendsto ?_) nhdsWithin_le_nhds
     exact continuousAt_const.mul ((continuousAt_const_cpow (ofReal_ne_zero.mpr pi_ne_zero)).comp
       (by fun_prop))
-  convert mul_one (2 : ℂ) ▸ (h'.mul h) using 2 with z
+  convert! mul_one (2 : ℂ) ▸ (h'.mul h) using 2 with z
   rw [Gammaℝ]
   ring_nf
 
@@ -187,7 +187,7 @@ lemma inv_Gammaℝ_two_sub {s : ℂ} (hs : ∀ (n : ℕ), s ≠ -n) :
     rcases n with - | m
     · rwa [Nat.cast_zero, neg_zero]
     · rw [Ne, sub_eq_iff_eq_add]
-      convert hs m using 2
+      convert! hs m using 2
       push_cast
       ring
   rw [(by ring : 2 - s = 1 - (s - 1)), inv_Gammaℝ_one_sub h',
diff --git a/Mathlib/Analysis/SpecialFunctions/Gamma/Deriv.lean b/Mathlib/Analysis/SpecialFunctions/Gamma/Deriv.lean
index f9d6e745bee19c..185a3ff403c56f 100644
--- a/Mathlib/Analysis/SpecialFunctions/Gamma/Deriv.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Gamma/Deriv.lean
@@ -50,7 +50,7 @@ transform of `log t * exp (-t)`. -/
 theorem hasDerivAt_GammaIntegral {s : ℂ} (hs : 0 < s.re) :
     HasDerivAt GammaIntegral (∫ t : ℝ in Ioi 0, t ^ (s - 1) * (Real.log t * Real.exp (-t))) s := by
   rw [GammaIntegral_eq_mellin]
-  convert (mellin_hasDerivAt_of_isBigO_rpow (E := ℂ) _ _ (lt_add_one _) _ hs).2
+  convert! (mellin_hasDerivAt_of_isBigO_rpow (E := ℂ) _ _ (lt_add_one _) _ hs).2
   · refine (Continuous.continuousOn ?_).locallyIntegrableOn measurableSet_Ioi
     exact continuous_ofReal.comp (Real.continuous_exp.comp continuous_neg)
   · rw [← isBigO_norm_left]
diff --git a/Mathlib/Analysis/SpecialFunctions/Gaussian/FourierTransform.lean b/Mathlib/Analysis/SpecialFunctions/Gaussian/FourierTransform.lean
index 640bb373d46507..f2ea3961909028 100644
--- a/Mathlib/Analysis/SpecialFunctions/Gaussian/FourierTransform.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Gaussian/FourierTransform.lean
@@ -245,7 +245,7 @@ theorem integrable_cexp_neg_sum_mul_add {ι : Type*} [Fintype ι] {b : ι → 
     Integrable (fun (v : ι → ℝ) ↦ cexp (-∑ i, b i * (v i : ℂ) ^ 2 + ∑ i, c i * v i)) := by
   simp_rw [← Finset.sum_neg_distrib, ← Finset.sum_add_distrib, Complex.exp_sum, ← neg_mul]
   apply Integrable.fintype_prod (f := fun i (v : ℝ) ↦ cexp (-b i * v ^ 2 + c i * v)) (fun i ↦ ?_)
-  convert integrable_cexp_quadratic (hb i) (c i) 0 using 3 with x
+  convert! integrable_cexp_quadratic (hb i) (c i) 0 using 3 with x
   simp only [add_zero]
 
 theorem integrable_cexp_neg_mul_sum_add {ι : Type*} [Fintype ι] (hb : 0 < b.re) (c : ι → ℂ) :
@@ -259,7 +259,7 @@ theorem integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace
   rw [← (PiLp.volume_preserving_toLp ι).integrable_comp_emb
     (MeasurableEquiv.toLp 2 _).measurableEmbedding]
   simp only [neg_mul, Function.comp_def]
-  convert integrable_cexp_neg_mul_sum_add hb (fun i ↦ c * w i) using 3 with v
+  convert! integrable_cexp_neg_mul_sum_add hb (fun i ↦ c * w i) using 3 with v
   simp only [EuclideanSpace.norm_eq, norm_eq_abs, sq_abs, PiLp.inner_apply, RCLike.inner_apply,
     conj_trivial, ofReal_sum, ofReal_mul, Finset.mul_sum, neg_mul, Finset.sum_neg_distrib,
     mul_assoc]
@@ -274,8 +274,7 @@ theorem integrable_cexp_neg_mul_sq_norm_add (hb : 0 < b.re) (c : ℂ) (w : V) :
     Integrable (fun (v : V) ↦ cexp (-b * ‖v‖ ^ 2 + c * ⟪w, v⟫)) := by
   let e := (stdOrthonormalBasis ℝ V).repr.symm
   rw [← e.measurePreserving.integrable_comp_emb e.toHomeomorph.measurableEmbedding]
-  convert integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace
-    hb c (e.symm w) with v
+  convert! integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace hb c (e.symm w) with v
   simp only [neg_mul, Function.comp_apply, LinearIsometryEquiv.norm_map,
     LinearIsometryEquiv.symm_symm,
     LinearIsometryEquiv.inner_map_eq_flip]
@@ -288,7 +287,7 @@ theorem integral_cexp_neg_sum_mul_add {ι : Type*} [Fintype ι] {b : ι → ℂ}
   rw [integral_fintype_prod_volume_eq_prod (f := fun i (v : ℝ) ↦ cexp (-b i * v ^ 2 + c i * v))]
   congr with i
   have : (-b i).re < 0 := by simpa using hb i
-  convert integral_cexp_quadratic this (c i) 0 using 1 <;> simp [div_neg]
+  convert! integral_cexp_quadratic this (c i) 0 using 1 <;> simp [div_neg]
 
 theorem integral_cexp_neg_mul_sum_add {ι : Type*} [Fintype ι] (hb : 0 < b.re) (c : ι → ℂ) :
     ∫ v : ι → ℝ, cexp (-b * ∑ i, (v i : ℂ) ^ 2 + ∑ i, c i * v i)
@@ -304,7 +303,7 @@ theorem integral_cexp_neg_mul_sq_norm_add_of_euclideanSpace
   rw [← (PiLp.volume_preserving_toLp ι).integral_comp
     (MeasurableEquiv.toLp 2 _).measurableEmbedding]
   simp only [neg_mul]
-  convert integral_cexp_neg_mul_sum_add hb (fun i ↦ c * w i) using 5 with _x y
+  convert! integral_cexp_neg_mul_sum_add hb (fun i ↦ c * w i) using 5 with _x y
   · simp only [EuclideanSpace.norm_eq, norm_eq_abs, sq_abs, neg_mul, neg_inj, mul_eq_mul_left_iff]
     norm_cast
     left
@@ -325,8 +324,8 @@ theorem integral_cexp_neg_mul_sq_norm_add
       (π / b) ^ (Module.finrank ℝ V / 2 : ℂ) * cexp (c ^ 2 * ‖w‖ ^ 2 / (4 * b)) := by
   let e := (stdOrthonormalBasis ℝ V).repr.symm
   rw [← e.measurePreserving.integral_comp e.toHomeomorph.measurableEmbedding]
-  convert integral_cexp_neg_mul_sq_norm_add_of_euclideanSpace
-    hb c (e.symm w) <;> simp [LinearIsometryEquiv.inner_map_eq_flip]
+  convert! integral_cexp_neg_mul_sq_norm_add_of_euclideanSpace hb c (e.symm w) <;>
+    simp [LinearIsometryEquiv.inner_map_eq_flip]
 
 theorem integral_cexp_neg_mul_sq_norm (hb : 0 < b.re) :
     ∫ v : V, cexp (-b * ‖v‖ ^ 2) = (π / b) ^ (Module.finrank ℝ V / 2 : ℂ) := by
@@ -335,7 +334,7 @@ theorem integral_cexp_neg_mul_sq_norm (hb : 0 < b.re) :
 theorem integral_rexp_neg_mul_sq_norm {b : ℝ} (hb : 0 < b) :
     ∫ v : V, rexp (-b * ‖v‖ ^ 2) = (π / b) ^ (Module.finrank ℝ V / 2 : ℝ) := by
   rw [← ofReal_inj]
-  convert integral_cexp_neg_mul_sq_norm (show 0 < (b : ℂ).re from hb) (V := V)
+  convert! integral_cexp_neg_mul_sq_norm (show 0 < (b : ℂ).re from hb) (V := V)
   · change ofRealLI (∫ (v : V), rexp (-b * ‖v‖ ^ 2)) = ∫ (v : V), cexp (-↑b * ↑‖v‖ ^ 2)
     rw [← ofRealLI.integral_comp_comm]
     simp [ofRealLI]
@@ -347,7 +346,7 @@ theorem _root_.fourier_gaussian_innerProductSpace' (hb : 0 < b.re) (x w : V) :
       (π / b) ^ (Module.finrank ℝ V / 2 : ℂ) * cexp (-π ^ 2 * ‖x - w‖ ^ 2 / b) := by
   simp only [neg_mul, fourier_eq', ofReal_neg, ofReal_mul, ofReal_ofNat,
     smul_eq_mul, ← Complex.exp_add, real_inner_comm w]
-  convert integral_cexp_neg_mul_sq_norm_add hb (2 * π * Complex.I) (x - w) using 3 with v
+  convert! integral_cexp_neg_mul_sq_norm_add hb (2 * π * Complex.I) (x - w) using 3 with v
   · congr 1
     simp [inner_sub_left]
     ring
diff --git a/Mathlib/Analysis/SpecialFunctions/Gaussian/GaussianIntegral.lean b/Mathlib/Analysis/SpecialFunctions/Gaussian/GaussianIntegral.lean
index 7974faebd6a6cb..ec4bc1bc43bcc3 100644
--- a/Mathlib/Analysis/SpecialFunctions/Gaussian/GaussianIntegral.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Gaussian/GaussianIntegral.lean
@@ -82,10 +82,10 @@ theorem integrableOn_rpow_mul_exp_neg_rpow {p s : ℝ} (hs : -1 < s) (hp : 1 ≤
         (ContinuousOn.mul (fun x hx => h_rpow x s hx) (fun x hx => ?_)) (IsLittleO.isBigO ?_)
       · rw [← Function.comp_def (fun x => exp (-x)) (· ^ p)]
         exact ContinuousAt.comp_continuousWithinAt (h_exp _) (h_rpow x p hx)
-      · convert rpow_mul_exp_neg_mul_rpow_isLittleO_exp_neg s hp (by simp : (0 : ℝ) < 1) using 3
+      · convert! rpow_mul_exp_neg_mul_rpow_isLittleO_exp_neg s hp (by simp : (0 : ℝ) < 1) using 3
         rw [neg_mul, one_mul]
   · simp_rw [← hp, Real.rpow_one]
-    convert Real.GammaIntegral_convergent (by linarith : 0 < s + 1) using 2
+    convert! Real.GammaIntegral_convergent (by linarith : 0 < s + 1) using 2
     rw [add_sub_cancel_right, mul_comm]
 
 theorem integrableOn_rpow_mul_exp_neg_mul_rpow {p s b : ℝ} (hs : -1 < s) (hp : 1 ≤ p) (hb : 0 < b) :
@@ -165,7 +165,7 @@ theorem integrable_mul_cexp_neg_mul_sq {b : ℂ} (hb : 0 < b.re) :
   · fun_prop
   have := (integrable_mul_exp_neg_mul_sq hb).hasFiniteIntegral
   rw [← hasFiniteIntegral_norm_iff] at this ⊢
-  convert this
+  convert! this
   rw [norm_mul, norm_mul, norm_cexp_neg_mul_sq b, norm_real, norm_of_nonneg (exp_pos _).le]
 
 theorem integral_mul_cexp_neg_mul_sq {b : ℂ} (hb : 0 < b.re) :
@@ -174,7 +174,7 @@ theorem integral_mul_cexp_neg_mul_sq {b : ℂ} (hb : 0 < b.re) :
   have A : ∀ x : ℂ, HasDerivAt (fun x => -(2 * b)⁻¹ * cexp (-b * x ^ 2))
     (x * cexp (-b * x ^ 2)) x := by
     intro x
-    convert ((hasDerivAt_pow 2 x).const_mul (-b)).cexp.const_mul (-(2 * b)⁻¹) using 1
+    convert! ((hasDerivAt_pow 2 x).const_mul (-b)).cexp.const_mul (-(2 * b)⁻¹) using 1
     field
   have B : Tendsto (fun y : ℝ ↦ -(2 * b)⁻¹ * cexp (-b * (y : ℂ) ^ 2))
     atTop (𝓝 (-(2 * b)⁻¹ * 0)) := by
@@ -182,8 +182,9 @@ theorem integral_mul_cexp_neg_mul_sq {b : ℂ} (hb : 0 < b.re) :
     simp_rw [norm_cexp_neg_mul_sq b]
     exact tendsto_exp_atBot.comp
       ((tendsto_pow_atTop two_ne_zero).const_mul_atTop_of_neg (neg_lt_zero.2 hb))
-  convert integral_Ioi_of_hasDerivAt_of_tendsto' (fun x _ => (A ↑x).comp_ofReal)
-    (integrable_mul_cexp_neg_mul_sq hb).integrableOn B using 1
+  convert!
+    integral_Ioi_of_hasDerivAt_of_tendsto' (fun x _ => (A ↑x).comp_ofReal)
+      (integrable_mul_cexp_neg_mul_sq hb).integrableOn B using 1
   simp only [mul_zero, ofReal_zero, zero_pow, Ne,
     not_false_iff, Complex.exp_zero, mul_one, sub_neg_eq_add, zero_add, reduceCtorEq]
 
@@ -229,7 +230,7 @@ theorem integral_gaussian (b : ℝ) : ∫ x : ℝ, exp (-b * x ^ 2) = √(π / b
   refine (sq_eq_sq₀ (by positivity) (by positivity)).1 ?_
   rw [← ofReal_inj, ofReal_pow, ← coe_algebraMap, RCLike.algebraMap_eq_ofReal, ← integral_ofReal,
     sq_sqrt (div_pos pi_pos hb).le, ← RCLike.algebraMap_eq_ofReal, coe_algebraMap, ofReal_div]
-  convert integral_gaussian_sq_complex (by rwa [ofReal_re] : 0 < (b : ℂ).re) with _ x
+  convert! integral_gaussian_sq_complex (by rwa [ofReal_re] : 0 < (b : ℂ).re) with _ x
   rw [ofReal_exp, ofReal_mul, ofReal_pow, ofReal_neg]
 
 theorem continuousAt_gaussian_integral (b : ℂ) (hb : 0 < re b) :
@@ -270,7 +271,7 @@ theorem integral_gaussian_complex {b : ℂ} (hb : 0 < re b) :
       · rw [← ofReal_one, ← ofReal_div]
       · rw [← ofReal_one, ← ofReal_ofNat, ← ofReal_div]
     rw [← ofReal_cpow, ofReal_inj]
-    · convert integral_gaussian (1 : ℝ) using 1
+    · convert! integral_gaussian (1 : ℝ) using 1
       rw [sqrt_eq_rpow]
     · rw [div_one]; exact pi_pos.le
   · -- squares of both sides agree
@@ -317,7 +318,7 @@ theorem integral_gaussian_Ioi (b : ℝ) :
     · rwa [← IntegrableOn, integrableOn_Ioi_exp_neg_mul_sq_iff, not_lt]
   rw [← RCLike.ofReal_inj (K := ℂ), ← integral_ofReal, ← RCLike.algebraMap_eq_ofReal,
     coe_algebraMap]
-  convert integral_gaussian_complex_Ioi (by rwa [ofReal_re] : 0 < (b : ℂ).re)
+  convert! integral_gaussian_complex_Ioi (by rwa [ofReal_re] : 0 < (b : ℂ).re)
   · simp
   · rw [sqrt_eq_rpow, ← ofReal_div, ofReal_div, ofReal_cpow]
     · simp
@@ -328,7 +329,7 @@ set_option linter.unusedSimpArgs false in
 /-- The special-value formula `Γ(1/2) = √π`, which is equivalent to the Gaussian integral. -/
 theorem Real.Gamma_one_half_eq : Real.Gamma (1 / 2) = √π := by
   rw [Gamma_eq_integral one_half_pos, ← integral_comp_rpow_Ioi_of_pos zero_lt_two]
-  convert congr_arg (fun x : ℝ => 2 * x) (integral_gaussian_Ioi 1) using 1
+  convert! congr_arg (fun x : ℝ => 2 * x) (integral_gaussian_Ioi 1) using 1
   · rw [← integral_const_mul]
     refine setIntegral_congr_fun measurableSet_Ioi fun x hx => ?_
     dsimp only
@@ -343,7 +344,7 @@ theorem Real.Gamma_one_half_eq : Real.Gamma (1 / 2) = √π := by
 
 /-- The special-value formula `Γ(1/2) = √π`, which is equivalent to the Gaussian integral. -/
 theorem Complex.Gamma_one_half_eq : Complex.Gamma (1 / 2) = (π : ℂ) ^ (1 / 2 : ℂ) := by
-  convert congr_arg ((↑) : ℝ → ℂ) Real.Gamma_one_half_eq
+  convert! congr_arg ((↑) : ℝ → ℂ) Real.Gamma_one_half_eq
   · simpa only [one_div, ofReal_inv, ofReal_ofNat] using Gamma_ofReal (1 / 2)
   · rw [sqrt_eq_rpow, ofReal_cpow pi_pos.le, ofReal_div, ofReal_ofNat, ofReal_one]
 
diff --git a/Mathlib/Analysis/SpecialFunctions/Gaussian/PoissonSummation.lean b/Mathlib/Analysis/SpecialFunctions/Gaussian/PoissonSummation.lean
index 37857a5dc55667..b5236856b0739a 100644
--- a/Mathlib/Analysis/SpecialFunctions/Gaussian/PoissonSummation.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Gaussian/PoissonSummation.lean
@@ -50,7 +50,7 @@ lemma rexp_neg_quadratic_isLittleO_rpow_atTop {a : ℝ} (ha : a < 0) (b s : ℝ)
 lemma cexp_neg_quadratic_isLittleO_rpow_atTop {a : ℂ} (ha : a.re < 0) (b : ℂ) (s : ℝ) :
     (fun x : ℝ ↦ cexp (a * x ^ 2 + b * x)) =o[atTop] (· ^ s) := by
   apply Asymptotics.IsLittleO.of_norm_left
-  convert rexp_neg_quadratic_isLittleO_rpow_atTop ha b.re s with x
+  convert! rexp_neg_quadratic_isLittleO_rpow_atTop ha b.re s with x
   simp_rw [Complex.norm_exp, add_re, ← ofReal_pow, mul_comm (_ : ℂ) ↑(_ : ℝ),
       re_ofReal_mul, mul_comm _ (re _)]
 
@@ -78,7 +78,7 @@ theorem tendsto_rpow_abs_mul_exp_neg_mul_sq_cocompact {a : ℝ} (ha : 0 < a) (s
 
 theorem isLittleO_exp_neg_mul_sq_cocompact {a : ℂ} (ha : 0 < a.re) (s : ℝ) :
     (fun x : ℝ => Complex.exp (-a * x ^ 2)) =o[cocompact ℝ] fun x : ℝ => |x| ^ s := by
-  convert cexp_neg_quadratic_isLittleO_abs_rpow_cocompact (?_ : (-a).re < 0) 0 s using 1
+  convert! cexp_neg_quadratic_isLittleO_abs_rpow_cocompact (?_ : (-a).re < 0) 0 s using 1
   · simp_rw [zero_mul, add_zero]
   · rwa [neg_re, neg_lt_zero]
 
@@ -103,7 +103,7 @@ theorem Complex.tsum_exp_neg_quadratic {a : ℂ} (ha : 0 < a.re) (b : ℂ) :
     contrapose! ha
     rw [ha, zero_re]
   have f_bd : f =O[cocompact ℝ] (fun x => |x| ^ (-2 : ℝ)) := by
-    convert (cexp_neg_quadratic_isLittleO_abs_rpow_cocompact ?_ _ (-2)).isBigO
+    convert! (cexp_neg_quadratic_isLittleO_abs_rpow_cocompact ?_ _ (-2)).isBigO
     rwa [neg_mul, neg_re, neg_lt_zero]
   have Ff_bd : (𝓕 f) =O[cocompact ℝ] (fun x => |x| ^ (-2 : ℝ)) := by
     rw [hFf]
@@ -115,7 +115,7 @@ theorem Complex.tsum_exp_neg_quadratic {a : ℂ} (ha : 0 < a.re) (b : ℂ) :
     refine ((cexp_neg_quadratic_isLittleO_abs_rpow_cocompact
       (?_) (-2 * ↑π * I * b / a) (-2)).isBigO.const_mul_left _).const_mul_left _
     rwa [neg_div, neg_re, neg_lt_zero]
-  convert Real.tsum_eq_tsum_fourier_of_rpow_decay hCf one_lt_two f_bd Ff_bd 0 using 1
+  convert! Real.tsum_eq_tsum_fourier_of_rpow_decay hCf one_lt_two f_bd Ff_bd 0 using 1
   · simp only [f, zero_add, ofReal_intCast]
   · rw [← tsum_mul_left]
     simp only [QuotientAddGroup.mk_zero, fourier_eval_zero, mul_one, hFf, ofReal_intCast]
diff --git a/Mathlib/Analysis/SpecialFunctions/ImproperIntegrals.lean b/Mathlib/Analysis/SpecialFunctions/ImproperIntegrals.lean
index 01f5993138b03f..125055d56bec26 100644
--- a/Mathlib/Analysis/SpecialFunctions/ImproperIntegrals.lean
+++ b/Mathlib/Analysis/SpecialFunctions/ImproperIntegrals.lean
@@ -117,7 +117,7 @@ theorem integrableOn_add_rpow_Ioi_of_lt {a c m : ℝ} (ha : a < -1) (hc : -m < c
     IntegrableOn (fun (x : ℝ) ↦ (x + m) ^ a) (Ioi c) := by
   have hd : ∀ x ∈ Ici c, HasDerivAt (fun t ↦ (t + m) ^ (a + 1) / (a + 1)) ((x + m) ^ a) x := by
     intro x hx
-    convert (((hasDerivAt_id _).add_const _).rpow_const _).div_const _ using 1
+    convert! (((hasDerivAt_id _).add_const _).rpow_const _).div_const _ using 1
     · simp [show a + 1 ≠ 0 by linarith]
     left; linarith [mem_Ici.mp hx, id_eq x]
   have ht : Tendsto (fun t ↦ ((t + m) ^ (a + 1)) / (a + 1)) atTop (nhds (0 / (a + 1))) := by
@@ -174,12 +174,12 @@ theorem integral_Ioi_rpow_of_lt {a : ℝ} (ha : a < -1) {c : ℝ} (hc : 0 < c) :
     ∫ t : ℝ in Ioi c, t ^ a = -c ^ (a + 1) / (a + 1) := by
   have hd : ∀ x ∈ Ici c, HasDerivAt (fun t => t ^ (a + 1) / (a + 1)) (x ^ a) x := by
     intro x hx
-    convert (hasDerivAt_rpow_const (p := a + 1) (Or.inl (hc.trans_le hx).ne')).div_const _ using 1
+    convert! (hasDerivAt_rpow_const (p := a + 1) (Or.inl (hc.trans_le hx).ne')).div_const _ using 1
     simp [show a + 1 ≠ 0 from ne_of_lt (by linarith), mul_comm]
   have ht : Tendsto (fun t => t ^ (a + 1) / (a + 1)) atTop (𝓝 (0 / (a + 1))) := by
     apply Tendsto.div_const
     simpa only [neg_neg] using tendsto_rpow_neg_atTop (by linarith : 0 < -(a + 1))
-  convert integral_Ioi_of_hasDerivAt_of_tendsto' hd (integrableOn_Ioi_rpow_of_lt ha hc) ht using 1
+  convert! integral_Ioi_of_hasDerivAt_of_tendsto' hd (integrableOn_Ioi_rpow_of_lt ha hc) ht using 1
   simp only [neg_div, zero_div, zero_sub]
 
 theorem integrableOn_Ioi_norm_cpow_of_lt {a : ℂ} (ha : a.re < -1) {c : ℝ} (hc : 0 < c) :
diff --git a/Mathlib/Analysis/SpecialFunctions/Integrability/Basic.lean b/Mathlib/Analysis/SpecialFunctions/Integrability/Basic.lean
index 5bfe0f4e1030c1..ba049d6ee37a70 100644
--- a/Mathlib/Analysis/SpecialFunctions/Integrability/Basic.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Integrability/Basic.lean
@@ -51,7 +51,7 @@ theorem intervalIntegrable_rpow' {r : ℝ} (h : -1 < r) :
     rw [intervalIntegrable_iff, uIoc_of_le hc]
     have hderiv : ∀ x ∈ Ioo 0 c, HasDerivAt (fun x : ℝ => x ^ (r + 1) / (r + 1)) (x ^ r) x := by
       intro x hx
-      convert (Real.hasDerivAt_rpow_const (p := r + 1) (Or.inl hx.1.ne')).div_const (r + 1) using 1
+      convert! (Real.hasDerivAt_rpow_const (p := r + 1) (Or.inl hx.1.ne')).div_const (r + 1) using 1
       simp [(by linarith : r + 1 ≠ 0)]
     apply integrableOn_deriv_of_nonneg _ hderiv
     · intro x hx; apply rpow_nonneg hx.1.le
diff --git a/Mathlib/Analysis/SpecialFunctions/Integrals/Basic.lean b/Mathlib/Analysis/SpecialFunctions/Integrals/Basic.lean
index 6d6facddf5b5d1..962a5e55889e4d 100644
--- a/Mathlib/Analysis/SpecialFunctions/Integrals/Basic.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Integrals/Basic.lean
@@ -152,7 +152,7 @@ theorem integral_rpow {r : ℝ} (h : -1 < r ∨ r ≠ -1 ∧ (0 : ℝ) ∉ [[a,
   have :
     (∫ x in a..b, (x : ℂ) ^ (r : ℂ)) = ((b : ℂ) ^ (r + 1 : ℂ) - (a : ℂ) ^ (r + 1 : ℂ)) / (r + 1) :=
     integral_cpow h'
-  apply_fun Complex.re at this; convert this
+  apply_fun Complex.re at this; convert! this
   · simp_rw [intervalIntegral_eq_integral_uIoc, Complex.real_smul, Complex.re_ofReal_mul, rpow_def,
       ← RCLike.re_eq_complex_re, smul_eq_mul]
     rw [integral_re]
@@ -382,15 +382,16 @@ theorem integral_mul_cpow_one_add_sq {t : ℂ} (ht : t ≠ -1) :
   apply integral_eq_sub_of_hasDerivAt
   · intro x _
     have f : HasDerivAt (fun y : ℂ => 1 + y ^ 2) (2 * x : ℂ) x := by
-      convert (hasDerivAt_pow 2 (x : ℂ)).const_add 1
+      convert! (hasDerivAt_pow 2 (x : ℂ)).const_add 1
       simp
     have g :
       ∀ {z : ℂ}, 0 < z.re → HasDerivAt (fun z => z ^ (t + 1) / (2 * (t + 1))) (z ^ t / 2) z := by
       intro z hz
-      convert (HasDerivAt.cpow_const (c := t + 1) (hasDerivAt_id _)
-        (Or.inl hz)).div_const (2 * (t + 1)) using 1
+      convert!
+        (HasDerivAt.cpow_const (c := t + 1) (hasDerivAt_id _) (Or.inl hz)).div_const
+          (2 * (t + 1)) using 1
       simp [field]
-    convert (HasDerivAt.comp (↑x) (g _) f).comp_ofReal using 1
+    convert! (HasDerivAt.comp (↑x) (g _) f).comp_ofReal using 1
     · ring
     · exact mod_cast add_pos_of_pos_of_nonneg zero_lt_one (sq_nonneg x)
   · apply Continuous.intervalIntegrable
@@ -409,7 +410,7 @@ theorem integral_mul_rpow_one_add_sq {t : ℝ} (ht : t ≠ -1) :
     rw [ofReal_cpow, ofReal_add, ofReal_pow, ofReal_one]
     exact add_nonneg zero_le_one (sq_nonneg x)
   rw [← ofReal_inj]
-  convert integral_mul_cpow_one_add_sq (_ : (t : ℂ) ≠ -1)
+  convert! integral_mul_cpow_one_add_sq (_ : (t : ℂ) ≠ -1)
   · rw [← intervalIntegral.integral_ofReal]
     congr with x : 1
     rw [ofReal_mul, this x t]
@@ -453,7 +454,7 @@ theorem integral_sin_pow :
       (sin a ^ (n + 1) * cos a - sin b ^ (n + 1) * cos b) / (n + 2) +
         (n + 1) / (n + 2) * ∫ x in a..b, sin x ^ n := by
   field_simp
-  convert eq_sub_iff_add_eq.mp (integral_sin_pow_aux n) using 1
+  convert! eq_sub_iff_add_eq.mp (integral_sin_pow_aux n) using 1
   ring
 
 @[simp]
@@ -526,7 +527,7 @@ theorem integral_cos_pow :
       (cos b ^ (n + 1) * sin b - cos a ^ (n + 1) * sin a) / (n + 2) +
         (n + 1) / (n + 2) * ∫ x in a..b, cos x ^ n := by
   field_simp
-  convert eq_sub_iff_add_eq.mp (integral_cos_pow_aux n) using 1
+  convert! eq_sub_iff_add_eq.mp (integral_cos_pow_aux n) using 1
   ring
 
 @[simp]
@@ -611,7 +612,7 @@ theorem integral_sin_pow_even_mul_cos_pow_even (m n : ℕ) :
 @[simp]
 theorem integral_sin_sq_mul_cos_sq :
     ∫ x in a..b, sin x ^ 2 * cos x ^ 2 = (b - a) / 8 - (sin (4 * b) - sin (4 * a)) / 32 := by
-  convert integral_sin_pow_even_mul_cos_pow_even 1 1 using 1
+  convert! integral_sin_pow_even_mul_cos_pow_even 1 1 using 1
   have h1 : ∀ c : ℝ, (↑1 - c) / ↑2 * ((↑1 + c) / ↑2) = (↑1 - c ^ 2) / 4 := fun c => by ring
   have h2 : Continuous fun x => cos (2 * x) ^ 2 := by fun_prop
   have h3 : ∀ x, cos x * sin x = sin (2 * x) / 2 := by intro; rw [sin_two_mul]; ring
diff --git a/Mathlib/Analysis/SpecialFunctions/Log/Basic.lean b/Mathlib/Analysis/SpecialFunctions/Log/Basic.lean
index 641e4fb4f88eac..f6c9ca89695e40 100644
--- a/Mathlib/Analysis/SpecialFunctions/Log/Basic.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Log/Basic.lean
@@ -305,7 +305,7 @@ theorem log_sqrt {x : ℝ} (hx : 0 ≤ x) : log (√x) = log x / 2 := by
 
 theorem log_le_sub_one_of_pos {x : ℝ} (hx : 0 < x) : log x ≤ x - 1 := by
   rw [le_sub_iff_add_le]
-  convert add_one_le_exp (log x)
+  convert! add_one_le_exp (log x)
   rw [exp_log hx]
 
 lemma one_sub_inv_le_log_of_pos (hx : 0 < x) : 1 - x⁻¹ ≤ log x := by
diff --git a/Mathlib/Analysis/SpecialFunctions/Log/Deriv.lean b/Mathlib/Analysis/SpecialFunctions/Log/Deriv.lean
index 498d28dd9a8062..a8ca2fea64a7fa 100644
--- a/Mathlib/Analysis/SpecialFunctions/Log/Deriv.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Log/Deriv.lean
@@ -44,7 +44,7 @@ theorem hasStrictDerivAt_log_of_pos (hx : 0 < x) : HasStrictDerivAt log x⁻¹ x
 
 theorem hasStrictDerivAt_log (hx : x ≠ 0) : HasStrictDerivAt log x⁻¹ x := by
   rcases hx.lt_or_gt with hx | hx
-  · convert (hasStrictDerivAt_log_of_pos (neg_pos.mpr hx)).comp x (hasStrictDerivAt_neg x) using 1
+  · convert! (hasStrictDerivAt_log_of_pos (neg_pos.mpr hx)).comp x (hasStrictDerivAt_neg x) using 1
     · ext y; exact (log_neg_eq_log y).symm
     · ring
   · exact hasStrictDerivAt_log_of_pos hx
@@ -75,7 +75,7 @@ theorem contDiffAt_log {n : ℕ∞ω} {x : ℝ} : ContDiffAt ℝ n log x ↔ x 
   refine ⟨fun h ↦ continuousAt_log_iff.1 h.continuousAt, fun hx ↦ ?_⟩
   have A y (hy : 0 < y) : ContDiffAt ℝ n log y := by
     apply expPartialHomeomorph.contDiffAt_symm_deriv (f₀' := y) hy.ne' (by simpa)
-    · convert hasDerivAt_exp (log y)
+    · convert! hasDerivAt_exp (log y)
       rw [exp_log hy]
     · exact analyticAt_rexp.contDiffAt
   rcases hx.lt_or_gt with hx | hx
@@ -83,7 +83,7 @@ theorem contDiffAt_log {n : ℕ∞ω} {x : ℝ} : ContDiffAt ℝ n log x ↔ x 
       apply ContDiffAt.comp
       · apply A _ (Left.neg_pos_iff.mpr hx)
       apply contDiffAt_id.neg
-    convert this
+    convert! this
     ext x
     simp
   · exact A x hx
@@ -227,7 +227,7 @@ theorem abs_log_sub_add_sum_range_le {x : ℝ} (h : |x| < 1) (n : ℕ) :
     have : HasDerivAt F ((∑ i ∈ range n, ↑(i + 1) * y ^ i / (↑i + 1)) + (-1) / (1 - y)) y :=
       .add (.fun_sum fun i _ ↦ (hasDerivAt_pow (i + 1) y).div_const ((i : ℝ) + 1))
         (((hasDerivAt_id y).const_sub _).log <| sub_ne_zero.2 hy.2.ne')
-    convert this using 1
+    convert! this using 1
     calc
       -y ^ n / (1 - y) = ∑ i ∈ Finset.range n, y ^ i + -1 / (1 - y) := by
         simp [field, geom_sum_eq hy.2.ne, sub_ne_zero.2 hy.2.ne, sub_ne_zero.2 hy.2.ne']
@@ -387,7 +387,7 @@ theorem hasSum_log_sub_log_of_abs_lt_one {x : ℝ} (h : |x| < 1) :
     ring_nf
   rw [← h_term_eq_goal, (mul_right_injective₀ (two_ne_zero' ℕ)).hasSum_iff]
   · have h₁ := (hasSum_pow_div_log_of_abs_lt_one (Eq.trans_lt (abs_neg x) h)).mul_left (-1)
-    convert h₁.add (hasSum_pow_div_log_of_abs_lt_one h) using 1
+    convert! h₁.add (hasSum_pow_div_log_of_abs_lt_one h) using 1
     ring_nf
   · intro m hm
     rw [range_two_mul, Set.mem_setOf_eq, ← Nat.even_add_one] at hm
@@ -403,7 +403,7 @@ theorem hasSum_log_one_add_inv {a : ℝ} (h : 0 < a) :
     · linarith
     · linarith
     · exact div_pos one_pos (by linarith)
-  convert hasSum_log_sub_log_of_abs_lt_one h₁ using 1
+  convert! hasSum_log_sub_log_of_abs_lt_one h₁ using 1
   have h₂ : (2 : ℝ) * a + 1 ≠ 0 := by linarith
   have h₃ := h.ne'
   rw [← log_div]
@@ -420,16 +420,17 @@ theorem hasSum_log_one_add {a : ℝ} (h : 0 ≤ a) :
       (log (1 + a)) := by
   obtain (rfl | ha0) := eq_or_ne a 0
   · simp [hasSum_zero]
-  · convert hasSum_log_one_add_inv (inv_pos.mpr (lt_of_le_of_ne h ha0.symm)) using 4
+  · convert! hasSum_log_one_add_inv (inv_pos.mpr (lt_of_le_of_ne h ha0.symm)) using 4
     all_goals simp [field, add_comm]
 
 lemma le_log_one_add_of_nonneg {x : ℝ} (hx : 0 ≤ x) : 2 * x / (x + 2) ≤ log (1 + x) := by
-  convert le_hasSum (hasSum_log_one_add hx) 0 (by intros; positivity) using 1
+  convert! le_hasSum (hasSum_log_one_add hx) 0 (by intros; positivity) using 1
   simp [field]
 
 lemma lt_log_one_add_of_pos {x : ℝ} (hx : 0 < x) : 2 * x / (x + 2) < log (1 + x) := by
-  convert lt_hasSum (hasSum_log_one_add hx.le) 0 (by intros; positivity)
-    1 (by positivity) (by positivity) using 1
+  convert!
+    lt_hasSum (hasSum_log_one_add hx.le) 0 (by intros; positivity) 1 (by positivity)
+      (by positivity) using 1
   simp [field]
 
 end Real
diff --git a/Mathlib/Analysis/SpecialFunctions/Log/ENNRealLogExp.lean b/Mathlib/Analysis/SpecialFunctions/Log/ENNRealLogExp.lean
index ac8f42fa1811b5..f1733727682ffd 100644
--- a/Mathlib/Analysis/SpecialFunctions/Log/ENNRealLogExp.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Log/ENNRealLogExp.lean
@@ -122,7 +122,7 @@ lemma _root_.EReal.tendsto_exp_nhds_top_nhds_top : Filter.Tendsto exp (𝓝 ⊤)
   continuous_exp.tendsto ⊤
 
 lemma _root_.EReal.tendsto_exp_nhds_zero_nhds_one : Filter.Tendsto exp (𝓝 0) (𝓝 1) := by
-  convert continuous_exp.tendsto 0
+  convert! continuous_exp.tendsto 0
   simp
 
 lemma _root_.EReal.tendsto_exp_nhds_bot_nhds_zero : Filter.Tendsto exp (𝓝 ⊥) (𝓝 0) :=
@@ -132,7 +132,7 @@ lemma tendsto_rpow_atTop_of_one_lt_base {b : ℝ≥0∞} (hb : 1 < b) :
     Filter.Tendsto (b ^ · : ℝ → ℝ≥0∞) Filter.atTop (𝓝 ⊤) := by
   simp_rw [ENNReal.rpow_eq_exp_mul_log]
   refine EReal.tendsto_exp_nhds_top_nhds_top.comp ?_
-  convert EReal.Tendsto.mul_const tendsto_coe_atTop _ _
+  convert! EReal.Tendsto.mul_const tendsto_coe_atTop _ _
   · rw [EReal.top_mul_of_pos (zero_lt_log_iff.2 hb)]
   all_goals simp
 
@@ -140,7 +140,7 @@ lemma tendsto_rpow_atTop_of_base_lt_one {b : ℝ≥0∞} (hb : b < 1) :
     Filter.Tendsto (b ^ · : ℝ → ℝ≥0∞) Filter.atTop (𝓝 0) := by
   simp_rw [ENNReal.rpow_eq_exp_mul_log]
   refine EReal.tendsto_exp_nhds_bot_nhds_zero.comp ?_
-  convert EReal.Tendsto.mul_const tendsto_coe_atTop _ _
+  convert! EReal.Tendsto.mul_const tendsto_coe_atTop _ _
   · rw [EReal.top_mul_of_neg (log_lt_zero_iff.2 hb)]
   all_goals simp
 
@@ -148,7 +148,7 @@ lemma tendsto_rpow_atBot_of_one_lt_base {b : ℝ≥0∞} (hb : 1 < b) :
     Filter.Tendsto (b ^ · : ℝ → ℝ≥0∞) Filter.atBot (𝓝 0) := by
   simp_rw [ENNReal.rpow_eq_exp_mul_log]
   refine EReal.tendsto_exp_nhds_bot_nhds_zero.comp ?_
-  convert EReal.Tendsto.mul_const tendsto_coe_atBot _ _
+  convert! EReal.Tendsto.mul_const tendsto_coe_atBot _ _
   · rw [EReal.bot_mul_of_pos (zero_lt_log_iff.2 hb)]
   all_goals simp
 
@@ -156,7 +156,7 @@ lemma tendsto_rpow_atBot_of_base_lt_one {b : ℝ≥0∞} (hb : b < 1) :
     Filter.Tendsto (b ^ · : ℝ → ℝ≥0∞) Filter.atBot (𝓝 ⊤) := by
   simp_rw [ENNReal.rpow_eq_exp_mul_log]
   refine EReal.tendsto_exp_nhds_top_nhds_top.comp ?_
-  convert EReal.Tendsto.mul_const tendsto_coe_atBot _ _
+  convert! EReal.Tendsto.mul_const tendsto_coe_atBot _ _
   · rw [EReal.bot_mul_of_neg (log_lt_zero_iff.2 hb)]
   all_goals simp
 
diff --git a/Mathlib/Analysis/SpecialFunctions/Log/Monotone.lean b/Mathlib/Analysis/SpecialFunctions/Log/Monotone.lean
index 849f0c54910b05..11c472c0be494e 100644
--- a/Mathlib/Analysis/SpecialFunctions/Log/Monotone.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Log/Monotone.lean
@@ -72,7 +72,7 @@ theorem log_div_self_rpow_antitoneOn {a : ℝ} (ha : 0 < a) :
     mul_div_assoc, mul_le_mul_iff_right₀ (one_div_pos.mpr ha)]
   have hbound {z : ℝ} (hz : z ∈ Ici (rexp a⁻¹)) : z ^ a ∈ {b | rexp 1 ≤ b} := by
     rw [mem_setOf_eq]
-    convert rpow_le_rpow _ hz (le_of_lt ha) using 1
+    convert! rpow_le_rpow _ hz (le_of_lt ha) using 1
     · simp only [← exp_mul, Real.exp_eq_exp, field]
     positivity
   refine log_div_self_antitoneOn (hbound hex) (hbound (hex.trans hxy)) ?_
@@ -80,7 +80,7 @@ theorem log_div_self_rpow_antitoneOn {a : ℝ} (ha : 0 < a) :
 
 theorem log_div_sqrt_antitoneOn : AntitoneOn (fun x : ℝ ↦ log x / √x) <| .Ici (exp 2) := by
   simp_rw [sqrt_eq_rpow]
-  convert log_div_self_rpow_antitoneOn one_half_pos
+  convert! log_div_self_rpow_antitoneOn one_half_pos
   norm_num
 
 end Real
diff --git a/Mathlib/Analysis/SpecialFunctions/Log/NegMulLog.lean b/Mathlib/Analysis/SpecialFunctions/Log/NegMulLog.lean
index 19ef6b7dacf6bd..da6eb99e59ea35 100644
--- a/Mathlib/Analysis/SpecialFunctions/Log/NegMulLog.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Log/NegMulLog.lean
@@ -55,7 +55,7 @@ lemma continuous_mul_log : Continuous fun x ↦ x * log x := by
   simp only [nhdsWithin_singleton, Filter.tendsto_sup]
   refine ⟨⟨tendsto_log_mul_self_nhdsLT_zero, ?_⟩, ?_⟩
   · simpa only [rpow_one] using tendsto_log_mul_rpow_nhdsGT_zero zero_lt_one
-  · convert tendsto_pure_nhds (fun x ↦ log x * x) 0
+  · convert! tendsto_pure_nhds (fun x ↦ log x * x) 0
     simp
 
 @[fun_prop]
diff --git a/Mathlib/Analysis/SpecialFunctions/Log/PosLog.lean b/Mathlib/Analysis/SpecialFunctions/Log/PosLog.lean
index 1d10fdb63a1995..c0f14e0220eb92 100644
--- a/Mathlib/Analysis/SpecialFunctions/Log/PosLog.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Log/PosLog.lean
@@ -197,7 +197,7 @@ lemma posLog_norm_sum_le {E : Type*} [SeminormedAddCommGroup E] {α : Type*} (s
 Estimate for `log⁺` of a sum. See `Real.posLog_sum` for a variant involving multiple summands.
 -/
 theorem posLog_add : log⁺ (x + y) ≤ log 2 + log⁺ x + log⁺ y := by
-  convert posLog_sum Finset.univ ![x, y] using 1 <;> simp [add_assoc]
+  convert! posLog_sum Finset.univ ![x, y] using 1 <;> simp [add_assoc]
 
 /--
 Variant of `posLog_add` for norms of elements in normed additive commutative groups, using
diff --git a/Mathlib/Analysis/SpecialFunctions/OrdinaryHypergeometric.lean b/Mathlib/Analysis/SpecialFunctions/OrdinaryHypergeometric.lean
index 54109c74f5976f..69e305c14fcc94 100644
--- a/Mathlib/Analysis/SpecialFunctions/OrdinaryHypergeometric.lean
+++ b/Mathlib/Analysis/SpecialFunctions/OrdinaryHypergeometric.lean
@@ -199,16 +199,16 @@ are non-positive integers. -/
 theorem ordinaryHypergeometricSeries_radius_eq_one
     (habc : ∀ kn : ℕ, ↑kn ≠ -a ∧ ↑kn ≠ -b ∧ ↑kn ≠ -c) :
     (ordinaryHypergeometricSeries 𝔸 a b c).radius = 1 := by
-  convert ofScalars_radius_eq_of_tendsto 𝔸 _ one_ne_zero ?_
+  convert! ofScalars_radius_eq_of_tendsto 𝔸 _ one_ne_zero ?_
   suffices Tendsto (fun k : ℕ ↦ (a + k)⁻¹ * (b + k)⁻¹ * (c + k) * ((1 : 𝕂) + k)) atTop (𝓝 1) by
     simp_rw [ordinaryHypergeometricSeries_norm_div_succ_norm a b c _ (fun n _ ↦ habc n)]
     simp only [← norm_inv, ← norm_mul, NNReal.coe_one]
-    convert Filter.Tendsto.norm this
+    convert! Filter.Tendsto.norm this
     exact norm_one.symm
   have (k : ℕ) : (a + k)⁻¹ * (b + k)⁻¹ * (c + k) * ((1 : 𝕂) + k) =
         (c + k) / (a + k) * ((1 + k) / (b + k)) := by field
   simp_rw [this]
   apply (mul_one (1 : 𝕂)) ▸ Filter.Tendsto.mul <;>
-  convert tendsto_add_mul_div_add_mul_atTop_nhds _ _ (1 : 𝕂) one_ne_zero <;> simp
+  convert! tendsto_add_mul_div_add_mul_atTop_nhds _ _ (1 : 𝕂) one_ne_zero <;> simp
 
 end RCLike
diff --git a/Mathlib/Analysis/SpecialFunctions/PolarCoord.lean b/Mathlib/Analysis/SpecialFunctions/PolarCoord.lean
index 3ca87f8a6ffbab..3f905e6b88a150 100644
--- a/Mathlib/Analysis/SpecialFunctions/PolarCoord.lean
+++ b/Mathlib/Analysis/SpecialFunctions/PolarCoord.lean
@@ -63,7 +63,7 @@ def polarCoord : OpenPartialHomeomorph (ℝ × ℝ) (ℝ × ℝ) where
     · conv_rhs => rw [← sqrt_sq (le_of_lt hr), ← one_mul (r ^ 2), ← sin_sq_add_cos_sq θ]
       congr 1
       ring
-    · convert Complex.arg_mul_cos_add_sin_mul_I hr ⟨hθ.1, hθ.2.le⟩
+    · convert! Complex.arg_mul_cos_add_sin_mul_I hr ⟨hθ.1, hθ.2.le⟩
       simp only [Complex.equivRealProd_symm_apply, Complex.ofReal_mul, Complex.ofReal_cos,
         Complex.ofReal_sin]
       ring
@@ -101,9 +101,11 @@ theorem hasFDerivAt_polarCoord_symm (p : ℝ × ℝ) :
     HasFDerivAt polarCoord.symm (fderivPolarCoordSymm p) p := by
   unfold fderivPolarCoordSymm
   rw [Matrix.toLin_finTwoProd_toContinuousLinearMap]
-  convert HasFDerivAt.prodMk (𝕜 := ℝ)
-    (hasFDerivAt_fst.mul ((hasDerivAt_cos p.2).comp_hasFDerivAt p hasFDerivAt_snd))
-    (hasFDerivAt_fst.mul ((hasDerivAt_sin p.2).comp_hasFDerivAt p hasFDerivAt_snd)) using 2 <;>
+  convert!
+    HasFDerivAt.prodMk (𝕜 := ℝ)
+      (hasFDerivAt_fst.mul ((hasDerivAt_cos p.2).comp_hasFDerivAt p hasFDerivAt_snd))
+      (hasFDerivAt_fst.mul ((hasDerivAt_sin p.2).comp_hasFDerivAt p hasFDerivAt_snd)) using
+    2 <;>
   simp [smul_smul, add_comm, neg_mul, smul_neg, neg_smul _ (ContinuousLinearMap.snd ℝ ℝ ℝ)]
 
 theorem det_fderivPolarCoordSymm (p : ℝ × ℝ) :
@@ -266,9 +268,10 @@ theorem integral_comp_pi_polarCoord_symm {E : Type*} [NormedAddCommGroup E] [Nor
     (∫ p in (Set.univ.pi fun _ : ι ↦ polarCoord.target),
       (∏ i, (p i).1) • f (fun i ↦ polarCoord.symm (p i))) = ∫ p, f p := by
   rw [← setIntegral_univ (f := f), ← setIntegral_congr_set pi_polarCoord_symm_target_ae_eq_univ]
-  convert (integral_image_eq_integral_abs_det_fderiv_smul volume measurableSet_pi_polarCoord_target
-    (fun p _ ↦ (hasFDerivAt_pi_polarCoord_symm p).hasFDerivWithinAt)
-      injOn_pi_polarCoord_symm f).symm using 1
+  convert!
+    (integral_image_eq_integral_abs_det_fderiv_smul volume measurableSet_pi_polarCoord_target
+        (fun p _ ↦ (hasFDerivAt_pi_polarCoord_symm p).hasFDerivWithinAt) injOn_pi_polarCoord_symm
+        f).symm using 1
   refine setIntegral_congr_fun measurableSet_pi_polarCoord_target fun x hx ↦ ?_
   simp_rw [det_fderivPiPolarCoordSymm, Finset.abs_prod, abs_fst_of_mem_pi_polarCoord_target hx]
 
@@ -285,9 +288,10 @@ theorem lintegral_comp_pi_polarCoord_symm (f : (ι → ℝ × ℝ) → ℝ≥0
     ∫⁻ p in (Set.univ.pi fun _ : ι ↦ polarCoord.target),
       (∏ i, .ofReal (p i).1) * f (fun i ↦ polarCoord.symm (p i)) = ∫⁻ p, f p := by
   rw [← setLIntegral_univ f, ← setLIntegral_congr pi_polarCoord_symm_target_ae_eq_univ]
-  convert (lintegral_image_eq_lintegral_abs_det_fderiv_mul volume measurableSet_pi_polarCoord_target
-    (fun p _ ↦ (hasFDerivAt_pi_polarCoord_symm p).hasFDerivWithinAt)
-      injOn_pi_polarCoord_symm f).symm using 1
+  convert!
+    (lintegral_image_eq_lintegral_abs_det_fderiv_mul volume measurableSet_pi_polarCoord_target
+        (fun p _ ↦ (hasFDerivAt_pi_polarCoord_symm p).hasFDerivWithinAt) injOn_pi_polarCoord_symm
+        f).symm using 1
   refine setLIntegral_congr_fun measurableSet_pi_polarCoord_target (fun x hx ↦ ?_)
   simp_rw [det_fderivPiPolarCoordSymm, Finset.abs_prod, ENNReal.ofReal_prod_of_nonneg (fun _ _ ↦
     abs_nonneg _), abs_fst_of_mem_pi_polarCoord_target hx]
diff --git a/Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean b/Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean
index e18a4589bdd58f..6e8052e52569d0 100644
--- a/Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean
@@ -107,12 +107,12 @@ theorem tendsto_rpow_div_mul_add (a b c : ℝ) (hb : 0 ≠ b) :
 
 /-- The function `x ^ (1 / x)` tends to `1` at `+∞`. -/
 theorem tendsto_rpow_div : Tendsto (fun x => x ^ ((1 : ℝ) / x)) atTop (𝓝 1) := by
-  convert tendsto_rpow_div_mul_add (1 : ℝ) _ (0 : ℝ) zero_ne_one
+  convert! tendsto_rpow_div_mul_add (1 : ℝ) _ (0 : ℝ) zero_ne_one
   ring
 
 /-- The function `x ^ (-1 / x)` tends to `1` at `+∞`. -/
 theorem tendsto_rpow_neg_div : Tendsto (fun x => x ^ (-(1 : ℝ) / x)) atTop (𝓝 1) := by
-  convert tendsto_rpow_div_mul_add (-(1 : ℝ)) _ (0 : ℝ) zero_ne_one
+  convert! tendsto_rpow_div_mul_add (-(1 : ℝ)) _ (0 : ℝ) zero_ne_one
   ring
 
 /-- The function `exp(x) / x ^ s` tends to `+∞` at `+∞`, for any real number `s`. -/
diff --git a/Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean b/Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean
index 0175e7acf4f2f2..b7d14ef68dde16 100644
--- a/Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean
@@ -304,9 +304,9 @@ theorem continuousAt_cpow_zero_of_re_pos {z : ℂ} (hz : 0 < z.re) :
   refine squeeze_zero (fun _ => norm_nonneg _) (fun _ => norm_cpow_le _ _) ?_
   simp only [div_eq_mul_inv, ← Real.exp_neg]
   refine Tendsto.zero_mul_isBoundedUnder_le ?_ ?_
-  · convert
-        (continuous_fst.norm.tendsto ((0 : ℂ), z)).rpow
-          ((continuous_re.comp continuous_snd).tendsto _) _ <;>
+  · convert!
+    (continuous_fst.norm.tendsto ((0 : ℂ), z)).rpow ((continuous_re.comp continuous_snd).tendsto _)
+      _ <;>
       simp [hz, Real.zero_rpow hz.ne']
   · simp only [Function.comp_def, Real.norm_eq_abs, abs_of_pos (Real.exp_pos _)]
     rcases exists_gt |im z| with ⟨C, hC⟩
@@ -457,11 +457,11 @@ private theorem continuousAt_rpow_const_of_pos {x : ℝ≥0∞} {y : ℝ} (h : 0
     ContinuousAt (fun a : ℝ≥0∞ => a ^ y) x := by
   by_cases hx : x = ⊤
   · rw [hx, ContinuousAt]
-    convert ENNReal.tendsto_rpow_at_top h
+    convert! ENNReal.tendsto_rpow_at_top h
     simp [h]
   lift x to ℝ≥0 using hx
   rw [continuousAt_coe_iff]
-  convert continuous_coe.continuousAt.comp (NNReal.continuousAt_rpow_const (Or.inr h.le)) using 1
+  convert! continuous_coe.continuousAt.comp (NNReal.continuousAt_rpow_const (Or.inr h.le)) using 1
   ext1 x
   simp [← coe_rpow_of_nonneg _ h.le]
 
@@ -479,7 +479,7 @@ theorem continuous_rpow_const {y : ℝ} : Continuous fun a : ℝ≥0∞ => a ^ y
 
 theorem tendsto_const_mul_rpow_nhds_zero_of_pos {c : ℝ≥0∞} (hc : c ≠ ∞) {y : ℝ} (hy : 0 < y) :
     Tendsto (fun x : ℝ≥0∞ => c * x ^ y) (𝓝 0) (𝓝 0) := by
-  convert ENNReal.Tendsto.const_mul (ENNReal.continuous_rpow_const.tendsto 0) _
+  convert! ENNReal.Tendsto.const_mul (ENNReal.continuous_rpow_const.tendsto 0) _
   · simp [hy]
   · exact Or.inr hc
 
diff --git a/Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean b/Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean
index b29c80a78adf64..566b8fd23b72c0 100644
--- a/Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean
@@ -86,7 +86,7 @@ theorem HasStrictFDerivAt.const_cpow (hf : HasStrictFDerivAt f f' x) (h0 : c ≠
 theorem HasFDerivAt.cpow (hf : HasFDerivAt f f' x) (hg : HasFDerivAt g g' x)
     (h0 : f x ∈ slitPlane) : HasFDerivAt (fun x => f x ^ g x)
       ((g x * f x ^ (g x - 1)) • f' + (f x ^ g x * Complex.log (f x)) • g') x := by
-  convert (@Complex.hasFDerivAt_cpow ((fun x => (f x, g x)) x) h0).comp x (hf.prodMk hg)
+  convert! (@Complex.hasFDerivAt_cpow ((fun x => (f x, g x)) x) h0).comp x (hf.prodMk hg)
 
 theorem HasFDerivAt.const_cpow (hf : HasFDerivAt f f' x) (h0 : c ≠ 0 ∨ f x ≠ 0) :
     HasFDerivAt (fun x => c ^ f x) ((c ^ f x * Complex.log c) • f') x :=
@@ -95,8 +95,8 @@ theorem HasFDerivAt.const_cpow (hf : HasFDerivAt f f' x) (h0 : c ≠ 0 ∨ f x 
 theorem HasFDerivWithinAt.cpow (hf : HasFDerivWithinAt f f' s x) (hg : HasFDerivWithinAt g g' s x)
     (h0 : f x ∈ slitPlane) : HasFDerivWithinAt (fun x => f x ^ g x)
       ((g x * f x ^ (g x - 1)) • f' + (f x ^ g x * Complex.log (f x)) • g') s x := by
-  convert (@Complex.hasFDerivAt_cpow ((fun x => (f x, g x)) x) h0).comp_hasFDerivWithinAt x
-    (hf.prodMk hg)
+  convert!
+    (@Complex.hasFDerivAt_cpow ((fun x => (f x, g x)) x) h0).comp_hasFDerivWithinAt x (hf.prodMk hg)
 
 theorem HasFDerivWithinAt.const_cpow (hf : HasFDerivWithinAt f f' s x) (h0 : c ≠ 0 ∨ f x ≠ 0) :
     HasFDerivWithinAt (fun x => c ^ f x) ((c ^ f x * Complex.log c) • f') s x :=
@@ -260,9 +260,9 @@ theorem hasDerivAt_ofReal_cpow_const' {x : ℝ} (hx : x ≠ 0) {r : ℂ} (hr : r
   rcases lt_or_gt_of_ne hx.symm with (hx | hx)
   · -- easy case : `0 < x`
     apply HasDerivAt.comp_ofReal (e := fun y => (y : ℂ) ^ (r + 1) / (r + 1))
-    convert HasDerivAt.div_const (𝕜 := ℂ) ?_ (r + 1) using 1
+    convert! HasDerivAt.div_const (𝕜 := ℂ) ?_ (r + 1) using 1
     · exact (mul_div_cancel_right₀ _ hr).symm
-    · convert HasDerivAt.cpow_const ?_ ?_ using 1
+    · convert! HasDerivAt.cpow_const ?_ ?_ using 1
       · rw [add_sub_cancel_right, mul_comm]; exact (mul_one _).symm
       · exact hasDerivAt_id (x : ℂ)
       · simp [hx]
@@ -275,20 +275,20 @@ theorem hasDerivAt_ofReal_cpow_const' {x : ℝ} (hx : x ≠ 0) {r : ℂ} (hr : r
     rw [ofReal_cpow_of_nonpos (le_of_lt hx)]
     suffices HasDerivAt (fun y : ℝ => (-↑y) ^ (r + 1) * exp (↑π * I * (r + 1)))
         ((r + 1) * (-↑x) ^ r * exp (↑π * I * r)) x by
-      convert this.div_const (r + 1) using 1
+      convert! this.div_const (r + 1) using 1
       conv_rhs => rw [mul_assoc, mul_comm, mul_div_cancel_right₀ _ hr]
     rw [mul_add ((π : ℂ) * _), mul_one, exp_add, exp_pi_mul_I, mul_comm (_ : ℂ) (-1 : ℂ),
       neg_one_mul]
     simp_rw [mul_neg, ← neg_mul, ← ofReal_neg]
     suffices HasDerivAt (fun y : ℝ => (↑(-y) : ℂ) ^ (r + 1)) (-(r + 1) * ↑(-x) ^ r) x by
-      convert this.neg.mul_const _ using 1; ring
+      convert! this.neg.mul_const _ using 1; ring
     suffices HasDerivAt (fun y : ℝ => (y : ℂ) ^ (r + 1)) ((r + 1) * ↑(-x) ^ r) (-x) by
-      convert @HasDerivAt.scomp ℝ _ ℂ _ _ x ℝ _ _ _ _ _ _ _ _ this (hasDerivAt_neg x) using 1
+      convert! @HasDerivAt.scomp ℝ _ ℂ _ _ x ℝ _ _ _ _ _ _ _ _ this (hasDerivAt_neg x) using 1
       rw [real_smul, ofReal_neg 1, ofReal_one]; ring
     suffices HasDerivAt (fun y : ℂ => y ^ (r + 1)) ((r + 1) * ↑(-x) ^ r) ↑(-x) by
       exact this.comp_ofReal
     conv in ↑_ ^ _ => rw [(by ring : r = r + 1 - 1)]
-    convert HasDerivAt.cpow_const ?_ ?_ using 1
+    convert! HasDerivAt.cpow_const ?_ ?_ using 1
     · rw [add_sub_cancel_right, add_sub_cancel_right]; exact (mul_one _).symm
     · exact hasDerivAt_id ((-x : ℝ) : ℂ)
     · simp [hx]
@@ -350,7 +350,7 @@ theorem hasStrictFDerivAt_rpow_of_pos (p : ℝ × ℝ) (hp : 0 < p.1) :
   have : (fun x : ℝ × ℝ => x.1 ^ x.2) =ᶠ[𝓝 p] fun x => exp (log x.1 * x.2) :=
     (continuousAt_fst.eventually (lt_mem_nhds hp)).mono fun p hp => rpow_def_of_pos hp _
   refine HasStrictFDerivAt.congr_of_eventuallyEq ?_ this.symm
-  convert ((hasStrictFDerivAt_fst.log hp.ne').fun_mul hasStrictFDerivAt_snd).exp using 1
+  convert! ((hasStrictFDerivAt_fst.log hp.ne').fun_mul hasStrictFDerivAt_snd).exp using 1
   rw [rpow_sub_one hp.ne', ← rpow_def_of_pos hp, smul_add, smul_smul, mul_div_left_comm,
     div_eq_mul_inv, smul_smul, smul_smul, mul_assoc, add_comm]
 
@@ -363,8 +363,9 @@ theorem hasStrictFDerivAt_rpow_of_neg (p : ℝ × ℝ) (hp : p.1 < 0) :
   have : (fun x : ℝ × ℝ => x.1 ^ x.2) =ᶠ[𝓝 p] fun x => exp (log x.1 * x.2) * cos (x.2 * π) :=
     (continuousAt_fst.eventually (gt_mem_nhds hp)).mono fun p hp => rpow_def_of_neg hp _
   refine HasStrictFDerivAt.congr_of_eventuallyEq ?_ this.symm
-  convert ((hasStrictFDerivAt_fst.log hp.ne).fun_mul hasStrictFDerivAt_snd).exp.fun_mul
-    (hasStrictFDerivAt_snd.mul_const π).cos using 1
+  convert!
+    ((hasStrictFDerivAt_fst.log hp.ne).fun_mul hasStrictFDerivAt_snd).exp.fun_mul
+      (hasStrictFDerivAt_snd.mul_const π).cos using 1
   simp_rw [rpow_sub_one hp.ne, smul_add, ← add_assoc, smul_smul, ← add_smul, ← mul_assoc,
     mul_comm (cos _), ← rpow_def_of_neg hp]
   rw [div_eq_mul_inv, add_comm]; congr 2 <;> ring
@@ -387,8 +388,9 @@ theorem differentiableAt_rpow_of_ne (p : ℝ × ℝ) (hp : p.1 ≠ 0) :
 theorem _root_.HasStrictDerivAt.rpow {f g : ℝ → ℝ} {f' g' : ℝ} (hf : HasStrictDerivAt f f' x)
     (hg : HasStrictDerivAt g g' x) (h : 0 < f x) : HasStrictDerivAt (fun x => f x ^ g x)
       (f' * g x * f x ^ (g x - 1) + g' * f x ^ g x * Real.log (f x)) x := by
-  convert (hasStrictFDerivAt_rpow_of_pos ((fun x => (f x, g x)) x) h).comp_hasStrictDerivAt x
-    (hf.prodMk hg) using 1
+  convert!
+    (hasStrictFDerivAt_rpow_of_pos ((fun x => (f x, g x)) x) h).comp_hasStrictDerivAt x
+      (hf.prodMk hg) using 1
   simp [mul_assoc, mul_comm]
 
 theorem hasStrictDerivAt_rpow_const_of_ne {x : ℝ} (hx : x ≠ 0) (p : ℝ) :
@@ -396,7 +398,7 @@ theorem hasStrictDerivAt_rpow_const_of_ne {x : ℝ} (hx : x ≠ 0) (p : ℝ) :
   rcases hx.lt_or_gt with hx | hx
   · have := (hasStrictFDerivAt_rpow_of_neg (x, p) hx).comp_hasStrictDerivAt x
       ((hasStrictDerivAt_id x).prodMk (hasStrictDerivAt_const x p))
-    convert this using 1; simp
+    convert! this using 1; simp
   · simpa using (hasStrictDerivAt_id x).rpow (hasStrictDerivAt_const x p) hx
 
 theorem hasStrictDerivAt_const_rpow {a : ℝ} (ha : 0 < a) (x : ℝ) :
@@ -669,7 +671,7 @@ variable {f g : ℝ → ℝ} {f' g' x y p : ℝ} {s : Set ℝ}
 theorem HasDerivWithinAt.rpow (hf : HasDerivWithinAt f f' s x) (hg : HasDerivWithinAt g g' s x)
     (h : 0 < f x) : HasDerivWithinAt (fun x => f x ^ g x)
       (f' * g x * f x ^ (g x - 1) + g' * f x ^ g x * Real.log (f x)) s x := by
-  convert (hf.hasFDerivWithinAt.rpow hg.hasFDerivWithinAt h).hasDerivWithinAt using 1
+  convert! (hf.hasFDerivWithinAt.rpow hg.hasFDerivWithinAt h).hasDerivWithinAt using 1
   dsimp; ring
 
 theorem HasDerivAt.rpow (hf : HasDerivAt f f' x) (hg : HasDerivAt g g' x) (h : 0 < f x) :
@@ -680,7 +682,7 @@ theorem HasDerivAt.rpow (hf : HasDerivAt f f' x) (hg : HasDerivAt g g' x) (h : 0
 
 theorem HasDerivWithinAt.rpow_const (hf : HasDerivWithinAt f f' s x) (hx : f x ≠ 0 ∨ 1 ≤ p) :
     HasDerivWithinAt (fun y => f y ^ p) (f' * p * f x ^ (p - 1)) s x := by
-  convert (hasDerivAt_rpow_const hx).comp_hasDerivWithinAt x hf using 1
+  convert! (hasDerivAt_rpow_const hx).comp_hasDerivWithinAt x hf using 1
   ring
 
 theorem HasDerivAt.rpow_const (hf : HasDerivAt f f' x) (hx : f x ≠ 0 ∨ 1 ≤ p) :
@@ -723,7 +725,7 @@ variable {a : ℝ}
 
 theorem HasDerivWithinAt.const_rpow (ha : 0 < a) (hf : HasDerivWithinAt f f' s x) :
     HasDerivWithinAt (a ^ f ·) (Real.log a * f' * a ^ f x) s x := by
-  convert (hasDerivWithinAt_const x s a).rpow hf ha using 1
+  convert! (hasDerivWithinAt_const x s a).rpow hf ha using 1
   ring
 
 theorem HasDerivAt.const_rpow (ha : 0 < a) (hf : HasDerivAt f f' x) :
diff --git a/Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean b/Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean
index 7fcd68993eee23..c76491e3102c03 100644
--- a/Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean
@@ -705,7 +705,7 @@ theorem mul_rpow_eq_ite (x y : ℝ≥0∞) (z : ℝ) :
   rcases eq_or_ne z 0 with (rfl | hz); · simp
   replace hz := hz.lt_or_gt
   wlog hxy : x ≤ y
-  · convert this y x z hz (le_of_not_ge hxy) using 2 <;> simp only [mul_comm, and_comm, or_comm]
+  · convert! this y x z hz (le_of_not_ge hxy) using 2 <;> simp only [mul_comm, and_comm, or_comm]
   rcases eq_or_ne x 0 with (rfl | hx0)
   · induction y <;> rcases hz with hz | hz <;> simp [*, hz.not_gt]
   rcases eq_or_ne y 0 with (rfl | hy0)
diff --git a/Mathlib/Analysis/SpecialFunctions/Pow/Real.lean b/Mathlib/Analysis/SpecialFunctions/Pow/Real.lean
index 441564fddc9a30..8c3d5bd70fd10e 100644
--- a/Mathlib/Analysis/SpecialFunctions/Pow/Real.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Pow/Real.lean
@@ -660,11 +660,11 @@ theorem rpow_le_one {x z : ℝ} (hx1 : 0 ≤ x) (hx2 : x ≤ 1) (hz : 0 ≤ z) :
   gcongr
 
 theorem rpow_lt_one_of_one_lt_of_neg {x z : ℝ} (hx : 1 < x) (hz : z < 0) : x ^ z < 1 := by
-  convert rpow_lt_rpow_of_exponent_lt hx hz
+  convert! rpow_lt_rpow_of_exponent_lt hx hz
   exact (rpow_zero x).symm
 
 theorem rpow_le_one_of_one_le_of_nonpos {x z : ℝ} (hx : 1 ≤ x) (hz : z ≤ 0) : x ^ z ≤ 1 := by
-  convert rpow_le_rpow_of_exponent_le hx hz
+  convert! rpow_le_rpow_of_exponent_le hx hz
   exact (rpow_zero x).symm
 
 theorem one_lt_rpow {x z : ℝ} (hx : 1 < x) (hz : 0 < z) : 1 < x ^ z := by
@@ -677,12 +677,12 @@ theorem one_le_rpow {x z : ℝ} (hx : 1 ≤ x) (hz : 0 ≤ z) : 1 ≤ x ^ z := b
 
 theorem one_lt_rpow_of_pos_of_lt_one_of_neg (hx1 : 0 < x) (hx2 : x < 1) (hz : z < 0) :
     1 < x ^ z := by
-  convert rpow_lt_rpow_of_exponent_gt hx1 hx2 hz
+  convert! rpow_lt_rpow_of_exponent_gt hx1 hx2 hz
   exact (rpow_zero x).symm
 
 theorem one_le_rpow_of_pos_of_le_one_of_nonpos (hx1 : 0 < x) (hx2 : x ≤ 1) (hz : z ≤ 0) :
     1 ≤ x ^ z := by
-  convert rpow_le_rpow_of_exponent_ge hx1 hx2 hz
+  convert! rpow_le_rpow_of_exponent_ge hx1 hx2 hz
   exact (rpow_zero x).symm
 
 theorem rpow_lt_one_iff_of_pos (hx : 0 < x) : x ^ y < 1 ↔ 1 < x ∧ y < 0 ∨ x < 1 ∧ 0 < y := by
diff --git a/Mathlib/Analysis/SpecialFunctions/Sigmoid.lean b/Mathlib/Analysis/SpecialFunctions/Sigmoid.lean
index 957e4634d6d5fd..a1707859907c38 100644
--- a/Mathlib/Analysis/SpecialFunctions/Sigmoid.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Sigmoid.lean
@@ -135,7 +135,7 @@ lemma tendsto_sigmoid_atBot : Tendsto sigmoid atBot (𝓝 0) :=
 
 lemma hasDerivAt_sigmoid (x : ℝ) :
     HasDerivAt sigmoid (sigmoid x * (1 - sigmoid x)) x := by
-  convert (hasDerivAt_neg' x |>.exp.const_add 1 |>.inv <| by positivity) using 1
+  convert! (hasDerivAt_neg' x |>.exp.const_add 1 |>.inv <| by positivity) using 1
   rw [← sigmoid_neg, ← sigmoid_mul_rexp_neg x, sigmoid_def]
   field [sq]
 
diff --git a/Mathlib/Analysis/SpecialFunctions/SmoothTransition.lean b/Mathlib/Analysis/SpecialFunctions/SmoothTransition.lean
index 5f2a1674a7de7e..cd24266ad8eb62 100644
--- a/Mathlib/Analysis/SpecialFunctions/SmoothTransition.lean
+++ b/Mathlib/Analysis/SpecialFunctions/SmoothTransition.lean
@@ -109,7 +109,7 @@ theorem hasDerivAt_polynomial_eval_inv_mul (p : ℝ[X]) (x : ℝ) :
     refine ((tendsto_polynomial_inv_mul_zero (p * X)).mono_left inf_le_left).congr fun x ↦ ?_
     simp [slope_def_field, div_eq_mul_inv, mul_right_comm]
   · have := ((p.hasDerivAt x⁻¹).mul (hasDerivAt_neg _).exp).comp x (hasDerivAt_inv hx.ne')
-    convert this.congr_of_eventuallyEq _ using 1
+    convert! this.congr_of_eventuallyEq _ using 1
     · simp [expNegInvGlue, hx.not_ge]
       ring
     · filter_upwards [lt_mem_nhds hx] with y hy
@@ -131,7 +131,7 @@ theorem contDiff_polynomial_eval_inv_mul {n : ℕ∞} (p : ℝ[X]) :
   | succ m ihm =>
     rw [show ((m + 1 : ℕ) : WithTop ℕ∞) = m + 1 from rfl]
     refine contDiff_succ_iff_deriv.2 ⟨differentiable_polynomial_eval_inv_mul _, by simp, ?_⟩
-    convert ihm (X ^ 2 * (p - derivative (R := ℝ) p)) using 2
+    convert! ihm (X ^ 2 * (p - derivative (R := ℝ) p)) using 2
     exact (hasDerivAt_polynomial_eval_inv_mul p _).deriv
 
 /-- The function `expNegInvGlue` is smooth. -/
diff --git a/Mathlib/Analysis/SpecialFunctions/Stirling.lean b/Mathlib/Analysis/SpecialFunctions/Stirling.lean
index c966bbaec1bf4b..3c2a3664a553a3 100644
--- a/Mathlib/Analysis/SpecialFunctions/Stirling.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Stirling.lean
@@ -79,7 +79,7 @@ theorem log_stirlingSeq_diff_hasSum (m : ℕ) :
   let f (k : ℕ) := (1 : ℝ) / (2 * k + 1) * ((1 / (2 * ↑(m + 1) + 1)) ^ 2) ^ k
   change HasSum (fun k => f (k + 1)) _
   rw [hasSum_nat_add_iff]
-  convert (hasSum_log_one_add_inv m.cast_add_one_pos).mul_left ((↑(m + 1) : ℝ) + 1 / 2) using 1
+  convert! (hasSum_log_one_add_inv m.cast_add_one_pos).mul_left ((↑(m + 1) : ℝ) + 1 / 2) using 1
   · ext k
     dsimp only [f]
     rw [← pow_mul, pow_add]
@@ -240,7 +240,7 @@ lemma factorial_isEquivalent_stirling :
   apply Asymptotics.isEquivalent_of_tendsto_one
   have : sqrt π ≠ 0 := by positivity
   nth_rewrite 2 [← div_self this]
-  convert tendsto_stirlingSeq_sqrt_pi.div tendsto_const_nhds this using 1
+  convert! tendsto_stirlingSeq_sqrt_pi.div tendsto_const_nhds this using 1
   ext n
   simp [field, stirlingSeq, mul_right_comm]
 
diff --git a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean
index a06fde5b158b41..1908802a7dd306 100644
--- a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean
@@ -155,7 +155,7 @@ theorem two_nsmul_eq_iff {ψ θ : Angle} : (2 : ℕ) • ψ = (2 : ℕ) • θ 
   simp_rw [← natCast_zsmul, Nat.cast_ofNat, two_zsmul_eq_iff]
 
 theorem two_nsmul_eq_zero_iff {θ : Angle} : (2 : ℕ) • θ = 0 ↔ θ = 0 ∨ θ = π := by
-  convert two_nsmul_eq_iff <;> simp
+  convert! two_nsmul_eq_iff <;> simp
 
 theorem two_nsmul_ne_zero_iff {θ : Angle} : (2 : ℕ) • θ ≠ 0 ↔ θ ≠ 0 ∧ θ ≠ π := by
   rw [← not_or, ← two_nsmul_eq_zero_iff]
@@ -463,7 +463,7 @@ theorem neg_pi_lt_toReal (θ : Angle) : -π < θ.toReal := by
 
 theorem toReal_le_pi (θ : Angle) : θ.toReal ≤ π := by
   induction θ using Real.Angle.induction_on
-  convert toIocMod_le_right two_pi_pos _ _
+  convert! toIocMod_le_right two_pi_pos _ _
   ring
 
 theorem abs_toReal_le_pi (θ : Angle) : |θ.toReal| ≤ π :=
@@ -580,11 +580,11 @@ theorem toReal_coe_eq_self_sub_two_mul_int_mul_pi_iff {θ : ℝ} {k : ℤ} :
 
 theorem toReal_coe_eq_self_sub_two_pi_iff {θ : ℝ} :
     (θ : Angle).toReal = θ - 2 * π ↔ θ ∈ Set.Ioc π (3 * π) := by
-  convert @toReal_coe_eq_self_sub_two_mul_int_mul_pi_iff θ 1 <;> norm_num
+  convert! @toReal_coe_eq_self_sub_two_mul_int_mul_pi_iff θ 1 <;> norm_num
 
 theorem toReal_coe_eq_self_add_two_pi_iff {θ : ℝ} :
     (θ : Angle).toReal = θ + 2 * π ↔ θ ∈ Set.Ioc (-3 * π) (-π) := by
-  convert @toReal_coe_eq_self_sub_two_mul_int_mul_pi_iff θ (-1) using 2 <;> norm_num
+  convert! @toReal_coe_eq_self_sub_two_mul_int_mul_pi_iff θ (-1) using 2 <;> norm_num
 
 theorem two_nsmul_toReal_eq_two_mul_sub_two_pi {θ : Angle} :
     ((2 : ℕ) • θ).toReal = 2 * θ.toReal - 2 * π ↔ π / 2 < θ.toReal := by
@@ -936,7 +936,7 @@ lemma abs_toReal_add_eq_two_pi_sub_abs_toReal_add_abs_toReal {θ ψ : Angle} (hs
   · obtain ⟨hθ', hψ'⟩ : (-θ).sign = 1 ∧ (-ψ).sign = 1 := by grind [sign_neg, neg_neg]
     have hsa' : (-θ + -ψ).sign ≠ 1 := by
       rwa [← hθ', ne_comm, ← neg_add, sign_neg, sign_neg, neg_injective.ne_iff]
-    convert abs_toReal_add_eq_two_pi_sub_abs_toReal_add_abs_toReal_aux hθ' hψ' hsa' using 1
+    convert! abs_toReal_add_eq_two_pi_sub_abs_toReal_add_abs_toReal_aux hθ' hψ' hsa' using 1
     all_goals simp [-neg_add_rev, ← neg_add, abs_toReal_neg]
   · grind [sign_eq_zero_iff, coe_pi_add_coe_pi]
   · exact abs_toReal_add_eq_two_pi_sub_abs_toReal_add_abs_toReal_aux h (hs ▸ h) (h ▸ hsa.symm)
diff --git a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean
index 75f958a523fd1d..87a236b2f5b280 100644
--- a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean
@@ -39,7 +39,7 @@ theorem tan_add
     tan (x + y) = (tan x + tan y) / (1 - tan x * tan y) := by
   simpa only [← Complex.ofReal_inj, Complex.ofReal_sub, Complex.ofReal_add, Complex.ofReal_div,
     Complex.ofReal_mul, Complex.ofReal_tan] using
-    @Complex.tan_add (x : ℂ) (y : ℂ) (by convert h <;> norm_cast)
+    @Complex.tan_add (x : ℂ) (y : ℂ) (by convert! h <;> norm_cast)
 
 theorem tan_add'
     (h : (∀ k : ℤ, x ≠ (2 * k + 1) * π / 2) ∧ ∀ l : ℤ, y ≠ (2 * l + 1) * π / 2) :
@@ -52,7 +52,7 @@ theorem tan_sub {x y : ℝ}
     tan (x - y) = (tan x - tan y) / (1 + tan x * tan y) := by
   simpa only [← Complex.ofReal_inj, Complex.ofReal_sub, Complex.ofReal_add, Complex.ofReal_div,
     Complex.ofReal_mul, Complex.ofReal_tan] using
-    @Complex.tan_sub (x : ℂ) (y : ℂ) (by convert h <;> norm_cast)
+    @Complex.tan_sub (x : ℂ) (y : ℂ) (by convert! h <;> norm_cast)
 
 theorem tan_sub' {x y : ℝ}
     (h : (∀ k : ℤ, x ≠ (2 * k + 1) * π / 2) ∧ ∀ l : ℤ, y ≠ (2 * l + 1) * π / 2) :
diff --git a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean
index ad33732b70832e..0b458980a6f4da 100644
--- a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean
@@ -969,34 +969,36 @@ theorem tan_int_mul_pi_sub (x : ℝ) (n : ℤ) : tan (n * π - x) = -tan x :=
   tan_neg x ▸ tan_periodic.int_mul_sub_eq n
 
 theorem tendsto_sin_pi_div_two : Tendsto sin (𝓝[<] (π / 2)) (𝓝 1) := by
-  convert continuous_sin.continuousWithinAt.tendsto
+  convert! continuous_sin.continuousWithinAt.tendsto
   simp
 
 theorem tendsto_cos_pi_div_two : Tendsto cos (𝓝[<] (π / 2)) (𝓝[>] 0) := by
   apply tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within
-  · convert continuous_cos.continuousWithinAt.tendsto
+  · convert! continuous_cos.continuousWithinAt.tendsto
     simp
   · filter_upwards [Ioo_mem_nhdsLT (neg_lt_self pi_div_two_pos)] with x hx
     exact cos_pos_of_mem_Ioo hx
 
 theorem tendsto_tan_pi_div_two : Tendsto tan (𝓝[<] (π / 2)) atTop := by
-  convert tendsto_cos_pi_div_two.inv_tendsto_nhdsGT_zero.atTop_mul_pos zero_lt_one
-    tendsto_sin_pi_div_two using 1
+  convert!
+    tendsto_cos_pi_div_two.inv_tendsto_nhdsGT_zero.atTop_mul_pos zero_lt_one
+      tendsto_sin_pi_div_two using 1
   simp only [Pi.inv_apply, ← div_eq_inv_mul, ← tan_eq_sin_div_cos]
 
 theorem tendsto_sin_neg_pi_div_two : Tendsto sin (𝓝[>] (-(π / 2))) (𝓝 (-1)) := by
-  convert continuous_sin.continuousWithinAt.tendsto using 2
+  convert! continuous_sin.continuousWithinAt.tendsto using 2
   simp
 
 theorem tendsto_cos_neg_pi_div_two : Tendsto cos (𝓝[>] (-(π / 2))) (𝓝[>] 0) := by
   apply tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within
-  · convert continuous_cos.continuousWithinAt.tendsto
+  · convert! continuous_cos.continuousWithinAt.tendsto
     simp
   · filter_upwards [Ioo_mem_nhdsGT (neg_lt_self pi_div_two_pos)] with x hx
     exact cos_pos_of_mem_Ioo hx
 
 theorem tendsto_tan_neg_pi_div_two : Tendsto tan (𝓝[>] (-(π / 2))) atBot := by
-  convert tendsto_cos_neg_pi_div_two.inv_tendsto_nhdsGT_zero.atTop_mul_neg (by simp)
+  convert!
+    tendsto_cos_neg_pi_div_two.inv_tendsto_nhdsGT_zero.atTop_mul_neg (by simp)
       tendsto_sin_neg_pi_div_two using 1
   simp only [Pi.inv_apply, ← div_eq_inv_mul, ← tan_eq_sin_div_cos]
 
@@ -1268,7 +1270,7 @@ theorem sinh_add_pi_mul_I (z : ℂ) : sinh (z + π * I) = -sinh z :=
   sinh_antiperiodic z
 
 theorem sinh_periodic : Function.Periodic sinh (2 * π * I) := by
-  convert sinh_antiperiodic.periodic_two_mul using 1
+  convert! sinh_antiperiodic.periodic_two_mul using 1
   ring
 
 @[simp]
@@ -1283,7 +1285,7 @@ theorem cosh_add_pi_mul_I (z : ℂ) : cosh (z + π * I) = -cosh z :=
   cosh_antiperiodic z
 
 theorem cosh_periodic : Function.Periodic cosh (2 * π * I) := by
-  convert cosh_antiperiodic.periodic_two_mul using 1
+  convert! cosh_antiperiodic.periodic_two_mul using 1
   ring
 
 @[simp]
diff --git a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Bounds.lean b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Bounds.lean
index 0b8c6ac67592ab..3b3720b8b28d92 100644
--- a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Bounds.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Bounds.lean
@@ -209,7 +209,7 @@ theorem cos_lt_one_div_sqrt_sq_add_one {x : ℝ} (hx1 : -(3 * π / 2) ≤ x) (hx
   suffices ∀ {y : ℝ}, 0 < y → y ≤ 3 * π / 2 → cos y < 1 / √(y ^ 2 + 1) by
     rcases lt_or_lt_iff_ne.mpr hx3.symm with ⟨h⟩
     · exact this h hx2
-    · convert this (by linarith : 0 < -x) (by linarith) using 1
+    · convert! this (by linarith : 0 < -x) (by linarith) using 1
       · rw [cos_neg]
       · rw [neg_sq]
   intro y hy1 hy2
diff --git a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev/ChebyshevGauss.lean b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev/ChebyshevGauss.lean
index ee57b6dd899082..f44143431db645 100644
--- a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev/ChebyshevGauss.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev/ChebyshevGauss.lean
@@ -55,7 +55,7 @@ private theorem sum_exp {n : ℕ} {k : ℤ} (hn : n ≠ 0) (hk : ¬ (2 * n : ℤ
     have hf {s a b t : ℂ} (h : s * a⁻¹ * b = t) (ha : a ≠ 0) (hb : b ≠ 0) : s = a / b * t := by
       linear_combination (norm := field) h * a / b
     apply hf this (Complex.exp_ne_zero _) (by grind [exp_sub_one_ne_zero])
-  convert geom_sum_mul (exp (k / n * π * I)) n using 1
+  convert! geom_sum_mul (exp (k / n * π * I)) n using 1
   · simp_rw [sum_mul]
     congr! 1 with i hi
     rw [← Complex.exp_nat_mul, ← Complex.exp_add]
diff --git a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev/Extremal.lean b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev/Extremal.lean
index 55e0f66353f5d6..1af1d845979ab0 100644
--- a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev/Extremal.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev/Extremal.lean
@@ -175,7 +175,7 @@ private theorem sumNodes_eq_coeff {n : ℕ} {P : ℝ[X]} (hP : P.degree ≤ n) :
     grw [hP]
     norm_cast
     simp
-  convert (Lagrange.coeff_eq_sum (strictAntiOn_node n).injOn this).symm using 2
+  convert! (Lagrange.coeff_eq_sum (strictAntiOn_node n).injOn this).symm using 2
   · exact Eq.symm (Nat.range_succ_eq_Iic n)
   · simp
 
@@ -194,8 +194,7 @@ private theorem negOnePow_mul_leadingCoeffC_pos {n i : ℕ} (hi : i ≤ n) :
 theorem coeff_le_of_forall_abs_le_one {n : ℕ} {P : ℝ[X]}
     (hPdeg : P.degree ≤ n) (hPbnd : ∀ x ∈ Set.Icc (-1) 1, |P.eval x| ≤ 1) :
     P.coeff n ≤ 2 ^ (n - 1) := by
-  convert sumNodes_le_sumNodes_T
-      (fun i hi => le_of_lt <| negOnePow_mul_leadingCoeffC_pos hi) hPbnd
+  convert! sumNodes_le_sumNodes_T (fun i hi => le_of_lt <| negOnePow_mul_leadingCoeffC_pos hi) hPbnd
   · rw [sumNodes_eq_coeff hPdeg]
   · rw [sumNodes_T_eq]
 
@@ -214,8 +213,7 @@ theorem leadingCoeff_le_of_forall_abs_le_one {n : ℕ} {P : ℝ[X]}
 theorem coeff_eq_iff_of_forall_abs_le_one {n : ℕ} {P : ℝ[X]}
     (hPdeg : P.degree ≤ n) (hPbnd : ∀ x ∈ Set.Icc (-1) 1, |P.eval x| ≤ 1) :
     P.coeff n = 2 ^ (n - 1) ↔ P = T ℝ n := by
-  convert sumNodes_eq_sumNodes_T_iff
-      (fun i hi => negOnePow_mul_leadingCoeffC_pos hi) hPdeg hPbnd
+  convert! sumNodes_eq_sumNodes_T_iff (fun i hi => negOnePow_mul_leadingCoeffC_pos hi) hPdeg hPbnd
   · rw [sumNodes_eq_coeff hPdeg]
   · rw [sumNodes_T_eq]
 
@@ -249,8 +247,9 @@ private theorem sumNodes_eq_eval_iterate_derivative {n k : ℕ} (hk : k ≤ n) (
   simp_rw [sumNodes, iterateDerivativeC]
   have h₁ : P.degree < (Finset.range (n + 1)).card := by
     rw [Finset.card_range]; grw [hP]; norm_cast; simp
-  convert (Lagrange.eval_iterate_derivative_eq_sum (strictAntiOn_node n).injOn h₁
-    (show k < _ by simp [hk]) x).symm
+  convert!
+    (Lagrange.eval_iterate_derivative_eq_sum (strictAntiOn_node n).injOn h₁
+        (show k < _ by simp [hk]) x).symm
   rw [Finset.mul_sum]
   grind [Nat.range_succ_eq_Iic, Nat.card_Iic]
 
@@ -288,8 +287,8 @@ theorem eval_iterate_derivative_le_of_forall_abs_le_one {n : ℕ} {P : ℝ[X]}
   by_cases! hk : n < k
   · rw [iterate_derivative_eq_zero_of_degree_lt (by grw [hPdeg]; simpa),
       iterate_derivative_eq_zero_of_degree_lt (by simp [hk])]
-  convert sumNodes_le_sumNodes_T
-    (fun i hi => negOnePow_mul_iterateDerivativeC_nonneg hi hx) hPbnd using 1
+  convert!
+    sumNodes_le_sumNodes_T (fun i hi => negOnePow_mul_iterateDerivativeC_nonneg hi hx) hPbnd using 1
   · rw [sumNodes_eq_eval_iterate_derivative hk x hPdeg]
   · rw [sumNodes_eq_eval_iterate_derivative hk x (le_of_eq (degree_T ℝ n))]
 
@@ -297,8 +296,9 @@ theorem eval_iterate_derivative_eq_iff_of_bounded {n : ℕ} {P : ℝ[X]}
     {k : ℕ} (hk₁ : 0 < k) (hk₂ : k ≤ n) {x : ℝ} (hx : 1 ≤ x)
     (hPdeg : P.degree ≤ n) (hPbnd : ∀ x ∈ Set.Icc (-1) 1, |P.eval x| ≤ 1) :
     (derivative^[k] P).eval x = (derivative^[k] (T ℝ n)).eval x ↔ P = T ℝ n := by
-  convert sumNodes_eq_sumNodes_T_iff
-    (fun i hi => negOnePow_mul_iterateDerivativeC_pos hk₁ hk₂ hi hx) hPdeg hPbnd using 2
+  convert!
+    sumNodes_eq_sumNodes_T_iff (fun i hi => negOnePow_mul_iterateDerivativeC_pos hk₁ hk₂ hi hx)
+      hPdeg hPbnd using 2
   · rw [sumNodes_eq_eval_iterate_derivative hk₂ x hPdeg]
   · rw [sumNodes_eq_eval_iterate_derivative hk₂ x (le_of_eq (degree_T ℝ n))]
 
diff --git a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev/Orthogonality.lean b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev/Orthogonality.lean
index 494efbc07e25bd..51998fd7926032 100644
--- a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev/Orthogonality.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev/Orthogonality.lean
@@ -72,7 +72,7 @@ theorem integrable_measureT {f : ℝ → ℝ} (hf : ContinuousOn f (Set.Icc (-1)
   rw [measureT, restrict_withDensity (by measurability),
     integrable_withDensity_iff (by fun_prop) (by simp)]
   unfold IntegrableOn at this
-  convert this
+  convert! this
 
 open Set in
 theorem integral_measureT_eq_integral_cos {f : ℝ → ℝ} :
diff --git a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev/RootsExtrema.lean b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev/RootsExtrema.lean
index c7032f200465f6..ce2395f4574158 100644
--- a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev/RootsExtrema.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev/RootsExtrema.lean
@@ -59,14 +59,14 @@ theorem one_lt_eval_T_real {n : ℤ} (hn : n ≠ 0) {x : ℝ} (hx : 1 < x) :
 theorem one_le_negOnePow_mul_eval_T_real (n : ℤ) {x : ℝ} (hx : x ≤ -1) :
     1 ≤ n.negOnePow * (T ℝ n).eval x := by
   rw [← neg_neg x, T_eval_neg]
-  convert one_le_eval_T_real n (le_neg_of_le_neg hx)
+  convert! one_le_eval_T_real n (le_neg_of_le_neg hx)
   rw [Int.cast_negOnePow, ← mul_assoc, ← mul_zpow]
   simp
 
 theorem one_lt_negOnePow_mul_eval_T_real {n : ℤ} (hn : n ≠ 0) {x : ℝ} (hx : x < -1) :
     1 < n.negOnePow * (T ℝ n).eval x := by
   rw [← neg_neg x, T_eval_neg]
-  convert one_lt_eval_T_real hn (lt_neg_of_lt_neg hx)
+  convert! one_lt_eval_T_real hn (lt_neg_of_lt_neg hx)
   rw [Int.cast_negOnePow, ← mul_assoc, ← mul_zpow]
   simp
 
@@ -102,7 +102,7 @@ theorem abs_eval_T_real_eq_one_iff {n : ℕ} (hn : n ≠ 0) (x : ℝ) :
       gcongr
       exact div_le_one_of_le₀ (arccos_le_pi x) (by positivity)
     refine ⟨k, by simpa using hkn, ?_⟩
-    convert congr(cos ($hk.symm / n))
+    convert! congr(cos ($hk.symm / n))
     rw [mul_div_cancel_left₀ _ (by simpa), cos_arccos (by grind) (by grind)]
   · rintro ⟨k, hk, rfl⟩
     rw [T_real_cos, abs_cos_eq_one_iff]
@@ -111,7 +111,7 @@ theorem abs_eval_T_real_eq_one_iff {n : ℕ} (hn : n ≠ 0) (x : ℝ) :
 theorem eval_T_real_cos_int_mul_pi_div {k : ℕ} {n : ℕ} (hn : n ≠ 0) :
     (T ℝ n).eval (cos (k * π / n)) = (k : ℤ).negOnePow := by
   rw [T_real_cos, Int.cast_negOnePow]
-  convert Real.cos_int_mul_pi k using 2
+  convert! Real.cos_int_mul_pi k using 2
   simp [field]
 
 theorem eval_T_real_eq_one_iff {n : ℕ} (hn : n ≠ 0) (x : ℝ) :
@@ -312,7 +312,7 @@ theorem irrational_of_isRoot_T_real {n : ℕ} {x : ℝ} (hroot : (T ℝ n).IsRoo
   obtain ⟨k, hk₁, hk₂⟩ := Finset.mem_image.mp hroot
   have hn : n ≠ 0 := by grind
   suffices Irrational (cos ((Rat.divInt (2 * k + 1) (2 * n)) * π)) by
-    rw [← hk₂]; convert this using 2; push_cast; field_simp
+    rw [← hk₂]; convert! this using 2; push_cast; field_simp
   apply irrational_cos_rat_mul_pi
   contrapose! hnz
   have : (Rat.divInt (2 * k + 1) (2 * n)).den = 2 * (n / n.gcd (2 * k + 1)) := calc
@@ -321,12 +321,12 @@ theorem irrational_of_isRoot_T_real {n : ℕ} {x : ℝ} (hroot : (T ℝ n).IsRoo
       Nat.mul_div_assoc _ (Nat.gcd_dvd_left ..)]
   have hn : 2 * k + 1 = n := Nat.eq_of_dvd_of_lt_two_mul (by simp) (Nat.gcd_eq_left_iff_dvd.mp <|
     Nat.eq_of_dvd_of_div_eq_one (Nat.gcd_dvd_left ..) (by grind [Rat.den_pos])) (by grind)
-  rw_mod_cast [← hk₂, hn]; convert cos_pi_div_two using 2; push_cast; field_simp
+  rw_mod_cast [← hk₂, hn]; convert! cos_pi_div_two using 2; push_cast; field_simp
 
 theorem abs_iterate_derivative_T_real_le (n : ℤ) (k : ℕ) {x : ℝ} (hx : |x| ≤ 1) :
     |(derivative^[k] (T ℝ n)).eval x| ≤ (derivative^[k] (T ℝ n)).eval 1 := by
   wlog hn : 0 ≤ n
-  · convert this (-n) k hx (by grind) using 1 <;> rw [T_neg]
+  · convert! this (-n) k hx (by grind) using 1 <;> rw [T_neg]
   lift n to ℕ using hn
   have := T_iterate_derivative_mem_span_T (R := ℝ) n k
   obtain ⟨f, hfsupp, hfderiv⟩ := Submodule.mem_span_set.mp this
diff --git a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean
index 824805a6d1f58f..7932da5e271491 100644
--- a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean
@@ -145,7 +145,7 @@ theorem tan_sub {x y : ℂ}
     rcases h with ⟨x_ne, minus_y_ne⟩ | ⟨x_eq, minus_y_eq⟩
     · refine .inl ⟨x_ne, fun l => ?_⟩
       rw [Ne, neg_eq_iff_eq_neg]
-      convert minus_y_ne (-l - 1) using 2
+      convert! minus_y_ne (-l - 1) using 2
       push_cast
       ring
     · refine .inr ⟨x_eq, ?_⟩
@@ -154,7 +154,7 @@ theorem tan_sub {x y : ℂ}
       push_cast
       ring
   rw [tan_neg] at this
-  convert this using 2
+  convert! this using 2
   ring
 
 theorem tan_sub' {x y : ℂ}
@@ -181,7 +181,7 @@ theorem tan_eq {z : ℂ}
         (∃ k : ℤ, (z.re : ℂ) = (2 * k + 1) * π / 2) ∧
           ∃ l : ℤ, (z.im : ℂ) * I = (2 * l + 1) * π / 2) :
     tan z = (tan z.re + tanh z.im * I) / (1 - tan z.re * tanh z.im * I) := by
-  convert tan_add_mul_I h; exact (re_add_im z).symm
+  convert! tan_add_mul_I h; exact (re_add_im z).symm
 
 /-- `tan x` takes the junk value `0` when `cos x = 0` -/
 lemma tan_eq_zero_of_cos_eq_zero {x} (h : cos x = 0) : tan x = 0 := by
@@ -237,7 +237,7 @@ theorem cos_surjective : Function.Surjective cos := by
     simp only [zero_add, one_ne_zero, mul_zero] at hw
   refine ⟨log w / I, cos_eq_iff_quadratic.2 ?_⟩
   rw [div_mul_cancel₀ _ I_ne_zero, exp_log w₀]
-  convert hw using 1
+  convert! hw using 1
   ring
 
 @[simp]
diff --git a/Mathlib/Analysis/SpecialFunctions/Trigonometric/ComplexDeriv.lean b/Mathlib/Analysis/SpecialFunctions/Trigonometric/ComplexDeriv.lean
index 50422d5b225f57..4d51e2e7c975cd 100644
--- a/Mathlib/Analysis/SpecialFunctions/Trigonometric/ComplexDeriv.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Trigonometric/ComplexDeriv.lean
@@ -26,7 +26,7 @@ open Set Filter
 open scoped Real
 
 theorem hasStrictDerivAt_tan {x : ℂ} (h : cos x ≠ 0) : HasStrictDerivAt tan (1 / cos x ^ 2) x := by
-  convert (hasStrictDerivAt_sin x).div (hasStrictDerivAt_cos x) h using 1
+  convert! (hasStrictDerivAt_sin x).div (hasStrictDerivAt_cos x) h using 1
   rw_mod_cast [← sin_sq_add_cos_sq x]
   ring
 
diff --git a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Cotangent.lean b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Cotangent.lean
index 8797ac0313c150..a1a2b1c90bed39 100644
--- a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Cotangent.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Cotangent.lean
@@ -404,7 +404,7 @@ theorem iteratedDerivWithin_cot_pi_mul_eq_mul_tsum_div_pow {k : ℕ} (hk : 1 ≤
     (hz : z ∈ ℍₒ) :
     iteratedDerivWithin k (fun x : ℂ ↦ π * cot (π * x)) ℍₒ z =
       (-1) ^ k * k ! * ∑' n : ℤ, 1 / (z + n) ^ (k + 1) := by
-  convert iteratedDerivWithin_cot_pi_mul_eq_mul_tsum_zpow hk hz with n
+  convert! iteratedDerivWithin_cot_pi_mul_eq_mul_tsum_zpow hk hz with n
   rw [show (-1 - k : ℤ) = -(k + 1 :) by norm_cast; lia, zpow_neg_coe_of_pos _ (by lia),
     one_div]
 
diff --git a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean
index 6642d8173ff07b..2ed674ee551988 100644
--- a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean
@@ -33,8 +33,11 @@ namespace Complex
 /-- The complex sine function is everywhere strictly differentiable, with the derivative `cos x`. -/
 theorem hasStrictDerivAt_sin (x : ℂ) : HasStrictDerivAt sin (cos x) x := by
   simp only [cos, div_eq_mul_inv]
-  convert ((((hasStrictDerivAt_id x).fun_neg.mul_const I).cexp.sub
-    ((hasStrictDerivAt_id x).mul_const I).cexp).mul_const I).mul_const (2 : ℂ)⁻¹ using 1
+  convert!
+    ((((hasStrictDerivAt_id x).fun_neg.mul_const I).cexp.sub
+              ((hasStrictDerivAt_id x).mul_const I).cexp).mul_const
+          I).mul_const
+      (2 : ℂ)⁻¹ using 1
   simp only [id]
   rw [sub_mul, mul_assoc, mul_assoc, I_mul_I, neg_one_mul, neg_neg, mul_one, one_mul, mul_assoc,
     I_mul_I, mul_neg_one, sub_neg_eq_add, add_comm]
@@ -82,8 +85,10 @@ theorem deriv_sin : deriv sin = cos :=
 `-sin x`. -/
 theorem hasStrictDerivAt_cos (x : ℂ) : HasStrictDerivAt cos (-sin x) x := by
   simp only [sin, div_eq_mul_inv, neg_mul_eq_neg_mul]
-  convert (((hasStrictDerivAt_id x).mul_const I).cexp.add
-    ((hasStrictDerivAt_id x).fun_neg.mul_const I).cexp).mul_const (2 : ℂ)⁻¹ using 1
+  convert!
+    (((hasStrictDerivAt_id x).mul_const I).cexp.add
+          ((hasStrictDerivAt_id x).fun_neg.mul_const I).cexp).mul_const
+      (2 : ℂ)⁻¹ using 1
   simp only [id]
   ring
 
diff --git a/Mathlib/Analysis/SpecialFunctions/Trigonometric/DerivHyp.lean b/Mathlib/Analysis/SpecialFunctions/Trigonometric/DerivHyp.lean
index 3c1dd210ba1950..bed1acdb86f3ba 100644
--- a/Mathlib/Analysis/SpecialFunctions/Trigonometric/DerivHyp.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Trigonometric/DerivHyp.lean
@@ -37,8 +37,8 @@ namespace Complex
 `cosh x`. -/
 theorem hasStrictDerivAt_sinh (x : ℂ) : HasStrictDerivAt sinh (cosh x) x := by
   simp only [cosh, div_eq_mul_inv]
-  convert ((hasStrictDerivAt_exp x).sub (hasStrictDerivAt_id x).fun_neg.cexp).mul_const (2 : ℂ)⁻¹
-    using 1
+  convert!
+    ((hasStrictDerivAt_exp x).sub (hasStrictDerivAt_id x).fun_neg.cexp).mul_const (2 : ℂ)⁻¹ using 1
   rw [id, mul_neg_one, sub_eq_add_neg, neg_neg]
 
 /-- The complex hyperbolic sine function is everywhere differentiable, with the derivative
@@ -84,8 +84,8 @@ theorem deriv_sinh : deriv sinh = cosh :=
 derivative `sinh x`. -/
 theorem hasStrictDerivAt_cosh (x : ℂ) : HasStrictDerivAt cosh (sinh x) x := by
   simp only [sinh, div_eq_mul_inv]
-  convert ((hasStrictDerivAt_exp x).add (hasStrictDerivAt_id x).fun_neg.cexp).mul_const (2 : ℂ)⁻¹
-    using 1
+  convert!
+    ((hasStrictDerivAt_exp x).add (hasStrictDerivAt_id x).fun_neg.cexp).mul_const (2 : ℂ)⁻¹ using 1
   rw [id, mul_neg_one, sub_eq_add_neg]
 
 /-- The complex hyperbolic cosine function is everywhere differentiable, with the derivative
diff --git a/Mathlib/Analysis/SpecialFunctions/Trigonometric/EulerSineProd.lean b/Mathlib/Analysis/SpecialFunctions/Trigonometric/EulerSineProd.lean
index 2b5e39a274e515..5efad8d26a4da7 100644
--- a/Mathlib/Analysis/SpecialFunctions/Trigonometric/EulerSineProd.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Trigonometric/EulerSineProd.lean
@@ -67,9 +67,9 @@ theorem integral_cos_mul_cos_pow_aux (hn : 2 ≤ n) (hz : z ≠ 0) :
     intro x _
     have b : HasDerivAt (fun y : ℝ => (cos y : ℂ)) (-sin x) x := by
       simpa using (hasDerivAt_cos x).ofReal_comp
-    convert HasDerivAt.comp x (hasDerivAt_pow _ _) b using 1
+    convert! HasDerivAt.comp x (hasDerivAt_pow _ _) b using 1
     ring
-  convert (config := { sameFun := true })
+  convert! (config := { sameFun := true })
     integral_mul_deriv_eq_deriv_mul der1 (fun x _ => antideriv_cos_comp_const_mul hz x) _ _ using 2
   · ext1 x; rw [mul_comm]
   · rw [Complex.ofReal_zero, mul_zero, Complex.sin_zero, zero_div, mul_zero, sub_zero,
@@ -92,7 +92,7 @@ theorem integral_sin_mul_sin_mul_cos_pow_eq (hn : 2 ≤ n) (hz : z ≠ 0) :
           ((cos x : ℂ) ^ n - (n - 1) * (sin x : ℂ) ^ 2 * (cos x : ℂ) ^ (n - 2)) x := by
     intro x _
     have c := HasDerivAt.comp (x : ℂ) (hasDerivAt_pow (n - 1) _) (Complex.hasDerivAt_cos x)
-    convert ((Complex.hasDerivAt_sin x).fun_mul c).comp_ofReal using 1
+    convert! ((Complex.hasDerivAt_sin x).fun_mul c).comp_ofReal using 1
     · simp only [Complex.ofReal_sin, Complex.ofReal_cos, Function.comp]
     · simp only [Complex.ofReal_cos, Complex.ofReal_sin]
       rw [mul_neg, mul_neg, ← sub_eq_add_neg, Function.comp_apply]
@@ -102,7 +102,7 @@ theorem integral_sin_mul_sin_mul_cos_pow_eq (hn : 2 ≤ n) (hz : z ≠ 0) :
           rw [Nat.cast_sub (one_le_two.trans hn), Nat.cast_one]
         rw [Nat.sub_sub, this]
         ring
-  convert
+  convert!
     integral_mul_deriv_eq_deriv_mul der1 (fun x _ => antideriv_sin_comp_const_mul hz x) _ _ using 1
   · refine integral_congr fun x _ => ?_
     ring_nf
@@ -139,7 +139,7 @@ theorem integral_cos_mul_cos_pow (hn : 2 ≤ n) (hz : z ≠ 0) :
   have := integral_cos_mul_cos_pow_aux hn hz
   rw [integral_sin_mul_sin_mul_cos_pow_eq hn hz, sub_eq_neg_add, mul_add, ← sub_eq_iff_eq_add]
     at this
-  convert congr_arg (fun u : ℂ => -u * (2 * z) ^ 2 / n ^ 2) this using 1 <;> field
+  convert! congr_arg (fun u : ℂ => -u * (2 * z) ^ 2 / n ^ 2) this using 1 <;> field
 
 /-- Note this also holds for `z = 0`, but we do not need this case for `sin_pi_mul_eq`. -/
 theorem integral_cos_mul_cos_pow_even (n : ℕ) (hz : z ≠ 0) :
@@ -147,7 +147,7 @@ theorem integral_cos_mul_cos_pow_even (n : ℕ) (hz : z ≠ 0) :
         ∫ x in (0 : ℝ)..π / 2, Complex.cos (2 * z * x) * (cos x : ℂ) ^ (2 * n + 2)) =
       (2 * n + 1 : ℂ) / (2 * n + 2) *
         ∫ x in (0 : ℝ)..π / 2, Complex.cos (2 * z * x) * (cos x : ℂ) ^ (2 * n) := by
-  convert integral_cos_mul_cos_pow (by lia : 2 ≤ 2 * n + 2) hz using 3
+  convert! integral_cos_mul_cos_pow (by lia : 2 ≤ 2 * n + 2) hz using 3
   · simp only [Nat.cast_add, Nat.cast_mul, Nat.cast_two]
     nth_rw 2 [← mul_one (2 : ℂ)]
     rw [← mul_add, mul_pow, ← div_div]
@@ -229,11 +229,11 @@ theorem sin_pi_mul_eq (z : ℂ) (n : ℕ) :
       rw [this, Complex.ofReal_mul, Complex.ofReal_div]
       have : (C : ℂ) ≠ 0 := Complex.ofReal_ne_zero.mpr (integral_cos_pow_pos _).ne'
       have : 2 * (n : ℂ) + 1 ≠ 0 := by
-        convert (Nat.cast_add_one_ne_zero (2 * n) : (↑(2 * n) + 1 : ℂ) ≠ 0)
+        convert! (Nat.cast_add_one_ne_zero (2 * n) : (↑(2 * n) + 1 : ℂ) ≠ 0)
         simp
       have : (n : ℂ) + 1 ≠ 0 := Nat.cast_add_one_ne_zero n
       simp [field]
-    convert integral_cos_mul_cos_pow_even n hz
+    convert! integral_cos_mul_cos_pow_even n hz
     rw [Nat.cast_succ]
 
 end IntegralRecursion
@@ -280,13 +280,13 @@ theorem _root_.Complex.tendsto_euler_sin_prod (z : ℂ) :
     Tendsto.congr (fun n => sin_pi_mul_eq z n) tendsto_const_nhds
   have : 𝓝 (Complex.sin (π * z)) = 𝓝 (Complex.sin (π * z) * 1) := by rw [mul_one]
   simp_rw [this, mul_div_assoc] at A
-  convert (tendsto_mul_iff_of_ne_zero _ one_ne_zero).mp A
+  convert! (tendsto_mul_iff_of_ne_zero _ one_ne_zero).mp A
   suffices Tendsto (fun n : ℕ =>
         (∫ x in (0 : ℝ)..π / 2, Complex.cos (2 * z * x) * (cos x : ℂ) ^ n) /
           (∫ x in (0 : ℝ)..π / 2, cos x ^ n : ℝ)) atTop (𝓝 1) from
     this.comp (tendsto_id.const_mul_atTop' zero_lt_two)
   have : ContinuousOn (fun x : ℝ ↦ Complex.cos (2 * z * x)) (Icc 0 (π / 2)) := by fun_prop
-  convert tendsto_integral_cos_pow_mul_div this using 1
+  convert! tendsto_integral_cos_pow_mul_div this using 1
   · ext1 n; congr 2 with x : 1; rw [mul_comm]
   · rw [Complex.ofReal_zero, mul_zero, Complex.cos_zero]
 
@@ -294,7 +294,7 @@ theorem _root_.Complex.tendsto_euler_sin_prod (z : ℂ) :
 theorem _root_.Real.tendsto_euler_sin_prod (x : ℝ) :
     Tendsto (fun n : ℕ => π * x * ∏ j ∈ Finset.range n, ((1 : ℝ) - x ^ 2 / ((j : ℝ) + 1) ^ 2))
       atTop (𝓝 <| sin (π * x)) := by
-  convert (Complex.continuous_re.tendsto _).comp (Complex.tendsto_euler_sin_prod x) using 1
+  convert! (Complex.continuous_re.tendsto _).comp (Complex.tendsto_euler_sin_prod x) using 1
   · ext1 n
     rw [Function.comp_apply, ← Complex.ofReal_mul, Complex.re_ofReal_mul]
     suffices
diff --git a/Mathlib/Analysis/SpecialFunctions/Trigonometric/InverseDeriv.lean b/Mathlib/Analysis/SpecialFunctions/Trigonometric/InverseDeriv.lean
index 63656e08066a62..2f102a8ae3e251 100644
--- a/Mathlib/Analysis/SpecialFunctions/Trigonometric/InverseDeriv.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Trigonometric/InverseDeriv.lean
@@ -61,14 +61,14 @@ theorem contDiffAt_arcsin {x : ℝ} (h₁ : x ≠ -1) (h₂ : x ≠ 1) {n : ℕ
 theorem hasDerivWithinAt_arcsin_Ici {x : ℝ} (h : x ≠ -1) :
     HasDerivWithinAt arcsin (1 / √(1 - x ^ 2)) (Ici x) x := by
   rcases eq_or_ne x 1 with (rfl | h')
-  · convert (hasDerivWithinAt_const (1 : ℝ) _ (π / 2)).congr _ _ <;>
+  · convert! (hasDerivWithinAt_const (1 : ℝ) _ (π / 2)).congr _ _ <;>
       simp +contextual [arcsin_of_one_le]
   · exact (hasDerivAt_arcsin h h').hasDerivWithinAt
 
 theorem hasDerivWithinAt_arcsin_Iic {x : ℝ} (h : x ≠ 1) :
     HasDerivWithinAt arcsin (1 / √(1 - x ^ 2)) (Iic x) x := by
   rcases em (x = -1) with (rfl | h')
-  · convert (hasDerivWithinAt_const (-1 : ℝ) _ (-(π / 2))).congr _ _ <;>
+  · convert! (hasDerivWithinAt_const (-1 : ℝ) _ (-(π / 2))).congr _ _ <;>
       simp +contextual [arcsin_of_le_neg_one]
   · exact (hasDerivAt_arcsin h' h).hasDerivWithinAt
 
diff --git a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Series.lean b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Series.lean
index 37d773c2794887..45714e812c4fa6 100644
--- a/Mathlib/Analysis/SpecialFunctions/Trigonometric/Series.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Trigonometric/Series.lean
@@ -42,7 +42,7 @@ theorem Complex.hasSum_cos' (z : ℂ) :
   simp_rw [← mul_comm 2 _] at this
   refine this.prod_fiberwise fun k => ?_
   dsimp only
-  convert hasSum_fintype (_ : Fin 2 → ℂ) using 1
+  convert! hasSum_fintype (_ : Fin 2 → ℂ) using 1
   rw [Fin.sum_univ_two]
   simp_rw [Fin.val_zero, Fin.val_one, add_zero, pow_succ, pow_mul, mul_pow, neg_sq, ← two_mul,
     neg_mul, mul_neg, neg_div, add_neg_cancel, zero_div, add_zero,
@@ -59,7 +59,7 @@ theorem Complex.hasSum_sin' (z : ℂ) :
   simp_rw [← mul_comm 2 _] at this
   refine this.prod_fiberwise fun k => ?_
   dsimp only
-  convert hasSum_fintype (_ : Fin 2 → ℂ) using 1
+  convert! hasSum_fintype (_ : Fin 2 → ℂ) using 1
   rw [Fin.sum_univ_two]
   simp_rw [Fin.val_zero, Fin.val_one, add_zero, pow_succ, pow_mul, mul_pow, neg_sq, sub_self,
     zero_mul, zero_div, zero_add, neg_mul, mul_neg, neg_div, ← neg_add', ← two_mul,
@@ -68,13 +68,13 @@ theorem Complex.hasSum_sin' (z : ℂ) :
 /-- The power series expansion of `Complex.cos`. -/
 theorem Complex.hasSum_cos (z : ℂ) :
     HasSum (fun n : ℕ => (-1) ^ n * z ^ (2 * n) / ↑(2 * n)!) (Complex.cos z) := by
-  convert Complex.hasSum_cos' z using 1
+  convert! Complex.hasSum_cos' z using 1
   simp_rw [mul_pow, pow_mul, Complex.I_sq, mul_comm]
 
 /-- The power series expansion of `Complex.sin`. -/
 theorem Complex.hasSum_sin (z : ℂ) :
     HasSum (fun n : ℕ => (-1) ^ n * z ^ (2 * n + 1) / ↑(2 * n + 1)!) (Complex.sin z) := by
-  convert Complex.hasSum_sin' z using 1
+  convert! Complex.hasSum_sin' z using 1
   simp_rw [mul_pow, pow_succ, pow_mul, Complex.I_sq, ← mul_assoc, mul_div_assoc, div_right_comm,
     div_self Complex.I_ne_zero, mul_comm _ ((-1 : ℂ) ^ _), mul_one_div, mul_div_assoc, mul_assoc]
 
diff --git a/Mathlib/Analysis/SpecificLimits/Basic.lean b/Mathlib/Analysis/SpecificLimits/Basic.lean
index 4857e7c7bbe409..a1aac4e3484e9e 100644
--- a/Mathlib/Analysis/SpecificLimits/Basic.lean
+++ b/Mathlib/Analysis/SpecificLimits/Basic.lean
@@ -38,14 +38,13 @@ theorem NNRat.tendsto_inv_atTop_nhds_zero_nat : Tendsto (fun n : ℕ ↦ (n : 
 theorem NNRat.tendsto_algebraMap_inv_atTop_nhds_zero_nat (𝕜 : Type*) [Semiring 𝕜]
     [Algebra ℚ≥0 𝕜] [TopologicalSpace 𝕜] [ContinuousSMul ℚ≥0 𝕜] :
     Tendsto (algebraMap ℚ≥0 𝕜 ∘ fun n : ℕ ↦ (n : ℚ≥0)⁻¹) atTop (𝓝 0) := by
-  convert (continuous_algebraMap ℚ≥0 𝕜).continuousAt.tendsto.comp
-    tendsto_inv_atTop_nhds_zero_nat
+  convert! (continuous_algebraMap ℚ≥0 𝕜).continuousAt.tendsto.comp tendsto_inv_atTop_nhds_zero_nat
   rw [map_zero]
 
 theorem tendsto_inv_atTop_nhds_zero_nat {𝕜 : Type*} [DivisionSemiring 𝕜] [CharZero 𝕜]
     [TopologicalSpace 𝕜] [ContinuousSMul ℚ≥0 𝕜] :
     Tendsto (fun n : ℕ ↦ (n : 𝕜)⁻¹) atTop (𝓝 0) := by
-  convert NNRat.tendsto_algebraMap_inv_atTop_nhds_zero_nat 𝕜
+  convert! NNRat.tendsto_algebraMap_inv_atTop_nhds_zero_nat 𝕜
   simp
 
 theorem tendsto_const_div_atTop_nhds_zero_nat {𝕜 : Type*} [DivisionSemiring 𝕜] [CharZero 𝕜]
@@ -77,7 +76,7 @@ theorem tendsto_algebraMap_inv_atTop_nhds_zero_nat {𝕜 : Type*} (A : Type*)
     [Semifield 𝕜] [CharZero 𝕜] [TopologicalSpace 𝕜] [ContinuousSMul ℚ≥0 𝕜]
     [Semiring A] [Algebra 𝕜 A] [TopologicalSpace A] [ContinuousSMul 𝕜 A] :
     Tendsto (algebraMap 𝕜 A ∘ fun n : ℕ ↦ (n : 𝕜)⁻¹) atTop (𝓝 0) := by
-  convert (continuous_algebraMap 𝕜 A).continuousAt.tendsto.comp tendsto_inv_atTop_nhds_zero_nat
+  convert! (continuous_algebraMap 𝕜 A).continuousAt.tendsto.comp tendsto_inv_atTop_nhds_zero_nat
   rw [map_zero]
 
 /-- The limit of `n / (n + x)` is 1, for any constant `x` (valid in `ℝ` or any topological division
@@ -85,7 +84,7 @@ algebra over `ℚ≥0`, e.g., `ℂ`). -/
 theorem tendsto_natCast_div_add_atTop {𝕜 : Type*} [DivisionSemiring 𝕜] [TopologicalSpace 𝕜]
     [CharZero 𝕜] [ContinuousSMul ℚ≥0 𝕜] [IsTopologicalSemiring 𝕜] [ContinuousInv₀ 𝕜] (x : 𝕜) :
     Tendsto (fun n : ℕ ↦ (n : 𝕜) / (n + x)) atTop (𝓝 1) := by
-  convert Tendsto.congr' ((eventually_ne_atTop 0).mp (Eventually.of_forall fun n hn ↦ _)) _
+  convert! Tendsto.congr' ((eventually_ne_atTop 0).mp (Eventually.of_forall fun n hn ↦ _)) _
   · exact fun n : ℕ ↦ 1 / (1 + x / n)
   · simp [Nat.cast_ne_zero.mpr hn, add_div']
   · have : 𝓝 (1 : 𝕜) = 𝓝 (1 / (1 + x * (0 : 𝕜))) := by
@@ -331,7 +330,7 @@ theorem tsum_geometric_of_lt_one {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) : ∑
   (hasSum_geometric_of_lt_one h₁ h₂).tsum_eq
 
 theorem hasSum_geometric_two : HasSum (fun n : ℕ ↦ ((1 : ℝ) / 2) ^ n) 2 := by
-  convert hasSum_geometric_of_lt_one _ _ <;> norm_num
+  convert! hasSum_geometric_of_lt_one _ _ <;> norm_num
 
 theorem summable_geometric_two : Summable fun n : ℕ ↦ ((1 : ℝ) / 2) ^ n :=
   ⟨_, hasSum_geometric_two⟩
@@ -348,7 +347,7 @@ theorem sum_geometric_two_le (n : ℕ) : (∑ i ∈ range n, (1 / (2 : ℝ)) ^ i
     intro i
     apply pow_nonneg
     norm_num
-  convert summable_geometric_two.sum_le_tsum (range n) (fun i _ ↦ this i)
+  convert! summable_geometric_two.sum_le_tsum (range n) (fun i _ ↦ this i)
   exact tsum_geometric_two.symm
 
 theorem tsum_geometric_inv_two : (∑' n : ℕ, (2 : ℝ)⁻¹ ^ n) = 2 :=
@@ -367,7 +366,8 @@ theorem tsum_geometric_inv_two_ge (n : ℕ) :
     le_add_iff_nonneg_left, pow_add, _root_.tsum_mul_right, tsum_geometric_inv_two]
 
 theorem hasSum_geometric_two' (a : ℝ) : HasSum (fun n : ℕ ↦ a / 2 / 2 ^ n) a := by
-  convert HasSum.mul_left (a / 2)
+  convert!
+    HasSum.mul_left (a / 2)
       (hasSum_geometric_of_lt_one (le_of_lt one_half_pos) one_half_lt_one) using 1
   · funext n
     simp only [one_div, inv_pow]
@@ -402,7 +402,7 @@ theorem ENNReal.tsum_geometric (r : ℝ≥0∞) : ∑' n : ℕ, r ^ n = (1 - r)
   rcases lt_or_ge r 1 with hr | hr
   · rcases ENNReal.lt_iff_exists_coe.1 hr with ⟨r, rfl, hr'⟩
     norm_cast at *
-    convert ENNReal.tsum_coe_eq (NNReal.hasSum_geometric hr)
+    convert! ENNReal.tsum_coe_eq (NNReal.hasSum_geometric hr)
     rw [ENNReal.coe_inv <| ne_of_gt <| tsub_pos_iff_lt.2 hr, coe_sub, coe_one]
   · rw [tsub_eq_zero_iff_le.mpr hr, ENNReal.inv_zero, ENNReal.tsum_eq_iSup_nat, iSup_eq_top]
     refine fun a ha ↦
@@ -464,7 +464,7 @@ include hu in
 `f n` to the limit of `f` is bounded above by `C * r^n / (1 - r)`. -/
 theorem edist_le_of_edist_le_geometric_of_tendsto {a : α} (ha : Tendsto f atTop (𝓝 a)) (n : ℕ) :
     edist (f n) a ≤ C * r ^ n / (1 - r) := by
-  convert edist_le_tsum_of_edist_le_of_tendsto _ hu ha _
+  convert! edist_le_tsum_of_edist_le_of_tendsto _ hu ha _
   simp only [pow_add, ENNReal.tsum_mul_left, ENNReal.tsum_geometric, div_eq_mul_inv, mul_assoc]
 
 include hu in
@@ -494,7 +494,7 @@ include hu ha in
 theorem edist_le_of_edist_le_geometric_two_of_tendsto (n : ℕ) : edist (f n) a ≤ 2 * C / 2 ^ n := by
   simp only [div_eq_mul_inv, ENNReal.inv_pow] at *
   rw [mul_assoc, mul_comm]
-  convert edist_le_of_edist_le_geometric_of_tendsto 2⁻¹ C hu ha n using 1
+  convert! edist_le_of_edist_le_geometric_of_tendsto 2⁻¹ C hu ha n using 1
   rw [ENNReal.one_sub_inv_two, div_eq_mul_inv, inv_inv]
 
 include hu ha in
@@ -540,7 +540,7 @@ theorem dist_le_of_le_geometric_of_tendsto₀ {a : α} (ha : Tendsto f atTop (
 theorem dist_le_of_le_geometric_of_tendsto {a : α} (ha : Tendsto f atTop (𝓝 a)) (n : ℕ) :
     dist (f n) a ≤ C * r ^ n / (1 - r) := by
   have := aux_hasSum_of_le_geometric hr hu
-  convert dist_le_tsum_of_dist_le_of_tendsto _ hu ⟨_, this⟩ ha n
+  convert! dist_le_tsum_of_dist_le_of_tendsto _ hu ⟨_, this⟩ ha n
   simp only [pow_add, mul_left_comm C, mul_div_right_comm]
   rw [mul_comm]
   exact (this.mul_left _).tsum_eq.symm
@@ -564,7 +564,7 @@ theorem dist_le_of_le_geometric_two_of_tendsto₀ {a : α} (ha : Tendsto f atTop
 `f n` to the limit of `f` is bounded above by `C / 2^n`. -/
 theorem dist_le_of_le_geometric_two_of_tendsto {a : α} (ha : Tendsto f atTop (𝓝 a)) (n : ℕ) :
     dist (f n) a ≤ C / 2 ^ n := by
-  convert dist_le_tsum_of_dist_le_of_tendsto _ hu₂ (summable_geometric_two' C) ha n
+  convert! dist_le_tsum_of_dist_le_of_tendsto _ hu₂ (summable_geometric_two' C) ha n
   simp only [add_comm n, pow_add, ← div_div]
   symm
   exact ((hasSum_geometric_two' C).div_const _).tsum_eq
diff --git a/Mathlib/Analysis/SpecificLimits/Fibonacci.lean b/Mathlib/Analysis/SpecificLimits/Fibonacci.lean
index 8423b2c198dab6..f7c6231eb10990 100644
--- a/Mathlib/Analysis/SpecificLimits/Fibonacci.lean
+++ b/Mathlib/Analysis/SpecificLimits/Fibonacci.lean
@@ -35,6 +35,6 @@ theorem tendsto_fib_succ_div_fib_atTop :
 /-- The limit of `fib n / fib (n + 1)` as `n → ∞` is the negative conjugate of the golden ratio. -/
 theorem tendsto_fib_div_fib_succ_atTop :
     Tendsto (fun n ↦ (fib n / fib (n + 1) : ℝ)) atTop (𝓝 (-ψ)) := by
-  convert tendsto_fib_succ_div_fib_atTop.inv₀ (by positivity) using 2
+  convert! tendsto_fib_succ_div_fib_atTop.inv₀ (by positivity) using 2
   · rw [inv_div]
   · rw [inv_goldenRatio]
diff --git a/Mathlib/Analysis/SpecificLimits/FloorPow.lean b/Mathlib/Analysis/SpecificLimits/FloorPow.lean
index fa299173faec20..34f9f3fb667f6b 100644
--- a/Mathlib/Analysis/SpecificLimits/FloorPow.lean
+++ b/Mathlib/Analysis/SpecificLimits/FloorPow.lean
@@ -203,7 +203,7 @@ theorem tendsto_div_of_monotone_of_tendsto_div_floor_pow (u : ℕ → ℝ) (l :
       exact tendsto_pow_atTop_atTop_of_one_lt (cone k)
   have B : Tendsto (fun n : ℕ => (⌊c k ^ (n + 1)⌋₊ : ℝ) / ⌊c k ^ n⌋₊) atTop (𝓝 (c k)) := by
     simp only [one_mul, div_one] at A
-    convert A using 1
+    convert! A using 1
     ext1 n
     field [(zero_lt_one.trans (cone k)).ne']
   filter_upwards [(tendsto_order.1 B).2 a hk] with n hn
diff --git a/Mathlib/Analysis/SpecificLimits/Normed.lean b/Mathlib/Analysis/SpecificLimits/Normed.lean
index 8defaef2b591c0..8403145edf7f25 100644
--- a/Mathlib/Analysis/SpecificLimits/Normed.lean
+++ b/Mathlib/Analysis/SpecificLimits/Normed.lean
@@ -298,7 +298,7 @@ theorem tsum_geometric_le_of_norm_lt_one (x : R) (h : ‖x‖ < 1) :
     refine le_trans (norm_add_le _ _) ?_
     have : ‖∑' b : ℕ, (fun n ↦ x ^ (n + 1)) b‖ ≤ (1 - ‖x‖)⁻¹ - 1 := by
       refine tsum_of_norm_bounded ?_ fun b ↦ norm_pow_le' _ (Nat.succ_pos b)
-      convert (hasSum_nat_add_iff' 1).mpr (hasSum_geometric_of_lt_one (norm_nonneg x) h)
+      convert! (hasSum_nat_add_iff' 1).mpr (hasSum_geometric_of_lt_one (norm_nonneg x) h)
       simp
     linarith
   · simp only [tsum_eq_zero_of_not_summable hx, norm_zero]
@@ -344,7 +344,7 @@ theorem geom_series_eq_inverse (x : R) (h : ‖x‖ < 1) :
 
 theorem hasSum_geom_series_inverse (x : R) (h : ‖x‖ < 1) :
     HasSum (fun i ↦ x ^ i) (1 - x)⁻¹ʳ := by
-  convert (summable_geometric_of_norm_lt_one h).hasSum
+  convert! (summable_geometric_of_norm_lt_one h).hasSum
   exact (geom_series_eq_inverse x h).symm
 
 lemma isUnit_one_sub_of_norm_lt_one {x : R} (h : ‖x‖ < 1) : IsUnit (1 - x) :=
@@ -448,8 +448,10 @@ lemma hasSum_choose_mul_geometric_of_norm_lt_one'
           _ ≤ (2 * n).choose k := choose_le_choose k (by lia)
           _ ≤ (2 * n) ^ k := Nat.choose_le_pow _ _
           _ = 2 ^ k * n ^ k := Nat.mul_pow 2 n k
-      convert hasSum_sum_range_mul_of_summable_norm' I1 ih.summable
-        (summable_norm_geometric_of_norm_lt_one hr) (summable_geometric_of_norm_lt_one hr) with n
+      convert!
+        hasSum_sum_range_mul_of_summable_norm' I1 ih.summable
+          (summable_norm_geometric_of_norm_lt_one hr) (summable_geometric_of_norm_lt_one hr) with
+        n
       · have : ∑ i ∈ Finset.range (n + 1), ↑((i + k).choose k) * r ^ i * r ^ (n - i) =
             ∑ i ∈ Finset.range (n + 1), ↑((i + k).choose k) * r ^ n := by
           apply Finset.sum_congr rfl (fun i hi ↦ ?_)
@@ -469,7 +471,7 @@ lemma tsum_choose_mul_geometric_of_norm_lt_one' (k : ℕ) {r : R} (hr : ‖r‖
 lemma hasSum_choose_mul_geometric_of_norm_lt_one
     (k : ℕ) {r : 𝕜} (hr : ‖r‖ < 1) :
     HasSum (fun n ↦ (n + k).choose k * r ^ n) (1 / (1 - r) ^ (k + 1)) := by
-  convert hasSum_choose_mul_geometric_of_norm_lt_one' k hr
+  convert! hasSum_choose_mul_geometric_of_norm_lt_one' k hr
   simp
 
 lemma tsum_choose_mul_geometric_of_norm_lt_one (k : ℕ) {r : 𝕜} (hr : ‖r‖ < 1) :
@@ -478,8 +480,8 @@ lemma tsum_choose_mul_geometric_of_norm_lt_one (k : ℕ) {r : 𝕜} (hr : ‖r
 
 lemma summable_descFactorial_mul_geometric_of_norm_lt_one (k : ℕ) {r : R} (hr : ‖r‖ < 1) :
     Summable (fun n ↦ (n + k).descFactorial k * r ^ n) := by
-  convert (summable_choose_mul_geometric_of_norm_lt_one k hr).mul_left (k.factorial : R)
-    using 2 with n
+  convert! (summable_choose_mul_geometric_of_norm_lt_one k hr).mul_left (k.factorial : R) using
+    2 with n
   simp [← mul_assoc, descFactorial_eq_factorial_mul_choose (n + k) k]
 
 open Polynomial in
@@ -505,7 +507,7 @@ theorem summable_pow_mul_geometric_of_norm_lt_one (k : ℕ) {r : R} (hr : ‖r
     simp_rw [mul_assoc]
     simp only [Finset.mem_range] at hi
     exact (hk _ hi).mul_left _
-  convert this using 1
+  convert! this using 1
   ext n
   simp [ha n, add_mul, sum_mul]
 
@@ -516,10 +518,10 @@ theorem hasSum_coe_mul_geometric_of_norm_lt_one'
     {x : R} (h : ‖x‖ < 1) :
     HasSum (fun n ↦ n * x ^ n : ℕ → R) (x * ((1 - x)⁻¹ʳ) ^ 2) := by
   have A : HasSum (fun (n : ℕ) ↦ (n + 1) * x ^ n) ((1 - x)⁻¹ʳ ^ 2) := by
-    convert hasSum_choose_mul_geometric_of_norm_lt_one' 1 h with n
+    convert! hasSum_choose_mul_geometric_of_norm_lt_one' 1 h with n
     simp
   have B : HasSum (fun (n : ℕ) ↦ x ^ n) ((1 - x)⁻¹ʳ) := hasSum_geom_series_inverse x h
-  convert A.sub B using 1
+  convert! A.sub B using 1
   · ext n
     simp [add_mul]
   · symm
@@ -538,7 +540,7 @@ theorem tsum_coe_mul_geometric_of_norm_lt_one'
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`, `HasSum` version. -/
 theorem hasSum_coe_mul_geometric_of_norm_lt_one {r : 𝕜} (hr : ‖r‖ < 1) :
     HasSum (fun n ↦ n * r ^ n : ℕ → 𝕜) (r / (1 - r) ^ 2) := by
-  convert hasSum_coe_mul_geometric_of_norm_lt_one' hr using 1
+  convert! hasSum_coe_mul_geometric_of_norm_lt_one' hr using 1
   simp [div_eq_mul_inv]
 
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`. -/
@@ -638,7 +640,7 @@ theorem summable_of_ratio_norm_eventually_le {α : Type*} [SeminormedAddCommGrou
     simp only
     conv_rhs => rw [mul_comm, ← zero_add N]
     refine le_geom (u := fun n ↦ ‖f (n + N)‖) hr₀ n fun i _ ↦ ?_
-    convert hN (i + N) (N.le_add_left i) using 3
+    convert! hN (i + N) (N.le_add_left i) using 3
     ac_rfl
   · refine .of_norm_bounded_eventually_nat summable_zero ?_
     filter_upwards [h] with _ hn
@@ -663,7 +665,7 @@ theorem not_summable_of_ratio_norm_eventually_ge {α : Type*} [SeminormedAddComm
   rw [← @summable_nat_add_iff α _ _ _ _ N]
   refine mt Summable.tendsto_atTop_zero
     fun h' ↦ not_tendsto_atTop_of_tendsto_nhds (tendsto_norm_zero.comp h') ?_
-  convert tendsto_atTop_of_geom_le _ hr _
+  convert! tendsto_atTop_of_geom_le _ hr _
   · refine lt_of_le_of_ne (norm_nonneg _) ?_
     intro h''
     specialize hN₀ N hNN₀
@@ -742,9 +744,9 @@ theorem Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded (hfa : Antitone
     CauchySeq fun n ↦ ∑ i ∈ range n, f i • z i := by
   have hfa' : Monotone fun n ↦ -f n := fun _ _ hab ↦ neg_le_neg <| hfa hab
   have hf0' : Tendsto (fun n ↦ -f n) atTop (𝓝 0) := by
-    convert hf0.neg
+    convert! hf0.neg
     simp
-  convert (hfa'.cauchySeq_series_mul_of_tendsto_zero_of_bounded hf0' hzb).neg
+  convert! (hfa'.cauchySeq_series_mul_of_tendsto_zero_of_bounded hf0' hzb).neg
   simp
 
 theorem norm_sum_neg_one_pow_le (n : ℕ) : ‖∑ i ∈ range n, (-1 : ℝ) ^ i‖ ≤ 1 := by
diff --git a/Mathlib/Analysis/SumIntegralComparisons.lean b/Mathlib/Analysis/SumIntegralComparisons.lean
index 3f94e17c23565f..8b7e0f244ba4bc 100644
--- a/Mathlib/Analysis/SumIntegralComparisons.lean
+++ b/Mathlib/Analysis/SumIntegralComparisons.lean
@@ -75,8 +75,10 @@ lemma integral_le_sum_Ico_of_le
     (hab : a ≤ b) (h : ∀ i ∈ Ico a b, ∀ x ∈ Ico (i : ℝ) (i + 1 : ℕ), g x ≤ f i)
     (hg : IntegrableOn g (Set.Ico a b)) :
     ∫ x in a..b, g x ≤ ∑ i ∈ Finset.Ico a b, f i := by
-  convert neg_le_neg (sum_Ico_le_integral_of_le (f := -f) (g := -g) hab
-    (fun i hi x hx ↦ neg_le_neg (h i hi x hx)) hg.neg) <;> simp
+  convert!
+    neg_le_neg
+      (sum_Ico_le_integral_of_le (f := -f) (g := -g) hab (fun i hi x hx ↦ neg_le_neg (h i hi x hx))
+        hg.neg) <;> simp
 
 theorem AntitoneOn.integral_le_sum (hf : AntitoneOn f (Icc x₀ (x₀ + a))) :
     (∫ x in x₀..x₀ + a, f x) ≤ ∑ i ∈ Finset.range a, f (x₀ + i) := by
@@ -90,7 +92,7 @@ theorem AntitoneOn.integral_le_sum (hf : AntitoneOn f (Icc x₀ (x₀ + a))) :
     · simp only [add_le_add_iff_left, Nat.cast_le, Nat.le_succ]
   calc
     ∫ x in x₀..x₀ + a, f x = ∑ i ∈ Finset.range a, ∫ x in x₀ + i..x₀ + (i + 1 : ℕ), f x := by
-      convert (intervalIntegral.sum_integral_adjacent_intervals hint).symm
+      convert! (intervalIntegral.sum_integral_adjacent_intervals hint).symm
       simp only [Nat.cast_zero, add_zero]
     _ ≤ ∑ i ∈ Finset.range a, ∫ _ in x₀ + i..x₀ + (i + 1 : ℕ), f (x₀ + i) := by
       gcongr with i hi
@@ -151,7 +153,7 @@ theorem AntitoneOn.sum_le_integral (hf : AntitoneOn f (Icc x₀ (x₀ + a))) :
       · refine mem_Icc.2 ⟨le_add_of_nonneg_right (Nat.cast_nonneg _), ?_⟩
         simp only [add_le_add_iff_left, Nat.cast_le, ia]
     _ = ∫ x in x₀..x₀ + a, f x := by
-      convert intervalIntegral.sum_integral_adjacent_intervals hint
+      convert! intervalIntegral.sum_integral_adjacent_intervals hint
       simp only [Nat.cast_zero, add_zero]
 
 theorem AntitoneOn.sum_le_integral_Ico (hab : a ≤ b) (hf : AntitoneOn f (Set.Icc a b)) :
diff --git a/Mathlib/Analysis/SumOverResidueClass.lean b/Mathlib/Analysis/SumOverResidueClass.lean
index 87d8ea7e7248a1..b29da2f5d98ff7 100644
--- a/Mathlib/Analysis/SumOverResidueClass.lean
+++ b/Mathlib/Analysis/SumOverResidueClass.lean
@@ -44,7 +44,7 @@ lemma summable_indicator_mod_iff_summable {R : Type*} [AddCommGroup R] [Topologi
       intro n hn
       contrapose! hn
       exact (Nat.range_mul_add m k).symm ▸ mem_of_indicator_ne_zero hn
-    convert (Function.Injective.summable_iff hg hg').symm using 3
+    convert! (Function.Injective.summable_iff hg hg').symm using 3
     simp only [Function.comp_apply, mem_setOf_eq, Nat.cast_add, Nat.cast_mul, CharP.cast_eq_zero,
       zero_mul, zero_add, le_add_iff_nonneg_left, zero_le, and_self, indicator_of_mem, g]
 
@@ -92,8 +92,9 @@ lemma summable_indicator_mod_iff {m : ℕ} [NeZero m] {f : ℕ → ℝ} (hf : An
     Summable ({n : ℕ | (n : ZMod m) = k}.indicator f) ↔ Summable f := by
   refine ⟨fun H ↦ ?_, fun H ↦ Summable.indicator H _⟩
   rw [Finset.sum_indicator_mod m f]
-  convert summable_sum (s := Finset.univ)
-    fun a _ ↦ summable_indicator_mod_iff_summable_indicator_mod hf a H
+  convert!
+    summable_sum (s := Finset.univ) fun a _ ↦
+      summable_indicator_mod_iff_summable_indicator_mod hf a H
   simp only [Finset.sum_apply]
 
 open ZMod
diff --git a/Mathlib/CategoryTheory/Abelian/Basic.lean b/Mathlib/CategoryTheory/Abelian/Basic.lean
index 06d807758cb9d0..9f7d3225a75779 100644
--- a/Mathlib/CategoryTheory/Abelian/Basic.lean
+++ b/Mathlib/CategoryTheory/Abelian/Basic.lean
@@ -208,7 +208,7 @@ lemma isNormalMonoCategory : IsNormalMonoCategory C where
           rw [KernelFork.ι_ofι] at hg
           rw [← cancel_mono f, hg, ← aux, KernelFork.ι_ofι]
         · simp only [KernelFork.ι_ofι, Category.assoc]
-          convert limit.lift_π s WalkingParallelPair.zero using 2
+          convert! limit.lift_π s WalkingParallelPair.zero using 2
           rw [IsIso.inv_comp_eq, eq_comm]
           exact (imageMonoFactorisation f).fac }⟩
 
@@ -235,7 +235,7 @@ lemma isNormalEpiCategory : IsNormalEpiCategory C where
           rw [CokernelCofork.π_ofπ] at hg
           rw [← cancel_epi f, hg, ← aux, CokernelCofork.π_ofπ]
         · simp only [CokernelCofork.π_ofπ, ← Category.assoc]
-          convert colimit.ι_desc s WalkingParallelPair.one using 2
+          convert! colimit.ι_desc s WalkingParallelPair.one using 2
           rw [IsIso.comp_inv_eq, IsIso.comp_inv_eq, eq_comm, ← imageMonoFactorisation_e']
           exact (imageMonoFactorisation f).fac }⟩
 
@@ -380,7 +380,7 @@ set_option backward.isDefEq.respectTransparency false in
 See `CategoryTheory.Abelian.ofCoimageImageComparisonIsIso` for the converse.
 -/
 instance : IsIso (coimageImageComparison f) := by
-  convert
+  convert!
     Iso.isIso_hom
       (IsImage.isoExt (coimageStrongEpiMonoFactorisation f).toMonoIsImage
         (imageStrongEpiMonoFactorisation f).toMonoIsImage)
diff --git a/Mathlib/CategoryTheory/Abelian/GrothendieckCategory/EnoughInjectives.lean b/Mathlib/CategoryTheory/Abelian/GrothendieckCategory/EnoughInjectives.lean
index 7f35272a940182..04ea5c03facb02 100644
--- a/Mathlib/CategoryTheory/Abelian/GrothendieckCategory/EnoughInjectives.lean
+++ b/Mathlib/CategoryTheory/Abelian/GrothendieckCategory/EnoughInjectives.lean
@@ -254,8 +254,8 @@ noncomputable def transfiniteCompositionOfShapeMapFromBot (j : J) :
   isColimit := colimitOfDiagramTerminal isTerminalTop _
   map_mem k hk := by
     dsimp [MonoOver.forget]
-    convert pushouts_ofLE_le_largerSubobject hG
-      (transfiniteIterate (largerSubobject hG) k.1 A₀) using 2
+    convert!
+      pushouts_ofLE_le_largerSubobject hG (transfiniteIterate (largerSubobject hG) k.1 A₀) using 2
     all_goals
       rw [Set.Iic.succ_eq_of_not_isMax hk,
         transfiniteIterate_succ _ _ _ (Set.not_isMax_coe _ hk)]
diff --git a/Mathlib/CategoryTheory/Abelian/NonPreadditive.lean b/Mathlib/CategoryTheory/Abelian/NonPreadditive.lean
index 8857a1aa064c6e..21e1139fae40f8 100644
--- a/Mathlib/CategoryTheory/Abelian/NonPreadditive.lean
+++ b/Mathlib/CategoryTheory/Abelian/NonPreadditive.lean
@@ -246,7 +246,7 @@ instance epi_r {A : C} : Epi (r A) := by
     · intro s m h
       haveI : Mono (prod.lift (𝟙 A) (0 : A ⟶ A)) := mono_of_mono_fac (prod.lift_fst _ _)
       apply (cancel_mono (prod.lift (𝟙 A) (0 : A ⟶ A))).1
-      convert h
+      convert! h
       apply Limits.prod.hom_ext <;> simp
   let hp2 : IsColimit (CokernelCofork.ofπ (Limits.prod.snd : A ⨯ A ⟶ A) hlp) :=
     epiIsCokernelOfKernel _ hp1
diff --git a/Mathlib/CategoryTheory/Abelian/Pseudoelements.lean b/Mathlib/CategoryTheory/Abelian/Pseudoelements.lean
index 495672a4b366ac..e7709d66db784b 100644
--- a/Mathlib/CategoryTheory/Abelian/Pseudoelements.lean
+++ b/Mathlib/CategoryTheory/Abelian/Pseudoelements.lean
@@ -272,7 +272,8 @@ theorem pseudo_injective_of_mono {P Q : C} (f : P ⟶ Q) [Mono f] : Function.Inj
   intro abar abar'
   induction abar, abar' using Quotient.inductionOn₂ with | _ a a'
   refine fun ha ↦ Quotient.sound ?_
-  have : (⟦(a.hom ≫ f : Over Q)⟧ : Quotient (setoid Q)) = ⟦↑(a'.hom ≫ f)⟧ := by convert ha
+  have : (⟦(a.hom ≫ f : Over Q)⟧ : Quotient (setoid Q)) = ⟦↑(a'.hom ≫ f)⟧ := by convert!
+    ha
   have ⟨R, p, q, ep, Eq, comm⟩ := Quotient.exact this
   exact ⟨R, p, q, ep, Eq, (cancel_mono f).1 <| by
     simp only [Category.assoc]
diff --git a/Mathlib/CategoryTheory/Adhesive/Basic.lean b/Mathlib/CategoryTheory/Adhesive/Basic.lean
index 7a11a34188b3e5..57f82845c4c328 100644
--- a/Mathlib/CategoryTheory/Adhesive/Basic.lean
+++ b/Mathlib/CategoryTheory/Adhesive/Basic.lean
@@ -94,8 +94,8 @@ theorem IsPushout.isVanKampen_iff (H : IsPushout f g h i) :
   · intro H F' c' α fα eα hα
     refine Iff.trans ?_
         ((H (F'.map WalkingSpan.Hom.fst) (F'.map WalkingSpan.Hom.snd) (c'.ι.app _) (c'.ι.app _)
-          (α.app _) (α.app _) (α.app _) fα (by convert hα WalkingSpan.Hom.fst)
-          (by convert hα WalkingSpan.Hom.snd) ?_ ?_ ?_).trans ?_)
+          (α.app _) (α.app _) (α.app _) fα (by convert! hα WalkingSpan.Hom.fst)
+          (by convert! hα WalkingSpan.Hom.snd) ?_ ?_ ?_).trans ?_)
     · have : F'.map WalkingSpan.Hom.fst ≫ c'.ι.app WalkingSpan.left =
           F'.map WalkingSpan.Hom.snd ≫ c'.ι.app WalkingSpan.right := by
         simp only [Cocone.w]
diff --git a/Mathlib/CategoryTheory/Adjunction/FullyFaithful.lean b/Mathlib/CategoryTheory/Adjunction/FullyFaithful.lean
index fcf8ee9bc006ff..5de687029c1d24 100644
--- a/Mathlib/CategoryTheory/Adjunction/FullyFaithful.lean
+++ b/Mathlib/CategoryTheory/Adjunction/FullyFaithful.lean
@@ -277,8 +277,10 @@ theorem isIso_map_unit_of_isLeftAdjoint_comp {E : Type*} [Category* E]
   let FF := FullyFaithful.ofFullyFaithful R
   apply isIso_of_coyoneda_map_bijective
   intro Y
-  convert ((adj2.homEquiv (R.obj (L.obj X)) Y).trans <| FF.homEquiv.symm.trans <|
-    (h.homEquiv X (S.obj Y)).trans (adj2.homEquiv X Y).symm).bijective using 1
+  convert!
+    ((adj2.homEquiv (R.obj (L.obj X)) Y).trans <|
+        FF.homEquiv.symm.trans <|
+          (h.homEquiv X (S.obj Y)).trans (adj2.homEquiv X Y).symm).bijective using 1
   ext x
   have := adj2.counit_naturality x
   simp_all [Adjunction.homEquiv]
diff --git a/Mathlib/CategoryTheory/Category/Basic.lean b/Mathlib/CategoryTheory/Category/Basic.lean
index 1a55f91f20c3e1..247a1928c37d7c 100644
--- a/Mathlib/CategoryTheory/Category/Basic.lean
+++ b/Mathlib/CategoryTheory/Category/Basic.lean
@@ -295,16 +295,16 @@ scoped infixr:80 " ≫= " => whisker_eq
 @[to_dual eq_of_comp_right_eq]
 theorem eq_of_comp_left_eq {f g : X ⟶ Y} (w : ∀ {Z : C} (h : Y ⟶ Z), f ≫ h = g ≫ h) :
     f = g := by
-  convert w (𝟙 Y) <;> simp
+  convert! w (𝟙 Y) <;> simp
 
 @[to_dual eq_of_comp_right_eq']
 theorem eq_of_comp_left_eq' (f g : X ⟶ Y)
     (w : (fun {Z} (h : Y ⟶ Z) => f ≫ h) = fun {Z} (h : Y ⟶ Z) => g ≫ h) : f = g :=
-  eq_of_comp_left_eq @fun Z h => by convert congr_fun (congr_fun w Z) h
+  eq_of_comp_left_eq @fun Z h => by convert! congr_fun (congr_fun w Z) h
 
 @[to_dual id_of_comp_right_id]
 theorem id_of_comp_left_id (f : X ⟶ X) (w : ∀ {Y : C} (g : X ⟶ Y), f ≫ g = g) : f = 𝟙 X := by
-  convert w (𝟙 X)
+  convert! w (𝟙 X)
   simp
 
 @[to_dual (reorder := f g' g) ite_comp]
@@ -344,7 +344,7 @@ theorem cancel_epi_assoc_iff (f : X ⟶ Y) [Epi f] {g h : Y ⟶ Z} {W : C} {k l
 
 @[to_dual]
 theorem cancel_epi_id (f : X ⟶ Y) [Epi f] {h : Y ⟶ Y} : f ≫ h = f ↔ h = 𝟙 Y := by
-  convert cancel_epi f
+  convert! cancel_epi f
   simp
 
 /-- The composition of epimorphisms is again an epimorphism. This version takes `Epi f` and `Epi g`
diff --git a/Mathlib/CategoryTheory/Category/PartialFun.lean b/Mathlib/CategoryTheory/Category/PartialFun.lean
index ecd59cab06f707..64b08617c38de7 100644
--- a/Mathlib/CategoryTheory/Category/PartialFun.lean
+++ b/Mathlib/CategoryTheory/Category/PartialFun.lean
@@ -111,7 +111,7 @@ noncomputable def partialFunToPointed : PartialFun ⥤ Pointed := by
       map := fun f => ⟨Option.elim' none fun a => (f a).toOption, rfl⟩
       map_id := fun X => Pointed.Hom.ext <| funext fun o => Option.recOn o rfl fun a => (by
         dsimp [CategoryStruct.id]
-        convert Part.some_toOption a)
+        convert! Part.some_toOption a)
       map_comp := fun f g => Pointed.Hom.ext <| funext fun o => Option.recOn o rfl fun a => by
         dsimp [CategoryStruct.comp]
         rw [Part.bind_toOption g (f a), Option.elim'_eq_elim] }
@@ -172,5 +172,5 @@ noncomputable def typeToPartialFunIsoPartialFunToPointed :
     fun f =>
     Pointed.Hom.ext <|
       funext fun a => Option.recOn a rfl fun a => by
-        convert Part.some_toOption _
+        convert! Part.some_toOption _
         simpa using (Part.get_eq_iff_mem (by trivial)).mp rfl
diff --git a/Mathlib/CategoryTheory/CofilteredSystem.lean b/Mathlib/CategoryTheory/CofilteredSystem.lean
index ae3d9b169742fd..b69d6870326a84 100644
--- a/Mathlib/CategoryTheory/CofilteredSystem.lean
+++ b/Mathlib/CategoryTheory/CofilteredSystem.lean
@@ -169,7 +169,7 @@ def toPreimages : J ⥤ Type v where
     rw [mem_iInter] at h ⊢
     intro f
     rw [← mem_preimage, preimage_preimage, mem_preimage]
-    convert h (g ≫ f); rw [F.map_comp]; rfl)
+    convert! h (g ≫ f); rw [F.map_comp]; rfl)
 
 instance toPreimages_finite [∀ j, Finite (F.obj j)] : ∀ j, Finite ((F.toPreimages s).obj j) :=
   fun _ => Subtype.finite
diff --git a/Mathlib/CategoryTheory/Comma/Final.lean b/Mathlib/CategoryTheory/Comma/Final.lean
index 45ef53f49668ff..7cfb87dbd53f62 100644
--- a/Mathlib/CategoryTheory/Comma/Final.lean
+++ b/Mathlib/CategoryTheory/Comma/Final.lean
@@ -57,7 +57,7 @@ private lemma final_fst_small [R.Final] : (fst L R).Final := by
     (Final.colimitIso (Grothendieck.pre (functor L) R) (grothendieckProj L ⋙ G)).symm ≪≫
     HasColimit.isoOfNatIso (Iso.refl _) ≪≫
     Final.colimitIso (grothendieckPrecompFunctorEquivalence L R).functor (fst L R ⋙ G)
-  convert i.isIso_inv
+  convert! i.isIso_inv
   apply colimit.hom_ext
   intro ⟨a, b, f⟩
   simp only [colimit.ι_pre, comp_obj, fst_obj, grothendieckPrecompFunctorEquivalence_functor,
diff --git a/Mathlib/CategoryTheory/Comma/StructuredArrow/Final.lean b/Mathlib/CategoryTheory/Comma/StructuredArrow/Final.lean
index 2f1b4b60f6abb4..73ac1c5cb28d5f 100644
--- a/Mathlib/CategoryTheory/Comma/StructuredArrow/Final.lean
+++ b/Mathlib/CategoryTheory/Comma/StructuredArrow/Final.lean
@@ -57,7 +57,7 @@ private lemma final_of_final_costructuredArrowToOver_small (L : A ⥤ T) (R : B
       _ ≅ colimit <| grothendieckProj (𝟭 T) ⋙ G :=
             Final.colimitIso _ _
       _ ≅ colimit G := (colimitIsoColimitGrothendieck (𝟭 T) G).symm
-  convert Iso.isIso_hom i
+  convert! Iso.isIso_hom i
   simp only [Iso.trans_def, comp_obj, grothendieckProj_obj, Grothendieck.pre_obj_base,
     Grothendieck.pre_obj_fiber, Iso.trans_assoc, Iso.trans_hom, Iso.symm_hom, i]
   rw [← Iso.inv_comp_eq, Iso.eq_inv_comp]
diff --git a/Mathlib/CategoryTheory/Dialectica/Monoidal.lean b/Mathlib/CategoryTheory/Dialectica/Monoidal.lean
index 1f2f7e26ffc636..720e1466f935d9 100644
--- a/Mathlib/CategoryTheory/Dialectica/Monoidal.lean
+++ b/Mathlib/CategoryTheory/Dialectica/Monoidal.lean
@@ -52,11 +52,11 @@ set_option backward.isDefEq.respectTransparency false in
     · have := (Subobject.pullback (prod.map π₁ π₁ :
         (X₁.src ⨯ Y₁.src) ⨯ X₂.tgt ⨯ Y₂.tgt ⟶ _)).monotone (Hom.le f)
       rw [← Subobject.pullback_comp, ← Subobject.pullback_comp] at this
-      convert this using 3 <;> simp
+      convert! this using 3 <;> simp
     · have := (Subobject.pullback (prod.map π₂ π₂ :
         (X₁.src ⨯ Y₁.src) ⨯ X₂.tgt ⨯ Y₂.tgt ⟶ _)).monotone (Hom.le g)
       rw [← Subobject.pullback_comp, ← Subobject.pullback_comp] at this
-      convert this using 3 <;> simp
+      convert! this using 3 <;> simp
 
 /-- The unit for the tensor `X ⊗ Y` in `Dial C`. -/
 @[simps] def tensorUnitImpl : Dial C := { src := ⊤_ _, tgt := ⊤_ _, rel := ⊤ }
diff --git a/Mathlib/CategoryTheory/DifferentialObject.lean b/Mathlib/CategoryTheory/DifferentialObject.lean
index 5f756fa36b4e6b..f955c315e588fa 100644
--- a/Mathlib/CategoryTheory/DifferentialObject.lean
+++ b/Mathlib/CategoryTheory/DifferentialObject.lean
@@ -311,16 +311,16 @@ instance : HasShift (DifferentialObject S C) S :=
       add := shiftFunctorAdd C
       assoc_hom_app := fun m₁ m₂ m₃ X => by
         ext1
-        convert shiftFunctorAdd_assoc_hom_app m₁ m₂ m₃ X.obj
+        convert! shiftFunctorAdd_assoc_hom_app m₁ m₂ m₃ X.obj
         dsimp [shiftFunctorAdd']
         simp
       zero_add_hom_app := fun n X => by
         ext1
-        convert shiftFunctorAdd_zero_add_hom_app n X.obj
+        convert! shiftFunctorAdd_zero_add_hom_app n X.obj
         simp
       add_zero_hom_app := fun n X => by
         ext1
-        convert shiftFunctorAdd_add_zero_hom_app n X.obj
+        convert! shiftFunctorAdd_add_zero_hom_app n X.obj
         simp }
 
 end
diff --git a/Mathlib/CategoryTheory/EffectiveEpi/Extensive.lean b/Mathlib/CategoryTheory/EffectiveEpi/Extensive.lean
index c311f3fb4b0695..056791f16214a0 100644
--- a/Mathlib/CategoryTheory/EffectiveEpi/Extensive.lean
+++ b/Mathlib/CategoryTheory/EffectiveEpi/Extensive.lean
@@ -39,15 +39,15 @@ instance [F.ReflectsEffectiveEpis] : F.ReflectsFiniteEffectiveEpiFamilies where
   reflects {α _ B} X π h := by
     simp only [← effectiveEpi_desc_iff_effectiveEpiFamily]
     apply F.effectiveEpi_of_map
-    convert (inferInstance :
-      EffectiveEpi (inv (sigmaComparison F X) ≫ (Sigma.desc (fun a ↦ F.map (π a)))))
+    convert!
+      (inferInstance :
+        EffectiveEpi (inv (sigmaComparison F X) ≫ (Sigma.desc (fun a ↦ F.map (π a)))))
     simp
 
 instance [F.PreservesEffectiveEpis] : F.PreservesFiniteEffectiveEpiFamilies where
   preserves {α _ B} X π h := by
     simp only [← effectiveEpi_desc_iff_effectiveEpiFamily]
-    convert (inferInstance :
-      EffectiveEpi ((sigmaComparison F X) ≫ (F.map (Sigma.desc π))))
+    convert! (inferInstance : EffectiveEpi ((sigmaComparison F X) ≫ (F.map (Sigma.desc π))))
     simp
 
 end CategoryTheory
diff --git a/Mathlib/CategoryTheory/Enriched/Basic.lean b/Mathlib/CategoryTheory/Enriched/Basic.lean
index 5b1c62e13158cd..0431277a7f98a9 100644
--- a/Mathlib/CategoryTheory/Enriched/Basic.lean
+++ b/Mathlib/CategoryTheory/Enriched/Basic.lean
@@ -127,14 +127,14 @@ instance : EnrichedCategory W (TransportEnrichment F C) where
     simp only [comp_whiskerRight, Category.assoc, Functor.LaxMonoidal.μ_natural_left_assoc,
       Functor.LaxMonoidal.left_unitality_inv_assoc]
     simp_rw [← F.map_comp]
-    convert F.map_id _
+    convert! F.map_id _
     simp
   comp_id X Y := by
     simp only [MonoidalCategory.whiskerLeft_comp, Category.assoc,
       Functor.LaxMonoidal.μ_natural_right_assoc,
       Functor.LaxMonoidal.right_unitality_inv_assoc]
     simp_rw [← F.map_comp]
-    convert F.map_id _
+    convert! F.map_id _
     simp
   assoc P Q R S := by
     rw [comp_whiskerRight, Category.assoc, μ_natural_left_assoc,
diff --git a/Mathlib/CategoryTheory/Extensive.lean b/Mathlib/CategoryTheory/Extensive.lean
index e3c7e717c6f9cd..9a0743bcf54162 100644
--- a/Mathlib/CategoryTheory/Extensive.lean
+++ b/Mathlib/CategoryTheory/Extensive.lean
@@ -253,7 +253,7 @@ instance types.finitaryExtensive : FinitaryExtensive (Type u) := by
       rcases f x with (⟨⟨⟩⟩ | ⟨⟨⟩⟩)
       exacts [Or.inl rfl, Or.inr rfl]
     let eX : { p : Z × PUnit // f p.fst = Sum.inl p.snd } ≃ { x : Z // f x = Sum.inl PUnit.unit } :=
-      ⟨fun p => ⟨p.1.1, by convert p.2⟩, fun x => ⟨⟨_, _⟩, x.2⟩, fun _ => by ext; rfl,
+      ⟨fun p => ⟨p.1.1, by convert! p.2⟩, fun x => ⟨⟨_, _⟩, x.2⟩, fun _ => by ext; rfl,
         fun _ => by ext; rfl⟩
     let eY : { p : Z × PUnit // f p.fst = Sum.inr p.snd } ≃ { x : Z // f x = Sum.inr PUnit.unit } :=
       ⟨fun p => ⟨p.1.1, p.2.trans (congr_arg Sum.inr <| Subsingleton.elim _ _)⟩,
@@ -301,10 +301,10 @@ noncomputable def finitaryExtensiveTopCatAux (Z : TopCat.{u})
     · rintro x ⟨⟨⟩, hx⟩; refine ⟨⟨⟨x, PUnit.unit⟩, hx.symm⟩, rfl⟩
   refine ((TopCat.binaryCofan_isColimit_iff _).mpr ⟨?_, ?_, ?_⟩).some
   · refine ⟨(Homeomorph.prodPUnit Z).isEmbedding.comp .subtypeVal, ?_⟩
-    convert f.hom.2.1 _ isOpen_range_inl
+    convert! f.hom.2.1 _ isOpen_range_inl
   · refine ⟨(Homeomorph.prodPUnit Z).isEmbedding.comp .subtypeVal, ?_⟩
-    convert f.hom.2.1 _ isOpen_range_inr
-  · convert Set.isCompl_range_inl_range_inr.preimage f
+    convert! f.hom.2.1 _ isOpen_range_inr
+  · convert! Set.isCompl_range_inl_range_inr.preimage f
 
 instance finitaryExtensive_TopCat : FinitaryExtensive TopCat.{u} := by
   rw [finitaryExtensive_iff_of_isTerminal TopCat.{u} _ TopCat.isTerminalPUnit _
@@ -329,7 +329,7 @@ instance finitaryExtensive_TopCat : FinitaryExtensive TopCat.{u} := by
         fun {l'} h₁ _ => TopCat.ext fun x =>
           hl' x (l' x) (ConcreteCategory.congr_hom h₁ x).symm⟩
       apply (IsEmbedding.inl (X := X') (Y := Y')).isInducing.continuous_iff.mpr
-      convert s.fst.hom.2 using 1
+      convert! s.fst.hom.2 using 1
       exact (funext hl).symm
     · refine ⟨⟨hαY.symm⟩, ⟨PullbackCone.isLimitAux' _ ?_⟩⟩
       intro s
@@ -347,7 +347,7 @@ instance finitaryExtensive_TopCat : FinitaryExtensive TopCat.{u} := by
         fun {l'} h₁ _ =>
           TopCat.ext fun x => hl' x (l' x) (ConcreteCategory.congr_hom h₁ x).symm⟩
       apply (IsEmbedding.inr (X := X') (Y := Y')).isInducing.continuous_iff.mpr
-      convert s.fst.hom.2 using 1
+      convert! s.fst.hom.2 using 1
       exact (funext hl).symm
   · intro Z f
     exact finitaryExtensiveTopCatAux Z f
@@ -591,11 +591,12 @@ lemma FinitaryPreExtensive.isPullback_sigmaDesc [HasPullbacks C] [FinitaryPreExt
       (Limits.Sigma.desc fun (p : ι × ι') ↦ pullback.fst (f p.1) (g p.2) ≫ Sigma.ι X p.1)
       (Limits.Sigma.desc fun (p : ι × ι') ↦ pullback.snd (f p.1) (g p.2) ≫ Sigma.ι Y p.2)
       (Limits.Sigma.desc f) (Limits.Sigma.desc g) := by
-  convert IsUniversalColimit.isPullback_prod_of_isColimit
-      (d := Cofan.mk _ (Sigma.ι fun (p : ι × ι') ↦ pullback (f p.1) (g p.2)))
-      (hd := coproductIsCoproduct (fun (p : ι × ι') ↦ pullback (f p.1) (g p.2)))
-      (a := Cofan.mk _ <| fun i ↦ Sigma.ι _ i) (b := Cofan.mk _ <| fun i ↦ Sigma.ι _ i)
-      ?_ ?_ f g (Sigma.desc f) (Sigma.desc g) (fun i j ↦ IsPullback.of_hasPullback (f i) (g j))
+  convert!
+    IsUniversalColimit.isPullback_prod_of_isColimit (d :=
+      Cofan.mk _ (Sigma.ι fun (p : ι × ι') ↦ pullback (f p.1) (g p.2))) (hd :=
+      coproductIsCoproduct (fun (p : ι × ι') ↦ pullback (f p.1) (g p.2))) (a :=
+      Cofan.mk _ <| fun i ↦ Sigma.ι _ i) (b := Cofan.mk _ <| fun i ↦ Sigma.ι _ i) ?_ ?_ f g
+      (Sigma.desc f) (Sigma.desc g) (fun i j ↦ IsPullback.of_hasPullback (f i) (g j))
   · ext
     simp [Cofan.IsColimit.desc, Sigma.ι, coproductIsCoproduct]
   · ext
diff --git a/Mathlib/CategoryTheory/Filtered/Basic.lean b/Mathlib/CategoryTheory/Filtered/Basic.lean
index abc400bfb542aa..a4f192619b9061 100644
--- a/Mathlib/CategoryTheory/Filtered/Basic.lean
+++ b/Mathlib/CategoryTheory/Filtered/Basic.lean
@@ -685,7 +685,7 @@ theorem _root_.CategoryTheory.Functor.ranges_directed (F : C ⥤ Type*) (j : C)
   let ⟨l, li, lk, e⟩ := cospan ij kj
   refine ⟨⟨l, lk ≫ kj⟩, e ▸ ?_, ?_⟩ <;>
     simp_rw [F.map_comp] <;>
-    convert Set.range_comp_subset_range _ _
+    convert! Set.range_comp_subset_range _ _
 
 /-- Given a "bowtie" of morphisms
 ```
diff --git a/Mathlib/CategoryTheory/FintypeCat.lean b/Mathlib/CategoryTheory/FintypeCat.lean
index 3d923a311c6891..5a91c38d3e71d0 100644
--- a/Mathlib/CategoryTheory/FintypeCat.lean
+++ b/Mathlib/CategoryTheory/FintypeCat.lean
@@ -234,9 +234,9 @@ attribute [local instance] FintypeCat.fintype in
 @[simp]
 theorem incl_mk_nat_card (n : ℕ) :
     Fintype.card (incl.obj (mk n)) = n := by
-  convert Finset.card_fin n
+  convert! Finset.card_fin n
   dsimp [incl, mk, len]
-  convert (Fintype.ofEquiv_card Equiv.ulift).symm
+  convert! (Fintype.ofEquiv_card Equiv.ulift).symm
 
 end Skeleton
 
diff --git a/Mathlib/CategoryTheory/Functor/Flat.lean b/Mathlib/CategoryTheory/Functor/Flat.lean
index c308abbe359157..2b41684d7e3f6b 100644
--- a/Mathlib/CategoryTheory/Functor/Flat.lean
+++ b/Mathlib/CategoryTheory/Functor/Flat.lean
@@ -222,7 +222,7 @@ theorem uniq {K : J ⥤ C} {c : Cone K} (hc : IsLimit c) (s : Cone (K ⋙ F))
     intro j
     injection c₀.π.naturality (BiconeHom.left j) with _ e₁
     injection c₀.π.naturality (BiconeHom.right j) with _ e₂
-    convert e₁.symm.trans e₂ <;> simp [c₁, c₂]
+    convert! e₁.symm.trans e₂ <;> simp [c₁, c₂]
   have : c.extend g₁.right = c.extend g₂.right := by
     unfold Cone.extend
     congr 1
diff --git a/Mathlib/CategoryTheory/Generator/Basic.lean b/Mathlib/CategoryTheory/Generator/Basic.lean
index 87b4a82f2d1ebe..08357f85ffbd76 100644
--- a/Mathlib/CategoryTheory/Generator/Basic.lean
+++ b/Mathlib/CategoryTheory/Generator/Basic.lean
@@ -703,7 +703,7 @@ theorem isSeparator_sigma {β : Type w} (f : β → C) [HasCoproduct f] :
 theorem isSeparator_coprod (G H : C) [HasBinaryCoproduct G H] :
     IsSeparator (G ⨿ H) ↔ ObjectProperty.IsSeparating (.pair G H) := by
   refine (isSeparator_iff_of_isColimit_cofan (coprodIsCoprod G H)).trans ?_
-  convert Iff.rfl
+  convert! Iff.rfl
   ext X
   simp only [ObjectProperty.pair_iff, ObjectProperty.ofObj_iff]
   constructor
@@ -750,7 +750,7 @@ theorem isCoseparator_pi {β : Type w} (f : β → C) [HasProduct f] :
 theorem isCoseparator_prod (G H : C) [HasBinaryProduct G H] :
     IsCoseparator (G ⨯ H) ↔ ObjectProperty.IsCoseparating (.pair G H) := by
   refine (isCoseparator_iff_of_isLimit_fan (prodIsProd G H)).trans ?_
-  convert Iff.rfl
+  convert! Iff.rfl
   ext X
   simp only [ObjectProperty.pair_iff, ObjectProperty.ofObj_iff]
   constructor
diff --git a/Mathlib/CategoryTheory/GlueData.lean b/Mathlib/CategoryTheory/GlueData.lean
index 36b36a3c217d35..1b82efaa98f426 100644
--- a/Mathlib/CategoryTheory/GlueData.lean
+++ b/Mathlib/CategoryTheory/GlueData.lean
@@ -398,7 +398,7 @@ instance (D : GlueData' C) (i j k : D.J) :
     infer_instance
   else
     have {X Y Z : C} (f : X ⟶ Y) (e : Z = X) : eqToHom e ≫ f ≍ f := by subst e; simp
-    convert D.f_hasPullback i j k hij hik <;> simp [GlueData'.f', hij, hik, this]
+    convert! D.f_hasPullback i j k hij hik <;> simp [GlueData'.f', hij, hik, this]
 
 open scoped Classical in
 /-- (Implementation detail) the constructed `GlueData.t'` from a `GlueData'`. -/
diff --git a/Mathlib/CategoryTheory/GradedObject/Monoidal.lean b/Mathlib/CategoryTheory/GradedObject/Monoidal.lean
index 5fe1ad5ce46d3e..7021c3ee257170 100644
--- a/Mathlib/CategoryTheory/GradedObject/Monoidal.lean
+++ b/Mathlib/CategoryTheory/GradedObject/Monoidal.lean
@@ -558,8 +558,9 @@ variable [DecidableEq I] [HasInitial C]
 lemma triangle :
     (associator X₁ tensorUnit X₃).hom ≫ tensorHom (𝟙 X₁) (leftUnitor X₃).hom =
       tensorHom (rightUnitor X₁).hom (𝟙 X₃) := by
-  convert mapBifunctor_triangle (curriedAssociatorNatIso C) (𝟙_ C)
-    (rightUnitorNatIso C) (leftUnitorNatIso C) (triangleIndexData I) X₁ X₃ (by simp)
+  convert!
+    mapBifunctor_triangle (curriedAssociatorNatIso C) (𝟙_ C) (rightUnitorNatIso C)
+      (leftUnitorNatIso C) (triangleIndexData I) X₁ X₃ (by simp)
   all_goals assumption
 
 end Triangle
diff --git a/Mathlib/CategoryTheory/Groupoid/FreeGroupoid.lean b/Mathlib/CategoryTheory/Groupoid/FreeGroupoid.lean
index 2e08b0ab9c9dfc..4e1115b66d2287 100644
--- a/Mathlib/CategoryTheory/Groupoid/FreeGroupoid.lean
+++ b/Mathlib/CategoryTheory/Groupoid/FreeGroupoid.lean
@@ -170,7 +170,7 @@ theorem lift_unique (φ : V ⥤q V') (Φ : Quiver.FreeGroupoid V ⥤ V')
     change Φ.map (Groupoid.inv ((Quotient.functor redStep).toPrefunctor.map f.toPath)) =
       Groupoid.inv (Φ.map ((Quotient.functor redStep).toPrefunctor.map f.toPath))
     have := Functor.map_inv Φ ((Quotient.functor redStep).toPrefunctor.map f.toPath)
-    convert this <;> simp only [Groupoid.inv_eq_inv]
+    convert! this <;> simp only [Groupoid.inv_eq_inv]
 
 end UniversalProperty
 
diff --git a/Mathlib/CategoryTheory/Groupoid/Subgroupoid.lean b/Mathlib/CategoryTheory/Groupoid/Subgroupoid.lean
index a50e4ef8887173..33fd840edbc5ca 100644
--- a/Mathlib/CategoryTheory/Groupoid/Subgroupoid.lean
+++ b/Mathlib/CategoryTheory/Groupoid/Subgroupoid.lean
@@ -117,7 +117,7 @@ theorem mem_objs_of_tgt {c d : C} {f : c ⟶ d} (h : f ∈ S.arrows c d) : d ∈
 
 theorem id_mem_of_nonempty_isotropy (c : C) : c ∈ objs S → 𝟙 c ∈ S.arrows c c := by
   rintro ⟨γ, hγ⟩
-  convert S.mul hγ (S.inv hγ)
+  convert! S.mul hγ (S.inv hγ)
   simp only [inv_eq_inv, IsIso.hom_inv_id]
 
 theorem id_mem_of_src {c d : C} {f : c ⟶ d} (h : f ∈ S.arrows c d) : 𝟙 c ∈ S.arrows c c :=
@@ -305,7 +305,7 @@ structure IsNormal : Prop extends IsWide S where
 
 theorem IsNormal.conj' {S : Subgroupoid C} (Sn : IsNormal S) :
     ∀ {c d} (p : d ⟶ c) {γ : c ⟶ c}, γ ∈ S.arrows c c → p ≫ γ ≫ Groupoid.inv p ∈ S.arrows d d :=
-  fun p γ hs => by convert Sn.conj (Groupoid.inv p) hs; simp
+  fun p γ hs => by convert! Sn.conj (Groupoid.inv p) hs; simp
 
 theorem IsNormal.conjugation_bij (Sn : IsNormal S) {c d} (p : c ⟶ d) :
     Set.BijOn (fun γ : c ⟶ c => Groupoid.inv p ≫ γ ≫ p) (S.arrows c c) (S.arrows d d) := by
@@ -481,7 +481,7 @@ theorem mem_map_objs_iff (hφ : Function.Injective φ.obj) (d : D) :
 
 @[simp]
 theorem map_objs_eq (hφ : Function.Injective φ.obj) : (map φ hφ S).objs = φ.obj '' S.objs := by
-  ext x; convert mem_map_objs_iff S φ hφ x
+  ext x; convert! mem_map_objs_iff S φ hφ x
 
 /-- The image of a functor injective on objects -/
 def im (hφ : Function.Injective φ.obj) :=
@@ -491,7 +491,7 @@ theorem mem_im_iff (hφ : Function.Injective φ.obj) {c d : D} (f : c ⟶ d) :
     f ∈ (im φ hφ).arrows c d ↔
       ∃ (a b : C) (g : a ⟶ b) (ha : φ.obj a = c) (hb : φ.obj b = d),
         f = eqToHom ha.symm ≫ φ.map g ≫ eqToHom hb := by
-  convert Map.arrows_iff φ hφ ⊤ f; simp only [Top.top, mem_univ, exists_true_left]
+  convert! Map.arrows_iff φ hφ ⊤ f; simp only [Top.top, mem_univ, exists_true_left]
 
 theorem mem_im_objs_iff (hφ : Function.Injective φ.obj) (d : D) :
     d ∈ (im φ hφ).objs ↔ ∃ c : C, φ.obj c = d := by
diff --git a/Mathlib/CategoryTheory/Idempotents/Basic.lean b/Mathlib/CategoryTheory/Idempotents/Basic.lean
index 406de0abd48412..2b9451e4caf30d 100644
--- a/Mathlib/CategoryTheory/Idempotents/Basic.lean
+++ b/Mathlib/CategoryTheory/Idempotents/Basic.lean
@@ -106,7 +106,7 @@ theorem isIdempotentComplete_iff_idempotents_have_kernels [Preadditive C] :
   constructor
   · intro h X p hp
     haveI : HasEqualizer (𝟙 X) (𝟙 X - p) := h X (𝟙 _ - p) (idem_of_id_sub_idem p hp)
-    convert hasKernel_of_hasEqualizer (𝟙 X) (𝟙 X - p)
+    convert! hasKernel_of_hasEqualizer (𝟙 X) (𝟙 X - p)
     rw [sub_sub_cancel]
   · intro h X p hp
     haveI : HasKernel (𝟙 _ - p) := h X (𝟙 _ - p) (idem_of_id_sub_idem p hp)
diff --git a/Mathlib/CategoryTheory/Limits/ConeCategory.lean b/Mathlib/CategoryTheory/Limits/ConeCategory.lean
index 4a9e2cb4b18545..bb46e976c3d0fa 100644
--- a/Mathlib/CategoryTheory/Limits/ConeCategory.lean
+++ b/Mathlib/CategoryTheory/Limits/ConeCategory.lean
@@ -139,7 +139,7 @@ def Cone.fromCostructuredArrow (F : J ⥤ C) : CostructuredArrow (const J) F ⥤
   map f :=
     { hom := f.left
       w := fun j => by
-        convert congr_fun (congr_arg NatTrans.app f.w) j
+        convert! congr_fun (congr_arg NatTrans.app f.w) j
         simp }
 
 /-- The category of cones on `F` is just the comma category `(Δ ↓ F)`, where `Δ` is the constant
diff --git a/Mathlib/CategoryTheory/Limits/Constructions/Equalizers.lean b/Mathlib/CategoryTheory/Limits/Constructions/Equalizers.lean
index 38c036ae6b4839..7cea64361478c4 100644
--- a/Mathlib/CategoryTheory/Limits/Constructions/Equalizers.lean
+++ b/Mathlib/CategoryTheory/Limits/Constructions/Equalizers.lean
@@ -50,7 +50,8 @@ abbrev pullbackFst (F : WalkingParallelPair ⥤ C) :
 set_option backward.isDefEq.respectTransparency false in
 theorem pullbackFst_eq_pullback_snd (F : WalkingParallelPair ⥤ C) :
     pullbackFst F = pullback.snd _ _ := by
-  convert (eq_whisker pullback.condition Limits.prod.fst :
+  convert!
+    (eq_whisker pullback.condition Limits.prod.fst :
       (_ : constructEqualizer F ⟶ F.obj WalkingParallelPair.zero) = _) <;> simp
 
 set_option backward.isDefEq.respectTransparency false in
@@ -60,8 +61,10 @@ abbrev equalizerCone (F : WalkingParallelPair ⥤ C) : Cone F :=
     (Fork.ofι (pullbackFst F)
       (by
         conv_rhs => rw [pullbackFst_eq_pullback_snd]
-        convert (eq_whisker pullback.condition Limits.prod.snd :
-          (_ : constructEqualizer F ⟶ F.obj WalkingParallelPair.one) = _) using 1 <;> simp))
+        convert!
+          (eq_whisker pullback.condition Limits.prod.snd :
+            (_ : constructEqualizer F ⟶ F.obj WalkingParallelPair.one) = _) using
+          1 <;> simp))
 
 set_option backward.isDefEq.respectTransparency false in
 /-- Show the equalizing cone is a limit -/
@@ -144,8 +147,9 @@ abbrev pushoutInl (F : WalkingParallelPair ⥤ C) :
 set_option backward.isDefEq.respectTransparency false in
 theorem pushoutInl_eq_pushout_inr (F : WalkingParallelPair ⥤ C) :
     pushoutInl F = pushout.inr _ _ := by
-  convert (whisker_eq Limits.coprod.inl pushout.condition :
-    (_ : F.obj _ ⟶ constructCoequalizer _) = _) <;> simp
+  convert!
+      (whisker_eq Limits.coprod.inl pushout.condition : (_ : F.obj _ ⟶ constructCoequalizer _) = _)
+    <;> simp
 
 set_option backward.isDefEq.respectTransparency false in
 /-- Define the equalizing cocone -/
@@ -153,8 +157,10 @@ abbrev coequalizerCocone (F : WalkingParallelPair ⥤ C) : Cocone F :=
   Cocone.ofCofork
     (Cofork.ofπ (pushoutInl F) (by
         conv_rhs => rw [pushoutInl_eq_pushout_inr]
-        convert (whisker_eq Limits.coprod.inr pushout.condition :
-          (_ : F.obj _ ⟶ constructCoequalizer _) = _) using 1 <;> simp))
+        convert!
+          (whisker_eq Limits.coprod.inr pushout.condition :
+            (_ : F.obj _ ⟶ constructCoequalizer _) = _) using
+          1 <;> simp))
 
 set_option backward.isDefEq.respectTransparency false in
 /-- Show the equalizing cocone is a colimit -/
diff --git a/Mathlib/CategoryTheory/Limits/Constructions/Filtered.lean b/Mathlib/CategoryTheory/Limits/Constructions/Filtered.lean
index b5c3cd57c5d2bd..41a5fd961958d7 100644
--- a/Mathlib/CategoryTheory/Limits/Constructions/Filtered.lean
+++ b/Mathlib/CategoryTheory/Limits/Constructions/Filtered.lean
@@ -71,7 +71,7 @@ def liftToFinsetColimitCocone [HasColimitsOfShape (Finset (Discrete α)) C]
         dsimp [liftToFinsetObj]
         apply colimit.hom_ext
         rintro ⟨⟨j, hj⟩⟩
-        convert h j using 1
+        convert! h j using 1
         · simp [← colimit.w (liftToFinsetObj F) ⟨⟨Finset.singleton_subset_iff.2 hj⟩⟩]
           rfl
         · simp }
@@ -106,8 +106,9 @@ def isColimitFiniteSubproductsCocone (f : α → C) [HasColimitsOfShape (Finset
       colimit.cocone_x, colimit.cocone_ι, finiteSubcoproductsCocone_ι_app]
     ext j
     rw [← Category.assoc]
-    convert IsColimit.comp_coconePointUniqueUpToIso_hom
-      (liftToFinsetColimitCocone (Discrete.functor f)).isColimit (colimit.isColimit _) j
+    convert!
+      IsColimit.comp_coconePointUniqueUpToIso_hom
+        (liftToFinsetColimitCocone (Discrete.functor f)).isColimit (colimit.isColimit _) j
     · simp [← colimit.w (liftToFinsetObj _) (homOfLE (x := {j.1}) (y := S) (by simp))]
     · simp))
 
@@ -211,7 +212,7 @@ def liftToFinsetLimitCone [HasLimitsOfShape (Finset (Discrete α))ᵒᵖ C]
         dsimp [liftToFinsetObj]
         apply limit.hom_ext
         rintro ⟨⟨j, hj⟩⟩
-        convert h j using 1
+        convert! h j using 1
         · simp [← limit.w (liftToFinsetObj F) ⟨⟨⟨Finset.singleton_subset_iff.2 hj⟩⟩⟩]
           rfl
         · simp }
diff --git a/Mathlib/CategoryTheory/Limits/Constructions/Over/Connected.lean b/Mathlib/CategoryTheory/Limits/Constructions/Over/Connected.lean
index 36f438aa5207e2..582dd78de6d928 100644
--- a/Mathlib/CategoryTheory/Limits/Constructions/Over/Connected.lean
+++ b/Mathlib/CategoryTheory/Limits/Constructions/Over/Connected.lean
@@ -58,7 +58,7 @@ def raiseCone [IsConnected J] {B : D} {F : J ⥤ CostructuredArrow K B}
     let z : (Functor.const J).obj (K.obj c.pt) ⟶ _ :=
       (CategoryTheory.Functor.constComp J c.pt K).inv ≫ Functor.whiskerRight c.π K ≫
         natTransInCostructuredArrow F
-    convert (nat_trans_from_is_connected z j (Classical.arbitrary J)) <;> simp [z]
+    convert! (nat_trans_from_is_connected z j (Classical.arbitrary J)) <;> simp [z]
   π.naturality X Y f := by
     apply CommaMorphism.ext
     · simpa using (c.w f).symm
diff --git a/Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean b/Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
index fe22d2d3cfa030..aabe63bf3de52c 100644
--- a/Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
+++ b/Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean
@@ -217,7 +217,7 @@ theorem colimitLimitToLimitColimit_surjective :
         ((curry.obj F).obj j').map (gf f) (F.map (𝟙 j' ×ₘ g j') (y j')) =
           ((curry.obj F).obj j').map (hf f) (F.map (f ×ₘ g j) (y j)) :=
         (w f).choose_spec.choose_spec.choose_spec
-      convert q using 1
+      convert! q using 1
       · simp [← comp_apply, -types_comp_apply]
       · simp [← comp_apply, -types_comp_apply, ← F.map_comp]
     clear_value kf gf hf
diff --git a/Mathlib/CategoryTheory/Limits/Final.lean b/Mathlib/CategoryTheory/Limits/Final.lean
index cf852bb62f3875..645d5405acbe7a 100644
--- a/Mathlib/CategoryTheory/Limits/Final.lean
+++ b/Mathlib/CategoryTheory/Limits/Final.lean
@@ -559,11 +559,11 @@ def induction {d : D} (Z : ∀ (X : C) (_ : F.obj X ⟶ d), Sort*)
       (CostructuredArrow.mk k₀) z
   · intro j₁ j₂ f a
     fapply h₁ _ _ _ _ f.left _ a
-    convert f.w
+    convert! f.w
     simp
   · intro j₁ j₂ f a
     fapply h₂ _ _ _ _ f.left _ a
-    convert f.w
+    convert! f.w
     simp
 
 variable {F G}
@@ -1118,7 +1118,7 @@ private lemma Grothendieck.final_map_small {C : Type u₁} [SmallCategory C] {F
   intro H
   let i := (colimitFiberwiseColimitIso _).symm ≪≫
     HasColimit.isoOfNatIso (fiberwiseColimitMapCompEquivalence α H) ≪≫ colimitFiberwiseColimitIso _
-  convert Iso.isIso_hom i
+  convert! Iso.isIso_hom i
   apply colimit.hom_ext
   intro X
   simp [i, fiberwiseColimitMapCompEquivalence]
diff --git a/Mathlib/CategoryTheory/Limits/FormalCoproducts/Basic.lean b/Mathlib/CategoryTheory/Limits/FormalCoproducts/Basic.lean
index 848f13e9f727df..feb2b4622392d0 100644
--- a/Mathlib/CategoryTheory/Limits/FormalCoproducts/Basic.lean
+++ b/Mathlib/CategoryTheory/Limits/FormalCoproducts/Basic.lean
@@ -310,7 +310,7 @@ def isLimitPullbackCone : IsLimit (pullbackCone f g pb) := by
     (fun s ↦ congrArg (·.1.snd)
       ((homPullbackEquiv f g pb hpb s.pt).right_inv ⟨(s.fst, s.snd), s.condition⟩))
     (fun s m h₁ h₂ ↦ ?_)
-  convert ((homPullbackEquiv f g pb hpb s.pt).left_inv m).symm using 3
+  convert! ((homPullbackEquiv f g pb hpb s.pt).left_inv m).symm using 3
   rw [← h₁, ← h₂]; rfl
 
 -- Arguments cannot be inferred.
diff --git a/Mathlib/CategoryTheory/Limits/IsLimit.lean b/Mathlib/CategoryTheory/Limits/IsLimit.lean
index adf3b35472cccf..cba5138452bf58 100644
--- a/Mathlib/CategoryTheory/Limits/IsLimit.lean
+++ b/Mathlib/CategoryTheory/Limits/IsLimit.lean
@@ -403,7 +403,7 @@ def homIso' (h : IsLimit t) (W : C) :
       { p : ∀ j, W ⟶ F.obj j // ∀ {j j'} (f : j ⟶ j'), p j ≫ F.map f = p j' } :=
   h.homIso W ≪≫
     { hom := ↾fun π =>
-        ⟨fun j => π.app j, fun f => by convert ← (π.naturality f).symm; apply id_comp⟩
+        ⟨fun j => π.app j, fun f => by convert! ← (π.naturality f).symm; apply id_comp⟩
       inv := ↾fun p =>
         { app := fun j => p.1 j
           naturality := fun j j' f => by dsimp; rw [id_comp]; exact (p.2 f).symm } }
@@ -419,7 +419,7 @@ def ofFaithful {t : Cone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D) [G
     uniq := fun s m w => by
       apply G.map_injective; rw [h]
       refine ht.uniq (mapCone G s) _ fun j => ?_
-      convert ← congrArg (fun f => G.map f) (w j)
+      convert! ← congrArg (fun f => G.map f) (w j)
       apply G.map_comp }
 
 /-- If `F` and `G` are naturally isomorphic, then `F.mapCone c` being a limit implies
@@ -901,7 +901,7 @@ def homIso' (h : IsColimit t) (W : C) :
       { p : ∀ j, F.obj j ⟶ W // ∀ {j j' : J} (f : j ⟶ j'), F.map f ≫ p j' = p j } :=
   h.homIso W ≪≫
     { hom := ↾fun ι =>
-        ⟨fun j => ι.app j, fun {j} {j'} f => by convert ← ι.naturality f; apply comp_id⟩
+        ⟨fun j => ι.app j, fun {j} {j'} f => by convert! ← ι.naturality f; apply comp_id⟩
       inv := ↾fun p =>
         { app := fun j => p.1 j
           naturality := fun j j' f => by dsimp; rw [comp_id]; exact p.2 f } }
@@ -918,7 +918,7 @@ def ofFaithful {t : Cocone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D)
     uniq := fun s m w => by
       apply G.map_injective; rw [h]
       refine ht.uniq (mapCocone G s) _ fun j => ?_
-      convert ← congrArg (fun f => G.map f) (w j)
+      convert! ← congrArg (fun f => G.map f) (w j)
       apply G.map_comp }
 
 /-- If `F` and `G` are naturally isomorphic, then `F.mapCocone c` being a colimit implies
diff --git a/Mathlib/CategoryTheory/Limits/MonoCoprod.lean b/Mathlib/CategoryTheory/Limits/MonoCoprod.lean
index dd9a000ab27c10..385439d45b5ae6 100644
--- a/Mathlib/CategoryTheory/Limits/MonoCoprod.lean
+++ b/Mathlib/CategoryTheory/Limits/MonoCoprod.lean
@@ -199,7 +199,7 @@ set_option backward.isDefEq.respectTransparency false in
 lemma mono_map'_of_injective [HasCoproduct (X ∘ ι)] [HasCoproduct X]
     [HasCoproduct (fun (k : ((Set.range ι)ᶜ : Set I)) => X k.1)] :
     Mono (Sigma.map' ι (fun j => 𝟙 ((X ∘ ι) j))) := by
-  convert mono_of_injective' X ι hι
+  convert! mono_of_injective' X ι hι
   apply Sigma.hom_ext
   intro j
   rw [Sigma.ι_comp_map', id_comp, colimit.ι_desc]
diff --git a/Mathlib/CategoryTheory/Limits/Preserves/Basic.lean b/Mathlib/CategoryTheory/Limits/Preserves/Basic.lean
index 56a9626d38051d..4779f298bbc38e 100644
--- a/Mathlib/CategoryTheory/Limits/Preserves/Basic.lean
+++ b/Mathlib/CategoryTheory/Limits/Preserves/Basic.lean
@@ -761,7 +761,7 @@ lemma isIso_app_coconePt_of_preservesColimit
     IsIso (α.app c.pt) := by
   let e := IsColimit.coconePointsIsoOfNatIso
     (isColimitOfPreserves L hc) (isColimitOfPreserves L' hc) (asIso (whiskerLeft K α))
-  convert (inferInstance : IsIso e.hom)
+  convert! (inferInstance : IsIso e.hom)
   apply (isColimitOfPreserves L hc).hom_ext fun j ↦ ?_
   simp only [Functor.comp_obj, Functor.mapCocone_pt, Functor.const_obj_obj, Functor.mapCocone_ι_app,
     NatTrans.naturality, IsColimit.coconePointsIsoOfNatIso_hom, asIso_hom, e]
diff --git a/Mathlib/CategoryTheory/Limits/Preserves/Grothendieck.lean b/Mathlib/CategoryTheory/Limits/Preserves/Grothendieck.lean
index 8431c9a21037e6..51ee1f9e2c9de1 100644
--- a/Mathlib/CategoryTheory/Limits/Preserves/Grothendieck.lean
+++ b/Mathlib/CategoryTheory/Limits/Preserves/Grothendieck.lean
@@ -83,7 +83,7 @@ instance preservesLimitsOfShape_colim_grothendieck [HasColimitsOfShape C H] [Has
       HasLimit.isoOfNatIso
        (associator _ _ _ ≪≫ isoWhiskerLeft _ fiberwiseColimCompColimIso)
   haveI : IsIso (limit.post K colim) := by
-    convert Iso.isIso_hom i₂
+    convert! Iso.isIso_hom i₂
     ext
     simp only [colim_obj, Functor.comp_obj, limit.post_π, colim_map, Iso.trans_def,
       Iso.trans_assoc, Iso.trans_hom, Category.assoc, HasLimit.isoOfNatIso_hom_π,
diff --git a/Mathlib/CategoryTheory/Limits/Preserves/Limits.lean b/Mathlib/CategoryTheory/Limits/Preserves/Limits.lean
index fd9a21ee408df2..ee81f17d04b6e6 100644
--- a/Mathlib/CategoryTheory/Limits/Preserves/Limits.lean
+++ b/Mathlib/CategoryTheory/Limits/Preserves/Limits.lean
@@ -99,7 +99,7 @@ variable [HasLimit F] [HasLimit (F ⋙ G)]
 preserves limits of `F`. -/
 lemma preservesLimit_of_isIso_post [IsIso (limit.post F G)] : PreservesLimit F G :=
   preservesLimit_of_preserves_limit_cone (limit.isLimit F) (by
-    convert IsLimit.ofPointIso (limit.isLimit (F ⋙ G))
+    convert! IsLimit.ofPointIso (limit.isLimit (F ⋙ G))
     assumption)
 
 end
@@ -172,7 +172,7 @@ variable [HasColimit F] [HasColimit (F ⋙ G)]
 preserves colimits of `F`. -/
 lemma preservesColimit_of_isIso_post [IsIso (colimit.post F G)] : PreservesColimit F G :=
   preservesColimit_of_preserves_colimit_cocone (colimit.isColimit F) (by
-    convert IsColimit.ofPointIso (colimit.isColimit (F ⋙ G))
+    convert! IsColimit.ofPointIso (colimit.isColimit (F ⋙ G))
     assumption)
 
 end
diff --git a/Mathlib/CategoryTheory/Limits/Presheaf.lean b/Mathlib/CategoryTheory/Limits/Presheaf.lean
index 8d8e7963efeeb0..2ff41881fb117c 100644
--- a/Mathlib/CategoryTheory/Limits/Presheaf.lean
+++ b/Mathlib/CategoryTheory/Limits/Presheaf.lean
@@ -396,7 +396,7 @@ instance (X : C) (Y : F.op.LeftExtension (yoneda.obj X)) :
   default := StructuredArrow.homMk
       (yonedaEquiv.symm (yonedaEquiv (F := F.op.comp Y.right) Y.hom)) (by
         ext Z f
-        convert (Y.hom.naturality_apply f.op _).symm
+        convert! (Y.hom.naturality_apply f.op _).symm
         simp)
   uniq φ := by
     ext1
diff --git a/Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean b/Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean
index b102163ffef8e9..acaad2c2669391 100644
--- a/Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean
+++ b/Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean
@@ -447,7 +447,7 @@ This means you may not be able to `simp` using this lemma unless you `open scope
 @[reassoc]
 theorem biproduct.ι_π [DecidableEq J] (f : J → C) [HasBiproduct f] (j j' : J) :
     biproduct.ι f j ≫ biproduct.π f j' = if h : j = j' then eqToHom (congr_arg f h) else 0 := by
-  convert (biproduct.bicone f).ι_π j j'
+  convert! (biproduct.bicone f).ι_π j j'
 
 @[reassoc] -- Not `simp` because `simp` can prove this
 theorem biproduct.ι_π_self (f : J → C) [HasBiproduct f] (j : J) :
diff --git a/Mathlib/CategoryTheory/Limits/Shapes/DisjointCoproduct.lean b/Mathlib/CategoryTheory/Limits/Shapes/DisjointCoproduct.lean
index b43755fdc4f0d6..806a00383a5065 100644
--- a/Mathlib/CategoryTheory/Limits/Shapes/DisjointCoproduct.lean
+++ b/Mathlib/CategoryTheory/Limits/Shapes/DisjointCoproduct.lean
@@ -240,7 +240,7 @@ attribute [instance 999] CoproductsOfShapeDisjoint.coproductDisjoint
 lemma BinaryCoproductsDisjoint.mk (H : ∀ (X Y : C), BinaryCoproductDisjoint X Y) :
     BinaryCoproductsDisjoint C where
   coproductDisjoint X := by
-    convert H (X .left) (X .right) using 2
+    convert! H (X .left) (X .right) using 2
     casesm WalkingPair <;> simp
 
 /-- If `C` has disjoint coproducts, any morphism out of initial is mono. Note it isn't true in
diff --git a/Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean b/Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean
index 1cdad676898b3c..216b2aed5ce5b9 100644
--- a/Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean
+++ b/Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean
@@ -896,7 +896,7 @@ def idFork (h : f = g) : Fork f g :=
 /-- The identity on `X` is an equalizer of `(f, g)`, if `f = g`. -/
 def isLimitIdFork (h : f = g) : IsLimit (idFork h) :=
   Fork.IsLimit.mk _ (fun s => Fork.ι s) (fun _ => Category.comp_id _) fun s m h => by
-    convert h
+    convert! h
     exact (Category.comp_id _).symm
 
 /-- Every equalizer of `(f, g)`, where `f = g`, is an isomorphism. -/
@@ -1114,7 +1114,7 @@ def idCofork (h : f = g) : Cofork f g :=
 /-- The identity on `Y` is a coequalizer of `(f, g)`, where `f = g`. -/
 def isColimitIdCofork (h : f = g) : IsColimit (idCofork h) :=
   Cofork.IsColimit.mk _ (fun s => Cofork.π s) (fun _ => Category.id_comp _) fun s m h => by
-    convert h
+    convert! h
     exact (Category.id_comp _).symm
 
 /-- Every coequalizer of `(f, g)`, where `f = g`, is an isomorphism. -/
diff --git a/Mathlib/CategoryTheory/Limits/Shapes/Images.lean b/Mathlib/CategoryTheory/Limits/Shapes/Images.lean
index 3e2eeaa88d8103..eb8f75af4fa6c2 100644
--- a/Mathlib/CategoryTheory/Limits/Shapes/Images.lean
+++ b/Mathlib/CategoryTheory/Limits/Shapes/Images.lean
@@ -488,7 +488,7 @@ theorem image.ext [HasImage f] {W : C} {g h : image f ⟶ W} [HasLimit (parallel
   have t : v ≫ q = 𝟙 (image f) :=
     (cancel_mono_id (image.ι f)).1
       (by
-        convert t₀ using 1
+        convert! t₀ using 1
         rw [Category.assoc])
   -- The proof from wikipedia next proves `q ≫ v = 𝟙 _`,
   -- and concludes that `equalizer g h ≅ image f`,
diff --git a/Mathlib/CategoryTheory/Limits/Shapes/KernelPair.lean b/Mathlib/CategoryTheory/Limits/Shapes/KernelPair.lean
index fc321c42ad0b46..ce65d956ac1222 100644
--- a/Mathlib/CategoryTheory/Limits/Shapes/KernelPair.lean
+++ b/Mathlib/CategoryTheory/Limits/Shapes/KernelPair.lean
@@ -219,7 +219,7 @@ theorem isIso_of_mono (h : IsKernelPair f a b) [Mono f] : IsIso a := by
 
 theorem of_isIso_of_mono [IsIso a] [Mono f] : IsKernelPair f a a := by
   change IsPullback _ _ _ _
-  convert (IsPullback.of_horiz_isIso ⟨(rfl : a ≫ 𝟙 X = _ )⟩).paste_vert (IsKernelPair.id_of_mono f)
+  convert! (IsPullback.of_horiz_isIso ⟨(rfl : a ≫ 𝟙 X = _)⟩).paste_vert (IsKernelPair.id_of_mono f)
   all_goals { simp }
 
 /-- The kernel pair provided by `HasPullback f f` fits into an `IsKernelPair`. -/
diff --git a/Mathlib/CategoryTheory/Limits/Shapes/NormalMono/Basic.lean b/Mathlib/CategoryTheory/Limits/Shapes/NormalMono/Basic.lean
index 92330068bb78c9..2c3305e06a5607 100644
--- a/Mathlib/CategoryTheory/Limits/Shapes/NormalMono/Basic.lean
+++ b/Mathlib/CategoryTheory/Limits/Shapes/NormalMono/Basic.lean
@@ -105,7 +105,7 @@ def normalOfIsPullbackSndOfNormal {P Q R S : C} {f : P ⟶ Q} {g : P ⟶ R} {h :
   isLimit := by
     letI gr := regularOfIsPullbackSndOfRegular hn.regularMono comm t
     have q := (HasZeroMorphisms.comp_zero k hn.Z).symm
-    convert gr.isLimit
+    convert! gr.isLimit
 
 /-- The first leg of a pullback cone is a normal monomorphism if the left component is too.
 
@@ -224,7 +224,7 @@ def normalOfIsPushoutSndOfNormal {P Q R S : C} {f : P ⟶ Q} {g : P ⟶ R} {h :
   isColimit := by
     letI hn := regularOfIsPushoutSndOfRegular gn.regularEpi comm t
     have q := (@zero_comp _ _ _ gn.W _ _ f).symm
-    convert hn.isColimit
+    convert! hn.isColimit
 
 /-- The first leg of a pushout cocone is a normal epimorphism if the left component is too.
 
diff --git a/Mathlib/CategoryTheory/Limits/Shapes/Opposites/Products.lean b/Mathlib/CategoryTheory/Limits/Shapes/Opposites/Products.lean
index 7de93693742bf8..c65f8d1d7ca20e 100644
--- a/Mathlib/CategoryTheory/Limits/Shapes/Opposites/Products.lean
+++ b/Mathlib/CategoryTheory/Limits/Shapes/Opposites/Products.lean
@@ -183,8 +183,9 @@ theorem desc_op_comp_opCoproductIsoProduct'_hom {c : Cofan Z} {f : Fan (op <| Z
 
 theorem desc_op_comp_opCoproductIsoProduct_hom [HasCoproduct Z] {X : C} (π : (a : α) → Z a ⟶ X) :
     (Sigma.desc π).op ≫ (opCoproductIsoProduct Z).hom = Pi.lift (fun a ↦ (π a).op) := by
-  convert desc_op_comp_opCoproductIsoProduct'_hom (coproductIsCoproduct Z)
-    (productIsProduct (op <| Z ·)) (Cofan.mk _ π)
+  convert!
+    desc_op_comp_opCoproductIsoProduct'_hom (coproductIsCoproduct Z) (productIsProduct (op <| Z ·))
+      (Cofan.mk _ π)
   · simp [Sigma.desc, coproductIsCoproduct]
   · simp [Pi.lift, productIsProduct]
 
@@ -279,8 +280,9 @@ theorem opProductIsoCoproduct'_inv_comp_lift {f : Fan Z} {c : Cofan (op <| Z ·)
 
 theorem opProductIsoCoproduct_inv_comp_lift [HasProduct Z] {X : C} (π : (a : α) → X ⟶ Z a) :
     (opProductIsoCoproduct Z).inv ≫ (Pi.lift π).op = Sigma.desc (fun a ↦ (π a).op) := by
-  convert opProductIsoCoproduct'_inv_comp_lift (productIsProduct Z)
-    (coproductIsCoproduct (op <| Z ·)) (Fan.mk _ π)
+  convert!
+    opProductIsoCoproduct'_inv_comp_lift (productIsProduct Z) (coproductIsCoproduct (op <| Z ·))
+      (Fan.mk _ π)
   · simp [Pi.lift, productIsProduct]
   · simp [Sigma.desc, coproductIsCoproduct]
 
@@ -293,7 +295,7 @@ variable {A B : C} [HasBinaryProduct A B]
 instance : HasBinaryCoproduct (op A) (op B) := by
   have : HasProduct fun x ↦ (WalkingPair.casesOn x A B : C) := ‹_›
   change HasCoproduct _
-  convert (inferInstance : HasCoproduct fun x ↦ op (WalkingPair.casesOn x A B : C)) with x
+  convert! (inferInstance : HasCoproduct fun x ↦ op (WalkingPair.casesOn x A B : C)) with x
   cases x <;> rfl
 
 set_option backward.isDefEq.respectTransparency false in
diff --git a/Mathlib/CategoryTheory/Limits/Shapes/Products.lean b/Mathlib/CategoryTheory/Limits/Shapes/Products.lean
index 2b72d3178df98d..c52658d3f22373 100644
--- a/Mathlib/CategoryTheory/Limits/Shapes/Products.lean
+++ b/Mathlib/CategoryTheory/Limits/Shapes/Products.lean
@@ -287,7 +287,7 @@ theorem Sigma.ι_desc {β : Type w} {f : β → C} [HasCoproduct f] {P : C} (p :
 
 set_option backward.isDefEq.respectTransparency false in
 instance {f : β → C} [HasCoproduct f] : IsIso (Sigma.desc (fun a ↦ Sigma.ι f a)) := by
-  convert IsIso.id _
+  convert! IsIso.id _
   ext
   simp
 
diff --git a/Mathlib/CategoryTheory/Limits/Shapes/Pullback/EquifiberedLimits.lean b/Mathlib/CategoryTheory/Limits/Shapes/Pullback/EquifiberedLimits.lean
index 947467c7538ec8..1ea969cc8900a0 100644
--- a/Mathlib/CategoryTheory/Limits/Shapes/Pullback/EquifiberedLimits.lean
+++ b/Mathlib/CategoryTheory/Limits/Shapes/Pullback/EquifiberedLimits.lean
@@ -66,8 +66,8 @@ instance (F : C ⥤ D) [∀ a b : C, HasProductsOfShape (a ⟶ b) D] :
     hasColimitsOfShape_of_equivalence (Discrete.equivalence Quiver.Hom.opEquiv)
   let e : Over F.op ≌ (Under F)ᵒᵖ := (postEquiv _ (opUnopEquiv _ _)).symm.trans (opEquivOpUnder F)
   rw [isClosedUnderColimitsOfShape_iff_op, ← isClosedUnderLimitsOfShape_inverseImage_iff _ _ e]
-  convert (inferInstance : IsClosedUnderLimitsOfShape
-    (fun f : Over F.op ↦ f.hom.Equifibered) Jᵒᵖ) with f
+  convert!
+    (inferInstance : IsClosedUnderLimitsOfShape (fun f : Over F.op ↦ f.hom.Equifibered) Jᵒᵖ) with f
   simp [e, MorphismProperty.cancel_left_of_respectsIso, ← coequifibered_unop_iff]
   rfl
 
diff --git a/Mathlib/CategoryTheory/Limits/Shapes/Pullback/IsPullback/BicartesianSq.lean b/Mathlib/CategoryTheory/Limits/Shapes/Pullback/IsPullback/BicartesianSq.lean
index 9fd133f613c86a..588cacb4f90c5c 100644
--- a/Mathlib/CategoryTheory/Limits/Shapes/Pullback/IsPullback/BicartesianSq.lean
+++ b/Mathlib/CategoryTheory/Limits/Shapes/Pullback/IsPullback/BicartesianSq.lean
@@ -66,7 +66,7 @@ variable {P X Y Z : C} {fst : P ⟶ X} {snd : P ⟶ Y} {f : X ⟶ Z} {g : Y ⟶
 
 theorem of_hasBinaryProduct [HasBinaryProduct X Y] :
     IsPullback Limits.prod.fst Limits.prod.snd (0 : X ⟶ 0) (0 : Y ⟶ 0) := by
-  convert @of_is_product _ _ X Y 0 _ (limit.isLimit _) HasZeroObject.zeroIsTerminal
+  convert! @of_is_product _ _ X Y 0 _ (limit.isLimit _) HasZeroObject.zeroIsTerminal
     <;> subsingleton
 
 set_option backward.isDefEq.respectTransparency false in
@@ -99,7 +99,7 @@ theorem zero_bot (X : C) : IsPullback (𝟙 X) (0 : X ⟶ 0) (0 : X ⟶ 0) (0 :
 
 theorem of_isBilimit {b : BinaryBicone X Y} (h : b.IsBilimit) :
     IsPullback b.fst b.snd (0 : X ⟶ 0) (0 : Y ⟶ 0) := by
-  convert IsPullback.of_is_product' h.isLimit HasZeroObject.zeroIsTerminal
+  convert! IsPullback.of_is_product' h.isLimit HasZeroObject.zeroIsTerminal
     <;> subsingleton
 
 @[simp]
@@ -176,7 +176,7 @@ variable {Z X Y P : C} {f : Z ⟶ X} {g : Z ⟶ Y} {inl : X ⟶ P} {inr : Y ⟶
 
 theorem of_hasBinaryCoproduct [HasBinaryCoproduct X Y] :
     IsPushout (0 : 0 ⟶ X) (0 : 0 ⟶ Y) coprod.inl coprod.inr := by
-  convert @of_is_coproduct _ _ 0 X Y _ (colimit.isColimit _) HasZeroObject.zeroIsInitial
+  convert! @of_is_coproduct _ _ 0 X Y _ (colimit.isColimit _) HasZeroObject.zeroIsInitial
     <;> subsingleton
 
 set_option backward.isDefEq.respectTransparency false in
@@ -212,7 +212,7 @@ theorem zero_top (X : C) : IsPushout (0 : (0 : C) ⟶ 0) (0 : 0 ⟶ X) (0 : 0 
 
 theorem of_isBilimit {b : BinaryBicone X Y} (h : b.IsBilimit) :
     IsPushout (0 : 0 ⟶ X) (0 : 0 ⟶ Y) b.inl b.inr := by
-  convert IsPushout.of_is_coproduct' h.isColimit HasZeroObject.zeroIsInitial
+  convert! IsPushout.of_is_coproduct' h.isColimit HasZeroObject.zeroIsInitial
     <;> subsingleton
 
 @[simp]
@@ -339,7 +339,7 @@ is a bi-Cartesian square.
 @[simp]
 theorem of_has_biproduct₁ [HasBinaryBiproduct X Y] :
     BicartesianSq biprod.fst biprod.snd (0 : X ⟶ 0) (0 : Y ⟶ 0) := by
-  convert of_is_biproduct₁ (BinaryBiproduct.isBilimit X Y)
+  convert! of_is_biproduct₁ (BinaryBiproduct.isBilimit X Y)
 
 /-- ```
    0 -----0---> X
@@ -354,7 +354,7 @@ is a bi-Cartesian square.
 @[simp]
 theorem of_has_biproduct₂ [HasBinaryBiproduct X Y] :
     BicartesianSq (0 : 0 ⟶ X) (0 : 0 ⟶ Y) biprod.inl biprod.inr := by
-  convert of_is_biproduct₂ (BinaryBiproduct.isBilimit X Y)
+  convert! of_is_biproduct₂ (BinaryBiproduct.isBilimit X Y)
 
 end BicartesianSq
 end CategoryTheory
diff --git a/Mathlib/CategoryTheory/Limits/Shapes/Pullback/Mono.lean b/Mathlib/CategoryTheory/Limits/Shapes/Pullback/Mono.lean
index 3415ed43d1b1a8..705894aae5d3af 100644
--- a/Mathlib/CategoryTheory/Limits/Shapes/Pullback/Mono.lean
+++ b/Mathlib/CategoryTheory/Limits/Shapes/Pullback/Mono.lean
@@ -165,7 +165,7 @@ instance hasPullback_of_right_factors_mono : HasPullback i (f ≫ i) := by
 instance pullback_snd_iso_of_right_factors_mono :
     IsIso (pullback.snd i (f ≫ i)) := by
   have := limit.isoLimitCone_hom_π ⟨_, pullbackIsPullbackOfCompMono (𝟙 _) f i⟩ WalkingCospan.right
-  convert (congrArg IsIso (show _ ≫ pullback.snd (𝟙 Z) f = _ from this)).mp inferInstance
+  convert! (congrArg IsIso (show _ ≫ pullback.snd (𝟙 Z) f = _ from this)).mp inferInstance
   · exact (Category.id_comp _).symm
   · exact (Category.id_comp _).symm
 
@@ -177,7 +177,7 @@ instance hasPullback_of_left_factors_mono : HasPullback (f ≫ i) i := by
 instance pullback_snd_iso_of_left_factors_mono :
     IsIso (pullback.fst (f ≫ i) i) := by
   have := limit.isoLimitCone_hom_π ⟨_, pullbackIsPullbackOfCompMono f (𝟙 _) i⟩ WalkingCospan.left
-  convert (congrArg IsIso (show _ ≫ pullback.fst f (𝟙 Z) = _ from this)).mp inferInstance
+  convert! (congrArg IsIso (show _ ≫ pullback.fst f (𝟙 Z) = _ from this)).mp inferInstance
   · exact (Category.id_comp _).symm
   · exact (Category.id_comp _).symm
 
@@ -343,9 +343,12 @@ instance hasPushout_of_right_factors_epi : HasPushout h (h ≫ f) := by
 set_option backward.isDefEq.respectTransparency false in
 instance pushout_inr_iso_of_right_factors_epi :
     IsIso (pushout.inr _ _ : _ ⟶ pushout h (h ≫ f)) := by
-  convert (congrArg IsIso (show pushout.inr _ _ ≫ _ = _ from colimit.isoColimitCocone_ι_inv
-    ⟨_, pushoutIsPushoutOfEpiComp (𝟙 _) f h⟩ WalkingSpan.right)).mp
-    inferInstance
+  convert!
+    (congrArg IsIso
+          (show pushout.inr _ _ ≫ _ = _ from
+            colimit.isoColimitCocone_ι_inv ⟨_, pushoutIsPushoutOfEpiComp (𝟙 _) f h⟩
+              WalkingSpan.right)).mp
+      inferInstance
   · apply (Category.comp_id _).symm
   · apply (Category.comp_id _).symm
 
@@ -357,9 +360,12 @@ instance hasPushout_of_left_factors_epi (f : X ⟶ Y) : HasPushout (h ≫ f) h :
 set_option backward.isDefEq.respectTransparency false in
 instance pushout_inl_iso_of_left_factors_epi (f : X ⟶ Y) :
     IsIso (pushout.inl _ _ : _ ⟶ pushout (h ≫ f) h) := by
-  convert (congrArg IsIso (show pushout.inl _ _ ≫ _ = _ from colimit.isoColimitCocone_ι_inv
-    ⟨_, pushoutIsPushoutOfEpiComp f (𝟙 _) h⟩ WalkingSpan.left)).mp
-        inferInstance
+  convert!
+    (congrArg IsIso
+          (show pushout.inl _ _ ≫ _ = _ from
+            colimit.isoColimitCocone_ι_inv ⟨_, pushoutIsPushoutOfEpiComp f (𝟙 _) h⟩
+              WalkingSpan.left)).mp
+      inferInstance
   · exact (Category.comp_id _).symm
   · exact (Category.comp_id _).symm
 
diff --git a/Mathlib/CategoryTheory/Limits/Shapes/ZeroObjects.lean b/Mathlib/CategoryTheory/Limits/Shapes/ZeroObjects.lean
index d4e98e703d840d..5ffb598b92c1c8 100644
--- a/Mathlib/CategoryTheory/Limits/Shapes/ZeroObjects.lean
+++ b/Mathlib/CategoryTheory/Limits/Shapes/ZeroObjects.lean
@@ -267,7 +267,7 @@ instance {X : C} (f : 0 ⟶ X) : Mono f where right_cancellation g h _ := by ext
 instance {X : C} (f : X ⟶ 0) : Epi f where left_cancellation g h _ := by ext
 
 instance zero_to_zero_isIso (f : (0 : C) ⟶ 0) : IsIso f := by
-  convert show IsIso (𝟙 (0 : C)) by infer_instance
+  convert! show IsIso (𝟙 (0 : C)) by infer_instance
   subsingleton
 
 /-- A zero object is in particular initial. -/
diff --git a/Mathlib/CategoryTheory/Limits/Types/Coequalizers.lean b/Mathlib/CategoryTheory/Limits/Types/Coequalizers.lean
index 793fd0d4b47a4d..1fca1ad2404cdb 100644
--- a/Mathlib/CategoryTheory/Limits/Types/Coequalizers.lean
+++ b/Mathlib/CategoryTheory/Limits/Types/Coequalizers.lean
@@ -67,7 +67,7 @@ theorem coequalizer_preimage_image_eq_of_preimage_eq (π : Y ⟶ Z) (e : f ≫ 
         inferInstance
     refine (eqv.eqvGen_iff.mp (Relation.EqvGen.mono lem (Quot.eqvGen_exact ?_))).mp hy
     apply e''
-    convert e'
+    convert! e'
   · exact fun hx => ⟨_, hx, rfl⟩
 
 /-- The categorical coequalizer in `Type u` is the quotient by `f g ~ g x`. -/
diff --git a/Mathlib/CategoryTheory/Limits/Types/ColimitType.lean b/Mathlib/CategoryTheory/Limits/Types/ColimitType.lean
index 6a5fea5f00437d..81389e5f412d98 100644
--- a/Mathlib/CategoryTheory/Limits/Types/ColimitType.lean
+++ b/Mathlib/CategoryTheory/Limits/Types/ColimitType.lean
@@ -226,7 +226,7 @@ lemma fac_apply (c' : CoconeTypes.{w₂} F) (j : J) (x : F.obj j) :
 lemma of_equiv {c' : CoconeTypes.{w₂} F} (e : c.pt ≃ c'.pt)
     (he : ∀ j x, c'.ι j x = e (c.ι j x)) : c'.IsColimit where
   bijective := by
-    convert Function.Bijective.comp e.bijective hc.bijective
+    convert! Function.Bijective.comp e.bijective hc.bijective
     ext y
     obtain ⟨j, x, rfl⟩ := F.ιColimitType_jointly_surjective y
     simp_all
@@ -237,7 +237,7 @@ lemma iff_bijective {c' : CoconeTypes.{w₂} F}
   refine ⟨fun hc' ↦ ?_, fun h ↦ hc.of_equiv (Equiv.ofBijective _ h) hf⟩
   have h₁ := hc.bijective
   rw [← Function.Bijective.of_comp_iff _ hc.bijective]
-  convert hc'.bijective
+  convert! hc'.bijective
   ext x
   obtain ⟨j, x, rfl⟩ := F.ιColimitType_jointly_surjective x
   simp [hf]
@@ -353,7 +353,7 @@ end CoconeTypes
 set_option backward.isDefEq.respectTransparency false in
 lemma isColimit_coconeTypes : F.coconeTypes.IsColimit where
   bijective := by
-    convert Function.bijective_id
+    convert! Function.bijective_id
     ext y
     obtain ⟨j, x, rfl⟩ := F.ιColimitType_jointly_surjective y
     rfl
diff --git a/Mathlib/CategoryTheory/Limits/Types/Filtered.lean b/Mathlib/CategoryTheory/Limits/Types/Filtered.lean
index 494d0160e8297f..f34079508815c2 100644
--- a/Mathlib/CategoryTheory/Limits/Types/Filtered.lean
+++ b/Mathlib/CategoryTheory/Limits/Types/Filtered.lean
@@ -131,7 +131,7 @@ theorem isColimit_eq_iff {t : Cocone F} (ht : IsColimit t) {i j : J} {xi : F.obj
   have : HasColimit F := ⟨_, ht⟩
   refine Iff.trans ?_ (colimit_eq_iff_aux F)
   rw [← (IsColimit.coconePointUniqueUpToIso ht (colimitCoconeIsColimit F)).toEquiv.injective.eq_iff]
-  convert Iff.rfl
+  convert! Iff.rfl
   · exact (congr_hom
       (IsColimit.comp_coconePointUniqueUpToIso_hom ht (colimitCoconeIsColimit F) _) xi).symm
   · exact (congr_hom
diff --git a/Mathlib/CategoryTheory/Limits/Types/Pushouts.lean b/Mathlib/CategoryTheory/Limits/Types/Pushouts.lean
index 415d4bc0160478..3482815250efe2 100644
--- a/Mathlib/CategoryTheory/Limits/Types/Pushouts.lean
+++ b/Mathlib/CategoryTheory/Limits/Types/Pushouts.lean
@@ -210,7 +210,7 @@ variable {f g}
 lemma pushoutCocone_inl_eq_inr_imp_of_iso {c c' : PushoutCocone f g} (e : c ≅ c')
     (x₁ : X₁) (x₂ : X₂) (h : c.inl x₁ = c.inr x₂) :
     c'.inl x₁ = c'.inr x₂ := by
-  convert congr_arg e.hom.hom h
+  convert! congr_arg e.hom.hom h
   · exact ConcreteCategory.congr_hom (e.hom.w WalkingSpan.left).symm x₁
   · exact ConcreteCategory.congr_hom (e.hom.w WalkingSpan.right).symm x₂
 
diff --git a/Mathlib/CategoryTheory/Limits/VanKampen.lean b/Mathlib/CategoryTheory/Limits/VanKampen.lean
index dd3865fc49ffec..6b1024e023ff11 100644
--- a/Mathlib/CategoryTheory/Limits/VanKampen.lean
+++ b/Mathlib/CategoryTheory/Limits/VanKampen.lean
@@ -179,10 +179,11 @@ theorem IsUniversalColimit.whiskerEquivalence {K : Type*} [Category* K] (e : J 
     {F : K ⥤ C} {c : Cocone F} (hc : IsUniversalColimit c) :
     IsUniversalColimit (c.whisker e.functor) := by
   intro F' c' α f e' hα H
-  convert hc (c'.whisker e.inverse) (whiskerLeft e.inverse α ≫ (e.invFunIdAssoc F).hom) f ?_
-    ((hα.whiskerLeft _).comp (.of_isIso _)) ?_ using 1
+  convert!
+    hc (c'.whisker e.inverse) (whiskerLeft e.inverse α ≫ (e.invFunIdAssoc F).hom) f ?_
+      ((hα.whiskerLeft _).comp (.of_isIso _)) ?_ using 1
   · exact (IsColimit.whiskerEquivalenceEquiv e.symm).nonempty_congr
-  · convert congr_arg (whiskerLeft e.inverse) e'
+  · convert! congr_arg (whiskerLeft e.inverse) e'
     ext
     simp
   · intro k
@@ -201,8 +202,9 @@ theorem IsVanKampenColimit.whiskerEquivalence {K : Type*} [Category* K] (e : J 
     {F : K ⥤ C} {c : Cocone F} (hc : IsVanKampenColimit c) :
     IsVanKampenColimit (c.whisker e.functor) := by
   intro F' c' α f e' hα
-  convert hc (c'.whisker e.inverse) (whiskerLeft e.inverse α ≫ (e.invFunIdAssoc F).hom) f ?_
-    ((hα.whiskerLeft _).comp (.of_isIso _)) using 1
+  convert!
+    hc (c'.whisker e.inverse) (whiskerLeft e.inverse α ≫ (e.invFunIdAssoc F).hom) f ?_
+      ((hα.whiskerLeft _).comp (.of_isIso _)) using 1
   · exact (IsColimit.whiskerEquivalenceEquiv e.symm).nonempty_congr
   · simp only [Functor.const_obj_obj, Functor.comp_obj, Cocone.whisker_pt, Cocone.whisker_ι,
       whiskerLeft_app, NatTrans.comp_app, Equivalence.invFunIdAssoc_hom_app, Functor.id_obj]
@@ -379,8 +381,9 @@ theorem IsVanKampenColimit.map_reflective [HasColimitsOfShape J C]
   have : f = (hl.coconePointUniqueUpToIso hr).hom ≫
     Gl.map (colimit.desc _ ⟨_, whiskerRight α' Gr ≫ c.2⟩) := by
     symm
-    convert @IsColimit.coconePointUniqueUpToIso_hom_desc _ _ _ _ ((F' ⋙ Gr) ⋙ Gl)
-      (Gl.mapCocone ⟨_, (whiskerRight α' Gr ≫ c.2 :)⟩) _ _ hl hr using 2
+    convert!
+      @IsColimit.coconePointUniqueUpToIso_hom_desc _ _ _ _ ((F' ⋙ Gr) ⋙ Gl)
+        (Gl.mapCocone ⟨_, (whiskerRight α' Gr ≫ c.2 :)⟩) _ _ hl hr using 2
     · apply hr.hom_ext
       intro j
       rw [hr.fac, Functor.mapCocone_ι_app, ← Gl.map_comp, colimit.cocone_ι, colimit.ι_desc]
@@ -397,7 +400,7 @@ theorem IsVanKampenColimit.map_reflective [HasColimitsOfShape J C]
   have := ((H (colimit.cocone <| F' ⋙ Gr) (whiskerRight α' Gr)
     (colimit.desc _ ⟨_, whiskerRight α' Gr ≫ c.2⟩) ?_ (hα'.whiskerRight Gr)).mp
     ⟨(getColimitCocone <| F' ⋙ Gr).2⟩ j).map Gl
-  · convert IsPullback.paste_vert _ this
+  · convert! IsPullback.paste_vert _ this
     refine IsPullback.of_vert_isIso ⟨?_⟩
     rw [← IsIso.inv_comp_eq, ← Category.assoc, NatIso.inv_inv_app]
     exact IsColimit.comp_coconePointUniqueUpToIso_hom hl hr _
@@ -704,7 +707,7 @@ theorem isPullback_initial_to_of_cofan_isVanKampen [HasInitial C] {ι : Type*} {
   clear_value f
   subst this
   have : ∀ i, Subsingleton (⊥_ C ⟶ (Discrete.functor f).obj i) := inferInstance
-  convert isPullback_of_cofan_isVanKampen hc i.as j.as
+  convert! isPullback_of_cofan_isVanKampen hc i.as j.as
   exact (if_neg (mt Discrete.ext hi.symm)).symm
 
 set_option backward.isDefEq.respectTransparency false in
@@ -718,7 +721,7 @@ theorem mono_of_cofan_isVanKampen [HasInitial C] {ι : Type*} {F : Discrete ι 
   subst this
   refine PullbackCone.mono_of_isLimitMkIdId _ (IsPullback.isLimit ?_)
   nth_rw 1 [← Category.id_comp (c.ι.app i)]
-  convert IsPullback.paste_vert _ (isPullback_of_cofan_isVanKampen hc i.as i.as)
+  convert! IsPullback.paste_vert _ (isPullback_of_cofan_isVanKampen hc i.as i.as)
   swap
   · exact (eqToHom (if_pos rfl).symm)
   · simp
diff --git a/Mathlib/CategoryTheory/Localization/Bousfield.lean b/Mathlib/CategoryTheory/Localization/Bousfield.lean
index 41bbb0279b0325..92f3b22c5a367b 100644
--- a/Mathlib/CategoryTheory/Localization/Bousfield.lean
+++ b/Mathlib/CategoryTheory/Localization/Bousfield.lean
@@ -162,17 +162,17 @@ lemma isoClosure_isColocal : P.isoClosure.isColocal = P.isColocal := by
 instance : P.isColocal.IsMultiplicative where
   id_mem _ _ _ := by simpa [id_comp] using Function.bijective_id
   comp_mem f g hf hg X hX := by
-    convert Function.Bijective.comp (hg X hX) (hf X hX)
+    convert! Function.Bijective.comp (hg X hX) (hf X hX)
     cat_disch
 
 instance : P.isColocal.HasTwoOutOfThreeProperty where
   of_postcomp f g hg hfg X hX := by
     rw [← Function.Bijective.of_comp_iff' (hg X hX)]
-    convert hfg X hX
+    convert! hfg X hX
     cat_disch
   of_precomp f g hf hfg X hX := by
     rw [← Function.Bijective.of_comp_iff _ (hf X hX)]
-    convert hfg X hX
+    convert! hfg X hX
     cat_disch
 
 lemma isColocal_of_isIso {X Y : C} (f : X ⟶ Y) [IsIso f] : P.isColocal f := fun Z _ => by
@@ -215,8 +215,9 @@ include adj
 
 lemma isLocal_adj_unit_app (X : D) : isLocal (· ∈ Set.range F.obj) (adj.unit.app X) := by
   rintro _ ⟨Y, rfl⟩
-  convert ((Functor.FullyFaithful.ofFullyFaithful F).homEquiv.symm.trans
-    (adj.homEquiv X Y)).bijective using 1
+  convert!
+    ((Functor.FullyFaithful.ofFullyFaithful F).homEquiv.symm.trans
+        (adj.homEquiv X Y)).bijective using 1
   dsimp [Adjunction.homEquiv]
   aesop
 
@@ -249,8 +250,9 @@ include adj
 
 lemma isColocal_adj_counit_app (X : C) : isColocal (· ∈ Set.range G.obj) (adj.counit.app X) := by
   rintro _ ⟨Y, rfl⟩
-  convert ((Functor.FullyFaithful.ofFullyFaithful G).homEquiv.symm.trans
-    (adj.homEquiv Y X).symm).bijective using 1
+  convert!
+    ((Functor.FullyFaithful.ofFullyFaithful G).homEquiv.symm.trans
+        (adj.homEquiv Y X).symm).bijective using 1
   dsimp [Adjunction.homEquiv]
   cat_disch
 
diff --git a/Mathlib/CategoryTheory/Localization/DerivabilityStructure/OfLocalizedEquivalences.lean b/Mathlib/CategoryTheory/Localization/DerivabilityStructure/OfLocalizedEquivalences.lean
index cb0d171a5c5e19..e0a0a88b47c3f9 100644
--- a/Mathlib/CategoryTheory/Localization/DerivabilityStructure/OfLocalizedEquivalences.lean
+++ b/Mathlib/CategoryTheory/Localization/DerivabilityStructure/OfLocalizedEquivalences.lean
@@ -75,8 +75,9 @@ lemma isLeftDerivabilityStructure_of_isLocalizedEquivalence
   letI : CatCommSq T.functor (L.functor ⋙ W₁'.Q) (R.functor ⋙ W₂'.Q) F :=
     CatCommSq.vComp (H₂ := B.functor) _ _ _ _ _ _
   have : (TwoSquare.hComp iso.inv e'.inv).GuitartExact := by
-    convert T.guitartExact_of_isLeftDerivabilityStructure' (L.functor ⋙ W₁'.Q)
-      (R.functor ⋙ W₂'.Q) F (CatCommSq.iso _ _ _ _)
+    convert!
+      T.guitartExact_of_isLeftDerivabilityStructure' (L.functor ⋙ W₁'.Q) (R.functor ⋙ W₂'.Q) F
+        (CatCommSq.iso _ _ _ _)
     ext
     simp [e', CatCommSq.iso, iso']
   rw [B.isLeftDerivabilityStructure_iff W₁'.Q W₂'.Q F e']
diff --git a/Mathlib/CategoryTheory/Localization/Monoidal/Basic.lean b/Mathlib/CategoryTheory/Localization/Monoidal/Basic.lean
index 00a1c9ebf884c0..2c3ea3a00dbeaf 100644
--- a/Mathlib/CategoryTheory/Localization/Monoidal/Basic.lean
+++ b/Mathlib/CategoryTheory/Localization/Monoidal/Basic.lean
@@ -432,7 +432,7 @@ lemma triangle (X Y : LocalizedMonoidal L W ε) :
     triangle_aux₁ _ _ _ e₁.symm ε.symm e₂.symm
   simp only [← this, Iso.symm_hom, Iso.symm_inv, assoc,
     ← id_tensorHom, ← tensor_comp, comp_id]
-  convert h₃
+  convert! h₃
   · exact triangle_aux₂ _ _ _ e₁ e₂
   · exact triangle_aux₃ _ _ _ e₁ e₂
 
diff --git a/Mathlib/CategoryTheory/Localization/Opposite.lean b/Mathlib/CategoryTheory/Localization/Opposite.lean
index efa7be661782f5..2f013c3161e766 100644
--- a/Mathlib/CategoryTheory/Localization/Opposite.lean
+++ b/Mathlib/CategoryTheory/Localization/Opposite.lean
@@ -37,7 +37,7 @@ def StrictUniversalPropertyFixedTarget.op {E : Type*} [Category* E]
   inverts := h.inverts.op
   lift F hF := (h.lift F.rightOp hF.rightOp).leftOp
   fac F hF := by
-    convert congr_arg Functor.leftOp (h.fac F.rightOp hF.rightOp)
+    convert! congr_arg Functor.leftOp (h.fac F.rightOp hF.rightOp)
   uniq F₁ F₂ eq := by
     suffices F₁.rightOp = F₂.rightOp by
       rw [← F₁.rightOp_leftOp_eq, ← F₂.rightOp_leftOp_eq, this]
diff --git a/Mathlib/CategoryTheory/Localization/StructuredArrow.lean b/Mathlib/CategoryTheory/Localization/StructuredArrow.lean
index 5f14cc4a57d957..7c41067c5f47bc 100644
--- a/Mathlib/CategoryTheory/Localization/StructuredArrow.lean
+++ b/Mathlib/CategoryTheory/Localization/StructuredArrow.lean
@@ -106,13 +106,13 @@ lemma induction_structuredArrow
     fun g ↦ P (structuredArrowEquiv W W.Q L g)
   rw [← (structuredArrowEquiv W W.Q L).apply_symm_apply g]
   apply induction_structuredArrow' W P'
-  · convert hP₀
+  · convert! hP₀
     simp
   · intro Y₁ Y₂ f φ hφ
-    convert hP₁ f (homEquiv W W.Q L φ) hφ
+    convert! hP₁ f (homEquiv W W.Q L φ) hφ
     simp [homEquiv_comp]
   · intro Y₁ Y₂ w hw φ hφ
-    convert hP₂ w hw (homEquiv W W.Q L φ) hφ
+    convert! hP₂ w hw (homEquiv W W.Q L φ) hφ
     simp [homEquiv_comp, homEquiv_isoOfHom_inv]
 
 end
diff --git a/Mathlib/CategoryTheory/Monoidal/Braided/Basic.lean b/Mathlib/CategoryTheory/Monoidal/Braided/Basic.lean
index a4a248c6f7b58e..7e7cbe96ea03b1 100644
--- a/Mathlib/CategoryTheory/Monoidal/Braided/Basic.lean
+++ b/Mathlib/CategoryTheory/Monoidal/Braided/Basic.lean
@@ -166,7 +166,7 @@ theorem yang_baxter' (X Y Z : C) :
     (β_ X Y).hom ▷ Z ⊗≫ Y ◁ (β_ X Z).hom ⊗≫ (β_ Y Z).hom ▷ X =
       𝟙 _ ⊗≫ (X ◁ (β_ Y Z).hom ⊗≫ (β_ X Z).hom ▷ Y ⊗≫ Z ◁ (β_ X Y).hom) ⊗≫ 𝟙 _ := by
   rw [← cancel_epi (α_ X Y Z).inv, ← cancel_mono (α_ Z Y X).hom]
-  convert yang_baxter X Y Z using 1
+  convert! yang_baxter X Y Z using 1
   all_goals monoidal
 
 theorem yang_baxter_iso (X Y Z : C) :
@@ -633,13 +633,13 @@ theorem tensorμ_natural {X₁ X₂ Y₁ Y₂ U₁ U₂ V₁ V₂ : C} (f₁ : X
 theorem tensorμ_natural_left {X₁ X₂ Y₁ Y₂ : C} (f₁ : X₁ ⟶ Y₁) (f₂ : X₂ ⟶ Y₂) (Z₁ Z₂ : C) :
     (f₁ ⊗ₘ f₂) ▷ (Z₁ ⊗ Z₂) ≫ tensorμ Y₁ Y₂ Z₁ Z₂ =
       tensorμ X₁ X₂ Z₁ Z₂ ≫ (f₁ ▷ Z₁ ⊗ₘ f₂ ▷ Z₂) := by
-  convert tensorμ_natural f₁ f₂ (𝟙 Z₁) (𝟙 Z₂) using 1 <;> simp
+  convert! tensorμ_natural f₁ f₂ (𝟙 Z₁) (𝟙 Z₂) using 1 <;> simp
 
 @[reassoc]
 theorem tensorμ_natural_right (Z₁ Z₂ : C) {X₁ X₂ Y₁ Y₂ : C} (f₁ : X₁ ⟶ Y₁) (f₂ : X₂ ⟶ Y₂) :
     (Z₁ ⊗ Z₂) ◁ (f₁ ⊗ₘ f₂) ≫ tensorμ Z₁ Z₂ Y₁ Y₂ =
       tensorμ Z₁ Z₂ X₁ X₂ ≫ (Z₁ ◁ f₁ ⊗ₘ Z₂ ◁ f₂) := by
-  convert tensorμ_natural (𝟙 Z₁) (𝟙 Z₂) f₁ f₂ using 1 <;> simp
+  convert! tensorμ_natural (𝟙 Z₁) (𝟙 Z₂) f₁ f₂ using 1 <;> simp
 
 @[reassoc]
 theorem tensor_left_unitality (X₁ X₂ : C) :
diff --git a/Mathlib/CategoryTheory/Monoidal/Closed/Functor.lean b/Mathlib/CategoryTheory/Monoidal/Closed/Functor.lean
index 43c6c9aa4afb03..b77627d3050310 100644
--- a/Mathlib/CategoryTheory/Monoidal/Closed/Functor.lean
+++ b/Mathlib/CategoryTheory/Monoidal/Closed/Functor.lean
@@ -86,7 +86,7 @@ set_option backward.isDefEq.respectTransparency false in
 theorem expComparison_ev (A B : C) :
     F.obj A ◁ ((expComparison F A).natTrans.app B) ≫ (ihom.ev (F.obj A)).app (F.obj B) =
       inv (prodComparison F _ _) ≫ F.map ((ihom.ev _).app _) := by
-  convert mateEquiv_counit _ _ (prodComparisonNatIso F A).inv B using 2
+  convert! mateEquiv_counit _ _ (prodComparisonNatIso F A).inv B using 2
   apply IsIso.inv_eq_of_hom_inv_id -- Porting note (https://github.com/leanprover-community/mathlib4/issues/11041): was `ext`
   simp only [prodComparisonNatTrans_app, prodComparisonNatIso_inv, NatIso.isIso_inv_app,
     IsIso.hom_inv_id]
@@ -95,7 +95,7 @@ set_option backward.isDefEq.respectTransparency false in
 theorem coev_expComparison (A B : C) :
     F.map ((ihom.coev A).app B) ≫ (expComparison F A).natTrans.app (A ⊗ B) =
       (ihom.coev _).app (F.obj B) ≫ (ihom (F.obj A)).map (inv (prodComparison F A B)) := by
-  convert unit_mateEquiv _ _ (prodComparisonNatIso F A).inv B using 3
+  convert! unit_mateEquiv _ _ (prodComparisonNatIso F A).inv B using 3
   apply IsIso.inv_eq_of_hom_inv_id -- Porting note (https://github.com/leanprover-community/mathlib4/issues/11041): was `ext`
   simp
 
diff --git a/Mathlib/CategoryTheory/Monoidal/Free/Coherence.lean b/Mathlib/CategoryTheory/Monoidal/Free/Coherence.lean
index 60505a12b403b0..3abb0d6ecda711 100644
--- a/Mathlib/CategoryTheory/Monoidal/Free/Coherence.lean
+++ b/Mathlib/CategoryTheory/Monoidal/Free/Coherence.lean
@@ -274,7 +274,7 @@ def normalizeIso : tensorFunc C ≅ normalize' C :=
   NatIso.ofComponents (normalizeIsoAux C) <| by
     intro X Y f
     ext ⟨n⟩
-    convert normalize_naturality n f using 1
+    convert! normalize_naturality n f using 1
     any_goals dsimp; rw [normalizeIsoApp_eq]
 
 /-- The isomorphism between an object and its normal form is natural. -/
diff --git a/Mathlib/CategoryTheory/Monoidal/Grp.lean b/Mathlib/CategoryTheory/Monoidal/Grp.lean
index 23c64ca9e1ef94..bac92072ab9b00 100644
--- a/Mathlib/CategoryTheory/Monoidal/Grp.lean
+++ b/Mathlib/CategoryTheory/Monoidal/Grp.lean
@@ -336,7 +336,7 @@ lemma toMonObj_injective {X : C} :
   suffices h₁.inv = h₂.inv by cases h₁; congr!
   apply lift_left_mul_ext (𝟙 _)
   rw [left_inv]
-  convert @left_inv _ _ _ _ h₁ using 2
+  convert! @left_inv _ _ _ _ h₁ using 2
   exacts [congr(($e.symm).mul), congr(($e.symm).one)]
 
 @[to_additive (attr := ext)]
diff --git a/Mathlib/CategoryTheory/Monoidal/Internal/Module.lean b/Mathlib/CategoryTheory/Monoidal/Internal/Module.lean
index b518401d7eee82..99fff9f427fd49 100644
--- a/Mathlib/CategoryTheory/Monoidal/Internal/Module.lean
+++ b/Mathlib/CategoryTheory/Monoidal/Internal/Module.lean
@@ -49,19 +49,19 @@ def MonObj.toRing (A : ModuleCat.{u} R) [MonObj A] : Ring A :=
     one := η[A] (1 : R)
     mul := fun x y => μ[A] (x ⊗ₜ y)
     one_mul := fun x => by
-      convert LinearMap.congr_fun (ModuleCat.hom_ext_iff.mp (one_mul A)) ((1 : R) ⊗ₜ x)
+      convert! LinearMap.congr_fun (ModuleCat.hom_ext_iff.mp (one_mul A)) ((1 : R) ⊗ₜ x)
       rw [MonoidalCategory.leftUnitor_hom_apply, one_smul]
     mul_one := fun x => by
-      convert LinearMap.congr_fun (ModuleCat.hom_ext_iff.mp (mul_one A)) (x ⊗ₜ (1 : R))
+      convert! LinearMap.congr_fun (ModuleCat.hom_ext_iff.mp (mul_one A)) (x ⊗ₜ (1 : R))
       rw [MonoidalCategory.rightUnitor_hom_apply, one_smul]
     mul_assoc := fun x y z => by
-      convert LinearMap.congr_fun (ModuleCat.hom_ext_iff.mp (mul_assoc A)) (x ⊗ₜ y ⊗ₜ z)
+      convert! LinearMap.congr_fun (ModuleCat.hom_ext_iff.mp (mul_assoc A)) (x ⊗ₜ y ⊗ₜ z)
     left_distrib := fun x y z => by
-      convert μ[A].hom.map_add (x ⊗ₜ y) (x ⊗ₜ z)
+      convert! μ[A].hom.map_add (x ⊗ₜ y) (x ⊗ₜ z)
       rw [← TensorProduct.tmul_add]
       rfl
     right_distrib := fun x y z => by
-      convert μ[A].hom.map_add (x ⊗ₜ z) (y ⊗ₜ z)
+      convert! μ[A].hom.map_add (x ⊗ₜ z) (y ⊗ₜ z)
       rw [← TensorProduct.add_tmul]
       rfl
     zero_mul := fun x => show μ[A] _ = 0 by
diff --git a/Mathlib/CategoryTheory/Monoidal/Internal/Types/Basic.lean b/Mathlib/CategoryTheory/Monoidal/Internal/Types/Basic.lean
index 085cda682d289c..505dea9ab5d083 100644
--- a/Mathlib/CategoryTheory/Monoidal/Internal/Types/Basic.lean
+++ b/Mathlib/CategoryTheory/Monoidal/Internal/Types/Basic.lean
@@ -31,9 +31,9 @@ namespace MonTypeEquivalenceMon
 instance monMonoid (A : Type u) [MonObj A] : Monoid A where
   one := η[A] PUnit.unit
   mul x y := μ[A] (x, y)
-  one_mul x := by convert congr_hom (CC := fun X ↦ X) (one_mul A) (PUnit.unit, x)
-  mul_one x := by convert congr_hom (CC := fun X ↦ X) (mul_one A) (x, PUnit.unit)
-  mul_assoc x y z := by convert congr_hom (CC := fun X ↦ X) (mul_assoc A) ((x, y), z)
+  one_mul x := by convert! congr_hom (CC := fun X ↦ X) (one_mul A) (PUnit.unit, x)
+  mul_one x := by convert! congr_hom (CC := fun X ↦ X) (mul_one A) (x, PUnit.unit)
+  mul_assoc x y z := by convert! congr_hom (CC := fun X ↦ X) (mul_assoc A) ((x, y), z)
 
 /-- Converting a monoid object in `Type` to a bundled monoid.
 -/
@@ -97,7 +97,8 @@ namespace CommMonTypeEquivalenceCommMon
 
 instance commMonCommMonoid (A : Type u) [MonObj A] [IsCommMonObj A] : CommMonoid A :=
   { MonTypeEquivalenceMon.monMonoid A with
-    mul_comm := fun x y => by convert congr_hom (CC := fun X ↦ X) (IsCommMonObj.mul_comm A) (y, x) }
+    mul_comm := fun x y => by
+      convert! congr_hom (CC := fun X ↦ X) (IsCommMonObj.mul_comm A) (y, x) }
 
 /-- Converting a commutative monoid object in `Type` to a bundled commutative monoid.
 -/
diff --git a/Mathlib/CategoryTheory/Monoidal/Internal/Types/CommGrp_.lean b/Mathlib/CategoryTheory/Monoidal/Internal/Types/CommGrp_.lean
index cf56adf826a27c..46038c4c81e68c 100644
--- a/Mathlib/CategoryTheory/Monoidal/Internal/Types/CommGrp_.lean
+++ b/Mathlib/CategoryTheory/Monoidal/Internal/Types/CommGrp_.lean
@@ -29,7 +29,8 @@ namespace CommGrpTypeEquivalenceCommGrp
 
 instance commGrpCommGroup (A : Type u) [GrpObj A] [IsCommMonObj A] : CommGroup A :=
   { GrpTypeEquivalenceGrp.grpGroup A with
-    mul_comm := fun x y => by convert congr_hom (CC := fun X ↦ X) (IsCommMonObj.mul_comm A) (y, x) }
+    mul_comm := fun x y => by
+      convert! congr_hom (CC := fun X ↦ X) (IsCommMonObj.mul_comm A) (y, x) }
 
 /-- Converting a commutative group object in `Type u` into a group. -/
 noncomputable def functor : CommGrp (Type u) ⥤ CommGrpCat.{u} where
diff --git a/Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean b/Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean
index f99b0fd913ea54..06ca90b22a06e3 100644
--- a/Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean
+++ b/Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean
@@ -118,11 +118,11 @@ lemma evaluation_coevaluation :
 
 lemma coevaluation_evaluation'' :
     Y ◁ η_ X Y ⊗≫ ε_ X Y ▷ Y = ⊗𝟙.hom := by
-  convert coevaluation_evaluation X Y <;> simp [monoidalComp]
+  convert! coevaluation_evaluation X Y <;> simp [monoidalComp]
 
 lemma evaluation_coevaluation'' :
     η_ X Y ▷ X ⊗≫ X ◁ ε_ X Y = ⊗𝟙.hom := by
-  convert evaluation_coevaluation X Y <;> simp [monoidalComp]
+  convert! evaluation_coevaluation X Y <;> simp [monoidalComp]
 
 end ExactPairing
 
diff --git a/Mathlib/CategoryTheory/Monoidal/Ring.lean b/Mathlib/CategoryTheory/Monoidal/Ring.lean
index 0f88054ea58544..7c998064df7e86 100644
--- a/Mathlib/CategoryTheory/Monoidal/Ring.lean
+++ b/Mathlib/CategoryTheory/Monoidal/Ring.lean
@@ -47,7 +47,7 @@ lemma mul_add_iff (R : C) [MonObj R] [AddMonObj R] :
     cat_disch
   · replace h := h (fst R (R ⊗ R)) (snd _ _ ≫ fst _ _) (snd _ _ ≫ snd _ _)
     simp only [Hom.mul_def, Hom.add_def] at h
-    convert h using 2
+    convert! h using 2
     · cat_disch
     · ext
       · simp only [lift_fst]
@@ -67,7 +67,7 @@ lemma add_mul_iff (R : C) [MonObj R] [AddMonObj R] :
     cat_disch
   · replace h := h (fst (R ⊗ R) R ≫ fst _ _) (fst _ _ ≫ snd _ _) (snd _ _)
     simp only [Hom.mul_def, Hom.add_def] at h
-    convert h using 2
+    convert! h using 2
     · cat_disch
     · ext
       · simp only [lift_fst]
diff --git a/Mathlib/CategoryTheory/MorphismProperty/Concrete.lean b/Mathlib/CategoryTheory/MorphismProperty/Concrete.lean
index 8a63916bbc0121..083328e2b51d15 100644
--- a/Mathlib/CategoryTheory/MorphismProperty/Concrete.lean
+++ b/Mathlib/CategoryTheory/MorphismProperty/Concrete.lean
@@ -52,7 +52,7 @@ theorem bijective_eq_sup :
 instance : (MorphismProperty.injective C).IsMultiplicative where
   id_mem X := by
     delta MorphismProperty.injective
-    convert injective_id
+    convert! injective_id
     aesop
   comp_mem f g hf hg := by
     delta MorphismProperty.injective
@@ -62,7 +62,7 @@ instance : (MorphismProperty.injective C).IsMultiplicative where
 instance : (MorphismProperty.surjective C).IsMultiplicative where
   id_mem X := by
     delta MorphismProperty.surjective
-    convert surjective_id
+    convert! surjective_id
     aesop
   comp_mem f g hf hg := by
     delta MorphismProperty.surjective
@@ -72,7 +72,7 @@ instance : (MorphismProperty.surjective C).IsMultiplicative where
 instance : (MorphismProperty.bijective C).IsMultiplicative where
   id_mem X := by
     delta MorphismProperty.bijective
-    convert bijective_id
+    convert! bijective_id
     aesop
   comp_mem f g hf hg := by
     delta MorphismProperty.bijective
diff --git a/Mathlib/CategoryTheory/MorphismProperty/Descent.lean b/Mathlib/CategoryTheory/MorphismProperty/Descent.lean
index 7c34987899f708..3a9a1dd63b87f1 100644
--- a/Mathlib/CategoryTheory/MorphismProperty/Descent.lean
+++ b/Mathlib/CategoryTheory/MorphismProperty/Descent.lean
@@ -137,7 +137,7 @@ lemma faithful_overPullback_of_isomorphisms_descendAlong
   refine ⟨fun {X} Y a b hab ↦ ?_⟩
   ext
   apply P.eq_of_isomorphisms_descendsAlong (Over.w a) (Over.w b) f hf
-  convert congr($(hab).left) <;> ext <;> simp
+  convert! congr($(hab).left) <;> ext <;> simp
 
 end DescendsAlong
 
diff --git a/Mathlib/CategoryTheory/MorphismProperty/TransfiniteComposition.lean b/Mathlib/CategoryTheory/MorphismProperty/TransfiniteComposition.lean
index 72d8094b66b1d2..4fa14df20f1198 100644
--- a/Mathlib/CategoryTheory/MorphismProperty/TransfiniteComposition.lean
+++ b/Mathlib/CategoryTheory/MorphismProperty/TransfiniteComposition.lean
@@ -90,7 +90,7 @@ def ofOrderIso {J' : Type w'} [LinearOrder J'] [OrderBot J']
       Arrow.mk (homOfLE (Order.le_succ (e j))) :=
         Arrow.ext rfl (e.map_succ j) rfl
     replace eq := congr_arg h.F.mapArrow.obj eq
-    convert this using 1
+    convert! this using 1
 
 /-- If `f` is a transfinite composition of shape `J` of morphisms
 in `W.inverseImage F`, then `F` is a transfinite composition of shape `J`
@@ -119,7 +119,7 @@ noncomputable def iic (j : J) :
       Arrow.mk (homOfLE (Order.le_succ i.1)) :=
         Arrow.ext rfl (Set.Iic.coe_succ_of_not_isMax hi) rfl
     replace eq := congr_arg h.F.mapArrow.obj eq
-    convert this using 1
+    convert! this using 1
 
 /-- A transfinite composition of shape `J` of morphisms in `W` induces a transfinite
 composition of shape `Set.Ici j` (for any `j : J`). -/
@@ -133,7 +133,7 @@ noncomputable def ici (j : J) :
       Arrow.mk (homOfLE (Order.le_succ i.1)) :=
         Arrow.ext rfl (coe_succ_of_mem (i.2.trans (Order.le_succ _))) rfl
     replace eq := congr_arg h.F.mapArrow.obj eq
-    convert this using 1
+    convert! this using 1
 
 end
 
@@ -153,7 +153,7 @@ def ofComposableArrows {n : ℕ} (F : ComposableArrows C n)
         Arrow.mk (homOfLE j.castSucc_le_succ) :=
           Arrow.ext rfl j.orderSucc_castSucc rfl
       replace eq := congr_arg F.mapArrow.obj eq
-      convert hF using 1
+      convert! hF using 1
     · rw [isMax_iff_eq_top] at hj
       exact (hj rfl).elim
 
diff --git a/Mathlib/CategoryTheory/ObjectProperty/ColimitsOfShape.lean b/Mathlib/CategoryTheory/ObjectProperty/ColimitsOfShape.lean
index 4dc38c510f5763..8a139de771dbf2 100644
--- a/Mathlib/CategoryTheory/ObjectProperty/ColimitsOfShape.lean
+++ b/Mathlib/CategoryTheory/ObjectProperty/ColimitsOfShape.lean
@@ -263,8 +263,9 @@ lemma isClosedUnderColimitsOfShape_inverseImage_iff (P : ObjectProperty D)
     (P.inverseImage e.functor).IsClosedUnderColimitsOfShape J ↔
       P.IsClosedUnderColimitsOfShape J := by
   refine ⟨fun H ↦ ?_, fun _ ↦ inferInstance⟩
-  convert (inferInstance :
-    ((P.inverseImage e.functor).inverseImage e.inverse).IsClosedUnderColimitsOfShape J)
+  convert!
+    (inferInstance :
+      ((P.inverseImage e.functor).inverseImage e.inverse).IsClosedUnderColimitsOfShape J)
   ext X
   simpa using P.prop_iff_of_iso (e.counitIso.app X).symm
 
diff --git a/Mathlib/CategoryTheory/ObjectProperty/LimitsOfShape.lean b/Mathlib/CategoryTheory/ObjectProperty/LimitsOfShape.lean
index c021be2476b31e..cdcf7de9067f26 100644
--- a/Mathlib/CategoryTheory/ObjectProperty/LimitsOfShape.lean
+++ b/Mathlib/CategoryTheory/ObjectProperty/LimitsOfShape.lean
@@ -264,8 +264,9 @@ lemma isClosedUnderLimitsOfShape_inverseImage_iff (P : ObjectProperty D)
     [P.IsClosedUnderIsomorphisms] (e : C ≌ D) :
     (P.inverseImage e.functor).IsClosedUnderLimitsOfShape J ↔ P.IsClosedUnderLimitsOfShape J := by
   refine ⟨fun H ↦ ?_, fun _ ↦ inferInstance⟩
-  convert (inferInstance :
-    ((P.inverseImage e.functor).inverseImage e.inverse).IsClosedUnderLimitsOfShape J)
+  convert!
+    (inferInstance :
+      ((P.inverseImage e.functor).inverseImage e.inverse).IsClosedUnderLimitsOfShape J)
   ext X
   simpa using P.prop_iff_of_iso (e.counitIso.app X).symm
 
diff --git a/Mathlib/CategoryTheory/ObjectProperty/Local.lean b/Mathlib/CategoryTheory/ObjectProperty/Local.lean
index 183ec366220069..34c82050ac45eb 100644
--- a/Mathlib/CategoryTheory/ObjectProperty/Local.lean
+++ b/Mathlib/CategoryTheory/ObjectProperty/Local.lean
@@ -67,13 +67,13 @@ lemma isColocal_iff (X : C) :
 instance : W.isLocal.IsClosedUnderIsomorphisms where
   of_iso {Z Z'} e hZ X Y f hf := by
     rw [← Function.Bijective.of_comp_iff _ (Iso.homToEquiv e).bijective]
-    convert (Iso.homToEquiv e).bijective.comp (hZ f hf) using 1
+    convert! (Iso.homToEquiv e).bijective.comp (hZ f hf) using 1
     aesop
 
 instance : W.isColocal.IsClosedUnderIsomorphisms where
   of_iso {X X'} e hX Y Z g hg := by
     rw [← Function.Bijective.of_comp_iff _ (Iso.homFromEquiv e).bijective]
-    convert (Iso.homFromEquiv e).bijective.comp (hX g hg) using 1
+    convert! (Iso.homFromEquiv e).bijective.comp (hX g hg) using 1
     aesop
 
 set_option backward.isDefEq.respectTransparency false in
diff --git a/Mathlib/CategoryTheory/PUnit.lean b/Mathlib/CategoryTheory/PUnit.lean
index fdbd8e6e56b429..5f91f44fc34588 100644
--- a/Mathlib/CategoryTheory/PUnit.lean
+++ b/Mathlib/CategoryTheory/PUnit.lean
@@ -69,8 +69,8 @@ theorem equiv_punit_iff_unique :
   · rintro ⟨h⟩
     refine ⟨⟨h.inverse.obj ⟨⟨⟩⟩⟩, fun x y => Nonempty.intro ?_⟩
     let f : x ⟶ y := by
-      have hx : x ⟶ h.inverse.obj ⟨⟨⟩⟩ := by convert h.unit.app x
-      have hy : h.inverse.obj ⟨⟨⟩⟩ ⟶ y := by convert h.unitInv.app y
+      have hx : x ⟶ h.inverse.obj ⟨⟨⟩⟩ := by convert! h.unit.app x
+      have hy : h.inverse.obj ⟨⟨⟩⟩ ⟶ y := by convert! h.unitInv.app y
       exact hx ≫ hy
     suffices sub : Subsingleton (x ⟶ y) from uniqueOfSubsingleton f
     have : ∀ z, z = h.unit.app x ≫ (h.functor ⋙ h.inverse).map z ≫ h.unitInv.app y := by
diff --git a/Mathlib/CategoryTheory/PathCategory/Basic.lean b/Mathlib/CategoryTheory/PathCategory/Basic.lean
index 9549706993a4e5..cd04540ca251d6 100644
--- a/Mathlib/CategoryTheory/PathCategory/Basic.lean
+++ b/Mathlib/CategoryTheory/PathCategory/Basic.lean
@@ -164,7 +164,7 @@ theorem lift_unique {C} [Category* C] (φ : V ⥤q C) (Φ : Paths V ⥤ C)
       -- Porting note: Had to do substitute `p.cons f'` and `f'.toPath` by their fully qualified
       -- versions in this `have` clause (elsewhere too).
       have : Φ.map (Quiver.Path.cons p f') = Φ.map p ≫ Φ.map (Quiver.Hom.toPath f') := by
-        convert Functor.map_comp Φ p (Quiver.Hom.toPath f')
+        convert! Functor.map_comp Φ p (Quiver.Hom.toPath f')
       rw [this, ih]
 
 /-- Two functors out of a path category are equal when they agree on singleton paths. -/
diff --git a/Mathlib/CategoryTheory/Preadditive/Biproducts.lean b/Mathlib/CategoryTheory/Preadditive/Biproducts.lean
index 523285ff76c393..34095e5b89f43d 100644
--- a/Mathlib/CategoryTheory/Preadditive/Biproducts.lean
+++ b/Mathlib/CategoryTheory/Preadditive/Biproducts.lean
@@ -659,9 +659,9 @@ instance subsingleton_preadditive_of_hasBinaryBiproducts {C : Type u} [Category.
   allEq := fun a b => by
     apply Preadditive.ext; funext X Y; apply AddCommGroup.ext; funext f g
     have h₁ := @biprod.add_eq_lift_id_desc _ _ a _ _ f g
-      (by convert (inferInstance : HasBinaryBiproduct X X); subsingleton)
+      (by convert! (inferInstance : HasBinaryBiproduct X X); subsingleton)
     have h₂ := @biprod.add_eq_lift_id_desc _ _ b _ _ f g
-      (by convert (inferInstance : HasBinaryBiproduct X X); subsingleton)
+      (by convert! (inferInstance : HasBinaryBiproduct X X); subsingleton)
     refine h₁.trans (Eq.trans ?_ h₂.symm)
     congr! 2 <;> subsingleton
 
@@ -910,7 +910,7 @@ lemma preservesBiproduct_of_mono_biproductComparison {f : J → C} [HasBiproduct
       (F.mapIso (biproduct.isoProduct f)).inv ≫
         biproductComparison F f ≫ (biproduct.isoProduct _).hom := by
     ext j
-    convert piComparison_comp_π F f j; simp [← Function.comp_def, ← Functor.map_comp]
+    convert! piComparison_comp_π F f j; simp [← Function.comp_def, ← Functor.map_comp]
   haveI : IsIso (biproductComparison F f) := isIso_of_mono_of_isSplitEpi _
   haveI : IsIso (piComparison F f) := by
     rw [that]
diff --git a/Mathlib/CategoryTheory/Preadditive/CommGrp_.lean b/Mathlib/CategoryTheory/Preadditive/CommGrp_.lean
index 684b5656c52595..addf37572e4426 100644
--- a/Mathlib/CategoryTheory/Preadditive/CommGrp_.lean
+++ b/Mathlib/CategoryTheory/Preadditive/CommGrp_.lean
@@ -72,11 +72,11 @@ def commGrpEquivalenceAux : CommGrp.forget C ⋙ toCommGrp C ≅
       mul_def, Iso.refl_hom, Category.comp_id, tensorHom_id, id_whiskerRight, Category.id_comp]
     apply monoidal_hom_ext
     · simp only [comp_add, lift_fst, lift_snd, add_zero]
-      convert (MonObj.lift_comp_one_right _ 0).symm
+      convert! (MonObj.lift_comp_one_right _ 0).symm
       · simp
       · infer_instance
     · simp only [comp_add, lift_fst, lift_snd, zero_add]
-      convert (MonObj.lift_comp_one_left 0 _).symm
+      convert! (MonObj.lift_comp_one_left 0 _).symm
       · simp
       · infer_instance
   · cat_disch
diff --git a/Mathlib/CategoryTheory/Preadditive/HomOrthogonal.lean b/Mathlib/CategoryTheory/Preadditive/HomOrthogonal.lean
index 1945741177ac21..71000d24f21c88 100644
--- a/Mathlib/CategoryTheory/Preadditive/HomOrthogonal.lean
+++ b/Mathlib/CategoryTheory/Preadditive/HomOrthogonal.lean
@@ -138,7 +138,7 @@ theorem matrixDecomposition_id (o : HomOrthogonal s) {α : Type} [Finite α] {f
   · cases h
     simp
   · simp only [Subtype.mk.injEq] at h
-    convert comp_zero
+    convert! comp_zero
     simpa using biproduct.ι_π_ne _ (Ne.symm h)
 
 set_option backward.isDefEq.respectTransparency false in
@@ -159,10 +159,10 @@ theorem matrixDecomposition_comp (o : HomOrthogonal s) {α β γ : Type} [Finite
   · intro b nm
     simp only [Set.mem_preimage, Set.mem_singleton_iff] at nm
     simp only [Category.assoc]
-    convert comp_zero
-    convert comp_zero
-    convert comp_zero
-    convert comp_zero
+    convert! comp_zero
+    convert! comp_zero
+    convert! comp_zero
+    convert! comp_zero
     simp only [o.eq_zero nm]
 
 section
diff --git a/Mathlib/CategoryTheory/Preadditive/Mat.lean b/Mathlib/CategoryTheory/Preadditive/Mat.lean
index e4c1a473beddfa..1b98566b5d70f3 100644
--- a/Mathlib/CategoryTheory/Preadditive/Mat.lean
+++ b/Mathlib/CategoryTheory/Preadditive/Mat.lean
@@ -574,7 +574,7 @@ def equivalenceSingleObjInverse : Mat_ (SingleObj Rᵐᵒᵖ) ⥤ Mat R where
     -- Porting note: this proof was automatic in mathlib3
     ext
     simp only [Mat_.comp_apply, comp_apply]
-    convert Finset.unop_sum _ _
+    convert! Finset.unop_sum _ _
 
 instance : (equivalenceSingleObjInverse R).Faithful where
   map_injective w := by
diff --git a/Mathlib/CategoryTheory/Quotient.lean b/Mathlib/CategoryTheory/Quotient.lean
index 4ce992e4714346..4c91ae7339a494 100644
--- a/Mathlib/CategoryTheory/Quotient.lean
+++ b/Mathlib/CategoryTheory/Quotient.lean
@@ -237,7 +237,7 @@ theorem functor_homRel_eq_compClosure_eqvGen {X Y : C} (f g : X ⟶ Y) :
 
 theorem compClosure.congruence :
     Congruence fun X Y => Relation.EqvGen (@HomRel.CompClosure C _ r X Y) := by
-  convert (inferInstance : Congruence (functor r).homRel)
+  convert! (inferInstance : Congruence (functor r).homRel)
   ext
   rw [functor_homRel_eq_compClosure_eqvGen]
 
diff --git a/Mathlib/CategoryTheory/Quotient/Preadditive.lean b/Mathlib/CategoryTheory/Quotient/Preadditive.lean
index 647f39174bec0b..633b61c185ff24 100644
--- a/Mathlib/CategoryTheory/Quotient/Preadditive.lean
+++ b/Mathlib/CategoryTheory/Quotient/Preadditive.lean
@@ -51,7 +51,7 @@ def neg (hr : ∀ ⦃X Y : C⦄ (f₁ f₂ g₁ g₂ : X ⟶ Y) (_ : r f₁ f₂
       simp only [HomRel.compClosure_iff_self] at hfg
       erw [functor_map_eq_iff]
       apply Congruence.equivalence.symm
-      convert hr f g _ _ hfg (Congruence.equivalence.refl (-f - g)) using 1 <;> abel)
+      convert! hr f g _ _ hfg (Congruence.equivalence.refl (-f - g)) using 1 <;> abel)
 
 end Preadditive
 
diff --git a/Mathlib/CategoryTheory/RegularCategory/Basic.lean b/Mathlib/CategoryTheory/RegularCategory/Basic.lean
index 62dc398e6be95e..d04cadd1890d83 100644
--- a/Mathlib/CategoryTheory/RegularCategory/Basic.lean
+++ b/Mathlib/CategoryTheory/RegularCategory/Basic.lean
@@ -129,7 +129,7 @@ instance : Mono (coequalizer.desc f pullback.condition) := by
     infer_instance
   -- We precompose with the epimorphism `g₁ ≫ pullback.snd e k₁`, and finish
   rw [← cancel_epi (g₁ ≫ pullback.snd e k₁)]
-  convert coequalizer.condition (pullback.fst f f) (pullback.snd f f) using 1
+  convert! coequalizer.condition (pullback.fst f f) (pullback.snd f f) using 1
   all_goals cat_disch
 
 set_option backward.isDefEq.respectTransparency false in
diff --git a/Mathlib/CategoryTheory/RepresentedBy.lean b/Mathlib/CategoryTheory/RepresentedBy.lean
index a7fc2eb6eac264..45e33521e77078 100644
--- a/Mathlib/CategoryTheory/RepresentedBy.lean
+++ b/Mathlib/CategoryTheory/RepresentedBy.lean
@@ -87,8 +87,9 @@ set_option backward.isDefEq.respectTransparency false in
 lemma RepresentableBy.isRepresentedBy (R : F.RepresentableBy X) :
     F.IsRepresentedBy (R.homEquiv (𝟙 X)) := by
   rw [IsRepresentedBy.iff_isIso_uliftYonedaEquiv]
-  convert (RepresentableBy.equivUliftYonedaIso _ _ <|
-    representableByUliftFunctorEquiv.{v}.symm R).isIso_hom
+  convert!
+    (RepresentableBy.equivUliftYonedaIso _ _ <|
+        representableByUliftFunctorEquiv.{v}.symm R).isIso_hom
   ext
   simpa [uliftYonedaEquiv] using (homEquiv_eq _ _).symm
 
diff --git a/Mathlib/CategoryTheory/Shift/Basic.lean b/Mathlib/CategoryTheory/Shift/Basic.lean
index 036efdbd74959b..4a3491159808c3 100644
--- a/Mathlib/CategoryTheory/Shift/Basic.lean
+++ b/Mathlib/CategoryTheory/Shift/Basic.lean
@@ -406,9 +406,11 @@ def shiftEquiv' (i j : A) (h : i + j = 0) : C ≌ C where
   counitIso := shiftFunctorCompIsoId C j i
     (by rw [← add_left_inj j, add_assoc, h, zero_add, add_zero])
   functor_unitIso_comp X := by
-    convert (equivOfTensorIsoUnit (shiftMonoidalFunctor C A) ⟨i⟩ ⟨j⟩ (Discrete.eqToIso h)
-      (Discrete.eqToIso (by dsimp; rw [← add_left_inj j, add_assoc, h, zero_add, add_zero]))
-      (Subsingleton.elim _ _)).functor_unitIso_comp X
+    convert!
+      (equivOfTensorIsoUnit (shiftMonoidalFunctor C A) ⟨i⟩ ⟨j⟩ (Discrete.eqToIso h)
+            (Discrete.eqToIso (by dsimp; rw [← add_left_inj j, add_assoc, h, zero_add, add_zero]))
+            (Subsingleton.elim _ _)).functor_unitIso_comp
+        X
     all_goals
       ext X
       dsimp [shiftFunctorCompIsoId, unitOfTensorIsoUnit,
diff --git a/Mathlib/CategoryTheory/Sites/Adjunction.lean b/Mathlib/CategoryTheory/Sites/Adjunction.lean
index abf7576039eb08..1cdfa9976d920a 100644
--- a/Mathlib/CategoryTheory/Sites/Adjunction.lean
+++ b/Mathlib/CategoryTheory/Sites/Adjunction.lean
@@ -90,8 +90,9 @@ lemma preservesSheafification_of_adjunction (adj : G ⊣ F) :
     dsimp
     intro R hR
     rw [← ((adj.whiskerRight Cᵒᵖ).homEquiv P R).comp_bijective]
-    convert (((adj.whiskerRight Cᵒᵖ).homEquiv Q R).trans
-      (hf.homEquiv (R ⋙ F) ((sheafCompose J F).obj ⟨R, hR⟩).property)).bijective
+    convert!
+      (((adj.whiskerRight Cᵒᵖ).homEquiv Q R).trans
+          (hf.homEquiv (R ⋙ F) ((sheafCompose J F).obj ⟨R, hR⟩).property)).bijective
     ext g X
     -- The rest of this proof was
     -- `dsimp [Adjunction.whiskerRight, Adjunction.mkOfUnitCounit]; simp` before https://github.com/leanprover-community/mathlib4/pull/16317.
diff --git a/Mathlib/CategoryTheory/Sites/Coherent/CoherentSheaves.lean b/Mathlib/CategoryTheory/Sites/Coherent/CoherentSheaves.lean
index 6469f299f6fe24..d277c096031618 100644
--- a/Mathlib/CategoryTheory/Sites/Coherent/CoherentSheaves.lean
+++ b/Mathlib/CategoryTheory/Sites/Coherent/CoherentSheaves.lean
@@ -57,7 +57,8 @@ theorem isSheaf_yoneda_obj (W : C) : Presieve.IsSheaf (coherentTopology C) (yone
   obtain ⟨t, t_amalg, t_uniq⟩ : ∃! t, x_ext.IsAmalgamation t :=
     (Sieve.forallYonedaIsSheaf_iff_colimit S).mpr ⟨h_colim⟩ W x_ext hx_ext
   refine ⟨t, ?_, ?_⟩
-  · convert Presieve.isAmalgamation_restrict (Sieve.le_generate (Presieve.ofArrows Y π)) _ _ t_amalg
+  · convert!
+    Presieve.isAmalgamation_restrict (Sieve.le_generate (Presieve.ofArrows Y π)) _ _ t_amalg
     exact (Presieve.restrict_extend hx).symm
   · exact fun y hy ↦ t_uniq y <| Presieve.isAmalgamation_sieveExtend x y hy
 
diff --git a/Mathlib/CategoryTheory/Sites/Coherent/Comparison.lean b/Mathlib/CategoryTheory/Sites/Coherent/Comparison.lean
index f31e4ef6792f4e..b09b1098ea1c02 100644
--- a/Mathlib/CategoryTheory/Sites/Coherent/Comparison.lean
+++ b/Mathlib/CategoryTheory/Sites/Coherent/Comparison.lean
@@ -95,7 +95,7 @@ theorem extensive_regular_generate_coherent [Preregular C] [FinitaryPreExtensive
         apply Coverage.saturate_of_superset _ this
         apply Coverage.Saturate.of
         refine Or.inl ⟨I, inferInstance, _, _, ⟨rfl, ?_⟩⟩
-        convert IsIso.id _
+        convert! IsIso.id _
         aesop
     | top => apply Coverage.Saturate.top
     | transitive Y T => apply Coverage.Saturate.transitive Y T <;> [assumption; assumption]
diff --git a/Mathlib/CategoryTheory/Sites/Coherent/LocallySurjective.lean b/Mathlib/CategoryTheory/Sites/Coherent/LocallySurjective.lean
index 70e7d37f41602c..775708dad935c7 100644
--- a/Mathlib/CategoryTheory/Sites/Coherent/LocallySurjective.lean
+++ b/Mathlib/CategoryTheory/Sites/Coherent/LocallySurjective.lean
@@ -126,7 +126,7 @@ lemma regularTopology.isLocallySurjective_sheaf_of_types [Preregular C] [Finitar
       NatTrans.op_app, Cofan.mk_ι_app, Functor.mapIso_symm, Iso.trans_hom, Iso.symm_hom,
       Functor.mapIso_inv, comp_apply, ← f.naturality_apply (Sigma.ι Z a).op, i']
     have : f.app ⟨Z a⟩ (x a) = G.map (π a).op y := (h' a).choose_spec
-    convert this
+    convert! this
     · rw [← Functor.map_comp_apply, opCoproductIsoProduct_inv_comp_ι, ← piComparison_comp_π]
       change ((PreservesProduct.iso F _).hom ≫ _) _ = _
       have := Types.productIso_hom_comp_eval (fun a ↦ F.obj (op (Z a))) a
diff --git a/Mathlib/CategoryTheory/Sites/Coherent/RegularSheaves.lean b/Mathlib/CategoryTheory/Sites/Coherent/RegularSheaves.lean
index 46eb44cd86094a..9eefb4036d6d12 100644
--- a/Mathlib/CategoryTheory/Sites/Coherent/RegularSheaves.lean
+++ b/Mathlib/CategoryTheory/Sites/Coherent/RegularSheaves.lean
@@ -288,8 +288,9 @@ lemma isSheaf_yoneda_obj [Preregular C] (W : C) :
   obtain ⟨t, t_amalg, t_uniq⟩ :=
     (Sieve.forallYonedaIsSheaf_iff_colimit S).mpr ⟨h_colim⟩ W x_ext hx_ext
   refine ⟨t, ?_, ?_⟩
-  · convert Presieve.isAmalgamation_restrict (Sieve.le_generate
-      (Presieve.ofArrows (fun () ↦ Y) (fun () ↦ f))) _ _ t_amalg
+  · convert!
+    Presieve.isAmalgamation_restrict
+      (Sieve.le_generate (Presieve.ofArrows (fun () ↦ Y) (fun () ↦ f))) _ _ t_amalg
     exact (Presieve.restrict_extend hx).symm
   · exact fun y hy ↦ t_uniq y <| Presieve.isAmalgamation_sieveExtend x y hy
 
diff --git a/Mathlib/CategoryTheory/Sites/Coherent/SheafComparison.lean b/Mathlib/CategoryTheory/Sites/Coherent/SheafComparison.lean
index c40711182c9df2..a50fd96a21b479 100644
--- a/Mathlib/CategoryTheory/Sites/Coherent/SheafComparison.lean
+++ b/Mathlib/CategoryTheory/Sites/Coherent/SheafComparison.lean
@@ -79,7 +79,7 @@ theorem exists_effectiveEpiFamily_iff_mem_induced (X : C) (S : Sieve X) :
       simpa using this
     · obtain ⟨W, g₁, g₂, h₁, h₂⟩ := H₂ a
       rw [h₂]
-      convert S.downward_closed h₁ (F.preimage (g₀ a ≫ g₂))
+      convert! S.downward_closed h₁ (F.preimage (g₀ a ≫ g₂))
       exact F.map_injective (by simp)
 
 lemma eq_induced : haveI := F.reflects_precoherent
@@ -179,7 +179,7 @@ theorem exists_effectiveEpi_iff_mem_induced (X : C) (S : Sieve X) :
       infer_instance
     · obtain ⟨W, g₁, g₂, h₁, h₂⟩ := H₂
       rw [h₂]
-      convert S.downward_closed h₁ (F.preimage (g₀ ≫ g₂))
+      convert! S.downward_closed h₁ (F.preimage (g₀ ≫ g₂))
       exact F.map_injective (by simp)
 
 lemma eq_induced : haveI := F.reflects_preregular
diff --git a/Mathlib/CategoryTheory/Sites/ConcreteSheafification.lean b/Mathlib/CategoryTheory/Sites/ConcreteSheafification.lean
index cd68d28468c49d..dfa6d6b49424c5 100644
--- a/Mathlib/CategoryTheory/Sites/ConcreteSheafification.lean
+++ b/Mathlib/CategoryTheory/Sites/ConcreteSheafification.lean
@@ -218,7 +218,7 @@ theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.Cover X} (x : Meq
     use W.unop, h1.unop, h2.unop
     ext I
     apply_fun Multiequalizer.ι (W.unop.index P) I at hh
-    convert hh
+    convert! hh
     all_goals
       dsimp [diagram]
       rw [← ConcreteCategory.comp_apply, Multiequalizer.lift_ι]
@@ -230,7 +230,7 @@ theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.Cover X} (x : Meq
     apply Concrete.multiequalizer_ext
     intro i
     apply_fun fun ee => ee i at e
-    convert e using 1
+    convert! e using 1
     all_goals
       dsimp [diagram]
       rw [← ConcreteCategory.comp_apply, Multiequalizer.lift_ι]
@@ -279,7 +279,7 @@ theorem sep {X : C} (P : Cᵒᵖ ⥤ D) (S : J.Cover X) (x y : ToType ((J.plusOb
   specialize hh IS
   let IW : (W IS).Arrow := I.toMiddle
   apply_fun fun e => e IW at hh
-  convert hh using 1
+  convert! hh using 1
   · exact x.congr_apply I.middle_spec.symm _
   · exact y.congr_apply I.middle_spec.symm _
 
diff --git a/Mathlib/CategoryTheory/Sites/CoproductSheafCondition.lean b/Mathlib/CategoryTheory/Sites/CoproductSheafCondition.lean
index 8db9f661cb7a0d..c14a8f86eb0419 100644
--- a/Mathlib/CategoryTheory/Sites/CoproductSheafCondition.lean
+++ b/Mathlib/CategoryTheory/Sites/CoproductSheafCondition.lean
@@ -96,7 +96,7 @@ lemma Presieve.isSheafFor_sigmaDesc_iff {ι : Type*} {X : ι → C} (f : ∀ i,
   have : PreservesLimit (Discrete.functor fun i ↦ op (E.toPreOneHypercover.X i)) F := by
     dsimp [E]; infer_instance
   have : PreservesLimit (Discrete.functor fun i ↦ op (E.toPreOneHypercover.Y' i)) F := by
-    convert Functor.Initial.preservesLimit_of_comp (Discrete.equivalence <| .sigmaPUnit _).inverse
+    convert! Functor.Initial.preservesLimit_of_comp (Discrete.equivalence <| .sigmaPUnit _).inverse
     assumption
   let equiv := (E.isLimitSigmaOfIsColimitEquiv hc hc' F).nonempty_congr
   rwa [isLimit_toPreOneHypercover_type_iff, isLimit_toPreOneHypercover_type_iff,
diff --git a/Mathlib/CategoryTheory/Sites/DenseSubsite/Basic.lean b/Mathlib/CategoryTheory/Sites/DenseSubsite/Basic.lean
index bbfc6cb11351f8..4e0eb417033bc2 100644
--- a/Mathlib/CategoryTheory/Sites/DenseSubsite/Basic.lean
+++ b/Mathlib/CategoryTheory/Sites/DenseSubsite/Basic.lean
@@ -475,7 +475,7 @@ lemma restrictHomEquivHom_naturality_left
 -/
 theorem iso_of_restrict_iso {ℱ ℱ' : Sheaf K A} (α : ℱ ⟶ ℱ') (i : IsIso (whiskerLeft G.op α.hom)) :
     IsIso α := by
-  convert (sheafIso (asIso (whiskerLeft G.op α.hom))).isIso_hom using 1
+  convert! (sheafIso (asIso (whiskerLeft G.op α.hom))).isIso_hom using 1
   ext1
   apply (sheafHom_eq _ _).symm
 
diff --git a/Mathlib/CategoryTheory/Sites/DenseSubsite/InducedTopology.lean b/Mathlib/CategoryTheory/Sites/DenseSubsite/InducedTopology.lean
index ba3659ce528019..742cbf547d080b 100644
--- a/Mathlib/CategoryTheory/Sites/DenseSubsite/InducedTopology.lean
+++ b/Mathlib/CategoryTheory/Sites/DenseSubsite/InducedTopology.lean
@@ -126,7 +126,7 @@ variable (J)
 
 instance over_forget_locallyCoverDense (X : C) : (Over.forget X).LocallyCoverDense J where
   functorPushforward_functorPullback_mem Y T := by
-    convert T.property
+    convert! T.property
     ext Z f
     constructor
     · rintro ⟨_, _, g', hg, rfl⟩
diff --git a/Mathlib/CategoryTheory/Sites/Descent/DescentData.lean b/Mathlib/CategoryTheory/Sites/Descent/DescentData.lean
index 97a6bc2d606588..e27ddb8f9a7e09 100644
--- a/Mathlib/CategoryTheory/Sites/Descent/DescentData.lean
+++ b/Mathlib/CategoryTheory/Sites/Descent/DescentData.lean
@@ -549,7 +549,7 @@ lemma bijective_toDescentData_map_iff (M N : F.obj (.mk (op S))) :
   rw [Presieve.isSheafFor_ofArrows_iff_bijective_toCompabible,
     ← (DescentData.subtypeCompatibleHomEquiv F f).bijective.of_comp_iff',
     ← Function.Bijective.of_comp_iff _ (presheafHomObjHomEquiv F).bijective]
-  convert Iff.rfl
+  convert! Iff.rfl
   ext φ : 1
   apply DescentData.subtypeCompatibleHomEquiv_toCompatible_presheafHomObjHomEquiv
 
@@ -560,7 +560,7 @@ lemma isPrestackFor_iff_isSheafFor {S : C} (R : Sieve S) :
   rw [isPrestackFor_iff, Functor.FullyFaithful.nonempty_iff_map_bijective]
   refine forall_congr' (fun M ↦ forall_congr' (fun N ↦ ?_))
   rw [bijective_toDescentData_map_iff]
-  convert Iff.rfl
+  convert! Iff.rfl
   refine le_antisymm ?_ ?_
   · rintro X f (hf : R.arrows f.left)
     obtain ⟨X, g, rfl⟩ := Over.mk_surjective X
@@ -578,7 +578,7 @@ lemma isPrestackFor_iff_isSheafFor' {S : C} (R : Sieve S) :
   rw [← Presieve.isSheafFor_iff_of_iso (F.overMapCompPresheafHomIso M N a),
     Presieve.isSheafFor_over_map_op_comp_iff (X' := Over.mk a)
       (e := Over.isoMk (Iso.refl _))] at h
-  convert h
+  convert! h
   refine le_antisymm ?_ ?_
   · intro Y f hf
     exact ⟨Over.mk f.left, Over.homMk f.left, Over.homMk (𝟙 _) (by simpa using Over.w f),
diff --git a/Mathlib/CategoryTheory/Sites/Descent/Precoverage.lean b/Mathlib/CategoryTheory/Sites/Descent/Precoverage.lean
index 01c2efc9c41b9c..7dfbba7e30a9e2 100644
--- a/Mathlib/CategoryTheory/Sites/Descent/Precoverage.lean
+++ b/Mathlib/CategoryTheory/Sites/Descent/Precoverage.lean
@@ -203,7 +203,7 @@ noncomputable def familyOfElements (i : ι) :
     Presieve.FamilyOfElements (F.presheafHom (D₁.obj i) (D₂.obj i)) (sieve f f' i).arrows :=
   fun Z q hq ↦
     mor w φ _ _ (sieve.fac (f := f) (f' := f') (q := Z.hom) (by
-      convert hq
+      convert! hq
       ext
       simpa using (Over.w q).symm))
 
diff --git a/Mathlib/CategoryTheory/Sites/Equivalence.lean b/Mathlib/CategoryTheory/Sites/Equivalence.lean
index b1a84418a95e38..d3e20a08f9dce9 100644
--- a/Mathlib/CategoryTheory/Sites/Equivalence.lean
+++ b/Mathlib/CategoryTheory/Sites/Equivalence.lean
@@ -55,7 +55,7 @@ namespace Equivalence
 instance (priority := 900) [G.IsEquivalence] : IsCoverDense G J where
   is_cover U := by
     let e := (asEquivalence G).symm
-    convert J.top_mem U
+    convert! J.top_mem U
     ext Y f
     simp only [Sieve.top_apply, iff_true]
     let g : e.inverse.obj _ ⟶ U := (e.unitInv.app Y) ≫ f
diff --git a/Mathlib/CategoryTheory/Sites/Grothendieck.lean b/Mathlib/CategoryTheory/Sites/Grothendieck.lean
index c990e6239237d3..c7caf6cf08eaa0 100644
--- a/Mathlib/CategoryTheory/Sites/Grothendieck.lean
+++ b/Mathlib/CategoryTheory/Sites/Grothendieck.lean
@@ -124,7 +124,7 @@ variable {J} in
 lemma pullback_mem_iff_of_isIso {i : X ⟶ Y} [IsIso i] {S : Sieve Y} :
     S.pullback i ∈ J _ ↔ S ∈ J _ := by
   refine ⟨fun H ↦ ?_, J.pullback_stable i⟩
-  convert J.pullback_stable (inv i) H
+  convert! J.pullback_stable (inv i) H
   rw [← Sieve.pullback_comp, IsIso.inv_hom_id, Sieve.pullback_id]
 
 @[grind .]
diff --git a/Mathlib/CategoryTheory/Sites/Hypercover/Homotopy.lean b/Mathlib/CategoryTheory/Sites/Hypercover/Homotopy.lean
index 13625777680dab..fddd49f702b794 100644
--- a/Mathlib/CategoryTheory/Sites/Hypercover/Homotopy.lean
+++ b/Mathlib/CategoryTheory/Sites/Hypercover/Homotopy.lean
@@ -184,7 +184,7 @@ lemma sieve₁'_cylinder (i j : Σ (i : E.I₀), F.I₁ (f.s₀ i) (g.s₀ i)) :
     simp_rw [← pullbackSymmetry_inv_comp_fst]
     apply (((cylinder f g).sieve₁' i j)).downward_closed
     rw [sieve₁']
-    convert Sieve.ofArrows_mk _ _ (ULift.up k)
+    convert! Sieve.ofArrows_mk _ _ (ULift.up k)
     simp [toPullback_cylinder f g ⟨k⟩]
 
 set_option backward.isDefEq.respectTransparency false in
diff --git a/Mathlib/CategoryTheory/Sites/Hypercover/Zero.lean b/Mathlib/CategoryTheory/Sites/Hypercover/Zero.lean
index 8bf2aae59fae77..343470a35f51fc 100644
--- a/Mathlib/CategoryTheory/Sites/Hypercover/Zero.lean
+++ b/Mathlib/CategoryTheory/Sites/Hypercover/Zero.lean
@@ -807,7 +807,7 @@ instance (E : ZeroHypercover.{w} J S) : ZeroHypercover.Small.{max u v} E where
       simp
     choose j h₁ h₂ using this
     refine ⟨ι, fun i ↦ j _ _ (.mk i), ?_⟩
-    convert E.mem₀
+    convert! E.mem₀
     exact le_antisymm (fun Z g ⟨i⟩ ↦ ⟨_⟩) (h ▸ fun Z g ⟨i⟩ ↦ .mk' i (h₁ _ _ _) (h₂ _ _ _))
 
 /-- Restrict a `w'`-small `0`-hypercover to a `w'`-`0`-hypercover. -/
@@ -871,7 +871,7 @@ lemma Small.inf {J K : Precoverage C} [Small.{w} J]
 instance [IsStableUnderBaseChange J] : RespectsIso J where
   of_iso {S E F} e h := by
     refine J.mem_coverings_of_isPullback (fun i ↦ E.f (e.inv.s₀ i)) ?_ (𝟙 S) _ (fun i ↦ ?_) ?_
-    · convert h
+    · convert! h
       exact Presieve.ofArrows_comp_eq_of_surjective _ (fun i ↦ ⟨e.hom.s₀ i, by simp⟩)
     · exact e.inv.h₀ i
     · intro i
diff --git a/Mathlib/CategoryTheory/Sites/IsSheafFor.lean b/Mathlib/CategoryTheory/Sites/IsSheafFor.lean
index 6c481804ee1e28..2f2cbc9c647a57 100644
--- a/Mathlib/CategoryTheory/Sites/IsSheafFor.lean
+++ b/Mathlib/CategoryTheory/Sites/IsSheafFor.lean
@@ -478,7 +478,7 @@ noncomputable def shrinkFunctorHomEquiv [LocallySmall.{w} C] {F : Cᵒᵖ ⥤ Ty
       naturality Y Z g := by
         ext ⟨f, hf⟩
         dsimp
-        convert t.2.to_sieveCompatible _ _ _
+        convert! t.2.to_sieveCompatible _ _ _
         simp only [Opposite.op_unop, shrinkYonedaObjObjEquiv_obj_map]
         rfl }
   left_inv t := by cat_disch
@@ -501,7 +501,7 @@ lemma shrinkFunctor_ι_comp_eq_iff_isAmalgamation [LocallySmall.{w} C] (F : Cᵒ
   · rintro rfl Y f hf
     simp [shrinkYonedaEquiv_naturality, shrinkYonedaEquiv_comp, shrinkYonedaEquiv_shrinkYoneda_map]
   · ext Y ⟨u, hu⟩
-    convert h (shrinkYonedaObjObjEquiv u) hu
+    convert! h (shrinkYonedaObjObjEquiv u) hu
     · rw [shrinkYonedaEquiv_naturality, shrinkYonedaEquiv_comp, shrinkYonedaEquiv_shrinkYoneda_map]
       simp
     · rw! [Equiv.symm_apply_apply]
@@ -870,7 +870,7 @@ lemma isSheafFor_pullback_iff (P : Cᵒᵖ ⥤ Type w) {X : C} (R : Sieve X)
   simp only [this, ← isSheafFor_iff_generate,
     isSheafFor_ofArrows_iff_bijective_toCompabible, ← e.bijective.of_comp_iff',
     ← Function.Bijective.of_comp_iff _ (P.mapIso (asIso f).symm.op).toEquiv.bijective]
-  convert Iff.rfl using 2
+  convert! Iff.rfl using 2
   ext
   simp [e]
 
@@ -895,7 +895,7 @@ lemma isSheafFor_over_map_op_comp_ofArrows_iff
         replace this := congr_arg (P.map φ.op) this
         dsimp at this
         simp only [← comp_apply, ← Functor.map_comp, ← op_comp] at this
-        convert this <;> cat_disch⟩
+        convert! this <;> cat_disch⟩
       invFun s := ⟨fun i ↦ s.val i, fun i₁ i₂ Z g₁ g₂ h ↦
         s.property i₁ i₂ _ ((Over.map p).map g₁) ((Over.map p).map g₂)
           (by simp only [← Functor.map_comp, h])⟩ }
@@ -912,7 +912,7 @@ lemma isSheafFor_over_map_op_comp_iff
   obtain ⟨ι, Z, g, rfl⟩ := R.exists_eq_ofArrows
   rw [← isSheafFor_iff_generate, isSheafFor_pullback_iff,
     isSheafFor_over_map_op_comp_ofArrows_iff, isSheafFor_iff_generate]
-  convert Iff.rfl
+  convert! Iff.rfl
   refine le_antisymm ?_ ?_
   · rintro W _ ⟨T, _, a, ⟨_, b, _, ⟨i⟩, rfl⟩, rfl⟩
     refine ⟨(Over.map p).obj (Z i), Over.homMk (a.left ≫ b.left) ?_, _, ⟨i⟩, ?_⟩
diff --git a/Mathlib/CategoryTheory/Sites/LeftExact.lean b/Mathlib/CategoryTheory/Sites/LeftExact.lean
index 580d3ee2f5a27f..52112f6067c2f6 100644
--- a/Mathlib/CategoryTheory/Sites/LeftExact.lean
+++ b/Mathlib/CategoryTheory/Sites/LeftExact.lean
@@ -293,8 +293,9 @@ set_option backward.isDefEq.respectTransparency false in
 @[reassoc (attr := simp)]
 lemma toSheafify_plusPlusIsoSheafify_hom (P : Cᵒᵖ ⥤ D) :
     J.toSheafify P ≫ (plusPlusIsoSheafify J D P).hom = toSheafify J P := by
-  convert Adjunction.unit_leftAdjointUniq_hom_app
-    (plusPlusAdjunction J D) (sheafificationAdjunction J D) P
+  convert!
+    Adjunction.unit_leftAdjointUniq_hom_app (plusPlusAdjunction J D) (sheafificationAdjunction J D)
+      P
   ext1 P
   dsimp [GrothendieckTopology.toSheafify, plusPlusAdjunction]
   rw [Category.comp_id]
diff --git a/Mathlib/CategoryTheory/Sites/LocallyInjective.lean b/Mathlib/CategoryTheory/Sites/LocallyInjective.lean
index cebb13c630641a..ec494c3b2b2958 100644
--- a/Mathlib/CategoryTheory/Sites/LocallyInjective.lean
+++ b/Mathlib/CategoryTheory/Sites/LocallyInjective.lean
@@ -80,7 +80,7 @@ lemma equalizerSieve_mem [IsLocallyInjective J φ]
 lemma isLocallyInjective_of_injective (hφ : ∀ (X : Cᵒᵖ), Function.Injective (φ.app X)) :
     IsLocallyInjective J φ where
   equalizerSieve_mem {X} x y h := by
-    convert J.top_mem X.unop
+    convert! J.top_mem X.unop
     ext Y f
     simp only [equalizerSieve_apply, op_unop, Sieve.top_apply, iff_true]
     apply hφ
diff --git a/Mathlib/CategoryTheory/Sites/LocallySurjective.lean b/Mathlib/CategoryTheory/Sites/LocallySurjective.lean
index 196eeae075878b..2687f17910070b 100644
--- a/Mathlib/CategoryTheory/Sites/LocallySurjective.lean
+++ b/Mathlib/CategoryTheory/Sites/LocallySurjective.lean
@@ -426,7 +426,7 @@ lemma imageSieve_cofanIsColimitDesc_shrinkYoneda_map
     obtain ⟨a : V ⟶ X i, rfl⟩ := shrinkYonedaObjObjEquiv.symm.surjective a
     refine ⟨_, a, _, ⟨i⟩, shrinkYonedaObjObjEquiv.symm.injective ?_⟩
     rw [← shrinkYoneda_map_app_shrinkYonedaObjObjEquiv_symm]
-    convert hw using 1
+    convert! hw using 1
     · exact (ConcreteCategory.congr_hom (NatTrans.congr_app
         ((Cofan.IsColimit.fac hc (fun i ↦ shrinkYoneda.{w}.map (f i))) i) (op V))
           (shrinkYonedaObjObjEquiv.symm a)).symm
diff --git a/Mathlib/CategoryTheory/Sites/Monoidal.lean b/Mathlib/CategoryTheory/Sites/Monoidal.lean
index 2f7c84550b8f40..7dea1989f7d62d 100644
--- a/Mathlib/CategoryTheory/Sites/Monoidal.lean
+++ b/Mathlib/CategoryTheory/Sites/Monoidal.lean
@@ -136,7 +136,7 @@ lemma whiskerLeft {G₁ G₂ : Cᵒᵖ ⥤ A} {g : G₁ ⟶ G₂} (hg : J.W g) (
     ((ihom.adjunction _).homEquiv _ _).bijective]
   rw [← Function.Bijective.of_comp_iff (g := MonoidalClosed.curry) _
     ((ihom.adjunction _).homEquiv _ _).bijective] at this
-  convert this using 1
+  convert! this using 1
   ext α : 1
   dsimp
   rw [curry_natural_left]
diff --git a/Mathlib/CategoryTheory/Sites/Over.lean b/Mathlib/CategoryTheory/Sites/Over.lean
index b82fef24c47312..78c1828f2090be 100644
--- a/Mathlib/CategoryTheory/Sites/Over.lean
+++ b/Mathlib/CategoryTheory/Sites/Over.lean
@@ -203,7 +203,7 @@ lemma overEquiv_functorPullback_post {D : Type*} [Category* D] (F : C ⥤ D) {X
   · intro Z g hg
     rw [Sieve.overEquiv_iff]
     dsimp [Presieve.functorPullback]
-    convert (Sieve.overEquiv_iff _ _).mp hg
+    convert! (Sieve.overEquiv_iff _ _).mp hg
     simp
 
 set_option backward.isDefEq.respectTransparency false in
@@ -282,8 +282,9 @@ lemma over_map_compatiblePreserving {X Y : C} (f : X ⟶ Y) :
       (by simpa using (Over.forget _).congr_map h.symm =≫ Z.hom)
     let e : (Over.map f).obj W' ≅ W := Over.isoMk (Iso.refl _)
       (by simpa [W'] using (Over.w f₁).symm)
-    convert congr_arg (F.obj.map e.inv.op)
-      (hx g₁' g₂' hg₁ hg₂ (by ext; exact (Over.forget _).congr_map h)) using 1
+    convert!
+      congr_arg (F.obj.map e.inv.op)
+        (hx g₁' g₂' hg₁ hg₂ (by ext; exact (Over.forget _).congr_map h)) using 1
     all_goals
       dsimp [e, W', g₁', g₂']
       rw [← Functor.map_comp_apply]
diff --git a/Mathlib/CategoryTheory/Sites/Plus.lean b/Mathlib/CategoryTheory/Sites/Plus.lean
index 8d06cb63682477..eedcef0bdc8507 100644
--- a/Mathlib/CategoryTheory/Sites/Plus.lean
+++ b/Mathlib/CategoryTheory/Sites/Plus.lean
@@ -116,7 +116,7 @@ def plusObj : Cᵒᵖ ⥤ D where
     let e := S.unop.pullbackId
     dsimp only [Functor.op, pullback_obj]
     rw [← colimit.w _ e.inv.op, ← Category.assoc]
-    convert Category.id_comp (colimit.ι (diagram J P (unop X)) S)
+    convert! Category.id_comp (colimit.ι (diagram J P (unop X)) S)
     refine Multiequalizer.hom_ext _ _ _ (fun I => ?_)
     dsimp
     simp only [Multiequalizer.lift_ι, Category.id_comp, Category.assoc]
@@ -243,8 +243,9 @@ theorem plusMap_toPlus : J.plusMap (J.toPlus P) = J.toPlus (J.plusObj P) := by
     ← Category.assoc, ← Category.assoc]
   congr 1
   refine Multiequalizer.hom_ext _ _ _ (fun II => ?_)
-  convert Multiequalizer.condition (S.unop.index P)
-    { fst := I, snd := II.base, r.Z := II.Y, r.g₁ := II.f, r.g₂ := 𝟙 II.Y } using 1
+  convert!
+    Multiequalizer.condition (S.unop.index P)
+      { fst := I, snd := II.base, r.Z := II.Y, r.g₁ := II.f, r.g₂ := 𝟙 II.Y } using 1
   all_goals simp
 
 set_option backward.isDefEq.respectTransparency false in
diff --git a/Mathlib/CategoryTheory/Sites/Point/Skyscraper.lean b/Mathlib/CategoryTheory/Sites/Point/Skyscraper.lean
index ddbe0afeb4b496..dfa2725d200c5f 100644
--- a/Mathlib/CategoryTheory/Sites/Point/Skyscraper.lean
+++ b/Mathlib/CategoryTheory/Sites/Point/Skyscraper.lean
@@ -252,7 +252,7 @@ lemma W_isInvertedBy_presheafFiber :
   rw [isIso_iff_coyoneda_map_bijective]
   intro M
   rw [← Function.Bijective.of_comp_iff' Φ.skyscraperPresheafHomEquiv.bijective]
-  convert (hf _ (Φ.isSheaf_skyscraperPresheaf M)).comp Φ.skyscraperPresheafHomEquiv.bijective
+  convert! (hf _ (Φ.isSheaf_skyscraperPresheaf M)).comp Φ.skyscraperPresheafHomEquiv.bijective
   ext g : 1
   simp [skyscraperPresheafHomEquiv_naturality_left]
 
diff --git a/Mathlib/CategoryTheory/Sites/Precoverage.lean b/Mathlib/CategoryTheory/Sites/Precoverage.lean
index c0a15ddcefc338..b0273725c31be0 100644
--- a/Mathlib/CategoryTheory/Sites/Precoverage.lean
+++ b/Mathlib/CategoryTheory/Sites/Precoverage.lean
@@ -142,7 +142,7 @@ lemma mem_coverings_of_isPullback {J : Precoverage C} [IsStableUnderBaseChange J
     exact .mk' (Sum.inr ⟨⟨_, _⟩, hg⟩) (by cat_disch) (by cat_disch)
   · refine IsStableUnderBaseChange.mem_coverings_of_isPullback (fun i ↦ f (a i)) ?_ g _
       (fun i ↦ p₂ (a i)) fun i ↦ h _
-    convert hR
+    convert! hR
     refine le_antisymm (fun Z g ⟨i⟩ ↦ .mk _) fun Z g hg ↦ ?_
     exact .mk' (Sum.inl ⟨⟨_, _⟩, hg⟩) (by cat_disch) (by cat_disch)
 
@@ -170,10 +170,10 @@ lemma comp_mem_coverings {J : Precoverage C} [IsStableUnderComposition J] {ι :
     exact .mk' ⟨Sum.inr ⟨⟨_, _⟩, hu⟩, .inl ⟨⟩⟩ hu.obj_idx.symm hu.eq_eqToHom_comp_hom_idx
   · refine IsStableUnderComposition.comp_mem_coverings (f := fun i ↦ f (incl i))
         (g := fun i j ↦ g (incl i) (fibincl i j)) ?_ fun i ↦ ?_
-    · convert hf
+    · convert! hf
       refine le_antisymm (fun T u ⟨p⟩ ↦ .mk _) fun T u hu ↦ ?_
       exact .mk' (Sum.inl ⟨⟨_, _⟩, hu⟩) (by cat_disch) (by cat_disch)
-    · convert hg (incl i)
+    · convert! hg (incl i)
       refine le_antisymm (fun T u ⟨p⟩ ↦ .mk _) fun T u hu ↦ ?_
       match i with
       | .inl i => exact .mk' ⟨⟨_, _⟩, hu⟩ (by cat_disch) (by cat_disch)
diff --git a/Mathlib/CategoryTheory/Sites/PreservesSheafification.lean b/Mathlib/CategoryTheory/Sites/PreservesSheafification.lean
index 1138c568349a3b..5e6eb777a91206 100644
--- a/Mathlib/CategoryTheory/Sites/PreservesSheafification.lean
+++ b/Mathlib/CategoryTheory/Sites/PreservesSheafification.lean
@@ -277,7 +277,7 @@ lemma sheafToPresheaf_map_sheafComposeNatTrans_eq_sheafifyCompIso_inv (P : Cᵒ
     rw [this]
     rfl
   apply ((plusPlusAdjunction J E).homEquiv _ _).injective
-  convert sheafComposeNatTrans_fac J F (plusPlusAdjunction J D) (plusPlusAdjunction J E) P
+  convert! sheafComposeNatTrans_fac J F (plusPlusAdjunction J D) (plusPlusAdjunction J E) P
   dsimp [plusPlusAdjunction]
   simp
 
diff --git a/Mathlib/CategoryTheory/Sites/Sheaf.lean b/Mathlib/CategoryTheory/Sites/Sheaf.lean
index d4b5e8c540a34e..482a40dbc9a933 100644
--- a/Mathlib/CategoryTheory/Sites/Sheaf.lean
+++ b/Mathlib/CategoryTheory/Sites/Sheaf.lean
@@ -110,7 +110,7 @@ def conesEquivSieveCompatibleFamily :
         have := x.2 f.unop.1.hom g.unop.hom.left f.unop.2
         dsimp at this ⊢
         rw [id_comp, ← this]
-        convert rfl
+        convert! rfl
         simp only [Over.w] }
 
 variable {P S E}
diff --git a/Mathlib/CategoryTheory/Sites/Sieves.lean b/Mathlib/CategoryTheory/Sites/Sieves.lean
index 0c4c9d76e45d69..582319b11d823f 100644
--- a/Mathlib/CategoryTheory/Sites/Sieves.lean
+++ b/Mathlib/CategoryTheory/Sites/Sieves.lean
@@ -707,7 +707,7 @@ lemma generate_eq_bot_iff (R : Presieve X) : generate R = ⊥ ↔ R = ⊥ := by
 lemma comp_mem_iff (i : X ⟶ Y) (f : Y ⟶ Z) [IsIso i] (S : Sieve Z) :
     S (i ≫ f) ↔ S f := by
   refine ⟨fun H ↦ ?_, fun H ↦ S.downward_closed H _⟩
-  convert S.downward_closed H (inv i)
+  convert! S.downward_closed H (inv i)
   simp
 
 section
diff --git a/Mathlib/CategoryTheory/Sites/Subsheaf.lean b/Mathlib/CategoryTheory/Sites/Subsheaf.lean
index 8191f45ebdbe1f..28abbe1c7137c2 100644
--- a/Mathlib/CategoryTheory/Sites/Subsheaf.lean
+++ b/Mathlib/CategoryTheory/Sites/Subsheaf.lean
@@ -68,7 +68,7 @@ def Subfunctor.sheafify : Subfunctor F where
 theorem Subfunctor.le_sheafify : G ≤ G.sheafify J := by
   intro U s hs
   change _ ∈ J _
-  convert J.top_mem U.unop
+  convert! J.top_mem U.unop
   rw [eq_top_iff]
   rintro V i -
   exact G.map i.op hs
@@ -201,13 +201,13 @@ alias Subpresheaf.to_sheafify_lift_unique := Subfunctor.to_sheafify_lift_unique
 theorem Subfunctor.sheafify_le (h : G ≤ G') (hF : Presieve.IsSheaf J F)
     (hG' : Presieve.IsSheaf J G'.toFunctor) : G.sheafify J ≤ G' := by
   intro U x hx
-  convert ((G.sheafifyLift (Subfunctor.homOfLe h) hG').app U ⟨x, hx⟩).2
+  convert! ((G.sheafifyLift (Subfunctor.homOfLe h) hG').app U ⟨x, hx⟩).2
   apply (hF _ hx).isSeparatedFor.ext
   intro V i hi
   have :=
     congr_arg (fun f : G.toFunctor ⟶ G'.toFunctor => (NatTrans.app f (op V) ⟨_, hi⟩).1)
       (G.to_sheafifyLift (Subfunctor.homOfLe h) hG')
-  convert this.symm
+  convert! this.symm
   rw [← Subfunctor.nat_trans_naturality]
   rfl
 
@@ -272,7 +272,7 @@ instance {F F' : Sheaf J (Type w)} (f : F ⟶ F') : Epi (Sheaf.toImage f) := by
   simp only [ObjectProperty.FullSubcategory.comp_hom, Sheaf.image_obj, Sheaf.toImage_hom,
     NatTrans.comp_app, Subfunctor.toFunctor_obj, comp_apply, op_unop, Subfunctor.toFunctor_map,
     ConcreteCategory.hom_ofHom, TypeCat.Fun.coe_mk, Subtype.ext_iff] at this E ⊢
-  convert this <;> exact E.symm
+  convert! this <;> exact E.symm
 
 /-- The mono factorization given by `image_sheaf` for a morphism. -/
 def imageMonoFactorization {F F' : Sheaf J (Type w)} (f : F ⟶ F') :
diff --git a/Mathlib/CategoryTheory/Sites/Types.lean b/Mathlib/CategoryTheory/Sites/Types.lean
index b06098d1e0e94f..a561d881fa36c4 100644
--- a/Mathlib/CategoryTheory/Sites/Types.lean
+++ b/Mathlib/CategoryTheory/Sites/Types.lean
@@ -56,10 +56,10 @@ theorem Presieve.isSheaf_yoneda' {α : Type u} :
   fun β _ hs x hx =>
   ⟨↾fun y => (x _ (hs y)).hom PUnit.unit , fun γ f h =>
     ConcreteCategory.hom_ext _ _ fun z => by
-      convert ConcreteCategory.congr_hom (hx (𝟙 _) (↾fun _ => z)
-        (hs <| f z) h rfl) PUnit.unit using 1,
+      convert!
+        ConcreteCategory.congr_hom (hx (𝟙 _) (↾fun _ => z) (hs <| f z) h rfl) PUnit.unit using 1,
       fun f hf => ConcreteCategory.hom_ext _ _ fun y => by
-        convert ConcreteCategory.congr_hom (hf _ (hs y)) PUnit.unit⟩
+        convert! ConcreteCategory.congr_hom (hf _ (hs y)) PUnit.unit⟩
 
 /-- The sheaf condition for `yoneda'`. -/
 theorem Presheaf.isSheaf_yoneda' {α : Type u} :
@@ -105,7 +105,7 @@ noncomputable def typesGlue (S : Type uᵒᵖ ⥤ Type u)
 theorem eval_typesGlue {S hs α} (f) : eval.{u} S α (typesGlue S hs α f) = f := by
   funext x
   apply (IsSheafFor.valid_glue _ _ _ <| ⟨PUnit.unit, fun _ => Subsingleton.elim _ _⟩).trans
-  convert ConcreteCategory.congr_hom (S.map_id _) _
+  convert! ConcreteCategory.congr_hom (S.map_id _) _
 
 theorem typesGlue_eval {S hs α} (s) : typesGlue.{u} S hs α (eval S α s) = s := by
   apply (hs.isSheafFor _ (generate_discretePresieve_mem α)).isSeparatedFor.ext
diff --git a/Mathlib/CategoryTheory/SmallObject/WellOrderInductionData.lean b/Mathlib/CategoryTheory/SmallObject/WellOrderInductionData.lean
index 19b9b5eb086aab..0a47e50c8fd0c6 100644
--- a/Mathlib/CategoryTheory/SmallObject/WellOrderInductionData.lean
+++ b/Mathlib/CategoryTheory/SmallObject/WellOrderInductionData.lean
@@ -221,10 +221,11 @@ def limit (j : J) (hj : Order.IsSuccLimit j)
     rw [d.map_lift _ _ _ _ (by simpa [bot_lt_iff_ne_bot] using hj.not_isMin)]
     simpa using (e ⊥ (by simpa [bot_lt_iff_ne_bot] using hj.not_isMin)).map_zero
   map_succ i hi := by
-    convert (e (Order.succ i) ((Order.IsSuccLimit.succ_lt_iff hj).mpr hi)).map_succ i
-      (by
-        simp only [Order.lt_succ_iff_not_isMax, not_isMax_iff]
-        exact ⟨_, hi⟩) using 1
+    convert!
+      (e (Order.succ i) ((Order.IsSuccLimit.succ_lt_iff hj).mpr hi)).map_succ i
+        (by
+          simp only [Order.lt_succ_iff_not_isMax, not_isMax_iff]
+          exact ⟨_, hi⟩) using 1
     · dsimp
       rw [map_id, id_apply, d.map_lift _ _ _ _ ((Order.IsSuccLimit.succ_lt_iff hj).mpr hi)]
     · congr 1
diff --git a/Mathlib/CategoryTheory/Subobject/Basic.lean b/Mathlib/CategoryTheory/Subobject/Basic.lean
index 6cca33b4b3c688..4866442c96b7c9 100644
--- a/Mathlib/CategoryTheory/Subobject/Basic.lean
+++ b/Mathlib/CategoryTheory/Subobject/Basic.lean
@@ -245,7 +245,7 @@ theorem mk_arrow (P : Subobject X) : mk P.arrow = P :=
 
 theorem le_of_comm {B : C} {X Y : Subobject B} (f : (X : C) ⟶ (Y : C)) (w : f ≫ Y.arrow = X.arrow) :
     X ≤ Y := by
-  convert mk_le_mk_of_comm _ w <;> simp
+  convert! mk_le_mk_of_comm _ w <;> simp
 
 theorem le_mk_of_comm {B A : C} {X : Subobject B} {f : A ⟶ B} [Mono f] (g : (X : C) ⟶ A)
     (w : g ≫ f = X.arrow) : X ≤ mk f :=
@@ -448,7 +448,7 @@ lemma mk_lt_mk_of_comm {X A₁ A₂ : C} {i₁ : A₁ ⟶ X} {i₂ : A₂ ⟶ X}
   · assumption
   · exfalso
     apply hf
-    convert (isoOfMkEqMk i₁ i₂ h).isIso_hom
+    convert! (isoOfMkEqMk i₁ i₂ h).isIso_hom
     rw [← cancel_mono i₂, isoOfMkEqMk_hom, ofMkLEMk_comp, fac]
 
 lemma mk_lt_mk_iff_of_comm {X A₁ A₂ : C} {i₁ : A₁ ⟶ X} {i₂ : A₂ ⟶ X} [Mono i₁] [Mono i₂]
@@ -529,12 +529,12 @@ def lowerEquivalence {A : C} {B : D} (e : MonoOver A ≌ MonoOver B) : Subobject
   inverse := lower e.inverse
   unitIso := by
     apply eqToIso
-    convert ThinSkeleton.map_iso_eq e.unitIso
+    convert! ThinSkeleton.map_iso_eq e.unitIso
     · exact ThinSkeleton.map_id_eq.symm
     · exact (ThinSkeleton.map_comp_eq _ _).symm
   counitIso := by
     apply eqToIso
-    convert ThinSkeleton.map_iso_eq e.counitIso
+    convert! ThinSkeleton.map_iso_eq e.counitIso
     · exact (ThinSkeleton.map_comp_eq _ _).symm
     · exact ThinSkeleton.map_id_eq.symm
 
diff --git a/Mathlib/CategoryTheory/Subobject/Classifier/Defs.lean b/Mathlib/CategoryTheory/Subobject/Classifier/Defs.lean
index 1d3ce7a8a04d9b..da73d95cb4b501 100644
--- a/Mathlib/CategoryTheory/Subobject/Classifier/Defs.lean
+++ b/Mathlib/CategoryTheory/Subobject/Classifier/Defs.lean
@@ -321,7 +321,7 @@ alias _root_.CategoryTheory.Classifier.truth_as_subobject := truth_as_subobject
 lemma surjective_χ {X : C} (φ : X ⟶ 𝒞.Ω) :
     ∃ (Z : C) (i : Z ⟶ X) (_ : Mono i), φ = 𝒞.χ i :=
   ⟨Limits.pullback φ 𝒞.truth, pullback.fst _ _, inferInstance, 𝒞.uniq _ (by
-    convert IsPullback.of_hasPullback φ 𝒞.truth)⟩
+    convert! IsPullback.of_hasPullback φ 𝒞.truth)⟩
 
 @[deprecated (since := "2026-03-06")]
 alias _root_.CategoryTheory.Classifier.surjective_χ := surjective_χ
@@ -456,7 +456,7 @@ lemma iso_inv_left_π :
     (h.iso m).inv.hom.left ≫ h.π m = Subobject.pullbackπ (h.χ m) h.Ω₀ := by
   dsimp only [π]
   rw [← Over.comp_left_assoc]
-  convert Category.id_comp _ using 2
+  convert! Category.id_comp _ using 2
   exact (MonoOver.forget _ ⋙ Over.forget _).congr_map (h.iso m).inv_hom_id
 
 @[deprecated (since := "2026-03-06")]
diff --git a/Mathlib/CategoryTheory/Subobject/Lattice.lean b/Mathlib/CategoryTheory/Subobject/Lattice.lean
index ee861db473397d..36a6cde1895a72 100644
--- a/Mathlib/CategoryTheory/Subobject/Lattice.lean
+++ b/Mathlib/CategoryTheory/Subobject/Lattice.lean
@@ -214,7 +214,7 @@ theorem top_eq_id (B : C) : (⊤ : Subobject B) = Subobject.mk (𝟙 B) :=
   rfl
 
 theorem underlyingIso_top_hom {B : C} : (underlyingIso (𝟙 B)).hom = (⊤ : Subobject B).arrow := by
-  convert underlyingIso_hom_comp_eq_mk (𝟙 B)
+  convert! underlyingIso_hom_comp_eq_mk (𝟙 B)
   simp only [comp_id]
 
 instance top_arrow_isIso {B : C} : IsIso (⊤ : Subobject B).arrow := by
@@ -443,7 +443,7 @@ theorem inf_eq_map_pullback' {A : C} (f₁ : MonoOver A) (f₂ : Subobject A) :
 
 theorem inf_eq_map_pullback {A : C} (f₁ : Subobject A) (f₂ : Subobject A) :
     (f₁ ⊓ f₂ : Subobject A) = (map f₁.arrow).obj ((pullback f₁.arrow).obj f₂) := by
-  convert inf_eq_map_pullback' (representative.obj f₁) f₂
+  convert! inf_eq_map_pullback' (representative.obj f₁) f₂
   ext1
   nth_rw 1 [← thinSkeleton_mk_representative_eq_self f₁]
   congr
@@ -611,7 +611,7 @@ theorem sInf_le {A : C} (s : Set (Subobject A)) (f) (hf : f ∈ s) : sInf s ≤
   · dsimp [sInf]
     simp only [Category.assoc, ← underlyingIso_hom_comp_eq_mk,
       Iso.cancel_iso_hom_left]
-    convert limit.w (wideCospan s) (WidePullbackShape.Hom.term _)
+    convert! limit.w (wideCospan s) (WidePullbackShape.Hom.term _)
     simp
 
 set_option backward.isDefEq.respectTransparency false in
diff --git a/Mathlib/CategoryTheory/Triangulated/Opposite/Triangulated.lean b/Mathlib/CategoryTheory/Triangulated/Opposite/Triangulated.lean
index 2d4267693fa464..db98c69fa84153 100644
--- a/Mathlib/CategoryTheory/Triangulated/Opposite/Triangulated.lean
+++ b/Mathlib/CategoryTheory/Triangulated/Opposite/Triangulated.lean
@@ -53,7 +53,7 @@ scoped instance [IsTriangulated C] : IsTriangulated Cᵒᵖ where
       exact congr($(Functor.map_injective _ congr($(eq₂).unop)).op).symm
     · have := op_distinguished _ o.mem
       dsimp at this
-      convert this using 2
+      convert! this using 2
       rw [Category.assoc, Functor.map_comp, Functor.map_comp,
         ← opShiftFunctorEquivalence_counitIso_hom_app_shift,
         ← opShiftFunctorEquivalence_counitIso_inv_naturality_assoc, Iso.inv_hom_id_app_assoc]
diff --git a/Mathlib/CategoryTheory/Triangulated/Pretriangulated.lean b/Mathlib/CategoryTheory/Triangulated/Pretriangulated.lean
index e08e2d2992feb9..30bedde4e50243 100644
--- a/Mathlib/CategoryTheory/Triangulated/Pretriangulated.lean
+++ b/Mathlib/CategoryTheory/Triangulated/Pretriangulated.lean
@@ -714,7 +714,7 @@ def isoTriangleOfIso₁₃ (T₁ T₂ : Triangle C) (hT₁ : T₁ ∈ distTriang
   have h₄ := (shiftFunctorCompIsoId C (-1 : ℤ) 1 (by simp)).inv.naturality e₃.hom
   dsimp at h₁ h₂ h₃ h₄
   refine Triangle.isoMk _ _ e₁ (Triangle.π₃.mapIso e) e₃ ?_ ?_ comm
-  · convert e.hom.comm₂ using 2
+  · convert! e.hom.comm₂ using 2
   · simp [← cancel_mono ((shiftFunctorCompIsoId C (-1) 1 (neg_add_cancel 1)).inv.app T₂.obj₃),
       ← h₃, assoc, h₁, h₄]
 
diff --git a/Mathlib/CategoryTheory/Triangulated/SpectralObject.lean b/Mathlib/CategoryTheory/Triangulated/SpectralObject.lean
index 8e62b7853cf869..8a698d63feeb9b 100644
--- a/Mathlib/CategoryTheory/Triangulated/SpectralObject.lean
+++ b/Mathlib/CategoryTheory/Triangulated/SpectralObject.lean
@@ -111,7 +111,7 @@ def precomp : SpectralObject C ι' where
     dsimp at this ⊢
     simp only [← Functor.map_comp_assoc, ← Functor.map_comp, Category.assoc,
       Iso.inv_hom_id, Functor.map_id, Category.comp_id] at this ⊢
-    convert this using 3
+    convert! this using 3
     · cat_disch
     · congr 2; cat_disch
   distinguished' D := by
@@ -133,7 +133,7 @@ def precomp : SpectralObject C ι' where
       rw [← cancel_epi (X.ω₁.map (F.mapComposableArrowsObjMk₁Iso _).inv)]
       simp only [← Functor.map_comp_assoc, ← Functor.map_comp, Category.assoc,
         Iso.inv_hom_id, Functor.map_id, Category.id_comp] at this ⊢
-      convert this.symm using 3
+      convert! this.symm using 3
       · congr; cat_disch
       · cat_disch
 
diff --git a/Mathlib/Combinatorics/Additive/AP/Three/Behrend.lean b/Mathlib/Combinatorics/Additive/AP/Three/Behrend.lean
index b6f8bce6902ee3..06729290aae937 100644
--- a/Mathlib/Combinatorics/Additive/AP/Three/Behrend.lean
+++ b/Mathlib/Combinatorics/Additive/AP/Three/Behrend.lean
@@ -75,7 +75,7 @@ lemma threeAPFree_sphere {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]
   obtain rfl | hr := eq_or_ne r 0
   · rw [sphere_zero]
     exact threeAPFree_singleton _
-  · convert threeAPFree_frontier isClosed_closedBall (strictConvex_closedBall ℝ x r)
+  · convert! threeAPFree_frontier isClosed_closedBall (strictConvex_closedBall ℝ x r)
     exact (frontier_closedBall _ hr).symm
 
 namespace Behrend
@@ -264,7 +264,7 @@ theorem bound_aux' (n d : ℕ) : ((d ^ n :) / (n * d ^ 2 :) : ℝ) ≤ rothNumbe
 
 theorem bound_aux (hd : d ≠ 0) (hn : 2 ≤ n) :
     (d ^ (n - 2 :) / n : ℝ) ≤ rothNumberNat ((2 * d - 1) ^ n) := by
-  convert bound_aux' n d using 1
+  convert! bound_aux' n d using 1
   rw [cast_mul, cast_pow, mul_comm, ← div_div, pow_sub₀ _ _ hn, ← div_eq_mul_inv, cast_pow]
   rwa [cast_ne_zero]
 
diff --git a/Mathlib/Combinatorics/Additive/AP/Three/Defs.lean b/Mathlib/Combinatorics/Additive/AP/Three/Defs.lean
index 0de18c194e9c72..5f0abedcd2d889 100644
--- a/Mathlib/Combinatorics/Additive/AP/Three/Defs.lean
+++ b/Mathlib/Combinatorics/Additive/AP/Three/Defs.lean
@@ -380,7 +380,7 @@ theorem mulRothNumber_map_mul_left :
     exact (threeGPFree_smul_set.1 hu).le_mulRothNumber hus
   · obtain ⟨u, hus, hcard, hu⟩ := mulRothNumber_spec s
     have h : ThreeGPFree (u.map <| mulLeftEmbedding a : Set α) := by rw [coe_map]; exact hu.smul_set
-    convert h.le_mulRothNumber (map_subset_map.2 hus) using 1
+    convert! h.le_mulRothNumber (map_subset_map.2 hus) using 1
     rw [card_map, hcard]
 
 @[to_additive (attr := simp)]
@@ -438,9 +438,9 @@ theorem rothNumberNat_zero : rothNumberNat 0 = 0 :=
 theorem addRothNumber_Ico (a b : ℕ) : addRothNumber (Ico a b) = rothNumberNat (b - a) := by
   obtain h | h := le_total b a
   · rw [Nat.sub_eq_zero_of_le h, Ico_eq_empty_of_le h, rothNumberNat_zero, addRothNumber_empty]
-  convert addRothNumber_map_add_left _ a
+  convert! addRothNumber_map_add_left _ a
   rw [range_eq_Ico, map_eq_image]
-  convert (image_add_left_Ico 0 (b - a) _).symm
+  convert! (image_add_left_Ico 0 (b - a) _).symm
   exact (add_tsub_cancel_of_le h).symm
 
 open Fin.NatCast in -- TODO: should this be refactored to avoid needing the coercion?
diff --git a/Mathlib/Combinatorics/Additive/Corner/Roth.lean b/Mathlib/Combinatorics/Additive/Corner/Roth.lean
index 4582bd977354ab..b012b8b6a77b39 100644
--- a/Mathlib/Combinatorics/Additive/Corner/Roth.lean
+++ b/Mathlib/Combinatorics/Additive/Corner/Roth.lean
@@ -92,7 +92,7 @@ theorem corners_theorem (ε : ℝ) (hε : 0 < ε) (hG : cornersTheoremBound ε 
   classical
   have h₁ := (farFromTriangleFree_graph hAε).le_card_cliqueFinset
   rw [card_triangles, card_triangleIndices] at h₁
-  convert h₁.trans (Nat.cast_le.2 <| card_le_univ _) using 1 <;> simp <;> ring
+  convert! h₁.trans (Nat.cast_le.2 <| card_le_univ _) using 1 <;> simp <;> ring
 
 open Fin.NatCast in -- TODO: refactor to avoid needing the coercion
 /-- The **corners theorem** for `ℕ`.
diff --git a/Mathlib/Combinatorics/Additive/FreimanHom.lean b/Mathlib/Combinatorics/Additive/FreimanHom.lean
index f03f52ab44c1af..b6a94309d77f9b 100644
--- a/Mathlib/Combinatorics/Additive/FreimanHom.lean
+++ b/Mathlib/Combinatorics/Additive/FreimanHom.lean
@@ -457,7 +457,7 @@ lemma isAddFreimanIso_Iio (hm : m ≠ 0) (hkmn : m * k ≤ n) :
   obtain _ | k := k
   · simp [← bot_eq_zero]
   have hkmn' : m * k ≤ n := (Nat.mul_le_mul_left _ k.le_succ).trans hkmn
-  convert isAddFreimanIso_Iic hm hkmn' using 1 <;> ext x
+  convert! isAddFreimanIso_Iic hm hkmn' using 1 <;> ext x
   · simp only [Nat.cast_add, Nat.cast_one, mem_Iio, lt_def, mem_Iic, le_iff_val_le_val,
       val_natCast, aux hm hkmn', Nat.mod_eq_of_lt]
     simp_rw [← Nat.cast_add_one]
diff --git a/Mathlib/Combinatorics/Additive/VerySmallDoubling.lean b/Mathlib/Combinatorics/Additive/VerySmallDoubling.lean
index 070ac20a2ddf91..5bfc35e3788361 100644
--- a/Mathlib/Combinatorics/Additive/VerySmallDoubling.lean
+++ b/Mathlib/Combinatorics/Additive/VerySmallDoubling.lean
@@ -166,7 +166,7 @@ def invMulSubgroup (A : Finset G) (h : #(A * A) < (3 / 2 : ℚ) * #A) : Subgroup
   mul_mem' := by
     norm_cast
     have h₁ x (hx : x ∈ A) y (hy : y ∈ A) : (1 / 2 : ℚ) * #A < #(x • A ∩ y • A) := by
-      convert lt_card_smul_inter_smul (by simpa using Rat.cast_strictMono (K := ℝ) h) hx hy
+      convert! lt_card_smul_inter_smul (by simpa using Rat.cast_strictMono (K := ℝ) h) hx hy
       norm_num
       simp [← Rat.cast_lt (K := ℝ)]
     intro a c ha hc
@@ -210,7 +210,7 @@ private lemma weak_invMulSubgroup_bound (h : #(A * A) < (3 / 2 : ℚ) * #A) :
     #(A⁻¹ * A) < 2 * #A := by
   have h₀ : A.Nonempty := nonempty_of_doubling h
   have h₁ a (ha : a ∈ A⁻¹ * A) : (1 / 2 : ℚ) * #A < #{xy ∈ A ×ˢ A | xy.1 * xy.2⁻¹ = a} := by
-    convert lt_card_mul_inv_eq (by simpa using Rat.cast_strictMono (K := ℝ) h) ha
+    convert! lt_card_mul_inv_eq (by simpa using Rat.cast_strictMono (K := ℝ) h) ha
     norm_num
     simp [← Rat.cast_lt (K := ℝ)]
   have h₂ : ∀ x ∈ A ×ˢ A, (fun ⟨x, y⟩ => x * y⁻¹) x ∈ A⁻¹ * A := by
diff --git a/Mathlib/Combinatorics/Configuration.lean b/Mathlib/Combinatorics/Configuration.lean
index a809cc259505d1..2b1f5a6ad5d985 100644
--- a/Mathlib/Combinatorics/Configuration.lean
+++ b/Mathlib/Combinatorics/Configuration.lean
@@ -450,7 +450,7 @@ theorem card_points [Fintype P] [Finite L] : Fintype.card P = order P L ^ 2 + or
   classical
     have h1 : Fintype.card { q // q ≠ p } + 1 = Fintype.card P := by
       apply (eq_tsub_iff_add_eq_of_le (Nat.succ_le_of_lt (Fintype.card_pos_iff.mpr ⟨p⟩))).mp
-      convert (Fintype.card_subtype_compl _).trans (congr_arg _ (Fintype.card_subtype_eq p))
+      convert! (Fintype.card_subtype_compl _).trans (congr_arg _ (Fintype.card_subtype_eq p))
     have h2 : ∀ l : { l : L // p ∈ l }, Fintype.card { q // q ∈ l.1 ∧ q ≠ p } = order P L := by
       intro l
       rw [← Fintype.card_congr (Equiv.subtypeSubtypeEquivSubtypeInter (· ∈ l.val) (· ≠ p)),
diff --git a/Mathlib/Combinatorics/Enumerative/Bell.lean b/Mathlib/Combinatorics/Enumerative/Bell.lean
index 51de56b170f4f0..00f5a2ddd4ba94 100644
--- a/Mathlib/Combinatorics/Enumerative/Bell.lean
+++ b/Mathlib/Combinatorics/Enumerative/Bell.lean
@@ -158,7 +158,7 @@ theorem uniformBell_one_right (m : ℕ) : uniformBell m 1 = 1 := by
 
 theorem uniformBell_mul_eq (m : ℕ) {n : ℕ} (hn : n ≠ 0) :
     uniformBell m n * n ! ^ m * m ! = (m * n)! := by
-  convert bell_mul_eq (replicate m n)
+  convert! bell_mul_eq (replicate m n)
   · simp only [map_replicate, prod_replicate]
   · simp only [toFinset_replicate]
     split_ifs with hm
diff --git a/Mathlib/Combinatorics/Enumerative/Composition.lean b/Mathlib/Combinatorics/Enumerative/Composition.lean
index 50787ee346fbb7..bf413e6446f813 100644
--- a/Mathlib/Combinatorics/Enumerative/Composition.lean
+++ b/Mathlib/Combinatorics/Enumerative/Composition.lean
@@ -222,7 +222,7 @@ theorem sizeUpTo_zero : c.sizeUpTo 0 = 0 := by simp [sizeUpTo]
 
 theorem sizeUpTo_ofLength_le (i : ℕ) (h : c.length ≤ i) : c.sizeUpTo i = n := by
   dsimp [sizeUpTo]
-  convert c.blocks_sum
+  convert! c.blocks_sum
   exact take_of_length_le h
 
 @[simp]
@@ -667,7 +667,7 @@ def recOnAppendSingle {motive : ∀ n, Composition n → Sort*} {n : ℕ} (c : C
       motive (n + (k + 1)) (append c (single (k + 1) k.succ_pos))) :
     motive n c :=
   reverse_reverse c ▸ c.reverse.recOnSingleAppend zero fun k n c ih ↦ by
-    convert append_single k n c.reverse ih using 1
+    convert! append_single k n c.reverse ih using 1
     · apply add_comm
     · rw [reverse_append, reverse_single]
       apply cast_heq
@@ -826,7 +826,7 @@ def compositionAsSetEquiv (n : ℕ) : CompositionAsSet n ≃ Finset (Fin (n - 1)
     · rintro (rfl | rfl | ⟨j, hj1, hj2⟩)
       · exact c.zero_mem
       · exact c.getLast_mem
-      · convert hj1
+      · convert! hj1
     · simp only [or_iff_not_imp_left, ← ne_eq, ← Fin.exists_succ_eq]
       rintro i_mem ⟨j, rfl⟩ i_ne_last
       rcases Nat.exists_add_one_eq.mpr j.pos with ⟨n, rfl⟩
@@ -888,7 +888,7 @@ theorem boundary_zero : (c.boundary ⟨0, c.card_boundaries_pos⟩ : Fin (n + 1)
 
 @[simp]
 theorem boundary_length : c.boundary ⟨c.length, c.length_lt_card_boundaries⟩ = Fin.last n := by
-  convert Finset.orderEmbOfFin_last rfl c.card_boundaries_pos
+  convert! Finset.orderEmbOfFin_last rfl c.card_boundaries_pos
   exact le_antisymm (Finset.le_max' _ _ c.getLast_mem) (Fin.le_last _)
 
 /-- Size of the `i`-th block in a `CompositionAsSet`, seen as a function on `Fin c.length`. -/
@@ -931,7 +931,7 @@ theorem mem_boundaries_iff_exists_blocks_sum_take_eq {j : Fin (n + 1)} :
     rw [← hi, c.blocks_partial_sum i.2]
     rfl
   · rintro ⟨i, hi, H⟩
-    convert (c.boundaries.orderIsoOfFin rfl ⟨i, hi⟩).2
+    convert! (c.boundaries.orderIsoOfFin rfl ⟨i, hi⟩).2
     have : c.boundary ⟨i, hi⟩ = j := by rwa [Fin.ext_iff, ← c.blocks_partial_sum hi]
     exact this.symm
 
diff --git a/Mathlib/Combinatorics/Enumerative/DyckWord.lean b/Mathlib/Combinatorics/Enumerative/DyckWord.lean
index fa5d2d4584f561..bfe4d869675eef 100644
--- a/Mathlib/Combinatorics/Enumerative/DyckWord.lean
+++ b/Mathlib/Combinatorics/Enumerative/DyckWord.lean
@@ -244,7 +244,7 @@ lemma semilength_eq_count_D : p.semilength = p.toList.count D := by
 @[simp]
 lemma two_mul_semilength_eq_length : 2 * p.semilength = p.toList.length := by
   nth_rw 1 [two_mul, semilength, p.count_U_eq_count_D, semilength]
-  convert (p.toList.length_eq_countP_add_countP (· == D)).symm
+  convert! (p.toList.length_eq_countP_add_countP (· == D)).symm
   rw [count]; congr!; rename_i s; cases s <;> tauto
 
 end Semilength
@@ -365,7 +365,7 @@ lemma outsidePart_add : (p + q).outsidePart = p.outsidePart + q := by
 @[simp]
 lemma insidePart_nest : p.nest.insidePart = p := by
   simp_rw [insidePart, nest_ne_zero, dite_false, firstReturn_nest]
-  convert p.denest_nest; rw [DyckWord.ext_iff]; apply take_of_length_le
+  convert! p.denest_nest; rw [DyckWord.ext_iff]; apply take_of_length_le
   simp_rw [nest, length_append, length_singleton]; lia
 
 @[simp]
@@ -545,7 +545,7 @@ instance {n : ℕ} : Fintype { p : DyckWord // p.semilength = n } :=
 theorem card_dyckWord_semilength_eq_catalan (n : ℕ) :
     Fintype.card { p : DyckWord // p.semilength = n } = catalan n := by
   rw [← Fintype.ofEquiv_card (equivTreesOfNumNodesEq n), ← treesOfNumNodesEq_card_eq_catalan]
-  convert Fintype.card_coe _
+  convert! Fintype.card_coe _
 
 end Tree
 
diff --git a/Mathlib/Combinatorics/Enumerative/IncidenceAlgebra.lean b/Mathlib/Combinatorics/Enumerative/IncidenceAlgebra.lean
index 6431aeb4db4971..453228069c5c0a 100644
--- a/Mathlib/Combinatorics/Enumerative/IncidenceAlgebra.lean
+++ b/Mathlib/Combinatorics/Enumerative/IncidenceAlgebra.lean
@@ -575,7 +575,7 @@ set_option backward.isDefEq.respectTransparency false in
 O'Donnell. -/
 lemma moebius_inversion_bot (f g : α → 𝕜) (h : ∀ x, g x = ∑ y ∈ Iic x, f y) (x : α) :
     f x = ∑ y ∈ Iic x, mu 𝕜 y x * g y := by
-  convert moebius_inversion_top (α := αᵒᵈ) f g h x using 3
+  convert! moebius_inversion_top (α := αᵒᵈ) f g h x using 3
   rw [← mu_toDual]; rfl
 
 end InversionBot
diff --git a/Mathlib/Combinatorics/Enumerative/InclusionExclusion.lean b/Mathlib/Combinatorics/Enumerative/InclusionExclusion.lean
index f7e31563ffc173..6758df6efd0420 100644
--- a/Mathlib/Combinatorics/Enumerative/InclusionExclusion.lean
+++ b/Mathlib/Combinatorics/Enumerative/InclusionExclusion.lean
@@ -105,7 +105,7 @@ variable [DecidableEq α]
 
 lemma prod_indicator_biUnion_finset_sub_indicator (hs : s.Nonempty) (S : ι → Finset α) (a : α) :
     ∏ i ∈ s, (Set.indicator (s.biUnion S) 1 a - Set.indicator (S i) 1 a) = (0 : ℤ) := by
-  convert prod_indicator_biUnion_sub_indicator hs (fun i ↦ S i) a
+  convert! prod_indicator_biUnion_sub_indicator hs (fun i ↦ S i) a
   simp
 
 /-- **Inclusion-exclusion principle** for the sum of a function over a union.
diff --git a/Mathlib/Combinatorics/Enumerative/Partition/Basic.lean b/Mathlib/Combinatorics/Enumerative/Partition/Basic.lean
index 6ce7063d65d58b..4bb7639e6fa7b9 100644
--- a/Mathlib/Combinatorics/Enumerative/Partition/Basic.lean
+++ b/Mathlib/Combinatorics/Enumerative/Partition/Basic.lean
@@ -154,7 +154,7 @@ theorem toFinsuppAntidiag_mem_finsuppAntidiag {n : ℕ} (p : Partition n) :
   have hp : p.parts.toFinset ⊆ Finset.Icc 1 n := by
     grind
   suffices ∑ m ∈ Finset.Icc 1 n, Multiset.count m p.parts * m = n by simpa [toFinsuppAntidiag, hp]
-  convert ← p.parts_sum
+  convert! ← p.parts_sum
   rw [Finset.sum_multiset_count]
   apply Finset.sum_subset hp
   suffices ∀ (x : ℕ), 1 ≤ x → x ≤ n → x ∉ p.parts → x ∉ p.parts ∨ x = 0 by simpa
diff --git a/Mathlib/Combinatorics/Enumerative/Partition/Glaisher.lean b/Mathlib/Combinatorics/Enumerative/Partition/Glaisher.lean
index 3337736c91f361..fbe261a305a3db 100644
--- a/Mathlib/Combinatorics/Enumerative/Partition/Glaisher.lean
+++ b/Mathlib/Combinatorics/Enumerative/Partition/Glaisher.lean
@@ -50,7 +50,7 @@ theorem hasProd_powerSeriesMk_card_restricted [IsTopologicalSemiring R]
     (p : ℕ → Prop) [DecidablePred p] :
     HasProd (fun i ↦ if p (i + 1) then ∑' j : ℕ, X ^ ((i + 1) * j) else 1)
     (PowerSeries.mk fun n ↦ (#(restricted n p) : R)) := by
-  convert hasProd_genFun (fun i c ↦ if p i then (1 : R) else 0) using 1
+  convert! hasProd_genFun (fun i c ↦ if p i then (1 : R) else 0) using 1
   · ext1 i
     split_ifs
     · rw [tsum_eq_zero_add' ?_]
@@ -81,7 +81,7 @@ theorem hasProd_powerSeriesMk_card_countRestricted {m : ℕ} (hm : 0 < m) :
     HasProd (fun i ↦ ∑ j ∈ range m, X ^ ((i + 1) * j))
     (PowerSeries.mk fun n ↦ (#(countRestricted n m) : R)) := by
   nontriviality R using Subsingleton.eq_one
-  convert hasProd_genFun (fun i c ↦ if c < m then (1 : R) else 0) using 1
+  convert! hasProd_genFun (fun i c ↦ if c < m then (1 : R) else 0) using 1
   · ext1 i
     rw [sum_range_eq_add_Ico _ hm, sum_Ico_eq_sum_range]
     congrm $(by simp) + ?_
diff --git a/Mathlib/Combinatorics/Graph/Basic.lean b/Mathlib/Combinatorics/Graph/Basic.lean
index 08c8020b193b3e..ee688ac483754e 100644
--- a/Mathlib/Combinatorics/Graph/Basic.lean
+++ b/Mathlib/Combinatorics/Graph/Basic.lean
@@ -354,7 +354,7 @@ to the definition of `Graph`, so it doesn't require equality of the edge sets.)
 protected lemma ext {G₁ G₂ : Graph α β} (hV : V(G₁) = V(G₂))
     (h : ∀ e x y, G₁.IsLink e x y ↔ G₂.IsLink e x y) : G₁ = G₂ := by
   rw [← G₁.mk_eq_self G₁.edge_mem_iff_exists_isLink, ← G₂.mk_eq_self G₂.edge_mem_iff_exists_isLink]
-  convert rfl using 2
+  convert! rfl using 2
   · exact hV.symm
   · simp [funext_iff, h]
   simp [edgeSet_eq_setOf_exists_isLink, h]
diff --git a/Mathlib/Combinatorics/HalesJewett.lean b/Mathlib/Combinatorics/HalesJewett.lean
index a897b271a1a7f4..bde1cc7b15b7d5 100644
--- a/Mathlib/Combinatorics/HalesJewett.lean
+++ b/Mathlib/Combinatorics/HalesJewett.lean
@@ -496,7 +496,7 @@ theorem exists_mono_in_high_dimension (α κ η) [Finite α] [Finite κ] [Finite
   refine ⟨ι × Shrink η, inferInstance, fun C ↦ ?_⟩
   obtain ⟨l, hl⟩ := hι fun x ↦ C fun (i, e) ↦ x i e
   refine ⟨l.toSubspace.reindex (equivShrink.{0} η).symm (Equiv.refl _) (Equiv.refl _), ?_⟩
-  convert hl.toSubspace.reindex
+  convert! hl.toSubspace.reindex
   simp
 
 /-- A variant of the **extended Hales-Jewett theorem** `exists_mono_in_high_dimension` where the
diff --git a/Mathlib/Combinatorics/Hall/Basic.lean b/Mathlib/Combinatorics/Hall/Basic.lean
index b9b392f5060a53..5d7cb118a5f2c8 100644
--- a/Mathlib/Combinatorics/Hall/Basic.lean
+++ b/Mathlib/Combinatorics/Hall/Basic.lean
@@ -77,7 +77,7 @@ theorem hallMatchingsOn.nonempty {ι : Type u} {α : Type v} [DecidableEq α] (t
     refine ⟨Classical.indefiniteDescription _ ?_⟩
     apply (all_card_le_biUnion_card_iff_existsInjective' fun i : ι' => t i).mp
     intro s'
-    convert h (s'.image (↑)) using 1
+    convert! h (s'.image (↑)) using 1
     · simp only [card_image_of_injective s' Subtype.coe_injective]
     · rw [image_biUnion]
 
diff --git a/Mathlib/Combinatorics/Hall/Finite.lean b/Mathlib/Combinatorics/Hall/Finite.lean
index 9ca804a778207b..3bd50b4a414a08 100644
--- a/Mathlib/Combinatorics/Hall/Finite.lean
+++ b/Mathlib/Combinatorics/Hall/Finite.lean
@@ -59,7 +59,7 @@ theorem hall_cond_of_erase {x : ι} (a : α)
   rw [image_nonempty, Finset.card_image_of_injective s' Subtype.coe_injective] at ha
   by_cases! he : s'.Nonempty
   · have ha' : #s' < #(s'.biUnion fun x => t x) := by
-      convert ha he fun h => by simpa [← h] using mem_univ x using 2
+      convert! ha he fun h => by simpa [← h] using mem_univ x using 2
       ext x
       simp only [mem_image, mem_biUnion, SetCoe.exists, exists_and_right,
         exists_eq_right]
@@ -126,7 +126,7 @@ theorem hall_cond_of_restrict {ι : Type u} {t : ι → Finset α} {s : Finset 
     #s' ≤ #(s'.biUnion fun a' => t a') := by
   classical
     rw [← card_image_of_injective s' Subtype.coe_injective]
-    convert ht (s'.image fun z => z.1) using 1
+    convert! ht (s'.image fun z => z.1) using 1
     apply congr_arg
     ext y
     simp
diff --git a/Mathlib/Combinatorics/Hindman.lean b/Mathlib/Combinatorics/Hindman.lean
index 7b45cb3734a45f..b22fbe7516e534 100644
--- a/Mathlib/Combinatorics/Hindman.lean
+++ b/Mathlib/Combinatorics/Hindman.lean
@@ -146,7 +146,7 @@ theorem exists_idempotent_ultrafilter_le_FP {M} [Semigroup M] (a : Stream' M) :
   have h := exists_idempotent_in_compact_subsemigroup ?_ S ?_ ?_ ?_
   · rcases h with ⟨U, hU, U_idem⟩
     refine ⟨U, U_idem, ?_⟩
-    convert Set.mem_iInter.mp hU 0
+    convert! Set.mem_iInter.mp hU 0
   · exact Ultrafilter.continuous_mul_left
   · apply IsCompact.nonempty_iInter_of_sequence_nonempty_isCompact_isClosed
     · intro n U hU
@@ -250,7 +250,7 @@ theorem FP.mul_two {M} [Semigroup M] (a : Stream' M) (i j : ℕ) (ij : i < j) :
   rcases Nat.exists_eq_add_of_le (Nat.succ_le_of_lt ij) with ⟨d, hd⟩
   have := FP.singleton (a.drop i).tail d
   rw [Stream'.tail_eq_drop, Stream'.get_drop, Stream'.get_drop] at this
-  convert this
+  convert! this
   lia
 
 @[to_additive]
diff --git a/Mathlib/Combinatorics/Matroid/Basic.lean b/Mathlib/Combinatorics/Matroid/Basic.lean
index 302fa328680035..d776d78b5dd7d7 100644
--- a/Mathlib/Combinatorics/Matroid/Basic.lean
+++ b/Mathlib/Combinatorics/Matroid/Basic.lean
@@ -827,7 +827,7 @@ theorem IsBasis.subset_ground (hI : M.IsBasis I X) : X ⊆ M.E :=
   hI.2
 
 theorem IsBasis.isBasis_inter_ground (hI : M.IsBasis I X) : M.IsBasis I (X ∩ M.E) := by
-  convert hI
+  convert! hI
   rw [inter_eq_self_of_subset_left hI.subset_ground]
 
 @[aesop unsafe 15% (rule_sets := [Matroid])]
@@ -1003,7 +1003,7 @@ theorem IsBasis.iUnion_isBasis_iUnion {ι : Type _} (X I : ι → Set α)
 
 theorem IsBasis.isBasis_iUnion {ι : Type _} [Nonempty ι] (X : ι → Set α)
     (hI : ∀ i, M.IsBasis I (X i)) : M.IsBasis I (⋃ i, X i) := by
-  convert IsBasis.iUnion_isBasis_iUnion X (fun _ ↦ I) (fun i ↦ hI i) _ <;> rw [iUnion_const]
+  convert! IsBasis.iUnion_isBasis_iUnion X (fun _ ↦ I) (fun i ↦ hI i) _ <;> rw [iUnion_const]
   exact (hI (Classical.arbitrary ι)).indep
 
 theorem IsBasis.isBasis_sUnion {Xs : Set (Set α)} (hne : Xs.Nonempty)
@@ -1028,11 +1028,11 @@ theorem IsBasis.union_isBasis_union (hIX : M.IsBasis I X) (hJY : M.IsBasis J Y)
 
 theorem IsBasis.isBasis_union (hIX : M.IsBasis I X) (hIY : M.IsBasis I Y) :
     M.IsBasis I (X ∪ Y) := by
-  convert hIX.union_isBasis_union hIY _ <;> rw [union_self]; exact hIX.indep
+  convert! hIX.union_isBasis_union hIY _ <;> rw [union_self]; exact hIX.indep
 
 theorem IsBasis.isBasis_union_of_subset (hI : M.IsBasis I X) (hJ : M.Indep J) (hIJ : I ⊆ J) :
     M.IsBasis J (J ∪ X) := by
-  convert hJ.isBasis_self.union_isBasis_union hI _ <;>
+  convert! hJ.isBasis_self.union_isBasis_union hI _ <;>
   rw [union_eq_self_of_subset_right hIJ]
   assumption
 
diff --git a/Mathlib/Combinatorics/Matroid/Circuit.lean b/Mathlib/Combinatorics/Matroid/Circuit.lean
index 4605ef5e10bf37..65f5e8634856d9 100644
--- a/Mathlib/Combinatorics/Matroid/Circuit.lean
+++ b/Mathlib/Combinatorics/Matroid/Circuit.lean
@@ -580,7 +580,7 @@ lemma isCocircuit_iff_minimal :
 /-- A cocircuit is a minimal set whose complement is nonspanning. -/
 lemma isCocircuit_iff_minimal_compl_nonspanning :
     M.IsCocircuit K ↔ Minimal (fun X ↦ ¬ M.Spanning (M.E \ X)) K := by
-  convert isCocircuit_iff_minimal with K
+  convert! isCocircuit_iff_minimal with K
   rw [spanning_iff_exists_isBase_subset]
   simp_rw [not_exists, subset_diff, not_and, not_disjoint_iff_nonempty_inter, ← and_imp,
     and_iff_left_of_imp IsBase.subset_ground, inter_comm K]
diff --git a/Mathlib/Combinatorics/Matroid/Closure.lean b/Mathlib/Combinatorics/Matroid/Closure.lean
index f9ab0a7f0b2ace..994aa22251fe46 100644
--- a/Mathlib/Combinatorics/Matroid/Closure.lean
+++ b/Mathlib/Combinatorics/Matroid/Closure.lean
@@ -106,7 +106,7 @@ lemma IsFlat.iInter {ι : Type*} [Nonempty ι] {Fs : ι → Set α}
     (iInter_subset _ (Classical.arbitrary _)).trans (hFs _).subset_ground⟩
   obtain ⟨J, hIJ, hJ⟩ := hI.indep.subset_isBasis_of_subset (hI.subset.trans (iInter_subset _ i))
   refine subset_union_right.trans ((hFs i).1 (X := Fs i ∪ X) hIJ ?_)
-  convert hIJ.isBasis_union (hIX.isBasis_union_of_subset hIJ.indep hJ) using 1
+  convert! hIJ.isBasis_union (hIX.isBasis_union_of_subset hIJ.indep hJ) using 1
   rw [← union_assoc, union_eq_self_of_subset_right hIJ.subset]
 
 /-- The property of being a flat gives rise to a `ClosureOperator` on the subsets of `M.E`,
@@ -118,7 +118,7 @@ def subtypeClosure (M : Matroid α) : ClosureOperator (Iic M.E) :=
     obtain (rfl | hne) := s.eq_empty_or_nonempty
     · simp
     have _ := hne.coe_sort
-    convert IsFlat.iInter (M := M) (Fs := fun (F : s) ↦ F.1.1) (fun F ↦ hs F.1 F.2)
+    convert! IsFlat.iInter (M := M) (Fs := fun (F : s) ↦ F.1.1) (fun F ↦ hs F.1 F.2)
     ext
     aesop
 
@@ -243,7 +243,7 @@ lemma mem_ground_of_mem_closure (he : e ∈ M.closure X) : e ∈ M.E :=
 lemma closure_iUnion_closure_eq_closure_iUnion (M : Matroid α) (Xs : ι → Set α) :
     M.closure (⋃ i, M.closure (Xs i)) = M.closure (⋃ i, Xs i) := by
   simp_rw [closure_eq_subtypeClosure, iUnion_inter, Subtype.coe_inj]
-  convert M.subtypeClosure.closure_iSup_closure (fun i ↦ ⟨Xs i ∩ M.E, inter_subset_right⟩) <;>
+  convert! M.subtypeClosure.closure_iSup_closure (fun i ↦ ⟨Xs i ∩ M.E, inter_subset_right⟩) <;>
   simp [← iUnion_inter, subtypeClosure]
 
 lemma closure_iUnion_congr (Xs Ys : ι → Set α) (h : ∀ i, M.closure (Xs i) = M.closure (Ys i)) :
@@ -489,8 +489,9 @@ lemma Indep.closure_sInter_eq_biInter_closure_of_forall_subset {Js : Set (Set α
 
 lemma closure_iInter_eq_iInter_closure_of_iUnion_indep [hι : Nonempty ι] (Is : ι → Set α)
     (h : M.Indep (⋃ i, Is i)) : M.closure (⋂ i, Is i) = (⋂ i, M.closure (Is i)) := by
-  convert h.closure_sInter_eq_biInter_closure_of_forall_subset (range_nonempty Is)
-    (by simp [subset_iUnion])
+  convert!
+    h.closure_sInter_eq_biInter_closure_of_forall_subset (range_nonempty Is)
+      (by simp [subset_iUnion])
   simp
 
 lemma closure_sInter_eq_biInter_closure_of_sUnion_indep (Is : Set (Set α)) (hIs : Is.Nonempty)
@@ -501,7 +502,7 @@ lemma closure_biInter_eq_biInter_closure_of_biUnion_indep {ι : Type*} {A : Set
     {I : ι → Set α} (h : M.Indep (⋃ i ∈ A, I i)) :
     M.closure (⋂ i ∈ A, I i) = ⋂ i ∈ A, M.closure (I i) := by
   have := hA.coe_sort
-  convert closure_iInter_eq_iInter_closure_of_iUnion_indep (Is := fun i : A ↦ I i) (by simpa) <;>
+  convert! closure_iInter_eq_iInter_closure_of_iUnion_indep (Is := fun i : A ↦ I i) (by simpa) <;>
   simp
 
 lemma Indep.closure_iInter_eq_biInter_closure_of_forall_subset [Nonempty ι] {Js : ι → Set α}
@@ -525,8 +526,9 @@ lemma Indep.inter_isBasis_biInter {ι : Type*} (hI : M.Indep I) {X : ι → Set
 
 lemma Indep.inter_isBasis_iInter [Nonempty ι] {X : ι → Set α} (hI : M.Indep I)
     (h : ∀ i, M.IsBasis ((X i) ∩ I) (X i)) : M.IsBasis ((⋂ i, X i) ∩ I) (⋂ i, X i) := by
-  convert hI.inter_isBasis_biInter (ι := PLift ι) univ_nonempty (X := fun i ↦ X i.down)
-    (by simpa using fun (i : PLift ι) ↦ h i.down) <;>
+  convert!
+    hI.inter_isBasis_biInter (ι := PLift ι) univ_nonempty (X := fun i ↦ X i.down)
+      (by simpa using fun (i : PLift ι) ↦ h i.down) <;>
   · simp only [mem_univ, iInter_true]
     exact (iInter_plift_down X).symm
 
@@ -596,7 +598,7 @@ lemma indep_iff_forall_notMem_closure_diff (hI : I ⊆ M.E := by aesop_mat) :
   use fun h e heI he ↦ ((h.closure_inter_eq_self_of_subset diff_subset).subset ⟨he, heI⟩).2 rfl
   intro h
   obtain ⟨J, hJ⟩ := M.exists_isBasis I
-  convert hJ.indep
+  convert! hJ.indep
   refine hJ.subset.antisymm' (fun e he ↦ by_contra fun heJ ↦ h he ?_)
   exact mem_of_mem_of_subset
     (hJ.subset_closure he) (M.closure_subset_closure (subset_diff_singleton hJ.subset heJ))
diff --git a/Mathlib/Combinatorics/Matroid/Dual.lean b/Mathlib/Combinatorics/Matroid/Dual.lean
index 4acdb3ebb8692e..fea37ed95c0f65 100644
--- a/Mathlib/Combinatorics/Matroid/Dual.lean
+++ b/Mathlib/Combinatorics/Matroid/Dual.lean
@@ -61,7 +61,7 @@ section dual
     rw [← compl_subset_compl, ← hIB.sdiff_eq_right, ← union_diff_distrib, diff_eq, compl_inter,
       compl_compl, union_subset_iff, compl_subset_compl] at hB''₂
     have hssu := (subset_inter (hB''₂.2) hIE).ssubset_of_ne
-      (by { rintro rfl; apply hI; convert hB''; simp [hB''.subset_ground] })
+      (by { rintro rfl; apply hI; convert! hB''; simp [hB''.subset_ground] })
     obtain ⟨e, ⟨(heB'' : e ∉ _), heE⟩, heI⟩ := exists_of_ssubset hssu
     use e
     simp_rw [mem_diff, insert_subset_iff, and_iff_left heI, and_iff_right heE, and_iff_right hIE]
diff --git a/Mathlib/Combinatorics/Matroid/Loop.lean b/Mathlib/Combinatorics/Matroid/Loop.lean
index bd9db75e142659..97b1e55756a990 100644
--- a/Mathlib/Combinatorics/Matroid/Loop.lean
+++ b/Mathlib/Combinatorics/Matroid/Loop.lean
@@ -365,7 +365,7 @@ lemma IsNonloop.isNonloop_of_mem_closure (he : M.IsNonloop e) (hef : e ∈ M.clo
     M.IsNonloop f := by
   rw [isNonloop_iff, and_comm]
   by_contra! h; apply he.not_isLoop
-  rw [isLoop_iff] at *; convert hef using 1
+  rw [isLoop_iff] at *; convert! hef using 1
   obtain (hf | hf) := em (f ∈ M.E)
   · rw [← closure_loops, ← insert_eq_of_mem (h hf), closure_insert_congr_right M.closure_loops,
       insert_empty_eq]
diff --git a/Mathlib/Combinatorics/Matroid/Sum.lean b/Mathlib/Combinatorics/Matroid/Sum.lean
index b933c19b6905e5..02ed7cc23695e2 100644
--- a/Mathlib/Combinatorics/Matroid/Sum.lean
+++ b/Mathlib/Combinatorics/Matroid/Sum.lean
@@ -143,7 +143,7 @@ lemma Finitary.sigma (h : ∀ i, (M i).Finitary) : (Matroid.sigma M).Finitary :=
   intro i
   apply indep_of_forall_finite_subset_indep
   intro J hJI hJ
-  convert hI (Sigma.mk i '' J) (by simpa) (hJ.image _) i
+  convert! hI (Sigma.mk i '' J) (by simpa) (hJ.image _) i
   rw [sigma_mk_preimage_image_eq_self]
 
 end Sigma
@@ -160,7 +160,7 @@ protected def sum' (M : ι → Matroid α) : Matroid (ι × α) :=
 @[simp] lemma sum'_indep_iff {I} :
     (Matroid.sum' M).Indep I ↔ ∀ i, (M i).Indep (Prod.mk i ⁻¹' I) := by
   simp only [Matroid.sum', mapEquiv_indep_iff, Equiv.sigmaEquivProd_symm_apply, sigma_indep_iff]
-  convert Iff.rfl
+  convert! Iff.rfl
   ext
   simp
 
@@ -172,14 +172,14 @@ protected def sum' (M : ι → Matroid α) : Matroid (ι × α) :=
 @[simp] lemma sum'_isBase_iff {B} :
     (Matroid.sum' M).IsBase B ↔ ∀ i, (M i).IsBase (Prod.mk i ⁻¹' B) := by
   simp only [Matroid.sum', mapEquiv_isBase_iff, Equiv.sigmaEquivProd_symm_apply, sigma_isBase_iff]
-  convert Iff.rfl
+  convert! Iff.rfl
   ext
   simp
 
 @[simp] lemma sum'_isBasis_iff {I X} :
     (Matroid.sum' M).IsBasis I X ↔ ∀ i, (M i).IsBasis (Prod.mk i ⁻¹' I) (Prod.mk i ⁻¹' X) := by
   simp only [Matroid.sum', mapEquiv_isBasis_iff, Equiv.sigmaEquivProd_symm_apply, sigma_isBasis_iff]
-  convert Iff.rfl <;>
+  convert! Iff.rfl <;>
   exact ext <| by simp
 
 lemma Finitary.sum' (h : ∀ i, (M i).Finitary) : (Matroid.sum' M).Finitary := by
@@ -242,7 +242,7 @@ set_option backward.isDefEq.respectTransparency false in
     (M.sum N).Indep I ↔ M.Indep (.inl ⁻¹' I) ∧ N.Indep (.inr ⁻¹' I) := by
   simp only [Matroid.sum, mapEquiv_indep_iff, Equiv.sumCongr_symm, Equiv.sumCongr_apply,
     Equiv.symm_symm, sigma_indep_iff, Bool.forall_bool]
-  convert Iff.rfl <;>
+  convert! Iff.rfl <;>
     simp [Set.ext_iff, Equiv.ulift, Equiv.sumEquivSigmaBool]
 
 set_option backward.isDefEq.respectTransparency false in
@@ -250,7 +250,7 @@ set_option backward.isDefEq.respectTransparency false in
     (M.sum N).IsBase B ↔ M.IsBase (.inl ⁻¹' B) ∧ N.IsBase (.inr ⁻¹' B) := by
   simp only [Matroid.sum, mapEquiv_isBase_iff, Equiv.sumCongr_symm, Equiv.sumCongr_apply,
     Equiv.symm_symm, sigma_isBase_iff, Bool.forall_bool]
-  convert Iff.rfl <;>
+  convert! Iff.rfl <;>
     simp [Set.ext_iff, Equiv.ulift, Equiv.sumEquivSigmaBool]
 
 set_option backward.isDefEq.respectTransparency false in
@@ -260,7 +260,7 @@ set_option backward.isDefEq.respectTransparency false in
   simp only [Matroid.sum, mapEquiv_isBasis_iff, Equiv.sumCongr_symm,
     Equiv.sumCongr_apply, Equiv.symm_symm, sigma_isBasis_iff, Bool.forall_bool,
     Equiv.sumEquivSigmaBool, Equiv.coe_fn_mk, Equiv.ulift]
-  convert Iff.rfl <;> exact ext <| by simp
+  convert! Iff.rfl <;> exact ext <| by simp
 
 end Sum
 
diff --git a/Mathlib/Combinatorics/Nullstellensatz.lean b/Mathlib/Combinatorics/Nullstellensatz.lean
index 12ebec3ddbbb7c..ab6494d1647864 100644
--- a/Mathlib/Combinatorics/Nullstellensatz.lean
+++ b/Mathlib/Combinatorics/Nullstellensatz.lean
@@ -78,14 +78,14 @@ theorem eq_zero_of_eval_zero_at_prod_finset {σ : Type*} [Finite σ] [IsDomain R
     apply h _ (fun i ↦ S (e i))
     · intro i
       classical
-      convert Hdeg (e i)
+      convert! Hdeg (e i)
       conv_lhs => rw [← e.symm_apply_apply i, degreeOf_rename_of_injective e.symm.injective]
     · intro x hx
       simp only [MvPolynomial.eval_rename]
       apply Heval
       intro s
       simp only [Function.comp_apply]
-      convert hx (e.symm s)
+      convert! hx (e.symm s)
       simp only [Equiv.apply_symm_apply]
   | h_empty =>
     suffices P = C (constantCoeff P) by
@@ -111,7 +111,7 @@ theorem eq_zero_of_eval_zero_at_prod_finset {σ : Type*} [Finite σ] [IsDomain R
         intro d hd
         simp only [hQ]
         rw [MvPolynomial.coeff_eval_eq_eval_coeff]
-        convert map_zero (MvPolynomial.eval x)
+        convert! map_zero (MvPolynomial.eval x)
         ext m
         simp only [coeff_zero]
         set n := (embDomain Function.Embedding.some m).update none d with hn
@@ -121,7 +121,7 @@ theorem eq_zero_of_eval_zero_at_prod_finset {σ : Type*} [Finite σ] [IsDomain R
         apply not_le.mpr hd
         rw [MvPolynomial.degreeOf_eq_sup]
         rw [← ne_eq, ← MvPolynomial.mem_support_iff] at hm
-        convert Finset.le_sup hm
+        convert! Finset.le_sup hm
         exact hn.1.symm
     ext m d
     simp only [Polynomial.coeff_zero, coeff_zero]
@@ -135,7 +135,7 @@ theorem eq_zero_of_eval_zero_at_prod_finset {σ : Type*} [Finite σ] [IsDomain R
       rw [eq_option_embedding_update_none_iff] at hn
       rw [hQ, ← hn.1, ← hn.2, optionEquivLeft_coeff_some_coeff_none, ← ne_eq,
         ← MvPolynomial.mem_support_iff] at he
-      convert Finset.le_sup he
+      convert! Finset.le_sup he
       rw [← hn.2, some_apply]
     · intro x hx
       specialize Heval' x hx
@@ -185,7 +185,7 @@ private lemma Alon.of_mem_P_support {ι : Type*} (i : ι) (S : Finset R) (m : ι
     rw [← Alon.degree_P]
     apply MonomialOrder.le_degree
     rw [mem_support_iff]
-    convert he
+    convert! he
   · rw [← hm]
     ext j
     by_cases hj : j = i
@@ -227,7 +227,7 @@ theorem combinatorial_nullstellensatz_exists_linearCombination
       linearCombination_apply, map_finsuppSum, Finsupp.sum, Finset.sum_eq_zero]
     intro i _
     rw [smul_eq_mul, map_mul]
-    convert mul_zero _
+    convert! mul_zero _
     rw [Alon.P, _root_.map_prod]
     apply Finset.prod_eq_zero (hx i)
     simp
diff --git a/Mathlib/Combinatorics/Optimization/ValuedCSP.lean b/Mathlib/Combinatorics/Optimization/ValuedCSP.lean
index da549dbbd49756..851c04232349f7 100644
--- a/Mathlib/Combinatorics/Optimization/ValuedCSP.lean
+++ b/Mathlib/Combinatorics/Optimization/ValuedCSP.lean
@@ -147,7 +147,7 @@ lemma Function.HasMaxCutPropertyAt.rows_lt_aux {C : Type*} [PartialOrder C]
   apply asymm
   obtain ⟨o, in_omega, rfl⟩ := rin
   change o (fun j => ![![a, b], ![b, a]] j 0) = o (fun j => ![![a, b], ![b, a]] j 1)
-  convert symmega ![a, b] ![b, a] (by simp [List.Perm.swap]) o in_omega using 2 <;>
+  convert! symmega ![a, b] ![b, a] (by simp [List.Perm.swap]) o in_omega using 2 <;>
     simp [Matrix.const_fin1_eq]
 
 variable {C : Type*} [AddCommMonoid C] [PartialOrder C] [IsOrderedCancelAddMonoid C]
@@ -177,7 +177,7 @@ lemma Function.HasMaxCutProperty.forbids_commutativeFractionalPolymorphism
     rw [two_nsmul, two_nsmul]
     exact add_lt_add half_sharp half_sharp
   have impos : 2 • (ω.map (fun _ => f ![a, b])).sum < ω.size • 2 • f ![a, b] := by
-    convert lt_of_lt_of_le sharp contr
+    convert! lt_of_lt_of_le sharp contr
     simp [FractionalOperation.tt, Multiset.map_map]
   have rhs_swap : ω.size • 2 • f ![a, b] = 2 • ω.size • f ![a, b] := nsmul_left_comm ..
   have distrib : (ω.map (fun _ => f ![a, b])).sum = ω.size • f ![a, b] := by simp
diff --git a/Mathlib/Combinatorics/SetFamily/AhlswedeZhang.lean b/Mathlib/Combinatorics/SetFamily/AhlswedeZhang.lean
index 37c2b8e97c20de..ac0a357e9bf3c3 100644
--- a/Mathlib/Combinatorics/SetFamily/AhlswedeZhang.lean
+++ b/Mathlib/Combinatorics/SetFamily/AhlswedeZhang.lean
@@ -96,7 +96,7 @@ private lemma Fintype.sum_div_mul_card_choose_card :
     rw [div_mul_cancel_right₀]
     exact cast_ne_zero.2 (choose_pos <| mem_range_succ_iff.1 hn).ne'
   simp only [Finset.sum_congr rfl this, mul_eq_mul_left_iff, cast_eq_zero]
-  convert Or.inl <| sum_range_reflect _ _ with a ha
+  convert! Or.inl <| sum_range_reflect _ _ with a ha
   rw [add_tsub_cancel_right, cast_sub (mem_range_succ_iff.mp ha)]
 
 end
diff --git a/Mathlib/Combinatorics/SetFamily/Compression/UV.lean b/Mathlib/Combinatorics/SetFamily/Compression/UV.lean
index 848a7b3c229c78..b7e413d1b0b399 100644
--- a/Mathlib/Combinatorics/SetFamily/Compression/UV.lean
+++ b/Mathlib/Combinatorics/SetFamily/Compression/UV.lean
@@ -349,7 +349,7 @@ theorem shadow_compression_subset_compression_shadow (u v : Finset α)
       rw [union_sdiff_distrib, ‹v \ u = v›]
       exact (erase_subset _ _).trans subset_union_right
     -- and then arguing that it's the same
-    convert this using 1
+    convert! this using 1
     rw [sdiff_union_erase_cancel (hus.trans subset_union_left) ‹x ∈ u›, erase_union_distrib,
       erase_insert ‹x ∉ s›, erase_eq_of_notMem ‹x ∉ v›, sdiff_erase (mem_union_right _ hyv),
       union_sdiff_cancel_right hsv]
@@ -375,7 +375,7 @@ theorem shadow_compression_subset_compression_shadow (u v : Finset α)
       refine sup_sdiff_mem_of_mem_compression (by rwa [hxy.eq]) ((erase_subset _ _).trans ‹_›) ?_
       rw [← sdiff_erase (mem_union_left _ <| hus hwu)]
       exact disjoint_sdiff
-    convert this using 1
+    convert! this using 1
     rw [insert_union_comm, insert_erase ‹w ∈ u›,
       sdiff_union_of_subset (hus.trans subset_union_left),
       sdiff_erase (mem_union_right _ ‹z ∈ v›), union_sdiff_cancel_right hsv]
@@ -385,7 +385,7 @@ theorem shadow_compression_subset_compression_shadow (u v : Finset α)
   have : (insert w ((s ∪ v) \ u) ∪ u) \ v ∈ 𝒜 :=
     sup_sdiff_mem_of_mem_compression ‹insert w ((s ∪ v) \ u) ∈ 𝒜'› ‹_›
       (disjoint_insert_right.2 ⟨‹_›, disjoint_sdiff⟩)
-  convert this using 1
+  convert! this using 1
   rw [insert_union, sdiff_union_of_subset (hus.trans subset_union_left),
     insert_sdiff_of_notMem _ (hwu ∘ hwB ∘ mem_union_right _), union_sdiff_cancel_right hsv]
 
diff --git a/Mathlib/Combinatorics/SetFamily/KruskalKatona.lean b/Mathlib/Combinatorics/SetFamily/KruskalKatona.lean
index f388fc0bfd201e..90c8e76eee6c17 100644
--- a/Mathlib/Combinatorics/SetFamily/KruskalKatona.lean
+++ b/Mathlib/Combinatorics/SetFamily/KruskalKatona.lean
@@ -290,7 +290,7 @@ theorem iterated_kk (h₁ : (𝒜 : Set (Finset (Fin n))).Sized r) (h₂ : #𝒞
   | zero => simpa
   | succ _ ih =>
     refine ih h₁.shadow (kruskal_katona h₁ h₂ h₃) ?_
-    convert h₃.shadow
+    convert! h₃.shadow
 
 /-- The **Lovasz formulation of the Kruskal-Katona theorem**.
 
@@ -350,7 +350,7 @@ theorem erdos_ko_rado {𝒜 : Finset (Finset (Fin n))} {r : ℕ}
     #𝒜 ≤ (n - 1).choose (r - 1) := by
   -- Take care of the r=0 case first: it's not very interesting.
   rcases Nat.eq_zero_or_pos r with b | h1r
-  · convert Nat.zero_le _
+  · convert! Nat.zero_le _
     rw [Finset.card_eq_zero, eq_empty_iff_forall_notMem]
     refine fun A HA ↦ h𝒜 HA HA ?_
     rw [disjoint_self_iff_empty, ← Finset.card_eq_zero, ← b]
@@ -377,15 +377,15 @@ theorem erdos_ko_rado {𝒜 : Finset (Finset (Fin n))} {r : ℕ}
   -- But this gives a contradiction: `n choose r < |𝒜| + |∂^[n-2k] 𝒜ᶜˢ|`
   have := calc
     n.choose r = (n - 1).choose (r - 1) + (n - 1).choose r := by
-      convert Nat.choose_succ_succ _ _ using 3 <;> rwa [Nat.sub_one, Nat.succ_pred_eq_of_pos]
+      convert! Nat.choose_succ_succ _ _ using 3 <;> rwa [Nat.sub_one, Nat.succ_pred_eq_of_pos]
     _ < #𝒜 + #(∂^[n - 2 * r] 𝒜ᶜˢ) := add_lt_add_of_lt_of_le size kk
     _ = #(𝒜 ∪ ∂^[n - 2 * r] 𝒜ᶜˢ) := by rw [card_union_of_disjoint ‹_›]
   apply this.not_ge
-  convert Set.Sized.card_le _
+  convert! Set.Sized.card_le _
   · rw [Fintype.card_fin]
   rw [coe_union, Set.sized_union]
   refine ⟨‹_›, ?_⟩
-  convert h𝒜bar.shadow_iterate
+  convert! h𝒜bar.shadow_iterate
   lia
 
 end Finset
diff --git a/Mathlib/Combinatorics/SetFamily/LYM.lean b/Mathlib/Combinatorics/SetFamily/LYM.lean
index 0f52fe96b02566..86cefa4a22f52c 100644
--- a/Mathlib/Combinatorics/SetFamily/LYM.lean
+++ b/Mathlib/Combinatorics/SetFamily/LYM.lean
@@ -102,7 +102,7 @@ theorem local_lubell_yamamoto_meshalkin_inequality_div (hr : r ≠ 0)
     · exact (hr rfl).elim
     rw [tsub_add_eq_add_tsub hr', add_tsub_add_eq_tsub_right] at h𝒜
     apply le_of_mul_le_mul_right _ (pos_iff_ne_zero.2 hr)
-    convert Nat.mul_le_mul_right ((Fintype.card α).choose r) h𝒜 using 1
+    convert! Nat.mul_le_mul_right ((Fintype.card α).choose r) h𝒜 using 1
     · simpa [mul_assoc, Nat.choose_succ_right_eq] using Or.inl (mul_comm _ _)
     · simp only [mul_assoc, choose_succ_right_eq, mul_eq_mul_left_iff]
       exact Or.inl (mul_comm _ _)
diff --git a/Mathlib/Combinatorics/SimpleGraph/Acyclic.lean b/Mathlib/Combinatorics/SimpleGraph/Acyclic.lean
index 8f7c72399e7c9a..e53b18581cdde3 100644
--- a/Mathlib/Combinatorics/SimpleGraph/Acyclic.lean
+++ b/Mathlib/Combinatorics/SimpleGraph/Acyclic.lean
@@ -412,7 +412,7 @@ theorem isAcyclic_sup_fromEdgeSet_iff {u v : V} :
   refine ⟨?_, fun ⟨hacyc, hreach⟩ ↦ hacyc.sup_edge_of_not_reachable <| by grind⟩
   refine fun hacyc ↦ ⟨hacyc.anti le_sup_left, fun hreach ↦ False.elim ?_⟩
   refine (isAcyclic_iff_forall_edge_isBridge.mp (e := s(u, v)) hacyc <| by simp [huv]).right ?_
-  convert hreach
+  convert! hreach
   simpa [deleteEdges_sup]
 
 /--
diff --git a/Mathlib/Combinatorics/SimpleGraph/Clique.lean b/Mathlib/Combinatorics/SimpleGraph/Clique.lean
index 6d5c164b94a8c6..34acf09b319b6f 100644
--- a/Mathlib/Combinatorics/SimpleGraph/Clique.lean
+++ b/Mathlib/Combinatorics/SimpleGraph/Clique.lean
@@ -483,7 +483,7 @@ protected theorem CliqueFree.replaceVertex [DecidableEq α] (h : G.CliqueFree n)
       refine Embedding.isContained ⟨φ.setValue x s, fun {a b} ↦ ?_⟩
       simp only [Embedding.coeFn_mk, Embedding.setValue, not_exists.mp ms, ite_false]
       rw [apply_ite (G.Adj · _), apply_ite (G.Adj _ ·), apply_ite (G.Adj _ ·)]
-      convert @hφ a b <;> simp only [← φ.apply_eq_iff_eq, SimpleGraph.irrefl, hx]
+      convert! @hφ a b <;> simp only [← φ.apply_eq_iff_eq, SimpleGraph.irrefl, hx]
   · refine Embedding.isContained ⟨φ, ?_⟩
     simp_rw [Set.mem_range, not_exists, ← ne_eq] at mt
     conv at hφ => enter [a, b]; rw [G.adj_replaceVertex_iff_of_ne _ (mt a) (mt b)]
diff --git a/Mathlib/Combinatorics/SimpleGraph/Coloring/VertexColoring.lean b/Mathlib/Combinatorics/SimpleGraph/Coloring/VertexColoring.lean
index d1588303b375c5..2de5c1f3f9d3a8 100644
--- a/Mathlib/Combinatorics/SimpleGraph/Coloring/VertexColoring.lean
+++ b/Mathlib/Combinatorics/SimpleGraph/Coloring/VertexColoring.lean
@@ -115,7 +115,7 @@ theorem Coloring.colorClasses_finite [Finite α] : C.colorClasses.Finite :=
 theorem Coloring.card_colorClasses_le [Fintype α] [Fintype C.colorClasses] :
     Fintype.card C.colorClasses ≤ Fintype.card α := by
   simp only [colorClasses]
-  convert Setoid.card_classes_ker_le C
+  convert! Setoid.card_classes_ker_le C
 
 theorem Coloring.not_adj_of_mem_colorClass {c : α} {v w : V} (hv : v ∈ C.colorClass c)
     (hw : w ∈ C.colorClass c) : ¬G.Adj v w := fun h => C.valid h (Eq.trans hv (Eq.symm hw))
diff --git a/Mathlib/Combinatorics/SimpleGraph/Connectivity/Connected.lean b/Mathlib/Combinatorics/SimpleGraph/Connectivity/Connected.lean
index d944916d38021b..f045486e9a2d6b 100644
--- a/Mathlib/Combinatorics/SimpleGraph/Connectivity/Connected.lean
+++ b/Mathlib/Combinatorics/SimpleGraph/Connectivity/Connected.lean
@@ -709,7 +709,7 @@ def homOfConnectedComponents (G : SimpleGraph V) {H : SimpleGraph V'}
   map_rel' := fun hab ↦ by
     have h : (G.connectedComponentMk _).toSimpleGraph.Adj ⟨_, rfl⟩
         ⟨_, ((G.connectedComponentMk _).mem_supp_congr_adj hab).1 rfl⟩ := by simpa using hab
-    convert (C (G.connectedComponentMk _)).map_rel h using 3 <;>
+    convert! (C (G.connectedComponentMk _)).map_rel h using 3 <;>
       rw [ConnectedComponent.connectedComponentMk_eq_of_adj hab]
 
 -- TODO: Extract as lemma about general equivalence relation
@@ -952,7 +952,7 @@ lemma Preconnected.induce_of_degree_eq_one (hG : G.Preconnected) {s : Set V}
   rintro ⟨u, hu⟩ ⟨v, hv⟩
   obtain ⟨p, hp⟩ := hG.exists_isPath u v
   constructor
-  convert p.induce s _
+  convert! p.induce s _
   rintro w hwp
   by_contra hws
   exact hp.not_mem_support_of_subsingleton_neighborSet (by grind) (by grind) (hs _ hws) hwp
diff --git a/Mathlib/Combinatorics/SimpleGraph/Connectivity/Subgraph.lean b/Mathlib/Combinatorics/SimpleGraph/Connectivity/Subgraph.lean
index 5cad961fe793a5..142079f0bae4b8 100644
--- a/Mathlib/Combinatorics/SimpleGraph/Connectivity/Subgraph.lean
+++ b/Mathlib/Combinatorics/SimpleGraph/Connectivity/Subgraph.lean
@@ -257,7 +257,7 @@ theorem finite_neighborSet_toSubgraph (p : G.Walk u v) : (p.toSubgraph.neighborS
 
 lemma toSubgraph_le_induce_support (p : G.Walk u v) :
     p.toSubgraph ≤ (⊤ : G.Subgraph).induce {v | v ∈ p.support} := by
-  convert Subgraph.le_induce_top_verts
+  convert! Subgraph.le_induce_top_verts
   exact p.verts_toSubgraph.symm
 
 theorem toSubgraph_adj_getVert {u v} (w : G.Walk u v) {i : ℕ} (hi : i < w.length) :
diff --git a/Mathlib/Combinatorics/SimpleGraph/Copy.lean b/Mathlib/Combinatorics/SimpleGraph/Copy.lean
index f3662614ba254e..f922c88f5216b8 100644
--- a/Mathlib/Combinatorics/SimpleGraph/Copy.lean
+++ b/Mathlib/Combinatorics/SimpleGraph/Copy.lean
@@ -482,7 +482,7 @@ noncomputable def labelledCopyCount (G : SimpleGraph V) (H : SimpleGraph W) : 
 
 @[simp] lemma labelledCopyCount_of_isEmpty [IsEmpty W] (G : SimpleGraph V) (H : SimpleGraph W) :
     G.labelledCopyCount H = 1 := by
-  convert Fintype.card_unique
+  convert! Fintype.card_unique
   exact { default := ⟨default, isEmptyElim⟩, uniq := fun _ ↦ Subsingleton.elim _ _ }
 
 @[simp] lemma labelledCopyCount_eq_zero : G.labelledCopyCount H = 0 ↔ H.Free G := by
@@ -524,11 +524,12 @@ lemma copyCount_le_labelledCopyCount [Fintype W] : G.copyCount H ≤ G.labelledC
 @[simp] lemma copyCount_bot (G : SimpleGraph V) : copyCount G (⊥ : SimpleGraph V) = 1 := by
   classical
   rw [copyCount]
-  convert card_singleton (α := G.Subgraph)
-    { verts := .univ
-      Adj := ⊥
-      adj_sub := False.elim
-      edge_vert := False.elim }
+  convert!
+    card_singleton (α := G.Subgraph)
+      { verts := .univ
+        Adj := ⊥
+        adj_sub := False.elim
+        edge_vert := False.elim }
   simp only [eq_singleton_iff_unique_mem, mem_filter_univ, Nonempty.forall]
   refine ⟨⟨⟨(Equiv.Set.univ _).symm, by simp⟩⟩, fun H' e ↦
     Subgraph.ext ((set_fintype_card_eq_univ_iff _).1 <| Fintype.card_congr e.toEquiv.symm) ?_⟩
diff --git a/Mathlib/Combinatorics/SimpleGraph/Dart.lean b/Mathlib/Combinatorics/SimpleGraph/Dart.lean
index 96be6e8b7b3875..651455db64474c 100644
--- a/Mathlib/Combinatorics/SimpleGraph/Dart.lean
+++ b/Mathlib/Combinatorics/SimpleGraph/Dart.lean
@@ -130,7 +130,7 @@ theorem dartOfNeighborSet_injective (v : V) : Function.Injective (G.dartOfNeighb
   fun e₁ e₂ h =>
   Subtype.ext <| by
     injection h with h'
-    convert congr_arg Prod.snd h'
+    convert! congr_arg Prod.snd h'
 
 instance nonempty_dart_top [Nontrivial V] : Nonempty (⊤ : SimpleGraph V).Dart := by
   obtain ⟨v, w, h⟩ := exists_pair_ne V
diff --git a/Mathlib/Combinatorics/SimpleGraph/DegreeSum.lean b/Mathlib/Combinatorics/SimpleGraph/DegreeSum.lean
index abfa2203d1a863..3b62bb027300c8 100644
--- a/Mathlib/Combinatorics/SimpleGraph/DegreeSum.lean
+++ b/Mathlib/Combinatorics/SimpleGraph/DegreeSum.lean
@@ -82,7 +82,7 @@ theorem dart_edge_fiber_card [DecidableEq V] (e : Sym2 V) (h : e ∈ G.edgeSet)
     #{d : G.Dart | d.edge = e} = 2 := by
   obtain ⟨v, w⟩ := e
   let d : G.Dart := ⟨(v, w), h⟩
-  convert congr_arg card d.edge_fiber
+  convert! congr_arg card d.edge_fiber
   rw [card_insert_of_notMem, card_singleton]
   rw [mem_singleton]
   exact d.symm_ne.symm
@@ -132,7 +132,7 @@ theorem even_card_odd_degree_vertices [Fintype V] [DecidableRel G.Adj] :
     rw [sum_congr (g := fun _v ↦ (1 : ZMod 2)) rfl] at h
     · simp only [mul_one, nsmul_eq_mul, sum_const, Ne] at h
       rw [← ZMod.natCast_eq_zero_iff_even]
-      convert h
+      convert! h
       exact ZMod.natCast_ne_zero_iff_odd.symm
     · intro v
       rw [mem_filter_univ, Ne, ZMod.natCast_eq_zero_iff_even, ZMod.natCast_eq_one_iff_odd,
diff --git a/Mathlib/Combinatorics/SimpleGraph/Extremal/Basic.lean b/Mathlib/Combinatorics/SimpleGraph/Extremal/Basic.lean
index a7fcb5c636b9a2..2bca2d3849bbfc 100644
--- a/Mathlib/Combinatorics/SimpleGraph/Extremal/Basic.lean
+++ b/Mathlib/Combinatorics/SimpleGraph/Extremal/Basic.lean
@@ -52,7 +52,7 @@ theorem exists_isExtremal_iff_exists (p : SimpleGraph V → Prop) :
     apply exists_max_image { G | p G } (#·.edgeFinset)
     use G, by simpa using hp
   use G', inferInstanceAs (DecidableRel G'.Adj)
-  exact ⟨by simpa using hp', fun _ _ hp ↦ by convert h _ (by simpa using hp)⟩
+  exact ⟨by simpa using hp', fun _ _ hp ↦ by convert! h _ (by simpa using hp)⟩
 
 /-- If `H` has at least one edge, then there exists an extremal `H.Free` graph. -/
 theorem exists_isExtremal_free {W : Type*} {H : SimpleGraph W} (h : H ≠ ⊥) :
@@ -96,7 +96,7 @@ theorem extremalNumber_of_fintypeCard_eq [Fintype V] (hc : card V = n) :
     rw [mem_filter, ← free_congr .refl (.map e G)]
     simpa using h
   rw [Iso.card_edgeFinset_eq (.map e G)]
-  convert @le_sup _ _ _ _ { G | H.Free G } (#·.edgeFinset) G' h'
+  convert! @le_sup _ _ _ _ {G | H.Free G} (#·.edgeFinset) G' h'
 
 variable [Fintype V] [DecidableRel G.Adj]
 
@@ -104,7 +104,7 @@ variable [Fintype V] [DecidableRel G.Adj]
 theorem card_edgeFinset_le_extremalNumber (h : H.Free G) :
     #G.edgeFinset ≤ extremalNumber (card V) H := by
   rw [extremalNumber_of_fintypeCard_eq rfl]
-  convert @le_sup _ _ _ _ { G | H.Free G } (#·.edgeFinset) G (by simpa using h)
+  convert! @le_sup _ _ _ _ {G | H.Free G} (#·.edgeFinset) G (by simpa using h)
 
 /-- If `G` has more than `extremalNumber (card V) H` edges, then `G` contains a copy of `H`. -/
 theorem IsContained.of_extremalNumber_lt_card_edgeFinset
@@ -118,7 +118,7 @@ theorem extremalNumber_le_iff (H : SimpleGraph W) (m : ℕ) :
     extremalNumber (card V) H ≤ m ↔
       ∀ ⦃G : SimpleGraph V⦄ [DecidableRel G.Adj], H.Free G → #G.edgeFinset ≤ m := by
   simp_rw [extremalNumber_of_fintypeCard_eq rfl, Finset.sup_le_iff, mem_filter_univ]
-  exact ⟨fun h _ _ h' ↦ by convert h _ h', fun h _ h' ↦ by convert h h'⟩
+  exact ⟨fun h _ _ h' ↦ by convert! h _ h', fun h _ h' ↦ by convert! h h'⟩
 
 /-- `extremalNumber (card V) H` is greater than `x` if and only if there exists a `H`-free simple
 graph `G` with more than `x` edges. -/
@@ -126,7 +126,8 @@ theorem lt_extremalNumber_iff (H : SimpleGraph W) (m : ℕ) :
     m < extremalNumber (card V) H ↔
       ∃ G : SimpleGraph V, ∃ _ : DecidableRel G.Adj, H.Free G ∧ m < #G.edgeFinset := by
   simp_rw [extremalNumber_of_fintypeCard_eq rfl, Finset.lt_sup_iff, mem_filter_univ]
-  exact ⟨fun ⟨_, h, h'⟩ ↦ ⟨_, _, h, h'⟩, fun ⟨_, _, h, h'⟩ ↦ ⟨_, h, by convert h'⟩⟩
+  exact ⟨fun ⟨_, h, h'⟩ ↦ ⟨_, _, h, h'⟩, fun ⟨_, _, h, h'⟩ ↦ ⟨_, h, by convert!
+    h'⟩⟩
 
 variable {R : Type*} [Semiring R] [LinearOrder R] [FloorSemiring R]
 
diff --git a/Mathlib/Combinatorics/SimpleGraph/Extremal/Turan.lean b/Mathlib/Combinatorics/SimpleGraph/Extremal/Turan.lean
index 3f74a28e62c4fa..40c4919868ec5d 100644
--- a/Mathlib/Combinatorics/SimpleGraph/Extremal/Turan.lean
+++ b/Mathlib/Combinatorics/SimpleGraph/Extremal/Turan.lean
@@ -190,7 +190,7 @@ lemma degree_eq_card_sub_part_card [DecidableEq V] :
       eq_tsub_of_add_eq (card_filter_add_card_filter_not _)
     _ = _ := by
       congr; ext; rw [mem_filter]
-      convert Finpartition.mem_part_ofSetoid_iff_rel.symm
+      convert! Finpartition.mem_part_ofSetoid_iff_rel.symm
       simp +instances [setoid]
 
 /-- The parts of a Turán-maximal graph form an equipartition. -/
@@ -243,8 +243,8 @@ theorem card_parts [DecidableEq V] : #h.finpartition.parts = min (card V) r := b
     exact exists_ne_map_eq_of_card_lt_of_maps_to (zc.symm ▸ l.2) fun a _ ↦
       fp.part_mem.2 (mem_univ a)
   use G ⊔ edge x y, inferInstance, cf.sup_edge x y
-  convert Nat.lt_add_one #G.edgeFinset
-  convert G.card_edgeFinset_sup_edge _ hn
+  convert! Nat.lt_add_one #G.edgeFinset
+  convert! G.card_edgeFinset_sup_edge _ hn
   rwa [h.not_adj_iff_part_eq]
 
 /-- **Turán's theorem**, forward direction.
@@ -373,7 +373,7 @@ theorem card_edgeFinset_turanGraph {n r : ℕ} :
   rcases r.eq_zero_or_pos with rfl | hr
   · rw [Nat.mod_zero, tsub_self, zero_mul, Nat.zero_div, zero_add]
     have := card_edgeFinset_top_eq_card_choose_two (V := Fin n)
-    rw [Fintype.card_fin] at this; convert this; exact turanGraph_zero
+    rw [Fintype.card_fin] at this; convert! this; exact turanGraph_zero
   · have ring₁ (n) : (n ^ 2 - (n % r) ^ 2) * (r - 1) / (2 * r) =
         n % r * (n / r) * (r - 1) + r * (r - 1) * (n / r) ^ 2 / 2 := by
       nth_rw 1 [← Nat.mod_add_div n r, Nat.sq_sub_sq, add_tsub_cancel_left,
@@ -383,7 +383,7 @@ theorem card_edgeFinset_turanGraph {n r : ℕ} :
     rcases lt_or_ge n r with h | h
     · rw [Nat.mod_eq_of_lt h, tsub_self, zero_mul, Nat.zero_div, zero_add]
       have := card_edgeFinset_top_eq_card_choose_two (V := Fin n)
-      rw [Fintype.card_fin] at this; convert this
+      rw [Fintype.card_fin] at this; convert! this
       rw [turanGraph_eq_top]; exact .inr h.le
     · let n' := n - r
       have n'r : n = n' + r := by lia
@@ -425,7 +425,7 @@ theorem CliqueFree.card_edgeFinset_le (cf : G.CliqueFree (r + 1)) :
     simp_rw [zero_tsub, mul_zero, Nat.mod_zero, Nat.div_zero, zero_add]
     exact card_edgeFinset_le_card_choose_two
   · obtain ⟨H, _, maxH⟩ := exists_isTuranMaximal (V := V) hr
-    convert maxH.2 cf
+    convert! maxH.2 cf
     rw [((isTuranMaximal_iff_nonempty_iso_turanGraph hr).mp maxH).some.card_edgeFinset_eq,
       card_edgeFinset_turanGraph]
 
diff --git a/Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean b/Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean
index 7dce7be3752083..d5732ebfe06576 100644
--- a/Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean
+++ b/Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean
@@ -95,7 +95,7 @@ theorem incMatrix_apply_eq_zero_iff : G.incMatrix R a e = 0 ↔ e ∉ G.incidenc
   simp only [incMatrix_apply, Set.indicator_apply_eq_zero, Pi.one_apply, one_ne_zero]
 
 theorem incMatrix_apply_eq_one_iff : G.incMatrix R a e = 1 ↔ e ∈ G.incidenceSet a := by
-  convert one_ne_zero.ite_eq_left_iff
+  convert! one_ne_zero.ite_eq_left_iff
   infer_instance
 
 end MulZeroOneClass
@@ -157,8 +157,8 @@ theorem incMatrix_mul_transpose_apply_of_adj (h : G.Adj a b) :
     (G.incMatrix R * (G.incMatrix R)ᵀ) a b = (1 : R) := by
   simp_rw [Matrix.mul_apply, Matrix.transpose_apply, incMatrix_apply_mul_incMatrix_apply,
     Set.indicator_apply, Pi.one_apply, sum_boole]
-  convert @Nat.cast_one R _
-  convert card_singleton s(a, b)
+  convert! @Nat.cast_one R _
+  convert! card_singleton s(a, b)
   rw [← coe_eq_singleton, coe_filter_univ]
   exact G.incidenceSet_inter_incidenceSet_of_adj h
 
diff --git a/Mathlib/Combinatorics/SimpleGraph/Maps.lean b/Mathlib/Combinatorics/SimpleGraph/Maps.lean
index ffc55e4671d0bc..7af785dbcc4cc5 100644
--- a/Mathlib/Combinatorics/SimpleGraph/Maps.lean
+++ b/Mathlib/Combinatorics/SimpleGraph/Maps.lean
@@ -652,12 +652,12 @@ def mapEdgeSet : G.edgeSet ≃ G'.edgeSet where
   left_inv := by
     rintro ⟨e, h⟩
     simp only [Hom.mapEdgeSet, RelEmbedding.toRelHom, Sym2.map_map, comp_apply, Subtype.mk.injEq]
-    convert congr_fun Sym2.map_id e
+    convert! congr_fun Sym2.map_id e
     exact RelIso.symm_apply_apply _ _
   right_inv := by
     rintro ⟨e, h⟩
     simp only [Hom.mapEdgeSet, RelEmbedding.toRelHom, Sym2.map_map, comp_apply, Subtype.mk.injEq]
-    convert congr_fun Sym2.map_id e
+    convert! congr_fun Sym2.map_id e
     exact RelIso.apply_symm_apply _ _
 
 /-- A graph isomorphism induces an equivalence of neighbor sets. -/
@@ -673,7 +673,7 @@ def mapNeighborSet (v : V) : G.neighborSet v ≃ G'.neighborSet (f v) where
 include f in
 theorem card_eq [Fintype V] [Fintype W] : Fintype.card V = Fintype.card W := by
   rw [← Fintype.ofEquiv_card f.toEquiv]
-  convert rfl
+  convert! rfl
 
 /-- Given a bijection, there is an embedding from the comapped graph into the original
 graph. -/
diff --git a/Mathlib/Combinatorics/SimpleGraph/Paths.lean b/Mathlib/Combinatorics/SimpleGraph/Paths.lean
index d9677005b6217c..d18682d5d425d0 100644
--- a/Mathlib/Combinatorics/SimpleGraph/Paths.lean
+++ b/Mathlib/Combinatorics/SimpleGraph/Paths.lean
@@ -147,7 +147,7 @@ theorem IsTrail.reverse {u v : V} (p : G.Walk u v) (h : p.IsTrail) : p.reverse.I
 theorem reverse_isTrail_iff {u v : V} (p : G.Walk u v) : p.reverse.IsTrail ↔ p.IsTrail := by
   constructor <;>
     · intro h
-      convert h.reverse _
+      convert! h.reverse _
       try rw [reverse_reverse]
 
 theorem IsTrail.of_append_left {u v w : V} {p : G.Walk u v} {q : G.Walk v w}
@@ -204,7 +204,7 @@ theorem IsPath.reverse {u v : V} {p : G.Walk u v} (h : p.IsPath) : p.reverse.IsP
 
 @[simp]
 theorem isPath_reverse_iff {u v : V} (p : G.Walk u v) : p.reverse.IsPath ↔ p.IsPath := by
-  constructor <;> intro h <;> convert h.reverse; simp
+  constructor <;> intro h <;> convert! h.reverse; simp
 
 theorem IsPath.of_append_left {u v w : V} {p : G.Walk u v} {q : G.Walk v w} :
     (p.append q).IsPath → p.IsPath := by
diff --git a/Mathlib/Combinatorics/SimpleGraph/Regularity/Chunk.lean b/Mathlib/Combinatorics/SimpleGraph/Regularity/Chunk.lean
index a73a398d68dfec..a5757901105fa7 100644
--- a/Mathlib/Combinatorics/SimpleGraph/Regularity/Chunk.lean
+++ b/Mathlib/Combinatorics/SimpleGraph/Regularity/Chunk.lean
@@ -113,8 +113,8 @@ private theorem card_nonuniformWitness_sdiff_biUnion_star (hV : V ∈ P.parts) (
     intro B hB
     unfold chunk
     split_ifs with h₁
-    · convert card_parts_equitabilise_subset_le _ (card_aux₁ h₁) hB
-    · convert card_parts_equitabilise_subset_le _ (card_aux₂ hP hU h₁) hB
+    · convert! card_parts_equitabilise_subset_le _ (card_aux₁ h₁) hB
+    · convert! card_parts_equitabilise_subset_le _ (card_aux₂ hP hU h₁) hB
   grw [sum_const, smul_eq_mul, card_filter_atomise_le_two_pow (s := U) hX,
     Finpartition.card_nonuniformWitnesses_le, filter_subset] <;> simp
 
@@ -364,12 +364,13 @@ private theorem abs_density_star_sub_density_le_eps (hPε : ↑100 ≤ ↑4 ^ #P
     (hε₁ : ε ≤ 1) {hU : U ∈ P.parts} {hV : V ∈ P.parts} (hUV' : U ≠ V) (hUV : ¬G.IsUniform ε U V) :
     |(G.edgeDensity ((star hP G ε hU V).biUnion id) ((star hP G ε hV U).biUnion id) : ℝ) -
       G.edgeDensity (G.nonuniformWitness ε U V) (G.nonuniformWitness ε V U)| ≤ ε / 5 := by
-  convert abs_edgeDensity_sub_edgeDensity_le_two_mul G.Adj
-    (biUnion_star_subset_nonuniformWitness hP G ε hU V)
-    (biUnion_star_subset_nonuniformWitness hP G ε hV U) (by sz_positivity)
-    (one_sub_eps_mul_card_nonuniformWitness_le_card_star hV hUV' hUV hPε hε₁)
-    (one_sub_eps_mul_card_nonuniformWitness_le_card_star hU hUV'.symm (fun hVU => hUV hVU.symm)
-      hPε hε₁) using 1
+  convert!
+    abs_edgeDensity_sub_edgeDensity_le_two_mul G.Adj
+      (biUnion_star_subset_nonuniformWitness hP G ε hU V)
+      (biUnion_star_subset_nonuniformWitness hP G ε hV U) (by sz_positivity)
+      (one_sub_eps_mul_card_nonuniformWitness_le_card_star hV hUV' hUV hPε hε₁)
+      (one_sub_eps_mul_card_nonuniformWitness_le_card_star hU hUV'.symm (fun hVU => hUV hVU.symm)
+        hPε hε₁) using 1
   linarith
 
 private theorem eps_le_card_star_div [Nonempty α] (hPα : #P.parts * 16 ^ #P.parts ≤ card α)
@@ -511,6 +512,6 @@ theorem edgeDensity_chunk_uniform [Nonempty α] (hPα : #P.parts * 16 ^ #P.parts
     rw [card_product, cast_mul, card_chunk (m_pos hPα).ne', card_chunk (m_pos hPα).ne', ←
       cast_mul, ← mul_pow]; norm_cast
   simp_rw [key]
-  convert sum_div_card_sq_le_sum_sq_div_card (α := ℝ)
+  convert! sum_div_card_sq_le_sum_sq_div_card (α := ℝ)
 
 end SzemerediRegularity
diff --git a/Mathlib/Combinatorics/SimpleGraph/Regularity/Uniform.lean b/Mathlib/Combinatorics/SimpleGraph/Regularity/Uniform.lean
index ab98927d895395..6c603a42151d94 100644
--- a/Mathlib/Combinatorics/SimpleGraph/Regularity/Uniform.lean
+++ b/Mathlib/Combinatorics/SimpleGraph/Regularity/Uniform.lean
@@ -347,8 +347,8 @@ lemma IsEquipartition.card_biUnion_offDiag_le (hε : 0 < ε) (hP : P.IsEquiparti
   refine (mul_le_mul_of_nonneg_left this <| by positivity).trans ?_
   suffices 1 ≤ ε / 4 * #P.parts by
     rw [mul_left_comm, ← sq]
-    convert mul_le_mul_of_nonneg_left this (mul_nonneg zero_le_two <| sq_nonneg (#A : 𝕜))
-      using 1 <;> ring
+    convert! mul_le_mul_of_nonneg_left this (mul_nonneg zero_le_two <| sq_nonneg (#A : 𝕜)) using 1
+      <;> ring
   rwa [← div_le_iff₀', one_div_div]
   positivity
 
diff --git a/Mathlib/Combinatorics/SimpleGraph/StronglyRegular.lean b/Mathlib/Combinatorics/SimpleGraph/StronglyRegular.lean
index 6e3ff1b129500f..5eade2756386cb 100644
--- a/Mathlib/Combinatorics/SimpleGraph/StronglyRegular.lean
+++ b/Mathlib/Combinatorics/SimpleGraph/StronglyRegular.lean
@@ -180,7 +180,7 @@ theorem IsSRGWith.param_eq
   letI := Classical.decEq V
   rw [← h.card, Fintype.card_pos_iff] at hn
   obtain ⟨v⟩ := hn
-  convert card_mul_eq_card_mul G.Adj (s := G.neighborFinset v) (t := Gᶜ.neighborFinset v) _ _
+  convert! card_mul_eq_card_mul G.Adj (s := G.neighborFinset v) (t := Gᶜ.neighborFinset v) _ _
   · simp [h.regular v]
   · simp [h.compl.regular v]
   · intro w hw
diff --git a/Mathlib/Combinatorics/SimpleGraph/Trails.lean b/Mathlib/Combinatorics/SimpleGraph/Trails.lean
index 6082d7b851a461..303e89003e5a02 100644
--- a/Mathlib/Combinatorics/SimpleGraph/Trails.lean
+++ b/Mathlib/Combinatorics/SimpleGraph/Trails.lean
@@ -126,7 +126,7 @@ theorem IsEulerian.edgesFinset_eq [Fintype G.edgeSet] {u v : V} {p : G.Walk u v}
 
 theorem IsEulerian.even_degree_iff {x u v : V} {p : G.Walk u v} (ht : p.IsEulerian) [Fintype V]
     [DecidableRel G.Adj] : Even (G.degree x) ↔ u ≠ v → x ≠ u ∧ x ≠ v := by
-  convert ht.isTrail.even_countP_edges_iff x
+  convert! ht.isTrail.even_countP_edges_iff x
   rw [← Multiset.coe_countP, Multiset.countP_eq_card_filter, ← card_incidenceFinset_eq_degree]
   change Multiset.card _ = _
   congr 1
diff --git a/Mathlib/Combinatorics/SimpleGraph/Triangle/Tripartite.lean b/Mathlib/Combinatorics/SimpleGraph/Triangle/Tripartite.lean
index ad30c9ad618e3b..81537b99c29372 100644
--- a/Mathlib/Combinatorics/SimpleGraph/Triangle/Tripartite.lean
+++ b/Mathlib/Combinatorics/SimpleGraph/Triangle/Tripartite.lean
@@ -241,7 +241,7 @@ lemma locallyLinear [ExplicitDisjoint t] [NoAccidental t] : (graph t).LocallyLin
   classical
   refine ⟨?_, fun x y hxy ↦ ?_⟩
   · unfold EdgeDisjointTriangles
-    convert map_toTriangle_disjoint t
+    convert! map_toTriangle_disjoint t
     rw [cliqueSet_eq_image, coe_map]
   · obtain ⟨z, hz, hxy⟩ := exists_mem_toTriangle hxy
     exact ⟨_, toTriangle_is3Clique hz, hxy⟩
diff --git a/Mathlib/Combinatorics/SimpleGraph/Walk/Basic.lean b/Mathlib/Combinatorics/SimpleGraph/Walk/Basic.lean
index ad961bcaa36987..a5290219dd659e 100644
--- a/Mathlib/Combinatorics/SimpleGraph/Walk/Basic.lean
+++ b/Mathlib/Combinatorics/SimpleGraph/Walk/Basic.lean
@@ -270,7 +270,7 @@ theorem mem_darts_iff_infix_support {u' v'} {p : G.Walk u v} (h : G.Adj u' v') :
     exact ⟨i, by grind, fun j hj ↦ by grind [fst_darts_getElem, snd_darts_getElem]⟩
   · have := h 0
     have := h 1
-    convert p.darts.getElem_mem (n := i) (by grind)
+    convert! p.darts.getElem_mem (n := i) (by grind)
       <;> grind [fst_darts_getElem, snd_darts_getElem]
 
 theorem mem_darts_iff_fst_snd_infix_support {p : G.Walk u v} {d : G.Dart} :
diff --git a/Mathlib/Combinatorics/SimpleGraph/Walk/Subwalks.lean b/Mathlib/Combinatorics/SimpleGraph/Walk/Subwalks.lean
index 9fd767ed9609e5..2b066c87d08144 100644
--- a/Mathlib/Combinatorics/SimpleGraph/Walk/Subwalks.lean
+++ b/Mathlib/Combinatorics/SimpleGraph/Walk/Subwalks.lean
@@ -157,7 +157,7 @@ theorem isSubwalk_toWalk_iff_mem_edges {p : G.Walk u v} (h : G.Adj u' v') :
   have ⟨d, hd, h⟩ := h
   rw [Dart.edge, Sym2.eq, Sym2.rel_iff'] at h
   refine h.imp (fun h ↦ ?_) (fun h ↦ ?_)
-    <;> convert hd using 2
+    <;> convert! hd using 2
     <;> exact h.symm
 
 theorem infix_support_iff_mem_edges {p : G.Walk u v} :
diff --git a/Mathlib/Combinatorics/Young/YoungDiagram.lean b/Mathlib/Combinatorics/Young/YoungDiagram.lean
index 05f06844c2d4eb..df7fa4f351b824 100644
--- a/Mathlib/Combinatorics/Young/YoungDiagram.lean
+++ b/Mathlib/Combinatorics/Young/YoungDiagram.lean
@@ -220,7 +220,7 @@ protected theorem le_of_transpose_le {μ ν : YoungDiagram} (h_le : μ.transpose
 @[simp]
 theorem transpose_le_iff {μ ν : YoungDiagram} : μ.transpose ≤ ν.transpose ↔ μ ≤ ν :=
   ⟨fun h => by
-    convert YoungDiagram.le_of_transpose_le h
+    convert! YoungDiagram.le_of_transpose_le h
     simp, fun h => by
     rw [← transpose_transpose μ] at h
     exact YoungDiagram.le_of_transpose_le h ⟩
@@ -313,7 +313,7 @@ theorem mem_col_iff {μ : YoungDiagram} {j : ℕ} {c : ℕ × ℕ} : c ∈ μ.co
 theorem mk_mem_col_iff {μ : YoungDiagram} {i j : ℕ} : (i, j) ∈ μ.col j ↔ (i, j) ∈ μ := by simp [col]
 
 protected theorem exists_notMem_col (μ : YoungDiagram) (j : ℕ) : ∃ i, (i, j) ∉ μ.cells := by
-  convert μ.transpose.exists_notMem_row j using 1
+  convert! μ.transpose.exists_notMem_row j using 1
   simp
 
 /-- Length of a column of a Young diagram -/
@@ -344,7 +344,7 @@ theorem colLen_eq_card (μ : YoungDiagram) {j : ℕ} : μ.colLen j = (μ.col j).
 
 @[gcongr, mono]
 theorem colLen_anti (μ : YoungDiagram) (j1 j2 : ℕ) (hj : j1 ≤ j2) : μ.colLen j2 ≤ μ.colLen j1 := by
-  convert μ.transpose.rowLen_anti j1 j2 hj using 1 <;> simp
+  convert! μ.transpose.rowLen_anti j1 j2 hj using 1 <;> simp
 
 end Columns
 
diff --git a/Mathlib/Computability/Ackermann.lean b/Mathlib/Computability/Ackermann.lean
index 0f467a8c10ef71..d100c4f3290f01 100644
--- a/Mathlib/Computability/Ackermann.lean
+++ b/Mathlib/Computability/Ackermann.lean
@@ -369,7 +369,7 @@ lemma eval_pappAck_step_succ (c : Code) (n) :
 
 lemma primrec_pappAck : Primrec pappAck := by
   suffices Primrec (Nat.rec Code.succ (fun _ c => pappAck.step c)) by
-    convert this using 2 with n; induction n <;> simp [pappAck, *]
+    convert! this using 2 with n; induction n <;> simp [pappAck, *]
   apply_rules [Primrec.nat_rec₁, primrec_pappAck_step.comp, Primrec.snd]
 
 @[simp]
diff --git a/Mathlib/Computability/ContextFreeGrammar.lean b/Mathlib/Computability/ContextFreeGrammar.lean
index f6142a08d7c695..d33ec96bc98206 100644
--- a/Mathlib/Computability/ContextFreeGrammar.lean
+++ b/Mathlib/Computability/ContextFreeGrammar.lean
@@ -316,7 +316,7 @@ protected lemma Derives.reverse (hg : g.Derives u v) : g.reverse.Derives u.rever
   | tail _ orig ih => exact ih.trans_produces orig.reverse
 
 lemma derives_reverse : g.reverse.Derives u.reverse v.reverse ↔ g.Derives u v :=
-  ⟨fun h ↦ by convert h.reverse <;> simp, .reverse⟩
+  ⟨fun h ↦ by convert! h.reverse <;> simp, .reverse⟩
 
 @[simp] lemma derives_reverse_comm : g.reverse.Derives u v ↔ g.Derives u.reverse v.reverse := by
   rw [iff_comm, ← derives_reverse, List.reverse_reverse, List.reverse_reverse]
diff --git a/Mathlib/Computability/Partrec.lean b/Mathlib/Computability/Partrec.lean
index c8363e6f90b16b..4d7662008a38d4 100644
--- a/Mathlib/Computability/Partrec.lean
+++ b/Mathlib/Computability/Partrec.lean
@@ -578,7 +578,7 @@ theorem bind_decode_iff {f : α → β → Option σ} :
 
 theorem map_decode_iff {f : α → β → σ} :
     (Computable₂ fun a n => (decode (α := β) n).map (f a)) ↔ Computable₂ f := by
-  convert (bind_decode_iff (f := fun a => Option.some ∘ f a)).trans option_some_iff
+  convert! (bind_decode_iff (f := fun a => Option.some ∘ f a)).trans option_some_iff
   apply Option.map_eq_bind
 
 theorem nat_rec {f : α → ℕ} {g : α → σ} {h : α → ℕ × σ → σ} (hf : Computable f) (hg : Computable g)
@@ -608,7 +608,7 @@ theorem option_bind {f : α → Option β} {g : α → β → Option σ} (hf : C
 
 theorem option_map {f : α → Option β} {g : α → β → σ} (hf : Computable f) (hg : Computable₂ g) :
     Computable fun a => (f a).map (g a) := by
-  convert option_bind hf (option_some.comp₂ hg)
+  convert! option_bind hf (option_some.comp₂ hg)
   apply Option.map_eq_bind
 
 theorem option_getD {f : α → Option β} {g : α → β} (hf : Computable f) (hg : Computable g) :
diff --git a/Mathlib/Computability/Primrec/Basic.lean b/Mathlib/Computability/Primrec/Basic.lean
index c1e2bc805b241a..83d9506be730ea 100644
--- a/Mathlib/Computability/Primrec/Basic.lean
+++ b/Mathlib/Computability/Primrec/Basic.lean
@@ -408,7 +408,7 @@ theorem Primrec₂.comp₂ {f : γ → δ → σ} {g : α → β → γ} {h : α
 
 protected lemma PrimrecPred.decide {p : α → Prop} [DecidablePred p] (hp : PrimrecPred p) :
     Primrec (fun a => decide (p a)) := by
-  convert hp.choose_spec
+  convert! hp.choose_spec
 
 lemma Primrec.primrecPred {p : α → Prop} [DecidablePred p]
     (hp : Primrec (fun a => decide (p a))) : PrimrecPred p :=
diff --git a/Mathlib/Computability/RE.lean b/Mathlib/Computability/RE.lean
index f27d90fdeb867f..3e5602b92a5fc6 100644
--- a/Mathlib/Computability/RE.lean
+++ b/Mathlib/Computability/RE.lean
@@ -135,7 +135,7 @@ variable {α} [Primcodable α]
 
 protected lemma ComputablePred.decide {p : α → Prop} [DecidablePred p] (hp : ComputablePred p) :
     Computable (fun a => decide (p a)) := by
-  convert hp.choose_spec
+  convert! hp.choose_spec
 
 lemma Computable.computablePred {p : α → Prop} [DecidablePred p]
     (hp : Computable (fun a => decide (p a))) : ComputablePred p :=
diff --git a/Mathlib/Computability/Reduce.lean b/Mathlib/Computability/Reduce.lean
index 475ab3a3e039e4..c7f16ff4f494d8 100644
--- a/Mathlib/Computability/Reduce.lean
+++ b/Mathlib/Computability/Reduce.lean
@@ -104,7 +104,7 @@ theorem OneOneReducible.of_equiv {α β} [Primcodable α] [Primcodable β] {e :
 
 theorem OneOneReducible.of_equiv_symm {α β} [Primcodable α] [Primcodable β] {e : α ≃ β}
     (q : β → Prop) (h : Computable e.symm) : q ≤₁ (q ∘ e) := by
-  convert OneOneReducible.of_equiv _ h; funext; simp
+  convert! OneOneReducible.of_equiv _ h; funext; simp
 
 instance stdRefl_oneOneReducible {α} [Primcodable α] : Std.Refl (@OneOneReducible α α _ _) where
   refl := oneOneReducible_refl
diff --git a/Mathlib/Computability/RegularExpressions.lean b/Mathlib/Computability/RegularExpressions.lean
index 4b3887a7e7eb32..27f759f5e87e2c 100644
--- a/Mathlib/Computability/RegularExpressions.lean
+++ b/Mathlib/Computability/RegularExpressions.lean
@@ -238,7 +238,7 @@ theorem mul_rmatch_iff (P Q : RegularExpression α) (x : List α) :
           rw [List.cons_append, List.cons_eq_cons] at h
           refine ⟨t, u, h.2, ?_, hQ⟩
           rw [rmatch] at hP
-          convert hP
+          convert! hP
           exact h.1
     · rw [ih]
       constructor <;> rintro ⟨t, u, h, hP, hQ⟩
@@ -248,7 +248,7 @@ theorem mul_rmatch_iff (P Q : RegularExpression α) (x : List α) :
         · rw [List.cons_append, List.cons_eq_cons] at h
           refine ⟨t, u, h.2, ?_, hQ⟩
           rw [rmatch] at hP
-          convert hP
+          convert! hP
           exact h.1
 
 theorem star_rmatch_iff (P : RegularExpression α) :
@@ -290,7 +290,7 @@ theorem star_rmatch_iff (P : RegularExpression α) :
           refine ⟨t, U.flatten, hsum.2, ?_, ?_⟩
           · specialize helem (b :: t) (by simp)
             rw [rmatch] at helem
-            convert helem.2
+            convert! helem.2
             exact hsum.1
           · grind
   termination_by t => (P, t.length)
diff --git a/Mathlib/Computability/TuringMachine/PostTuringMachine.lean b/Mathlib/Computability/TuringMachine/PostTuringMachine.lean
index 7654227c40a73c..d3aa8197fc4152 100644
--- a/Mathlib/Computability/TuringMachine/PostTuringMachine.lean
+++ b/Mathlib/Computability/TuringMachine/PostTuringMachine.lean
@@ -774,7 +774,7 @@ theorem trTape'_move_left (L R : ListBlank Γ) :
   | nil => cases e; rfl
   | cons b l₁ IH =>
     simp only [List.length, iterate_succ_apply]
-    convert IH e
+    convert! IH e
     simp only [ListBlank.tail_cons, ListBlank.append, Tape.move_left_mk', ListBlank.head_cons]
 
 theorem trTape'_move_right (L R : ListBlank Γ) :
diff --git a/Mathlib/Computability/TuringMachine/StackTuringMachine.lean b/Mathlib/Computability/TuringMachine/StackTuringMachine.lean
index 77dcba24dc80da..4923358a8a6e32 100644
--- a/Mathlib/Computability/TuringMachine/StackTuringMachine.lean
+++ b/Mathlib/Computability/TuringMachine/StackTuringMachine.lean
@@ -366,7 +366,7 @@ set_option backward.isDefEq.respectTransparency false in
 theorem addBottom_map (L : ListBlank (∀ k, Option (Γ k))) :
     (addBottom L).map ⟨Prod.snd, by rfl⟩ = L := by
   simp only [addBottom, ListBlank.map_cons]
-  convert ListBlank.cons_head_tail L
+  convert! ListBlank.cons_head_tail L
   generalize ListBlank.tail L = L'
   refine L'.induction_on fun l ↦ ?_; simp
 
diff --git a/Mathlib/Computability/TuringMachine/ToPartrec.lean b/Mathlib/Computability/TuringMachine/ToPartrec.lean
index 53bb370df0bef6..161c480fb874ac 100644
--- a/Mathlib/Computability/TuringMachine/ToPartrec.lean
+++ b/Mathlib/Computability/TuringMachine/ToPartrec.lean
@@ -604,7 +604,7 @@ theorem move_ok {p k₁ k₂ q s L₁ o L₂} {S : K' → List Γ'} (h₁ : k₁
     rw [e₃] at e
     cases e
     simp only [List.head?_cons, e₂, List.tail_cons, cond_false]
-    convert @IH _ (update (update S k₁ Sk) k₂ (a :: S k₂)) _ using 2 <;>
+    convert! @IH _ (update (update S k₁ Sk) k₂ (a :: S k₂)) _ using 2 <;>
       simp [Function.update_of_ne, h₁, h₁.symm, e₃, List.reverseAux]
     simp [Function.update_comm h₁.symm]
 
@@ -621,14 +621,14 @@ theorem move₂_ok {p k₁ k₂ q s L₁ o L₂} {S : K' → List Γ'} (h₁ : k
   simp only [TM2.step, Option.mem_def, Option.elim]
   cases o <;> simp only <;> rw [tr]
     <;> simp only [id, TM2.stepAux, Option.isSome, cond_true, cond_false]
-  · convert move_ok h₁.2.1.symm (splitAtPred_false _) using 2
+  · convert! move_ok h₁.2.1.symm (splitAtPred_false _) using 2
     simp only [Function.update_comm h₁.1, Function.update_idem]
     rw [show update S rev [] = S by rw [← h₂, Function.update_eq_self]]
     simp only [Function.update_of_ne h₁.2.2.symm, Function.update_of_ne h₁.2.1,
       Function.update_of_ne h₁.1.symm, List.reverseAux_eq, h₂, Function.update_self,
       List.append_nil, List.reverse_reverse]
   · simp only [Option.getD_some]
-    convert move_ok h₁.2.1.symm (splitAtPred_false _) using 2
+    convert! move_ok h₁.2.1.symm (splitAtPred_false _) using 2
     simp only [h₂, Function.update_comm h₁.1, List.reverseAux_eq, Function.update_self,
       List.append_nil, Function.update_idem]
     rw [show update S rev [] = S by rw [← h₂, Function.update_eq_self]]
@@ -661,7 +661,7 @@ theorem clear_ok {p k q s L₁ o L₂} {S : K' → List Γ'} (e : splitAtPred p
     rw [e₃] at e
     cases e
     simp only [List.head?_cons, e₂, List.tail_cons, cond_false]
-    convert @IH _ (update S k Sk) _ using 2 <;> simp [e₃]
+    convert! @IH _ (update S k Sk) _ using 2 <;> simp [e₃]
 
 theorem copy_ok (q s a b c d) :
     Reaches₁ (TM2.step tr) ⟨some (Λ'.copy q), s, K'.elim a b c d⟩
@@ -715,7 +715,7 @@ theorem head_main_ok {q s L} {c d : List Γ'} :
   rw [if_neg (show o ≠ some Γ'.consₗ by cases L <;> simp [o])]
   refine (clear_ok (splitAtPred_eq _ _ _ none [] ?_ ⟨rfl, rfl⟩)).trans ?_
   · exact fun x h => Bool.decide_false (trList_ne_consₗ _ _ h)
-  convert unrev_ok using 2; simp [List.reverseAux_eq]
+  convert! unrev_ok using 2; simp [List.reverseAux_eq]
 
 theorem head_stack_ok {q s L₁ L₂ L₃} :
     Reaches₁ (TM2.step tr)
@@ -731,7 +731,7 @@ theorem head_stack_ok {q s L₁ L₂ L₃} :
     simp only [TM2.step, Option.mem_def, TM2.stepAux, ite_true, id_eq, trList, List.nil_append,
       elim_update_stack, elim_rev, List.reverseAux_nil, elim_update_rev, Function.update_self,
       List.headI_nil, trNat_default]
-    convert unrev_ok using 2
+    convert! unrev_ok using 2
     simp
   · refine
       TransGen.trans
@@ -748,7 +748,7 @@ theorem head_stack_ok {q s L₁ L₂ L₃} :
           (splitAtPred_eq _ _ (trList L₂) (some Γ'.consₗ) L₃
             (fun x h => Bool.decide_false (trList_ne_consₗ _ _ h)) ⟨rfl, by simp⟩))
         ?_
-    convert unrev_ok using 2
+    convert! unrev_ok using 2
     simp [List.reverseAux_eq]
 
 theorem succ_ok {q s n} {c d : List Γ'} :
@@ -758,7 +758,7 @@ theorem succ_ok {q s n} {c d : List Γ'} :
   rcases (n : Num) with - | a
   · refine TransGen.head rfl ?_
     simp only [Option.mem_def]
-    convert unrev_ok using 1
+    convert! unrev_ok using 1
     simp only [elim_update_rev, elim_rev, elim_main, List.reverseAux_nil, elim_update_main]
     rfl
   simp only [trNum, Num.succ, Num.succ']
@@ -769,7 +769,7 @@ theorem succ_ok {q s n} {c d : List Γ'} :
     obtain ⟨l₁', l₂', s', e, h⟩ := this []
     simp only [List.reverseAux] at e
     refine h.trans ?_
-    convert unrev_ok using 2
+    convert! unrev_ok using 2
     simp [e, List.reverseAux_eq]
   induction a generalizing s with intro l₁
   | one =>
@@ -803,7 +803,7 @@ theorem pred_ok (q₁ q₂ s v) (c d : List Γ') : ∃ s',
   · simp only [trPosNum, Num.succ', List.singleton_append, List.nil_append]
     refine TransGen.head rfl ?_
     rw [tr]; simp only [pop', TM2.stepAux]
-    convert unrev_ok using 2
+    convert! unrev_ok using 2
     simp
   simp only [Num.succ']
   suffices ∀ l₁, ∃ l₁' l₂' s',
@@ -814,7 +814,7 @@ theorem pred_ok (q₁ q₂ s v) (c d : List Γ') : ∃ s',
     obtain ⟨l₁', l₂', s', e, h⟩ := this []
     simp only [List.reverseAux] at e
     refine h.trans ?_
-    convert unrev_ok using 2
+    convert! unrev_ok using 2
     simp [e, List.reverseAux_eq]
   induction a generalizing s with intro l₁
   | one =>
@@ -843,7 +843,7 @@ theorem trNormal_respects (c k v s) :
   | succ => refine ⟨_, ⟨none, rfl⟩, head_main_ok.trans succ_ok⟩
   | tail =>
     let o : Option Γ' := List.casesOn v none fun _ _ => some Γ'.cons
-    refine ⟨_, ⟨o, rfl⟩, ?_⟩; convert clear_ok _ using 2
+    refine ⟨_, ⟨o, rfl⟩, ?_⟩; convert! clear_ok _ using 2
     · simp; rfl
     swap
     refine splitAtPred_eq _ _ (trNat v.headI) _ _ (trNat_natEnd _) ?_
@@ -854,7 +854,7 @@ theorem trNormal_respects (c k v s) :
     simp only [TM2.step, Option.mem_def, elim_stack, elim_update_stack, elim_update_main,
       elim_main, elim_rev, elim_update_rev]
     refine (copy_ok _ none [] (trList v).reverse _ _).trans ?_
-    convert h₂ using 2
+    convert! h₂ using 2
     simp [List.reverseAux_eq, trContStack]
   | comp f _ _ IHg => exact IHg (Cont.comp f k) v s
   | case f g IHf IHg =>
@@ -918,9 +918,9 @@ theorem tr_ret_respects (k v s) : ∃ b₂,
     · obtain ⟨s', h₁, h₂⟩ := trNormal_respects f (Cont.fix f k) v.tail (some Γ'.cons)
       refine ⟨_, h₁, TransGen.head rfl <| TransGen.trans ?_ h₂⟩
       rw [trCont, tr]; simp only [pop', TM2.stepAux, elim_main, this.1]
-      convert clear_ok (splitAtPred_eq _ _ (trNat v.headI).tail (some Γ'.cons) _ _ _) using 2
+      convert! clear_ok (splitAtPred_eq _ _ (trNat v.headI).tail (some Γ'.cons) _ _ _) using 2
       · simp
-        convert rfl
+        convert! rfl
       · exact fun x h => trNat_natEnd _ _ (List.tail_subset _ h)
       · exact ⟨rfl, this.2⟩
 
diff --git a/Mathlib/Condensed/Discrete/LocallyConstant.lean b/Mathlib/Condensed/Discrete/LocallyConstant.lean
index 6ec60e11b2fc81..89820ffc889623 100644
--- a/Mathlib/Condensed/Discrete/LocallyConstant.lean
+++ b/Mathlib/Condensed/Discrete/LocallyConstant.lean
@@ -188,7 +188,7 @@ noncomputable def componentHom (a : Fiber (f.comap g.hom.hom)) :
   ConcreteCategory.ofHom
   { toFun x := ⟨g x.val, by
       simp only [Fiber.mk, Set.mem_preimage, Set.mem_singleton_iff]
-      convert map_eq_image _ _ x
+      convert! map_eq_image _ _ x
       exact map_preimage_eq_image_map _ _ a⟩
     continuous_toFun := by
       -- term mode gives "unknown free variable" error.
@@ -293,7 +293,7 @@ noncomputable def counit [HasExplicitFiniteCoproducts.{u} P] : haveI := CompHaus
     rw [this]
     apply congrArg
     symm
-    convert (b.preimage).prop
+    convert! (b.preimage).prop
     exact (mem_iff_eq_image (g.hom.app _ ∘ f) _ _).symm
 
 /--
diff --git a/Mathlib/Control/EquivFunctor.lean b/Mathlib/Control/EquivFunctor.lean
index 9330cfa6896c78..2f8a214334db27 100644
--- a/Mathlib/Control/EquivFunctor.lean
+++ b/Mathlib/Control/EquivFunctor.lean
@@ -51,10 +51,10 @@ def mapEquiv : f α ≃ f β where
   toFun := EquivFunctor.map e
   invFun := EquivFunctor.map e.symm
   left_inv x := by
-    convert (congr_fun (EquivFunctor.map_trans' e e.symm) x).symm
+    convert! (congr_fun (EquivFunctor.map_trans' e e.symm) x).symm
     simp
   right_inv y := by
-    convert (congr_fun (EquivFunctor.map_trans' e.symm e) y).symm
+    convert! (congr_fun (EquivFunctor.map_trans' e.symm e) y).symm
     simp
 
 @[simp]
diff --git a/Mathlib/Data/Complex/Basic.lean b/Mathlib/Data/Complex/Basic.lean
index 3ee3811181808a..969f69b3353927 100644
--- a/Mathlib/Data/Complex/Basic.lean
+++ b/Mathlib/Data/Complex/Basic.lean
@@ -785,7 +785,7 @@ lemma reProdIm_subset_iff {s s₁ t t₁ : Set ℝ} : s ×ℂ t ⊆ s₁ ×ℂ t
 /-- If `s ⊆ s₁ ⊆ ℝ` and `t ⊆ t₁ ⊆ ℝ`, then `s × t ⊆ s₁ × t₁` in `ℂ`. -/
 lemma reProdIm_subset_iff' {s s₁ t t₁ : Set ℝ} :
     s ×ℂ t ⊆ s₁ ×ℂ t₁ ↔ s ⊆ s₁ ∧ t ⊆ t₁ ∨ s = ∅ ∨ t = ∅ := by
-  convert prod_subset_prod_iff
+  convert! prod_subset_prod_iff
   exact reProdIm_subset_iff
 
 variable {s t : Set ℝ}
diff --git a/Mathlib/Data/DFinsupp/BigOperators.lean b/Mathlib/Data/DFinsupp/BigOperators.lean
index 57f35c60c4e735..133fb0907527c0 100644
--- a/Mathlib/Data/DFinsupp/BigOperators.lean
+++ b/Mathlib/Data/DFinsupp/BigOperators.lean
@@ -238,14 +238,14 @@ def sumZeroHom [∀ i, Zero (β i)] [AddCommMonoid γ] (φ : ∀ i, ZeroHom (β
       · intro i H1 H2
         rw [Finset.mem_inter] at H2
         simp only [Multiset.mem_toFinset] at H1 H2
-        convert map_zero (φ i)
+        convert! map_zero (φ i)
         exact (hy i).resolve_left (mt (And.intro H1) H2)
       · intro i _
         rfl
       · intro i H1 H2
         rw [Finset.mem_inter] at H2
         simp only [Multiset.mem_toFinset] at H1 H2
-        convert map_zero (φ i)
+        convert! map_zero (φ i)
         exact (hx i).resolve_left (mt (fun H3 => And.intro H3 H1) H2)
   map_zero' := by
     simp only [toFun_eq_coe, coe_zero, Pi.zero_apply, map_zero, Finset.sum_const_zero]; rfl
@@ -316,7 +316,7 @@ theorem sumAddHom_single [∀ i, AddZeroClass (β i)] [AddCommMonoid γ] (φ : 
 theorem sumAddHom_piSingle [∀ i, AddZeroClass (β i)] [AddCommMonoid γ] (i) (φ : β i →+ γ) :
     sumAddHom (Pi.single i φ) = φ.comp (evalAddMonoidHom i) :=
   AddMonoidHom.toZeroHom_injective <| by
-    convert sumZeroHom_piSingle i φ.toZeroHom using 1
+    convert! sumZeroHom_piSingle i φ.toZeroHom using 1
     rw [DFinsupp.sumAddHom_toZeroHom]
     conv_lhs =>
       enter [1, i]
diff --git a/Mathlib/Data/DFinsupp/Interval.lean b/Mathlib/Data/DFinsupp/Interval.lean
index 49a2401f5c65c6..fb5a449a44609f 100644
--- a/Mathlib/Data/DFinsupp/Interval.lean
+++ b/Mathlib/Data/DFinsupp/Interval.lean
@@ -37,7 +37,7 @@ def dfinsupp (s : Finset ι) (t : ∀ i, Finset (α i)) : Finset (Π₀ i, α i)
     ⟨fun f => DFinsupp.mk s fun i => f i i.2, by
       refine (mk_injective _).comp fun f g h => ?_
       ext i hi
-      convert congr_fun h ⟨i, hi⟩⟩
+      convert! congr_fun h ⟨i, hi⟩⟩
 
 @[simp]
 theorem card_dfinsupp (s : Finset ι) (t : ∀ i, Finset (α i)) : #(s.dfinsupp t) = ∏ i ∈ s, #(t i) :=
@@ -50,7 +50,7 @@ theorem mem_dfinsupp_iff : f ∈ s.dfinsupp t ↔ f.support ⊆ s ∧ ∀ i ∈
   · rintro ⟨f, hf, rfl⟩
     rw [Function.Embedding.coeFn_mk]
     refine ⟨support_mk_subset, fun i hi => ?_⟩
-    convert mem_pi.1 hf i hi
+    convert! mem_pi.1 hf i hi
     exact mk_of_mem hi
   · refine fun h => ⟨fun i _ => f i, mem_pi.2 h.2, ?_⟩
     ext i
diff --git a/Mathlib/Data/DFinsupp/WellFounded.lean b/Mathlib/Data/DFinsupp/WellFounded.lean
index cfb1a360951f3b..9826cab5551827 100644
--- a/Mathlib/Data/DFinsupp/WellFounded.lean
+++ b/Mathlib/Data/DFinsupp/WellFounded.lean
@@ -105,9 +105,10 @@ theorem Lex.acc_of_single_erase [DecidableEq ι] {x : Π₀ i, α i} (i : ι)
     (hs : Acc (DFinsupp.Lex r s) <| single i (x i)) (hu : Acc (DFinsupp.Lex r s) <| x.erase i) :
     Acc (DFinsupp.Lex r s) x := by
   classical
-    convert ← @Acc.of_fibration _ _ _ _ _ (lex_fibration r s) ⟨{i}, _⟩
-      (InvImage.accessible snd <| hs.prod_gameAdd hu)
-    convert piecewise_single_erase x i
+    convert! ←
+      @Acc.of_fibration _ _ _ _ _ (lex_fibration r s) ⟨{ i }, _⟩
+        (InvImage.accessible snd <| hs.prod_gameAdd hu)
+    convert! piecewise_single_erase x i
 
 theorem Lex.acc_zero (hbot : ∀ ⦃i a⦄, ¬s i a 0) : Acc (DFinsupp.Lex r s) 0 :=
   Acc.intro 0 fun _ ⟨_, _, h⟩ => (hbot h).elim
@@ -187,7 +188,7 @@ variable (r : ι → ι → Prop) {s : ∀ i, α i → α i → Prop}
 theorem Pi.Lex.wellFounded [IsStrictTotalOrder ι r] [Finite ι] (hs : ∀ i, WellFounded (s i)) :
     WellFounded (Pi.Lex r (fun {i} ↦ s i)) := by
   obtain h | ⟨⟨x⟩⟩ := isEmpty_or_nonempty (∀ i, α i)
-  · convert emptyWf.wf
+  · convert! emptyWf.wf
   letI : ∀ i, Zero (α i) := fun i => ⟨(hs i).min ⊤ ⟨x i, trivial⟩⟩
   haveI := Fintype.ofFinite ι
   refine InvImage.wf equivFunOnFintype.symm (Lex.wellFounded' (fun i a => ?_) hs ?_)
@@ -244,7 +245,7 @@ instance Pi.wellFoundedLT [Finite ι] [∀ i, Preorder (α i)] [hw : ∀ i, Well
     WellFoundedLT (∀ i, α i) :=
   ⟨by
     obtain h | ⟨⟨x⟩⟩ := isEmpty_or_nonempty (∀ i, α i)
-    · convert emptyWf.wf
+    · convert! emptyWf.wf
     letI : ∀ i, Zero (α i) := fun i => ⟨(hw i).wf.min ⊤ ⟨x i, trivial⟩⟩
     haveI := Fintype.ofFinite ι
     refine InvImage.wf equivFunOnFintype.symm (DFinsupp.wellFoundedLT fun i a => ?_).wf
diff --git a/Mathlib/Data/ENNReal/Operations.lean b/Mathlib/Data/ENNReal/Operations.lean
index 929dd53e955b26..1736a377358493 100644
--- a/Mathlib/Data/ENNReal/Operations.lean
+++ b/Mathlib/Data/ENNReal/Operations.lean
@@ -179,11 +179,11 @@ theorem add_ne_top : a + b ≠ ∞ ↔ a ≠ ∞ ∧ b ≠ ∞ := by simpa only
 protected lemma Finiteness.add_ne_top {a b : ℝ≥0∞} (ha : a ≠ ∞) (hb : b ≠ ∞) : a + b ≠ ∞ :=
   ENNReal.add_ne_top.2 ⟨ha, hb⟩
 
-theorem mul_top' : a * ∞ = if a = 0 then 0 else ∞ := by convert WithTop.mul_top' a
+theorem mul_top' : a * ∞ = if a = 0 then 0 else ∞ := by convert! WithTop.mul_top' a
 
 @[simp] theorem mul_top (h : a ≠ 0) : a * ∞ = ∞ := WithTop.mul_top h
 
-theorem top_mul' : ∞ * a = if a = 0 then 0 else ∞ := by convert WithTop.top_mul' a
+theorem top_mul' : ∞ * a = if a = 0 then 0 else ∞ := by convert! WithTop.top_mul' a
 
 @[simp] theorem top_mul (h : a ≠ 0) : ∞ * a = ∞ := WithTop.top_mul h
 
diff --git a/Mathlib/Data/EReal/Operations.lean b/Mathlib/Data/EReal/Operations.lean
index 2454d12fef8baf..d815387a89f3e8 100644
--- a/Mathlib/Data/EReal/Operations.lean
+++ b/Mathlib/Data/EReal/Operations.lean
@@ -811,7 +811,7 @@ lemma nsmul_eq_mul (n : ℕ) (x : EReal) : n • x = n * x := by
   | zero => rw [zero_smul, Nat.cast_zero, zero_mul]
   | succ n ih =>
     rw [succ_nsmul, ih, Nat.cast_succ]
-    convert (EReal.right_distrib_of_nonneg _ _).symm <;> simp
+    convert! (EReal.right_distrib_of_nonneg _ _).symm <;> simp
 
 end EReal
 
diff --git a/Mathlib/Data/Fin/Tuple/Basic.lean b/Mathlib/Data/Fin/Tuple/Basic.lean
index f83904d503e3aa..afa7f0ab0e7fc1 100644
--- a/Mathlib/Data/Fin/Tuple/Basic.lean
+++ b/Mathlib/Data/Fin/Tuple/Basic.lean
@@ -196,7 +196,7 @@ theorem consCases_cons {motive : (∀ i : Fin n.succ, α i) → Sort v}
 def consInduction {α : Sort*} {motive : ∀ {n : ℕ}, (Fin n → α) → Sort v} (elim0 : motive Fin.elim0)
     (cons : ∀ {n} (x₀) (x : Fin n → α), motive x → motive (Fin.cons x₀ x)) :
     ∀ {n : ℕ} (x : Fin n → α), motive x
-  | 0, x => by convert elim0
+  | 0, x => by convert! elim0
   | _ + 1, x => consCases (fun _ _ ↦ cons _ _ <| consInduction elim0 cons _) x
 
 theorem cons_injective_of_injective {α} {x₀ : α} {x : Fin n → α} (hx₀ : x₀ ∉ Set.range x)
@@ -511,12 +511,12 @@ def snoc (p : ∀ i : Fin n, α i.castSucc) (x : α (last n)) (i : Fin (n + 1))
 theorem init_snoc : init (snoc p x) = p := by
   ext i
   simp only [init, snoc, val_castSucc, is_lt, dite_true]
-  convert cast_eq rfl (p i)
+  convert! cast_eq rfl (p i)
 
 @[simp]
 theorem snoc_castSucc : snoc p x i.castSucc = p i := by
   simp only [snoc, val_castSucc, is_lt, dite_true]
-  convert cast_eq rfl (p i)
+  convert! cast_eq rfl (p i)
 
 @[simp]
 theorem snoc_apply_zero [NeZero n] : snoc p x 0 = p 0 := snoc_castSucc x p 0
@@ -729,7 +729,7 @@ def snocInduction {α : Sort*}
     (elim0 : motive Fin.elim0)
     (snoc : ∀ {n} (x : Fin n → α) (x₀), motive x → motive (Fin.snoc x x₀)) :
     ∀ {n : ℕ} (x : Fin n → α), motive x
-  | 0, x => by convert elim0
+  | 0, x => by convert! elim0
   | _ + 1, x => snocCases (fun _ _ ↦ snoc _ _ <| snocInduction elim0 snoc _) x
 
 theorem snoc_injective_of_injective {α} {x₀ : α} {x : Fin n → α}
@@ -802,7 +802,7 @@ theorem forall_fin_add_pi {γ : Fin (m + n) → Sort*} {P : (∀ i, γ i) → Pr
       (∀ (vₘ : ∀ i, γ (castAdd n i)) (vₙ : ∀ j, γ (natAdd m j)), P (addCases vₘ vₙ)) where
   mp hv vm vn := hv (addCases vm vn)
   mpr h v := by
-    convert h (fun i => v (castAdd n i)) (fun j => v (natAdd m j))
+    convert! h (fun i => v (castAdd n i)) (fun j => v (natAdd m j))
     exact (addCases_castAdd_natAdd v).symm
 
 lemma exists_iff_castSucc {P : Fin (n + 1) → Prop} :
@@ -926,7 +926,7 @@ theorem insertNth_zero (x : α 0) (p : ∀ j : Fin n, α (succAbove 0 j)) :
       cons x fun j ↦ _root_.cast (congr_arg α (congr_fun succAbove_zero j)) (p j) := by
   refine insertNth_eq_iff.2 ⟨by simp, ?_⟩
   ext j
-  convert (cons_succ x p j).symm
+  convert! (cons_succ x p j).symm
 
 @[simp]
 theorem insertNth_zero' (x : β) (p : Fin n → β) : @insertNth _ (fun _ ↦ β) 0 x p = cons x p := by
diff --git a/Mathlib/Data/Finite/Prod.lean b/Mathlib/Data/Finite/Prod.lean
index ba49a9e0ede989..7b421a871790c3 100644
--- a/Mathlib/Data/Finite/Prod.lean
+++ b/Mathlib/Data/Finite/Prod.lean
@@ -62,7 +62,7 @@ instance Function.Embedding.finite {α β : Sort*} [Finite β] : Finite (α ↪
 
 instance Equiv.finite_right {α β : Sort*} [Finite β] : Finite (α ≃ β) :=
   Finite.of_injective Equiv.toEmbedding fun e₁ e₂ h => Equiv.ext <| by
-    convert DFunLike.congr_fun h using 0
+    convert! DFunLike.congr_fun h using 0
 
 instance Equiv.finite_left {α β : Sort*} [Finite α] : Finite (α ≃ β) :=
   Finite.of_equiv _ ⟨Equiv.symm, Equiv.symm, Equiv.symm_symm, Equiv.symm_symm⟩
diff --git a/Mathlib/Data/Finset/DenselyOrdered.lean b/Mathlib/Data/Finset/DenselyOrdered.lean
index e6ecebf37a28c4..628be41a4d3098 100644
--- a/Mathlib/Data/Finset/DenselyOrdered.lean
+++ b/Mathlib/Data/Finset/DenselyOrdered.lean
@@ -22,7 +22,7 @@ variable {α : Type*} [LinearOrder α] [DenselyOrdered α]
 theorem Finset.exists_between {s t : Finset α}
     (hs : s.Nonempty) (ht : t.Nonempty) (H : ∀ x ∈ s, ∀ y ∈ t, x < y) :
     ∃ b, (∀ x ∈ s, x < b) ∧ (∀ y ∈ t, b < y) := by
-  convert _root_.exists_between (a₁ := s.max' hs) (a₂ := t.min' ht) (by simp_all) <;> simp
+  convert! _root_.exists_between (a₁ := s.max' hs) (a₂ := t.min' ht) (by simp_all) <;> simp
 
 theorem Finset.exists_between' (s t : Finset α) [NoMaxOrder α] [NoMinOrder α] [Nonempty α]
     (H : ∀ x ∈ s, ∀ y ∈ t, x < y) : ∃ b, (∀ x ∈ s, x < b) ∧ (∀ y ∈ t, b < y) := by
@@ -35,10 +35,12 @@ theorem Finset.exists_between' (s t : Finset α) [NoMaxOrder α] [NoMinOrder α]
 theorem Set.Finite.exists_between {s t : Set α}
     (hsf : s.Finite) (hs : s.Nonempty) (htf : t.Finite) (ht : t.Nonempty)
     (H : ∀ x ∈ s, ∀ y ∈ t, x < y) : ∃ b, (∀ x ∈ s, x < b) ∧ (∀ y ∈ t, b < y) := by
-  convert Finset.exists_between (s := hsf.toFinset) (t := htf.toFinset)
-    (by simpa) (by simpa) (by simpa) using 1; simp
+  convert!
+    Finset.exists_between (s := hsf.toFinset) (t := htf.toFinset) (by simpa) (by simpa)
+      (by simpa) using
+    1; simp
 
 theorem Set.Finite.exists_between' [NoMaxOrder α] [NoMinOrder α] [Nonempty α]
     {s t : Set α} (hs : s.Finite) (ht : t.Finite)
     (H : ∀ x ∈ s, ∀ y ∈ t, x < y) : ∃ b, (∀ x ∈ s, x < b) ∧ (∀ y ∈ t, b < y) := by
-  convert hs.toFinset.exists_between' ht.toFinset (by simpa) using 1; simp
+  convert! hs.toFinset.exists_between' ht.toFinset (by simpa) using 1; simp
diff --git a/Mathlib/Data/Finset/Finsupp.lean b/Mathlib/Data/Finset/Finsupp.lean
index 0eec0ed4dc5e78..0976494946549d 100644
--- a/Mathlib/Data/Finset/Finsupp.lean
+++ b/Mathlib/Data/Finset/Finsupp.lean
@@ -52,7 +52,7 @@ theorem mem_finsupp_iff {t : ι → Finset α} :
   refine mem_map.trans ⟨?_, ?_⟩
   · rintro ⟨f, hf, rfl⟩
     refine ⟨support_indicator_subset _ _, fun i hi => ?_⟩
-    convert mem_pi.1 hf i hi
+    convert! mem_pi.1 hf i hi
     exact indicator_of_mem hi _
   · refine fun h => ⟨fun i _ => f i, mem_pi.2 h.2, ?_⟩
     ext i
diff --git a/Mathlib/Data/Finset/Image.lean b/Mathlib/Data/Finset/Image.lean
index be28b6058eaa6e..01438ea6be936a 100644
--- a/Mathlib/Data/Finset/Image.lean
+++ b/Mathlib/Data/Finset/Image.lean
@@ -637,7 +637,7 @@ subtype. -/
 theorem map_subtype_subset {t : Set α} (s : Finset t) : ↑(s.map (Embedding.subtype _)) ⊆ t := by
   intro a ha
   rw [mem_coe] at ha
-  convert property_of_mem_map_subtype s ha
+  convert! property_of_mem_map_subtype s ha
 
 end Subtype
 
diff --git a/Mathlib/Data/Finset/NoncommProd.lean b/Mathlib/Data/Finset/NoncommProd.lean
index 85415d966e9d41..6c245360b212f7 100644
--- a/Mathlib/Data/Finset/NoncommProd.lean
+++ b/Mathlib/Data/Finset/NoncommProd.lean
@@ -409,7 +409,7 @@ theorem noncommProd_mulSingle [Fintype ι] [DecidableEq ι] (x : ∀ i, M i) :
   case a =>
     intro i _ j _ _
     exact Pi.mulSingle_apply_commute x i j
-  convert (noncommProd_congr (insert_erase (mem_univ i)).symm _ _).trans _
+  convert! (noncommProd_congr (insert_erase (mem_univ i)).symm _ _).trans _
   · intro j
     exact Pi.mulSingle j (x j) i
   · intro j _; dsimp
diff --git a/Mathlib/Data/Finset/PiInduction.lean b/Mathlib/Data/Finset/PiInduction.lean
index 21650d0a599b94..42e846a75ec20e 100644
--- a/Mathlib/Data/Finset/PiInduction.lean
+++ b/Mathlib/Data/Finset/PiInduction.lean
@@ -48,7 +48,7 @@ theorem induction_on_pi_of_choice (r : ∀ i, α i → Finset (α i) → Prop)
   induction hs : univ.sigma f using Finset.strongInductionOn generalizing f with | _ s ihs
   subst s
   rcases eq_empty_or_nonempty (univ.sigma f) with he | hne
-  · convert h0 using 1
+  · convert! h0 using 1
     simpa [funext_iff] using he
   · rcases sigma_nonempty.1 hne with ⟨i, -, hi⟩
     rcases H_ex i (f i) hi with ⟨x, x_mem, hr⟩
diff --git a/Mathlib/Data/Finset/Sort.lean b/Mathlib/Data/Finset/Sort.lean
index ddfc5d8329bb9e..6d84598bc9cd61 100644
--- a/Mathlib/Data/Finset/Sort.lean
+++ b/Mathlib/Data/Finset/Sort.lean
@@ -304,8 +304,8 @@ lemma orderEmbOfFin_compl_singleton {n : ℕ} {i : Fin (n + 1)} {k : ℕ}
         (Fin.succAboveOrderEmb i) := by
   apply DFunLike.coe_injective
   rw [eq_comm]
-  convert orderEmbOfFin_unique _ (fun x ↦ ?_)
-    ((Fin.strictMono_succAbove _).comp (Fin.cast_strictMono _))
+  convert!
+    orderEmbOfFin_unique _ (fun x ↦ ?_) ((Fin.strictMono_succAbove _).comp (Fin.cast_strictMono _))
   · simp
   · simp [← h, card_compl]
 
diff --git a/Mathlib/Data/Finset/Sym.lean b/Mathlib/Data/Finset/Sym.lean
index 8dd49cbdb52f53..07d6e1e91b2e75 100644
--- a/Mathlib/Data/Finset/Sym.lean
+++ b/Mathlib/Data/Finset/Sym.lean
@@ -206,7 +206,7 @@ lemma sym_map [DecidableEq β] {n : ℕ} (g : α ↪ β) (s : Finset α) :
       rw [← hi]
       exact (hd e he).choose_spec.1
     · simp only [Sym.map_map, Function.comp_apply, g']
-      convert Sym.attach_map_coe d with ⟨x, hx⟩ hx'
+      convert! Sym.attach_map_coe d with ⟨x, hx⟩ hx'
       exact (hd x hx).choose_spec.2
   · rw [← hd', Sym.mem_map] at hd
     obtain ⟨a, ha, rfl⟩ := hd
@@ -275,7 +275,7 @@ theorem sym_filterNe_mem {m : Sym α n} (a : α) (h : m ∈ s.sym n) :
   for `0 ≤ i ≤ n`. -/
 @[simps]
 def symInsertEquiv (h : a ∉ s) : (insert a s).sym n ≃ Σ i : Fin (n + 1), s.sym (n - i) where
-  toFun m := ⟨_, (m.1.filterNe a).2, by convert sym_filterNe_mem a m.2; rw [erase_insert h]⟩
+  toFun m := ⟨_, (m.1.filterNe a).2, by convert! sym_filterNe_mem a m.2; rw [erase_insert h]⟩
   invFun m := ⟨m.2.1.fill a m.1, sym_fill_mem a m.2.2⟩
   left_inv m := Subtype.ext <| m.1.fill_filterNe a
   right_inv := fun ⟨i, m, hm⟩ ↦ by
diff --git a/Mathlib/Data/Finsupp/Basic.lean b/Mathlib/Data/Finsupp/Basic.lean
index e46c8caa20f633..682adeef183b67 100644
--- a/Mathlib/Data/Finsupp/Basic.lean
+++ b/Mathlib/Data/Finsupp/Basic.lean
@@ -363,7 +363,7 @@ theorem mapDomain_apply' (S : Set α) {f : α → β} (x : α →₀ M) (hS : (x
     simp_rw [single_apply]
     by_cases hax : a ∈ x.support
     · rw [← Finset.add_sum_erase _ _ hax, if_pos rfl]
-      convert add_zero (x a)
+      convert! add_zero (x a)
       refine Finset.sum_eq_zero fun i hi => if_neg ?_
       exact (hf.mono hS).ne (Finset.mem_of_mem_erase hi) hax (Finset.ne_of_mem_erase hi)
     · rw [notMem_support_iff.1 hax]
@@ -1391,7 +1391,7 @@ end Sigma
 
 lemma mem_range_embDomain_iff [AddCommMonoid M] (f : α ↪ β) (x : β →₀ M) :
     x ∈ Set.range (embDomain f) ↔ ↑x.support ⊆ Set.range f := by
-  convert mem_range_mapDomain_iff _ f.injective _
+  convert! mem_range_mapDomain_iff _ f.injective _
   · ext; rw [embDomain_eq_mapDomain]
   · grind
 
diff --git a/Mathlib/Data/Finsupp/BigOperators.lean b/Mathlib/Data/Finsupp/BigOperators.lean
index 92c0d964d5863e..107461dea1c411 100644
--- a/Mathlib/Data/Finsupp/BigOperators.lean
+++ b/Mathlib/Data/Finsupp/BigOperators.lean
@@ -54,7 +54,7 @@ theorem Multiset.support_sum_subset [AddCommMonoid M] (s : Multiset (ι →₀ M
 
 theorem Finset.support_sum_subset [AddCommMonoid M] (s : Finset (ι →₀ M)) :
     (s.sum id).support ⊆ Finset.sup s Finsupp.support := by
-  classical convert Multiset.support_sum_subset s.1; simp
+  classical convert! Multiset.support_sum_subset s.1; simp
 
 theorem List.mem_foldr_sup_support_iff [Zero M] {l : List (ι →₀ M)} {x : ι} :
     x ∈ l.foldr (Finsupp.support · ⊔ ·) ∅ ↔ ∃ f ∈ l, x ∈ f.support := by
@@ -101,7 +101,7 @@ theorem Multiset.support_sum_eq [AddCommMonoid M] (s : Multiset (ι →₀ M))
   induction s using Quot.inductionOn with | _ a
   obtain ⟨l, hl, hd⟩ := hs
   suffices a.Pairwise (_root_.Disjoint on Finsupp.support) by
-    convert List.support_sum_eq a this
+    convert! List.support_sum_eq a this
     dsimp only [Function.comp_def]
     simp only [quot_mk_to_coe'', map_coe, sup_coe,
       Finset.sup_eq_union, Finset.bot_eq_empty, List.foldr_map]
@@ -113,7 +113,7 @@ theorem Finset.support_sum_eq [AddCommMonoid M] (s : Finset (ι →₀ M))
     (s.sum id).support = Finset.sup s Finsupp.support := by
   classical
   suffices s.1.Pairwise (_root_.Disjoint on Finsupp.support) by
-    convert Multiset.support_sum_eq s.1 this
+    convert! Multiset.support_sum_eq s.1 this
     exact (Finset.sum_val _).symm
   obtain ⟨l, hl, hn⟩ : ∃ l : List (ι →₀ M), l.toFinset = s ∧ l.Nodup := by
     refine ⟨s.toList, ?_, Finset.nodup_toList _⟩
diff --git a/Mathlib/Data/Finsupp/Defs.lean b/Mathlib/Data/Finsupp/Defs.lean
index 9dd1af7cb0c80c..2b2ed3a0d43935 100644
--- a/Mathlib/Data/Finsupp/Defs.lean
+++ b/Mathlib/Data/Finsupp/Defs.lean
@@ -498,7 +498,7 @@ theorem zipWith_apply {f : M → N → O} {hf : f 0 0 = 0} {g₁ : α →₀ M}
 
 theorem support_zipWith [D : DecidableEq α] {f : M → N → O} {hf : f 0 0 = 0} {g₁ : α →₀ M}
     {g₂ : α →₀ N} : (zipWith f hf g₁ g₂).support ⊆ g₁.support ∪ g₂.support := by
-  convert support_onFinset_subset
+  convert! support_onFinset_subset
 
 end ZipWith
 
diff --git a/Mathlib/Data/Fintype/List.lean b/Mathlib/Data/Fintype/List.lean
index 579f66e96c1498..dfe147b8cfe811 100644
--- a/Mathlib/Data/Fintype/List.lean
+++ b/Mathlib/Data/Fintype/List.lean
@@ -67,7 +67,7 @@ instance fintypeNodupList [Fintype α] : Fintype { l : List α // l.Nodup } := b
     constructor
     · simp only [Finset.coe_toList]
       rfl
-    · convert Finset.nodup_toList (Finset.univ.powerset : Finset (Finset α))
+    · convert! Finset.nodup_toList (Finset.univ.powerset : Finset (Finset α))
       ext l
       unfold Nodup
       refine Pairwise.iff ?_
@@ -99,7 +99,7 @@ instance fintypeNodupList [Fintype α] : Fintype { l : List α // l.Nodup } := b
     constructor
     · intro h
       rcases h with ⟨f, hf⟩
-      convert f.nodup
+      convert! f.nodup
       rw [hf]
       rfl
     · intro h
diff --git a/Mathlib/Data/Fintype/Option.lean b/Mathlib/Data/Fintype/Option.lean
index 9a1284c63aa876..8fc9cd0d1c2da6 100644
--- a/Mathlib/Data/Fintype/Option.lean
+++ b/Mathlib/Data/Fintype/Option.lean
@@ -92,11 +92,11 @@ theorem induction_empty_option {P : ∀ (α : Type u) [Fintype α], Prop}
     (h_empty : P PEmpty) (h_option : ∀ (α) [Fintype α], P α → P (Option α)) (α : Type u)
     [h_fintype : Fintype α] : P α := by
   obtain ⟨p⟩ :=
-    let f_empty := fun i => by convert h_empty
+    let f_empty := fun i => by convert! h_empty
     let h_option : ∀ {α : Type u} [Fintype α] [DecidableEq α],
           (∀ (h : Fintype α), P α) → ∀ (h : Fintype (Option α)), P (Option α) := by
       rintro α hα - Pα hα'
-      convert h_option α (Pα _)
+      convert! h_option α (Pα _)
     @truncRecEmptyOption (fun α => ∀ h, @P α h) (@fun α β e hα hβ => @of_equiv α β hβ e (hα _))
       f_empty h_option α _ (Classical.decEq α)
   exact p _
diff --git a/Mathlib/Data/Fintype/Order.lean b/Mathlib/Data/Fintype/Order.lean
index e4a5f7b738f08f..616051ccc6ca7f 100644
--- a/Mathlib/Data/Fintype/Order.lean
+++ b/Mathlib/Data/Fintype/Order.lean
@@ -102,12 +102,12 @@ noncomputable abbrev toCompleteDistribLatticeMinimalAxioms [DistribLattice α] [
     CompleteDistribLattice.MinimalAxioms α where
   __ := toCompleteLattice α
   iInf_sup_le_sup_sInf := fun a s => by
-    convert (Finset.inf_sup_distrib_left s.toFinset id a).ge using 1
+    convert! (Finset.inf_sup_distrib_left s.toFinset id a).ge using 1
     rw [Finset.inf_eq_iInf]
     simp_rw [Set.mem_toFinset]
     rfl
   inf_sSup_le_iSup_inf := fun a s => by
-    convert (Finset.sup_inf_distrib_left s.toFinset id a).le using 1
+    convert! (Finset.sup_inf_distrib_left s.toFinset id a).le using 1
     rw [Finset.sup_eq_iSup]
     simp_rw [Set.mem_toFinset]
     rfl
@@ -187,7 +187,7 @@ variable {α : Type*} {r : α → α → Prop} [IsTrans α r] {β γ : Type*} [N
 
 theorem Directed.finite_set_le (D : Directed r f) {s : Set γ} (hs : s.Finite) :
     ∃ z, ∀ i ∈ s, r (f i) (f z) := by
-  convert D.finset_le hs.toFinset using 3; rw [Set.Finite.mem_toFinset]
+  convert! D.finset_le hs.toFinset using 3; rw [Set.Finite.mem_toFinset]
 
 lemma Directed.finite_le {ι κ : Sort*} [Nonempty ι] [Finite κ] {f : ι → α} (hf : Directed r f)
     (g : κ → ι) : ∃ z, ∀ i, r (f (g i)) (f z) := by
diff --git a/Mathlib/Data/Fintype/Sets.lean b/Mathlib/Data/Fintype/Sets.lean
index d87519b73b3f13..ff1de4545097ef 100644
--- a/Mathlib/Data/Fintype/Sets.lean
+++ b/Mathlib/Data/Fintype/Sets.lean
@@ -275,7 +275,7 @@ sets on a finite type are finite.) -/
 noncomputable def finsetEquivSet : Finset α ≃ Set α where
   toFun := (↑)
   invFun := by classical exact fun s => s.toFinset
-  left_inv s := by convert Finset.toFinset_coe s
+  left_inv s := by convert! Finset.toFinset_coe s
   right_inv s := by classical exact s.coe_toFinset
 
 @[simp, norm_cast] lemma coe_finsetEquivSet : ⇑finsetEquivSet = ((↑) : Finset α → Set α) := rfl
diff --git a/Mathlib/Data/Fintype/Sum.lean b/Mathlib/Data/Fintype/Sum.lean
index 1e0154e21fe59d..13aa5d06ecb0d5 100644
--- a/Mathlib/Data/Fintype/Sum.lean
+++ b/Mathlib/Data/Fintype/Sum.lean
@@ -132,14 +132,14 @@ theorem Fintype.card_subtype_or (p q : α → Prop) [Fintype { x // p x }] [Fint
     [Fintype { x // p x ∨ q x }] :
     Fintype.card { x // p x ∨ q x } ≤ Fintype.card { x // p x } + Fintype.card { x // q x } := by
   classical
-    convert Fintype.card_le_of_embedding (subtypeOrLeftEmbedding p q)
+    convert! Fintype.card_le_of_embedding (subtypeOrLeftEmbedding p q)
     rw [Fintype.card_sum]
 
 theorem Fintype.card_subtype_or_disjoint (p q : α → Prop) (h : Disjoint p q) [Fintype { x // p x }]
     [Fintype { x // q x }] [Fintype { x // p x ∨ q x }] :
     Fintype.card { x // p x ∨ q x } = Fintype.card { x // p x } + Fintype.card { x // q x } := by
   classical
-    convert Fintype.card_congr (subtypeOrEquiv p q h)
+    convert! Fintype.card_congr (subtypeOrEquiv p q h)
     simp
 
 theorem Fintype.card_subtype_eq_or_eq_of_ne {α : Type*} [Fintype α] [DecidableEq α] {a b : α}
diff --git a/Mathlib/Data/Int/Basic.lean b/Mathlib/Data/Int/Basic.lean
index fe3824cdc1ec02..894581f3ab530a 100644
--- a/Mathlib/Data/Int/Basic.lean
+++ b/Mathlib/Data/Int/Basic.lean
@@ -58,7 +58,7 @@ lemma natAbs_surjective : natAbs.Surjective := fun n => ⟨n, natAbs_natCast n
 
 lemma pow_right_injective (h : 1 < a.natAbs) : ((a ^ ·) : ℕ → ℤ).Injective := by
   refine (?_ : (natAbs ∘ (a ^ · : ℕ → ℤ)).Injective).of_comp
-  convert Nat.pow_right_injective h using 2
+  convert! Nat.pow_right_injective h using 2
   rw [Function.comp_apply, natAbs_pow]
 
 /-! ### dvd -/
diff --git a/Mathlib/Data/Int/ConditionallyCompleteOrder.lean b/Mathlib/Data/Int/ConditionallyCompleteOrder.lean
index 299035a95dfac5..80503f26eb3e2a 100644
--- a/Mathlib/Data/Int/ConditionallyCompleteOrder.lean
+++ b/Mathlib/Data/Int/ConditionallyCompleteOrder.lean
@@ -49,7 +49,7 @@ theorem csSup_eq_greatestOfBdd {s : Set ℤ} [DecidablePred (· ∈ s)] (b : ℤ
     (Hinh : ∃ z : ℤ, z ∈ s) : sSup s = greatestOfBdd b Hb Hinh := by
   have : s.Nonempty ∧ BddAbove s := ⟨Hinh, b, Hb⟩
   simp only [sSup, dif_pos this]
-  convert (coe_greatestOfBdd_eq Hb (Classical.choose_spec (⟨b, Hb⟩ : BddAbove s)) Hinh).symm
+  convert! (coe_greatestOfBdd_eq Hb (Classical.choose_spec (⟨b, Hb⟩ : BddAbove s)) Hinh).symm
 
 @[deprecated (since := "2025-12-24")] alias csSup_eq_greatest_of_bdd := csSup_eq_greatestOfBdd
 
@@ -66,7 +66,7 @@ theorem csInf_eq_leastOfBdd {s : Set ℤ} [DecidablePred (· ∈ s)] (b : ℤ) (
     (Hinh : ∃ z : ℤ, z ∈ s) : sInf s = leastOfBdd b Hb Hinh := by
   have : s.Nonempty ∧ BddBelow s := ⟨Hinh, b, Hb⟩
   simp only [sInf, dif_pos this]
-  convert (coe_leastOfBdd_eq Hb (Classical.choose_spec (⟨b, Hb⟩ : BddBelow s)) Hinh).symm
+  convert! (coe_leastOfBdd_eq Hb (Classical.choose_spec (⟨b, Hb⟩ : BddBelow s)) Hinh).symm
 
 @[deprecated (since := "2025-12-24")] alias csInf_eq_least_of_bdd := csInf_eq_leastOfBdd
 
@@ -80,11 +80,11 @@ theorem csInf_of_not_bddBelow {s : Set ℤ} (h : ¬BddBelow s) : sInf s = 0 :=
 @[deprecated (since := "2025-12-24")] alias csInf_of_not_bdd_below := csInf_of_not_bddBelow
 
 theorem csSup_mem {s : Set ℤ} (h1 : s.Nonempty) (h2 : BddAbove s) : sSup s ∈ s := by
-  convert (greatestOfBdd _ (Classical.choose_spec h2) h1).2.1
+  convert! (greatestOfBdd _ (Classical.choose_spec h2) h1).2.1
   exact dif_pos ⟨h1, h2⟩
 
 theorem csInf_mem {s : Set ℤ} (h1 : s.Nonempty) (h2 : BddBelow s) : sInf s ∈ s := by
-  convert (leastOfBdd _ (Classical.choose_spec h2) h1).2.1
+  convert! (leastOfBdd _ (Classical.choose_spec h2) h1).2.1
   exact dif_pos ⟨h1, h2⟩
 
 end Int
diff --git a/Mathlib/Data/Int/ModEq.lean b/Mathlib/Data/Int/ModEq.lean
index f4a2043b4d9c99..44132ff8bff28c 100644
--- a/Mathlib/Data/Int/ModEq.lean
+++ b/Mathlib/Data/Int/ModEq.lean
@@ -142,7 +142,7 @@ protected theorem mul_right' (h : a ≡ b [ZMOD n]) : a * c ≡ b * c [ZMOD n *
 
 @[gcongr]
 protected theorem add (h₁ : a ≡ b [ZMOD n]) (h₂ : c ≡ d [ZMOD n]) : a + c ≡ b + d [ZMOD n] :=
-  modEq_iff_dvd.2 <| by convert Int.dvd_add h₁.dvd h₂.dvd using 1; lia
+  modEq_iff_dvd.2 <| by convert! Int.dvd_add h₁.dvd h₂.dvd using 1; lia
 
 protected theorem add_left (c : ℤ) (h : a ≡ b [ZMOD n]) : c + a ≡ c + b [ZMOD n] :=
   ModEq.rfl.add h
@@ -219,7 +219,7 @@ theorem cancel_left_div_gcd (hm : 0 < m) (h : c * a ≡ c * b [ZMOD m]) : a ≡
   cancel_right_div_gcd hm <| by simpa [mul_comm] using h
 
 theorem of_div (h : a / c ≡ b / c [ZMOD m / c]) (ha : c ∣ a) (ha : c ∣ b) (ha : c ∣ m) :
-    a ≡ b [ZMOD m] := by convert h.mul_left' <;> rwa [Int.mul_ediv_cancel']
+    a ≡ b [ZMOD m] := by convert! h.mul_left' <;> rwa [Int.mul_ediv_cancel']
 
 /-- Cancel left multiplication on both sides of the `≡` and in the modulus.
 
@@ -358,7 +358,7 @@ theorem modEq_and_modEq_iff_modEq_lcm {a b m n : ℤ} :
 
 theorem modEq_and_modEq_iff_modEq_mul {a b m n : ℤ} (hmn : m.natAbs.Coprime n.natAbs) :
     a ≡ b [ZMOD m] ∧ a ≡ b [ZMOD n] ↔ a ≡ b [ZMOD m * n] := by
-  convert ← modEq_and_modEq_iff_modEq_lcm using 1
+  convert! ← modEq_and_modEq_iff_modEq_lcm using 1
   rw [lcm_eq_mul_iff.mpr (.inr <| .inr hmn), ← natAbs_mul, modEq_natAbs]
 
 theorem gcd_a_modEq (a b : ℕ) : (a : ℤ) * Nat.gcdA a b ≡ Nat.gcd a b [ZMOD b] := by
diff --git a/Mathlib/Data/List/AList.lean b/Mathlib/Data/List/AList.lean
index 74630c14047305..69b8bcdd3809c6 100644
--- a/Mathlib/Data/List/AList.lean
+++ b/Mathlib/Data/List/AList.lean
@@ -352,7 +352,7 @@ theorem insertRec_insert {C : AList β → Sort*} (H0 : C ∅)
       IH c.1 c.2 ⟨l, hl⟩ h (@insertRec α β _ C H0 IH ⟨l, hl⟩) by
     cases c
     apply eq_of_heq
-    convert this <;> rw [insert_of_notMem h]
+    convert! this <;> rw [insert_of_notMem h]
   rw [insertRec]
   apply cast_heq
 
diff --git a/Mathlib/Data/List/Basic.lean b/Mathlib/Data/List/Basic.lean
index 433d9cb9364d19..b6f64d90dca234 100644
--- a/Mathlib/Data/List/Basic.lean
+++ b/Mathlib/Data/List/Basic.lean
@@ -665,7 +665,7 @@ theorem get_reverse' (l : List α) (n) (hn') :
   simp
 
 theorem eq_cons_of_length_one {l : List α} (h : l.length = 1) : l = [l.get ⟨0, by lia⟩] := by
-  refine ext_get (by convert h) (by grind)
+  refine ext_get (by convert! h) (by grind)
 
 end deprecated
 
diff --git a/Mathlib/Data/List/Cycle.lean b/Mathlib/Data/List/Cycle.lean
index f4b5d31effd0e0..05afb88727f8f8 100644
--- a/Mathlib/Data/List/Cycle.lean
+++ b/Mathlib/Data/List/Cycle.lean
@@ -388,7 +388,7 @@ theorem prev_reverse_eq_next (l : List α) (h : Nodup l) (x : α) (hx : x ∈ l)
 
 theorem next_reverse_eq_prev (l : List α) (h : Nodup l) (x : α) (hx : x ∈ l) :
     next l.reverse x (mem_reverse.mpr hx) = prev l x hx := by
-  convert (prev_reverse_eq_next l.reverse (nodup_reverse.mpr h) x (mem_reverse.mpr hx)).symm
+  convert! (prev_reverse_eq_next l.reverse (nodup_reverse.mpr h) x (mem_reverse.mpr hx)).symm
   exact (reverse_reverse l).symm
 
 theorem isRotated_next_eq {l l' : List α} (h : l ~r l') (hn : Nodup l) {x : α} (hx : x ∈ l) :
diff --git a/Mathlib/Data/List/Infix.lean b/Mathlib/Data/List/Infix.lean
index 74f4fa9e5dcb1b..7241a120eff011 100644
--- a/Mathlib/Data/List/Infix.lean
+++ b/Mathlib/Data/List/Infix.lean
@@ -116,7 +116,7 @@ theorem concat_get_prefix {x y : List α} (h : x <+: y) (hl : x.length < y.lengt
     x ++ [y.get ⟨x.length, hl⟩] <+: y := by
   use y.drop (x.length + 1)
   nth_rw 1 [List.prefix_iff_eq_take.mp h]
-  convert List.take_append_drop (x.length + 1) y using 2
+  convert! List.take_append_drop (x.length + 1) y using 2
   rw [← List.take_concat_get, List.concat_eq_append]; rfl
 
 theorem prefix_append_drop {l₁ l₂ : List α} (h : l₁ <+: l₂) :
diff --git a/Mathlib/Data/List/Intervals.lean b/Mathlib/Data/List/Intervals.lean
index 08abbc956649a2..01427527620c81 100644
--- a/Mathlib/Data/List/Intervals.lean
+++ b/Mathlib/Data/List/Intervals.lean
@@ -83,7 +83,7 @@ theorem eq_empty_iff {n m : ℕ} : Ico n m = [] ↔ m ≤ n :=
 theorem append_consecutive {n m l : ℕ} (hnm : n ≤ m) (hml : m ≤ l) :
     Ico n m ++ Ico m l = Ico n l := by
   dsimp only [Ico]
-  convert range'_append using 2
+  convert! range'_append using 2
   · rw [Nat.one_mul, Nat.add_sub_cancel' hnm]
   · lia
 
@@ -99,7 +99,7 @@ theorem inter_consecutive (n m l : ℕ) : Ico n m ∩ Ico m l = [] := by
 @[simp]
 theorem bagInter_consecutive (n m l : Nat) :
     @List.bagInter ℕ instBEqOfDecidableEq (Ico n m) (Ico m l) = [] :=
-  (bagInter_nil_iff_inter_nil _ _).2 (by convert inter_consecutive n m l)
+  (bagInter_nil_iff_inter_nil _ _).2 (by convert! inter_consecutive n m l)
 
 @[simp]
 theorem succ_singleton {n : ℕ} : Ico n (n + 1) = [n] := by
diff --git a/Mathlib/Data/List/Perm/Basic.lean b/Mathlib/Data/List/Perm/Basic.lean
index 0e9e02f85c1429..c1bc8b988698fa 100644
--- a/Mathlib/Data/List/Perm/Basic.lean
+++ b/Mathlib/Data/List/Perm/Basic.lean
@@ -164,7 +164,7 @@ end Rel
 lemma count_eq_count_filter_add [DecidableEq α] (P : α → Prop) [DecidablePred P]
     (l : List α) (a : α) :
     count a l = count a (l.filter P) + count a (l.filter (¬ P ·)) := by
-  convert countP_eq_countP_filter_add l _ P
+  convert! countP_eq_countP_filter_add l _ P
   simp only [decide_not]
 
 theorem Perm.foldl_eq {f : β → α → β} {l₁ l₂ : List α} [rcomm : RightCommutative f] (p : l₁ ~ l₂) :
diff --git a/Mathlib/Data/List/Sublists.lean b/Mathlib/Data/List/Sublists.lean
index fc230ed022ea0b..e41e39c15a6b50 100644
--- a/Mathlib/Data/List/Sublists.lean
+++ b/Mathlib/Data/List/Sublists.lean
@@ -331,7 +331,7 @@ protected alias ⟨Nodup.of_sublists', _⟩ := nodup_sublists'
 
 theorem nodup_sublistsLen (n : ℕ) {l : List α} (h : Nodup l) : (sublistsLen n l).Nodup := by
   have : Pairwise (· ≠ ·) l.sublists' := Pairwise.imp
-    (fun h => Lex.to_ne (by convert h using 3; simp [eq_comm])) h.sublists'
+    (fun h => Lex.to_ne (by convert! h using 3; simp [eq_comm])) h.sublists'
   exact this.sublist (sublistsLen_sublist_sublists' _ _)
 
 theorem sublists_map (f : α → β) : ∀ (l : List α),
diff --git a/Mathlib/Data/List/TakeWhile.lean b/Mathlib/Data/List/TakeWhile.lean
index 8e1ed94d7de509..d5f37e4fa7f80c 100644
--- a/Mathlib/Data/List/TakeWhile.lean
+++ b/Mathlib/Data/List/TakeWhile.lean
@@ -114,7 +114,7 @@ lemma find?_eq_head?_dropWhile_not :
 
 lemma find?_not_eq_head?_dropWhile :
     l.find? (fun x ↦ !(p x)) = (l.dropWhile p).head? := by
-  convert l.find?_eq_head?_dropWhile_not ?_
+  convert! l.find?_eq_head?_dropWhile_not ?_
   simp
 
 variable {p} {l}
@@ -125,7 +125,7 @@ lemma find?_eq_head_dropWhile_not (h : ∃ x ∈ l, p x) :
 
 lemma find?_not_eq_head_dropWhile (h : ∃ x ∈ l, ¬p x) :
     l.find? (fun x ↦ !(p x)) = some ((l.dropWhile p).head (by simpa using h)) := by
-  convert l.find?_eq_head_dropWhile_not ?_
+  convert! l.find?_eq_head_dropWhile_not ?_
   · simp
   · simpa using h
 
diff --git a/Mathlib/Data/List/ToFinsupp.lean b/Mathlib/Data/List/ToFinsupp.lean
index 5c6ee73ccf756d..d7499e9849650d 100644
--- a/Mathlib/Data/List/ToFinsupp.lean
+++ b/Mathlib/Data/List/ToFinsupp.lean
@@ -112,7 +112,7 @@ theorem toFinsupp_cons_eq_single_add_embDomain {R : Type*} [AddZeroClass R] (x :
     toFinsupp (x::xs) =
       Finsupp.single 0 x + (toFinsupp xs).embDomain (addRightEmbedding 1) := by
   classical
-    convert toFinsupp_append [x] xs using 3
+    convert! toFinsupp_append [x] xs using 3
     · exact (toFinsupp_singleton x).symm
     · ext n
       exact add_comm n 1
diff --git a/Mathlib/Data/Matrix/Invertible.lean b/Mathlib/Data/Matrix/Invertible.lean
index 728b99934521fd..1ddc70e5caf5e9 100644
--- a/Mathlib/Data/Matrix/Invertible.lean
+++ b/Mathlib/Data/Matrix/Invertible.lean
@@ -112,7 +112,7 @@ instance invertibleTranspose [Invertible A] : Invertible Aᵀ where
 
 lemma transpose_invOf [Invertible A] [Invertible Aᵀ] : (⅟A)ᵀ = ⅟(Aᵀ) := by
   letI := invertibleTranspose A
-  convert (rfl : _ = ⅟(Aᵀ))
+  convert! (rfl : _ = ⅟(Aᵀ))
 
 /-- `Aᵀ` is invertible when `A` is. -/
 @[implicit_reducible]
@@ -199,7 +199,7 @@ See `Matrix.invOf_add_mul_mul'` for the Binomial Inverse Theorem. -/
 theorem invOf_add_mul_mul [Invertible (A + U * C * V)] :
     ⅟(A + U * C * V) = ⅟A - ⅟A * U * ⅟(⅟C + V * ⅟A * U) * V * ⅟A := by
   letI := invertibleAddMulMul A U C V
-  convert (rfl : ⅟(A + U * C * V) = _)
+  convert! (rfl : ⅟(A + U * C * V) = _)
 
 end Woodbury
 
@@ -243,7 +243,7 @@ See `Matrix.invOf_add_mul_mul` for the Woodbury identity. -/
 theorem invOf_add_mul_mul' [Invertible (A + U * C * V)] :
     ⅟(A + U * C * V) = ⅟A - ⅟A * U * C * ⅟(C + C * V * ⅟A * U * C) * C * V * ⅟A := by
   letI := invertibleAddMulMul' A U C V
-  convert (rfl : ⅟(A + U * C * V) = _)
+  convert! (rfl : ⅟(A + U * C * V) = _)
 
 end BinomialInverseTheorem
 
diff --git a/Mathlib/Data/Matrix/Mul.lean b/Mathlib/Data/Matrix/Mul.lean
index f97ebaa6a7338e..5cdb2a47f5e0a5 100644
--- a/Mathlib/Data/Matrix/Mul.lean
+++ b/Mathlib/Data/Matrix/Mul.lean
@@ -164,34 +164,34 @@ variable [DecidableEq m] [NonUnitalNonAssocSemiring α] (u v w : m → α)
 theorem diagonal_dotProduct (i : m) : diagonal v i ⬝ᵥ w = v i * w i := by
   have : ∀ j ≠ i, diagonal v i j * w j = 0 := fun j hij => by
     simp [diagonal_apply_ne' _ hij]
-  convert Finset.sum_eq_single i (fun j _ => this j) _ using 1 <;> simp
+  convert! Finset.sum_eq_single i (fun j _ => this j) _ using 1 <;> simp
 
 
 @[simp]
 theorem dotProduct_diagonal (i : m) : v ⬝ᵥ diagonal w i = v i * w i := by
   have : ∀ j ≠ i, v j * diagonal w i j = 0 := fun j hij => by
     simp [diagonal_apply_ne' _ hij]
-  convert Finset.sum_eq_single i (fun j _ => this j) _ using 1 <;> simp
+  convert! Finset.sum_eq_single i (fun j _ => this j) _ using 1 <;> simp
 
 @[simp]
 theorem dotProduct_diagonal' (i : m) : (v ⬝ᵥ fun j => diagonal w j i) = v i * w i := by
   have : ∀ j ≠ i, v j * diagonal w j i = 0 := fun j hij => by
     simp [diagonal_apply_ne _ hij]
-  convert Finset.sum_eq_single i (fun j _ => this j) _ using 1 <;> simp
+  convert! Finset.sum_eq_single i (fun j _ => this j) _ using 1 <;> simp
 
 @[simp]
 theorem single_dotProduct (x : α) (i : m) : Pi.single i x ⬝ᵥ v = x * v i := by
 -- Porting note: added `(_ : m → α)`
   have : ∀ j ≠ i, (Pi.single i x : m → α) j * v j = 0 := fun j hij => by
     simp [Pi.single_eq_of_ne hij]
-  convert Finset.sum_eq_single i (fun j _ => this j) _ using 1 <;> simp
+  convert! Finset.sum_eq_single i (fun j _ => this j) _ using 1 <;> simp
 
 @[simp]
 theorem dotProduct_single (x : α) (i : m) : v ⬝ᵥ Pi.single i x = v i * x := by
 -- Porting note: added `(_ : m → α)`
   have : ∀ j ≠ i, v j * (Pi.single i x : m → α) j = 0 := fun j hij => by
     simp [Pi.single_eq_of_ne hij]
-  convert Finset.sum_eq_single i (fun j _ => this j) _ using 1 <;> simp
+  convert! Finset.sum_eq_single i (fun j _ => this j) _ using 1 <;> simp
 
 end NonUnitalNonAssocSemiringDecidable
 
diff --git a/Mathlib/Data/Multiset/AddSub.lean b/Mathlib/Data/Multiset/AddSub.lean
index 2e9155ac924f12..3f50a550897135 100644
--- a/Mathlib/Data/Multiset/AddSub.lean
+++ b/Mathlib/Data/Multiset/AddSub.lean
@@ -258,13 +258,13 @@ theorem card_erase_eq_ite {a : α} {s : Multiset α} :
 @[simp]
 theorem count_erase_self (a : α) (s : Multiset α) : count a (erase s a) = count a s - 1 :=
   Quotient.inductionOn s fun l => by
-    convert List.count_erase_self (a := a) (l := l) <;> rw [← coe_count] <;> simp
+    convert! List.count_erase_self (a := a) (l := l) <;> rw [← coe_count] <;> simp
 
 @[simp]
 theorem count_erase_of_ne {a b : α} (ab : a ≠ b) (s : Multiset α) :
     count a (erase s b) = count a s :=
   Quotient.inductionOn s fun l => by
-    convert List.count_erase_of_ne ab (l := l) <;> rw [← coe_count] <;> simp
+    convert! List.count_erase_of_ne ab (l := l) <;> rw [← coe_count] <;> simp
 
 end Erase
 
diff --git a/Mathlib/Data/Multiset/Filter.lean b/Mathlib/Data/Multiset/Filter.lean
index 111a922dbf9ec6..b94cfdfdf47f57 100644
--- a/Mathlib/Data/Multiset/Filter.lean
+++ b/Mathlib/Data/Multiset/Filter.lean
@@ -277,7 +277,7 @@ theorem countP_filter (q) [DecidablePred q] (s : Multiset α) :
 theorem countP_eq_countP_filter_add (s) (p q : α → Prop) [DecidablePred p] [DecidablePred q] :
     countP p s = (filter q s).countP p + (filter (fun a => ¬q a) s).countP p :=
   Quot.inductionOn s fun l => by
-    convert l.countP_eq_countP_filter_add (p ·) (q ·)
+    convert! l.countP_eq_countP_filter_add (p ·) (q ·)
     simp
 
 theorem countP_map (f : α → β) (s : Multiset α) (p : β → Prop) [DecidablePred p] :
diff --git a/Mathlib/Data/Multiset/Fintype.lean b/Mathlib/Data/Multiset/Fintype.lean
index 850c5cb3141696..e447b437ff83b2 100644
--- a/Mathlib/Data/Multiset/Fintype.lean
+++ b/Mathlib/Data/Multiset/Fintype.lean
@@ -250,9 +250,9 @@ def consEquiv {v : α} : v ::ₘ m ≃ Option m where
     by_cases hv : x.1 = v
     · simp only [hv, true_and] at h ⊢
       apply lt_of_le_of_ne (Nat.le_of_lt_add_one _) h
-      convert x.2.2 using 1
+      convert! x.2.2 using 1
       simp [hv]
-    · convert x.2.2 using 1
+    · convert! x.2.2 using 1
       exact (count_cons_of_ne hv _).symm
     ⟩⟩
   invFun x := x.elim ⟨v, ⟨m.count v, by simp⟩⟩ (fun x ↦ ⟨x.1, x.2.castLE (count_le_count_cons ..)⟩)
diff --git a/Mathlib/Data/Multiset/Replicate.lean b/Mathlib/Data/Multiset/Replicate.lean
index 50e521eb2bea8f..2681e862857bad 100644
--- a/Mathlib/Data/Multiset/Replicate.lean
+++ b/Mathlib/Data/Multiset/Replicate.lean
@@ -113,11 +113,11 @@ variable [DecidableEq α] {s t u : Multiset α}
 
 @[simp]
 theorem count_replicate_self (a : α) (n : ℕ) : count a (replicate n a) = n := by
-  convert List.count_replicate_self (a := a)
+  convert! List.count_replicate_self (a := a)
   rw [← coe_count, coe_replicate]
 
 theorem count_replicate (a b : α) (n : ℕ) : count a (replicate n b) = if b = a then n else 0 := by
-  convert List.count_replicate (a := a)
+  convert! List.count_replicate (a := a)
   · rw [← coe_count, coe_replicate]
   · simp
 
diff --git a/Mathlib/Data/NNRat/Lemmas.lean b/Mathlib/Data/NNRat/Lemmas.lean
index df6aac7d808201..7c0c1d60f5aef0 100644
--- a/Mathlib/Data/NNRat/Lemmas.lean
+++ b/Mathlib/Data/NNRat/Lemmas.lean
@@ -66,23 +66,23 @@ protected def rec {α : ℚ≥0 → Sort*} (h : ∀ m n : ℕ, α (m / n)) (q :
 theorem mul_num (q₁ q₂ : ℚ≥0) :
     (q₁ * q₂).num = q₁.num * q₂.num / Nat.gcd (q₁.num * q₂.num) (q₁.den * q₂.den) := by
   zify
-  convert Rat.mul_num q₁ q₂ <;> norm_cast
+  convert! Rat.mul_num q₁ q₂ <;> norm_cast
 
 theorem mul_den (q₁ q₂ : ℚ≥0) :
     (q₁ * q₂).den = q₁.den * q₂.den / Nat.gcd (q₁.num * q₂.num) (q₁.den * q₂.den) := by
-  convert Rat.mul_den q₁ q₂
+  convert! Rat.mul_den q₁ q₂
   norm_cast
 
 /-- A version of `NNRat.mul_den` without division. -/
 theorem den_mul_den_eq_den_mul_gcd (q₁ q₂ : ℚ≥0) :
     q₁.den * q₂.den = (q₁ * q₂).den * ((q₁.num * q₂.num).gcd (q₁.den * q₂.den)) := by
-  convert Rat.den_mul_den_eq_den_mul_gcd q₁ q₂
+  convert! Rat.den_mul_den_eq_den_mul_gcd q₁ q₂
   norm_cast
 
 /-- A version of `NNRat.mul_num` without division. -/
 theorem num_mul_num_eq_num_mul_gcd (q₁ q₂ : ℚ≥0) :
     q₁.num * q₂.num = (q₁ * q₂).num * ((q₁.num * q₂.num).gcd (q₁.den * q₂.den)) := by
   zify
-  convert Rat.num_mul_num_eq_num_mul_gcd q₁ q₂ <;> norm_cast
+  convert! Rat.num_mul_num_eq_num_mul_gcd q₁ q₂ <;> norm_cast
 
 end NNRat
diff --git a/Mathlib/Data/Nat/Bitwise.lean b/Mathlib/Data/Nat/Bitwise.lean
index c5d09a3ba76a3c..4e490227eefbb8 100644
--- a/Mathlib/Data/Nat/Bitwise.lean
+++ b/Mathlib/Data/Nat/Bitwise.lean
@@ -204,14 +204,14 @@ theorem lt_of_testBit {n m : ℕ} (i : ℕ) (hn : testBit n i = false) (hm : tes
       · subst hi
         simp only [testBit_bit_zero] at hn hm
         have : n = m :=
-          eq_of_testBit_eq fun i => by convert hnm (i + 1) (Nat.zero_lt_succ _) using 1
+          eq_of_testBit_eq fun i => by convert! hnm (i + 1) (Nat.zero_lt_succ _) using 1
           <;> rw [testBit_bit_succ]
         rw [hn, hm, this, bit_false, bit_true]
         exact Nat.lt_succ_self _
       · obtain ⟨i', rfl⟩ := exists_eq_succ_of_ne_zero hi
         simp only [testBit_bit_succ] at hn hm
         have := hn' _ hn hm fun j hj => by
-          convert hnm j.succ (succ_lt_succ hj) using 1 <;> rw [testBit_bit_succ]
+          convert! hnm j.succ (succ_lt_succ hj) using 1 <;> rw [testBit_bit_succ]
         exact bit_lt_bit b b' this
 
 theorem bitwise_swap {f : Bool → Bool → Bool} :
diff --git a/Mathlib/Data/Nat/Cast/Order/Basic.lean b/Mathlib/Data/Nat/Cast/Order/Basic.lean
index fc0cd1ca6d5813..575cb7470728b0 100644
--- a/Mathlib/Data/Nat/Cast/Order/Basic.lean
+++ b/Mathlib/Data/Nat/Cast/Order/Basic.lean
@@ -52,7 +52,7 @@ variable [NeZero (1 : α)]
 
 theorem cast_add_one_pos (n : ℕ) : 0 < (n : α) + 1 := by
   apply zero_lt_one.trans_le
-  convert (@mono_cast α _).imp (?_ : 1 ≤ n + 1)
+  convert! (@mono_cast α _).imp (?_ : 1 ≤ n + 1)
   <;> simp
 
 /-- See also `Nat.cast_pos`, specialised for an `OrderedSemiring`. -/
diff --git a/Mathlib/Data/Nat/Choose/Multinomial.lean b/Mathlib/Data/Nat/Choose/Multinomial.lean
index 4ab629a678e318..a9ed09a52cd00c 100644
--- a/Mathlib/Data/Nat/Choose/Multinomial.lean
+++ b/Mathlib/Data/Nat/Choose/Multinomial.lean
@@ -238,7 +238,7 @@ noncomputable def countPerms [DecidableEq α] (m : Multiset α) : ℕ :=
 theorem countPerms_filter_ne [DecidableEq α] (a : α) (m : Multiset α) :
     m.countPerms = m.card.choose (m.count a) * (m.filter (a ≠ ·)).countPerms := by
   dsimp only [countPerms]
-  convert Finsupp.multinomial_update a _
+  convert! Finsupp.multinomial_update a _
   · rw [← Finsupp.card_toMultiset, m.toFinsupp_toMultiset]
   · ext1 a
     rw [toFinsupp_apply, count_filter, Finsupp.coe_update]
@@ -322,8 +322,8 @@ theorem sum_pow_of_commute (x : α → R) (s : Finset α)
     · rw [_root_.pow_zero, Fintype.sum_subsingleton]
       swap
       · exact ⟨0, by simp [eq_iff_true_of_subsingleton]⟩
-      convert (@one_mul R _ _).symm
-      convert @Nat.cast_one R _
+      convert! (@one_mul R _ _).symm
+      convert! @Nat.cast_one R _
       simp
     · rw [_root_.pow_succ, mul_zero]
       haveI : IsEmpty (Finset.sym (∅ : Finset α) n.succ) := Finset.instIsEmpty
@@ -355,7 +355,7 @@ lemma sum_pow_eq_sum_piAntidiag (s : Finset α) (f : α → R) (n : ℕ) :
 theorem sum_pow (x : α → R) (n : ℕ) :
     s.sum x ^ n = ∑ k ∈ s.sym n, k.val.countPerms * (k.val.map x).prod := by
   conv_rhs => rw [← sum_coe_sort]
-  convert sum_pow_of_commute x s (fun _ _ _ _ _ ↦ Commute.all ..) n
+  convert! sum_pow_of_commute x s (fun _ _ _ _ _ ↦ Commute.all ..) n
   rw [Multiset.noncommProd_eq_prod]
 
 end CommSemiring
diff --git a/Mathlib/Data/Nat/Choose/Sum.lean b/Mathlib/Data/Nat/Choose/Sum.lean
index 9f2e202cc1f691..bd330feba8b9b3 100644
--- a/Mathlib/Data/Nat/Choose/Sum.lean
+++ b/Mathlib/Data/Nat/Choose/Sum.lean
@@ -147,7 +147,7 @@ we have to decompose the remaining interval `[0, i)` into `k + 1` intervals, hen
 lemma sum_range_add_choose (n k : ℕ) :
     ∑ i ∈ Finset.range (n + 1), (i + k).choose k = (n + k + 1).choose (k + 1) := by
   rw [← sum_Icc_choose, range_eq_Ico]
-  convert (sum_map _ (addRightEmbedding k) (·.choose k)).symm using 2
+  convert! (sum_map _ (addRightEmbedding k) (·.choose k)).symm using 2
   rw [map_add_right_Ico, zero_add, add_right_comm, Ico_add_one_right_eq_Icc]
 
 /-- Summing `i * (n.choose i)` for `i ∈ [0, n]` gives `n * 2 ^ (n - 1)`. -/
diff --git a/Mathlib/Data/Nat/Digits/Defs.lean b/Mathlib/Data/Nat/Digits/Defs.lean
index ab040111a55c17..a8af782476861e 100644
--- a/Mathlib/Data/Nat/Digits/Defs.lean
+++ b/Mathlib/Data/Nat/Digits/Defs.lean
@@ -227,7 +227,7 @@ theorem digits_ofDigits (b : ℕ) (h : 1 < b) (L : List ℕ) (w₁ : ∀ l ∈ L
         exact List.mem_cons_of_mem _ m
       · intro h
         rw [List.getLast_cons h] at w₂
-        convert w₂
+        convert! w₂
     · exact w₁ d List.mem_cons_self
     · by_cases h' : L = []
       · rcases h' with rfl
@@ -275,7 +275,7 @@ theorem digits_eq_nil_iff_eq_zero {b n : ℕ} : digits b n = [] ↔ n = 0 := by
   constructor
   · intro h
     have : ofDigits b (digits b n) = ofDigits b [] := by rw [h]
-    convert this
+    convert! this
     rw [ofDigits_digits]
   · rintro rfl
     simp
@@ -383,7 +383,7 @@ theorem ofDigits_lt_base_pow_length {b : ℕ} {l : List ℕ} (hb : 1 < b) (hl :
 
 /-- Any number m is less than (b+2)^(number of digits in the base b + 2 representation of m) -/
 theorem lt_base_pow_length_digits' {b m : ℕ} : m < (b + 2) ^ (digits (b + 2) m).length := by
-  convert @ofDigits_lt_base_pow_length' b (digits (b + 2) m) fun _ => digits_lt_base'
+  convert! @ofDigits_lt_base_pow_length' b (digits (b + 2) m) fun _ => digits_lt_base'
   rw [ofDigits_digits (b + 2) m]
 
 /-- Any number m is less than b^(number of digits in the base b representation of m) -/
@@ -455,8 +455,9 @@ lemma ofDigits_div_pow_eq_ofDigits_drop
 -/
 lemma self_div_pow_eq_ofDigits_drop {p : ℕ} (i n : ℕ) (h : 2 ≤ p) :
     n / p ^ i = ofDigits p ((p.digits n).drop i) := by
-  convert ofDigits_div_pow_eq_ofDigits_drop i (zero_lt_of_lt h) (p.digits n)
-    (fun l hl ↦ digits_lt_base h hl)
+  convert!
+    ofDigits_div_pow_eq_ofDigits_drop i (zero_lt_of_lt h) (p.digits n)
+      (fun l hl ↦ digits_lt_base h hl)
   exact (ofDigits_digits p n).symm
 
 /-- Interpreting as a base `p` number and modulo `p^i` is the same as taking the first `i` digits.
@@ -484,8 +485,9 @@ lemma ofDigits_mod_pow_eq_ofDigits_take
 -/
 lemma self_mod_pow_eq_ofDigits_take {p : ℕ} (i n : ℕ) (h : 2 ≤ p) :
     n % p ^ i = ofDigits p ((p.digits n).take i) := by
-  convert ofDigits_mod_pow_eq_ofDigits_take i (zero_lt_of_lt h) (p.digits n)
-    (fun l hl ↦ digits_lt_base h hl)
+  convert!
+    ofDigits_mod_pow_eq_ofDigits_take i (zero_lt_of_lt h) (p.digits n)
+      (fun l hl ↦ digits_lt_base h hl)
   exact (ofDigits_digits p n).symm
 
 /-! ### `Nat.toDigits` length -/
diff --git a/Mathlib/Data/Nat/Digits/Lemmas.lean b/Mathlib/Data/Nat/Digits/Lemmas.lean
index 54710594e597fd..4aae05517589dc 100644
--- a/Mathlib/Data/Nat/Digits/Lemmas.lean
+++ b/Mathlib/Data/Nat/Digits/Lemmas.lean
@@ -139,7 +139,7 @@ theorem pow_length_le_mul_ofDigits {b : ℕ} {l : List ℕ} (hl : l ≠ []) (hl2
   apply Nat.mul_le_mul_left
   refine le_trans ?_ (Nat.le_add_left _ _)
   have : 0 < l.getLast hl := by rwa [pos_iff_ne_zero]
-  convert Nat.mul_le_mul_left ((b + 2) ^ (l.length - 1)) this using 1
+  convert! Nat.mul_le_mul_left ((b + 2) ^ (l.length - 1)) this using 1
   rw [Nat.mul_one]
 
 /-- Any non-zero natural number `m` is greater than
@@ -148,8 +148,7 @@ theorem pow_length_le_mul_ofDigits {b : ℕ} {l : List ℕ} (hl : l ≠ []) (hl2
 theorem base_pow_length_digits_le' (b m : ℕ) (hm : m ≠ 0) :
     (b + 2) ^ (digits (b + 2) m).length ≤ (b + 2) * m := by
   have : digits (b + 2) m ≠ [] := digits_ne_nil_iff_ne_zero.mpr hm
-  convert @pow_length_le_mul_ofDigits b (digits (b + 2) m)
-    this (getLast_digit_ne_zero _ hm)
+  convert! @pow_length_le_mul_ofDigits b (digits (b + 2) m) this (getLast_digit_ne_zero _ hm)
   rw [ofDigits_digits]
 
 /-- Any non-zero natural number `m` is greater than
@@ -201,8 +200,9 @@ theorem sub_one_mul_sum_log_div_pow_eq_sub_sum_digits {p : ℕ} (n : ℕ) :
   obtain h | rfl | h : 1 < p ∨ 1 = p ∨ p < 1 := trichotomous 1 p
   · rcases eq_or_ne n 0 with rfl | hn
     · simp
-    · convert sub_one_mul_sum_div_pow_eq_sub_sum_digits (p.digits n) (getLast_digit_ne_zero p hn) <|
-          (fun l a ↦ digits_lt_base h a)
+    · convert!
+      sub_one_mul_sum_div_pow_eq_sub_sum_digits (p.digits n) (getLast_digit_ne_zero p hn) <|
+        (fun l a ↦ digits_lt_base h a)
       · refine (length_digits p n h hn).symm
       all_goals exact (ofDigits_digits p n).symm
   · simp
@@ -288,7 +288,7 @@ theorem modEq_digits_sum (b b' : ℕ) (h : b' % b = 1) (n : ℕ) : n ≡ (digits
     congr
     · skip
     · rw [← ofDigits_digits b' n]
-  convert ofDigits_modEq b' b (digits b' n)
+  convert! ofDigits_modEq b' b (digits b' n)
   exact h.symm
 
 theorem zmodeq_ofDigits_digits (b b' : ℕ) (c : ℤ) (h : b' ≡ c [ZMOD b]) (n : ℕ) :
@@ -421,7 +421,7 @@ This spelling can be helpful for some proofs.
 theorem _root_.Nat.bijOn_ofDigits' {b : ℕ} (hb : 1 < b) (l : ℕ) :
     Set.BijOn (ofDigits b) (fixedLengthDigits hb l) (Finset.range (b ^ l)) := by
   rw [fixedLengthDigits, Set.coe_toFinset]
-  convert bijOn_ofDigits hb l
+  convert! bijOn_ofDigits hb l
   ext; simp
 
 /--
@@ -431,7 +431,7 @@ This spelling can be helpful for some proofs.
 theorem _root_.Nat.bijOn_digitsAppend' {b : ℕ} (hb : 1 < b) (l : ℕ) :
     Set.BijOn (digitsAppend b l) (Finset.range (b ^ l)) (fixedLengthDigits hb l) := by
   rw [fixedLengthDigits, Set.coe_toFinset]
-  convert bijOn_digitsAppend hb l
+  convert! bijOn_digitsAppend hb l
   ext; simp
 
 @[simp]
diff --git a/Mathlib/Data/Nat/Factorization/Induction.lean b/Mathlib/Data/Nat/Factorization/Induction.lean
index b4d7f97e8d9be3..cbae182d598614 100644
--- a/Mathlib/Data/Nat/Factorization/Induction.lean
+++ b/Mathlib/Data/Nat/Factorization/Induction.lean
@@ -37,7 +37,7 @@ def recOnPrimePow {motive : ℕ → Sort*} (zero : motive 0) (one : motive 1)
       letI t := (k + 2).factorization p
       haveI hpt : p ^ t ∣ k + 2 := ordProj_dvd _ _
       haveI htp : 0 < t := hp.factorization_pos_of_dvd (k + 1).succ_ne_zero (k + 2).minFac_dvd
-      convert prime_pow_mul ((k + 2) / p ^ t) p t hp _ htp (hk _ (Nat.div_lt_of_lt_mul _)) using 1
+      convert! prime_pow_mul ((k + 2) / p ^ t) p t hp _ htp (hk _ (Nat.div_lt_of_lt_mul _)) using 1
       · rw [Nat.mul_div_cancel' hpt]
       · rw [Nat.dvd_div_iff_mul_dvd hpt, ← Nat.pow_succ]
         exact pow_succ_factorization_not_dvd (k + 1).succ_ne_zero hp
diff --git a/Mathlib/Data/Nat/GCD/Basic.lean b/Mathlib/Data/Nat/GCD/Basic.lean
index 26cceb810a4f00..07ccc5131cdb6f 100644
--- a/Mathlib/Data/Nat/GCD/Basic.lean
+++ b/Mathlib/Data/Nat/GCD/Basic.lean
@@ -206,7 +206,7 @@ theorem gcd_mul_of_coprime_of_dvd {a b c : ℕ} (hac : Coprime a c) (b_dvd_c : b
     gcd (a * b) c = b := by
   rcases exists_eq_mul_left_of_dvd b_dvd_c with ⟨d, rfl⟩
   rw [gcd_mul_right]
-  convert one_mul b
+  convert! one_mul b
   exact Coprime.coprime_mul_right_right hac
 
 theorem Coprime.eq_of_mul_eq_zero {m n : ℕ} (h : m.Coprime n) (hmn : m * n = 0) :
diff --git a/Mathlib/Data/Nat/Lattice.lean b/Mathlib/Data/Nat/Lattice.lean
index f5483169011237..1c215c142aa6ef 100644
--- a/Mathlib/Data/Nat/Lattice.lean
+++ b/Mathlib/Data/Nat/Lattice.lean
@@ -168,7 +168,7 @@ theorem sInf_add {n : ℕ} {p : ℕ → Prop} (hn : n ≤ sInf { m | p m }) :
 theorem sInf_add' {n : ℕ} {p : ℕ → Prop} (h : 0 < sInf { m | p m }) :
     sInf { m | p m } + n = sInf { m | p (m - n) } := by
   suffices h₁ : n ≤ sInf {m | p (m - n)} by
-    convert sInf_add h₁
+    convert! sInf_add h₁
     simp_rw [Nat.add_sub_cancel_right]
   obtain ⟨m, hm⟩ := nonempty_of_pos_sInf h
   refine
diff --git a/Mathlib/Data/Nat/ModEq.lean b/Mathlib/Data/Nat/ModEq.lean
index cc8b1a9aed7540..22f5deb78a5c55 100644
--- a/Mathlib/Data/Nat/ModEq.lean
+++ b/Mathlib/Data/Nat/ModEq.lean
@@ -167,7 +167,7 @@ protected theorem add_left_cancel (h₁ : a ≡ b [MOD n]) (h₂ : a + c ≡ b +
     c ≡ d [MOD n] := by
   simp only [modEq_iff_dvd, Int.natCast_add] at *
   rw [add_sub_add_comm] at h₂
-  convert Int.dvd_sub h₂ h₁ using 1
+  convert! Int.dvd_sub h₂ h₁ using 1
   rw [add_sub_cancel_left]
 
 protected theorem add_left_cancel' (c : ℕ) (h : c + a ≡ c + b [MOD n]) : a ≡ b [MOD n] :=
@@ -251,7 +251,7 @@ For cancelling right multiplication on both sides of the `≡`, see `nat.modeq.m
 lemma of_mul_right (m : ℕ) : a ≡ b [MOD n * m] → a ≡ b [MOD n] := mul_comm m n ▸ of_mul_left _
 
 theorem of_div (h : a / c ≡ b / c [MOD m / c]) (ha : c ∣ a) (ha : c ∣ b) (ha : c ∣ m) :
-    a ≡ b [MOD m] := by convert h.mul_left' c <;> rwa [Nat.mul_div_cancel']
+    a ≡ b [MOD m] := by convert! h.mul_left' c <;> rwa [Nat.mul_div_cancel']
 
 end ModEq
 
@@ -462,7 +462,7 @@ def chineseRemainder' (h : a ≡ b [MOD gcd n m]) : { k // k ≡ a [MOD n] ∧ k
 
 /-- The natural number less than `n*m` congruent to `a` mod `n` and `b` mod `m` -/
 def chineseRemainder (co : n.Coprime m) (a b : ℕ) : { k // k ≡ a [MOD n] ∧ k ≡ b [MOD m] } :=
-  chineseRemainder' (by convert @modEq_one a b)
+  chineseRemainder' (by convert! @modEq_one a b)
 
 theorem chineseRemainder'_lt_lcm (h : a ≡ b [MOD gcd n m]) (hn : n ≠ 0) (hm : m ≠ 0) :
     ↑(chineseRemainder' h) < lcm n m := by
diff --git a/Mathlib/Data/Nat/Multiplicity.lean b/Mathlib/Data/Nat/Multiplicity.lean
index 5ed0419e2691e5..f0e56408451f24 100644
--- a/Mathlib/Data/Nat/Multiplicity.lean
+++ b/Mathlib/Data/Nat/Multiplicity.lean
@@ -211,7 +211,7 @@ theorem emultiplicity_choose' {p n k b : ℕ} (hp : p.Prime) (hnb : log p (n + k
 theorem emultiplicity_choose {p n k b : ℕ} (hp : p.Prime) (hkn : k ≤ n) (hnb : log p n < b) :
     emultiplicity p (choose n k) = #{i ∈ Ico 1 b | p ^ i ≤ k % p ^ i + (n - k) % p ^ i} := by
   have := Nat.sub_add_cancel hkn
-  convert @emultiplicity_choose' p (n - k) k b hp _
+  convert! @emultiplicity_choose' p (n - k) k b hp _
   · rw [this]
   exact this.symm ▸ hnb
 
diff --git a/Mathlib/Data/Nat/Nth.lean b/Mathlib/Data/Nat/Nth.lean
index 71232827fc3f6a..0edf7e79df4707 100644
--- a/Mathlib/Data/Nat/Nth.lean
+++ b/Mathlib/Data/Nat/Nth.lean
@@ -236,7 +236,7 @@ theorem nth_zero : nth p 0 = sInf (setOf p) := by rw [nth_eq_sInf]; simp
 theorem nth_zero_of_zero (h : p 0) : nth p 0 = 0 := by simp [nth_zero, h]
 
 theorem nth_zero_of_exists [DecidablePred p] (h : ∃ n, p n) : nth p 0 = Nat.find h := by
-  rw [nth_zero]; convert Nat.sInf_def h
+  rw [nth_zero]; convert! Nat.sInf_def h
 
 theorem nth_eq_zero {n} :
     nth p n = 0 ↔ p 0 ∧ n = 0 ∨ ∃ hf : (setOf p).Finite, #hf.toFinset ≤ n := by
@@ -351,9 +351,9 @@ lemma nth_comp_of_strictMono {n : ℕ} {f : ℕ → ℕ} (hf : StrictMono f)
     repeat nth_rw 1 [nth_eq_sInf]
     have h0' : ∀ k', (p k' ∧ ∀ k < n + 1, nth p k < k') → k' ∈ Set.range f := fun _ h ↦ h0 _ h.1
     rw [← hs h0', ← hf.monotone.map_csInf]
-    · convert rfl using 8 with k m' hm
+    · convert! rfl using 8 with k m' hm
       nth_rw 2 [← hf.lt_iff_lt]
-      convert Iff.rfl using 2
+      convert! Iff.rfl using 2
       exact ih m' (Nat.lt_add_one_iff.mp hm) fun hfi ↦ hm.trans (h hfi)
     · rcases h0 _ (nth_mem _ h) with ⟨t, ht⟩
       exact ⟨t, ht ▸ (nth_mem _ h), fun _ hk ↦ ht ▸ nth_lt_nth' hk h⟩
diff --git a/Mathlib/Data/Nat/Set.lean b/Mathlib/Data/Nat/Set.lean
index f5fd105bc14585..950d1dbde02f5b 100644
--- a/Mathlib/Data/Nat/Set.lean
+++ b/Mathlib/Data/Nat/Set.lean
@@ -36,7 +36,7 @@ theorem range_of_succ (f : ℕ → α) : {f 0} ∪ range (f ∘ succ) = range f
 theorem range_rec {α : Type*} (x : α) (f : ℕ → α → α) :
     (Set.range fun n => Nat.rec x f n : Set α) =
       {x} ∪ Set.range fun n => Nat.rec (f 0 x) (f ∘ succ) n := by
-  convert (range_of_succ (fun n => Nat.rec x f n : ℕ → α)).symm using 4
+  convert! (range_of_succ (fun n => Nat.rec x f n : ℕ → α)).symm using 4
   dsimp
   rename_i n
   induction n with
diff --git a/Mathlib/Data/Nat/Squarefree.lean b/Mathlib/Data/Nat/Squarefree.lean
index 593cb5fb0d0634..f4fb20713370c4 100644
--- a/Mathlib/Data/Nat/Squarefree.lean
+++ b/Mathlib/Data/Nat/Squarefree.lean
@@ -322,9 +322,10 @@ theorem sq_mul_squarefree_of_pos {n : ℕ} (hn : 0 < n) :
   rw [Nat.isUnit_iff]
   by_contra hx
   refine Nat.lt_le_asymm ?_ (Finset.le_max' S ((b * x) ^ 2) ?_)
-  · convert lt_mul_of_one_lt_right hlts
-      (one_lt_pow two_ne_zero (one_lt_iff_ne_zero_and_ne_one.mpr ⟨fun h => by simp_all, hx⟩))
-      using 1
+  · convert!
+      lt_mul_of_one_lt_right hlts
+        (one_lt_pow two_ne_zero (one_lt_iff_ne_zero_and_ne_one.mpr ⟨fun h => by simp_all, hx⟩))
+    using 1
     rw [mul_pow]
   · simp_rw [S, hsa, Finset.mem_filter, Finset.mem_range]
     refine ⟨Nat.lt_succ_iff.mpr (le_of_dvd hn ?_), ?_, ⟨b * x, rfl⟩⟩ <;> use y <;> rw [hy] <;> ring
diff --git a/Mathlib/Data/Nat/Totient.lean b/Mathlib/Data/Nat/Totient.lean
index 82ed34fccf49ac..4a0b3dd32e0d8b 100644
--- a/Mathlib/Data/Nat/Totient.lean
+++ b/Mathlib/Data/Nat/Totient.lean
@@ -172,7 +172,7 @@ theorem sum_totient (n : ℕ) : n.divisors.sum φ = n := by
   exact sum_congr rfl fun x hx => totient_div_of_dvd (dvd_of_mem_divisors hx)
 
 theorem sum_totient' (n : ℕ) : ∑ m ∈ range n.succ with m ∣ n, φ m = n := by
-  convert sum_totient _ using 1
+  convert! sum_totient _ using 1
   simp only [Nat.divisors, sum_filter, range_eq_Ico]
   rw [sum_eq_sum_Ico_succ_bot] <;> simp
 
diff --git a/Mathlib/Data/Num/Prime.lean b/Mathlib/Data/Num/Prime.lean
index 8587208f30d454..05de04fe8517c3 100644
--- a/Mathlib/Data/Num/Prime.lean
+++ b/Mathlib/Data/Num/Prime.lean
@@ -52,7 +52,7 @@ theorem minFacAux_to_nat {fuel : ℕ} {n k : PosNum} (h : Nat.sqrt n < fuel + k.
     simp_rw [← mul_to_nat]
     simp only [cast_lt, dvd_to_nat]
     split_ifs <;> try rfl
-    rw [ih] <;> [congr; convert Nat.lt_succ_of_lt h using 1] <;>
+    rw [ih] <;> [congr; convert! Nat.lt_succ_of_lt h using 1] <;>
       simp only [cast_bit1, cast_succ, Nat.succ_eq_add_one, add_assoc,
         add_left_comm, ← one_add_one_eq_two]
 
diff --git a/Mathlib/Data/PFun.lean b/Mathlib/Data/PFun.lean
index 492e088a0f39df..ac172bc651d0b5 100644
--- a/Mathlib/Data/PFun.lean
+++ b/Mathlib/Data/PFun.lean
@@ -305,7 +305,7 @@ def fixInduction' {C : α → Sort*} {f : α →. β ⊕ α} {b : β} {a : α}
   refine fixInduction h fun a' h ih => ?_
   rcases e : (f a').get (dom_of_mem_fix h) with b' | a'' <;> replace e : _ ∈ f a' := ⟨_, e⟩
   · apply hbase
-    convert e
+    convert! e
     exact Part.mem_unique h (fix_stop e)
   · exact hind _ _ (fix_fwd h e) e (ih _ e)
 
diff --git a/Mathlib/Data/Prod/Lex.lean b/Mathlib/Data/Prod/Lex.lean
index 6eebf8dda44b85..36daf39da9ebf5 100644
--- a/Mathlib/Data/Prod/Lex.lean
+++ b/Mathlib/Data/Prod/Lex.lean
@@ -196,7 +196,7 @@ instance instLinearOrder (α β : Type*) [LinearOrder α] [LinearOrder β] : Lin
     have : Std.LawfulLTOrd (α ×ₗ β) := ⟨by
       simp [compare_def, compareLex, compareOn, Ordering.then_eq_lt, toLex_lt_toLex,
         compare_lt_iff_lt]⟩
-    convert Std.LawfulLTCmp.eq_compareOfLessAndEq (cmp := compare) a b
+    convert! Std.LawfulLTCmp.eq_compareOfLessAndEq (cmp := compare) a b
 
 @[to_dual]
 instance orderBot [PartialOrder α] [Preorder β] [OrderBot α] [OrderBot β] : OrderBot (α ×ₗ β) where
diff --git a/Mathlib/Data/QPF/Univariate/Basic.lean b/Mathlib/Data/QPF/Univariate/Basic.lean
index cafb4578dd5c9b..c7ede75799d102 100644
--- a/Mathlib/Data/QPF/Univariate/Basic.lean
+++ b/Mathlib/Data/QPF/Univariate/Basic.lean
@@ -311,7 +311,7 @@ theorem Fix.ind (p : Fix F → Prop) (h : ∀ x : F (Fix F), Liftp p x → p (Fi
   apply h
   rw [liftp_iff]
   refine ⟨_, _, rfl, ?_⟩
-  convert ih
+  convert! ih
 
 end QPF
 
diff --git a/Mathlib/Data/Rat/Star.lean b/Mathlib/Data/Rat/Star.lean
index 4654c29151d80e..0e10b183895b52 100644
--- a/Mathlib/Data/Rat/Star.lean
+++ b/Mathlib/Data/Rat/Star.lean
@@ -49,7 +49,7 @@ namespace Rat
 
 @[simp] lemma addSubmonoid_closure_range_pow {n : ℕ} (hn₀ : n ≠ 0) (hn : Even n) :
     closure (range fun x : ℚ ↦ x ^ n) = nonneg _ := by
-  convert (AddMonoidHom.map_mclosure NNRat.coeHom <| range fun x ↦ x ^ n).symm
+  convert! (AddMonoidHom.map_mclosure NNRat.coeHom <| range fun x ↦ x ^ n).symm
   · have (x : ℚ) : ∃ y : ℚ≥0, y ^ n = x ^ n := ⟨x.nnabs, by simp [hn.pow_abs]⟩
     simp [subset_antisymm_iff, range_subset_iff, this]
   · ext
diff --git a/Mathlib/Data/Real/Archimedean.lean b/Mathlib/Data/Real/Archimedean.lean
index f3f1887b4ed9de..27eb96d5d109a8 100644
--- a/Mathlib/Data/Real/Archimedean.lean
+++ b/Mathlib/Data/Real/Archimedean.lean
@@ -176,7 +176,7 @@ theorem sInf_univ : sInf (@Set.univ ℝ) = 0 := by
 
 @[simp] lemma iSup_of_isEmpty [IsEmpty ι] (f : ι → ℝ) : ⨆ i, f i = 0 := by
   dsimp [iSup]
-  convert Real.sSup_empty
+  convert! Real.sSup_empty
   rw [Set.range_eq_empty_iff]
   infer_instance
 
diff --git a/Mathlib/Data/Real/Basic.lean b/Mathlib/Data/Real/Basic.lean
index 0962408a023fe2..2f5810c41fc767 100644
--- a/Mathlib/Data/Real/Basic.lean
+++ b/Mathlib/Data/Real/Basic.lean
@@ -349,7 +349,7 @@ theorem ratCast_lt {x y : ℚ} : (x : ℝ) < (y : ℝ) ↔ x < y := by
   exact const_lt
 
 protected theorem zero_lt_one : (0 : ℝ) < 1 := by
-  convert ratCast_lt.2 zero_lt_one <;> simp [← ofCauchy_ratCast, ofCauchy_one, ofCauchy_zero]
+  convert! ratCast_lt.2 zero_lt_one <;> simp [← ofCauchy_ratCast, ofCauchy_one, ofCauchy_zero]
 
 instance instNontrivial : Nontrivial ℝ where
   exists_pair_ne := ⟨0, 1, Real.zero_lt_one.ne⟩
diff --git a/Mathlib/Data/Real/ConjExponents.lean b/Mathlib/Data/Real/ConjExponents.lean
index 06f66035c76433..e923a5955d86f6 100644
--- a/Mathlib/Data/Real/ConjExponents.lean
+++ b/Mathlib/Data/Real/ConjExponents.lean
@@ -152,7 +152,7 @@ theorem sub_one_pos : 0 < p - 1 := sub_pos.2 h.lt
 theorem sub_one_ne_zero : p - 1 ≠ 0 := h.sub_one_pos.ne'
 
 theorem conjugate_eq : q = p / (p - 1) := by
-  convert inv_inv q ▸ congr($(h.symm.inv_sub_inv_eq_inv.symm)⁻¹) using 1
+  convert! inv_inv q ▸ congr($(h.symm.inv_sub_inv_eq_inv.symm)⁻¹) using 1
   field [h.ne_zero]
 
 lemma conjExponent_eq : conjExponent p = q := h.conjugate_eq.symm
diff --git a/Mathlib/Data/Real/Embedding.lean b/Mathlib/Data/Real/Embedding.lean
index 38310ed8f8d397..51ff4fed81ba88 100644
--- a/Mathlib/Data/Real/Embedding.lean
+++ b/Mathlib/Data/Real/Embedding.lean
@@ -132,7 +132,7 @@ theorem ratLt_add (x y : M) : ratLt (x + y) = ratLt x + ratLt y := by
     · have hk' : 1 + (k • a.num • 1 - k • a.den • y) ≤ k • a.den • x - 1 := by
         rw [smul_add, smul_sub, smul_add, le_sub_iff_add_le, ← sub_le_iff_le_add] at hk
         rw [le_sub_iff_add_le]
-        convert hk using 1
+        convert! hk using 1
         abel
       have : k • a.num • 1 - k • a.den • y < m • 1 :=
         lt_of_lt_of_le (lt_add_of_pos_left _ zero_lt_one) (by simpa using hk'.trans hm1)
diff --git a/Mathlib/Data/Real/Sqrt.lean b/Mathlib/Data/Real/Sqrt.lean
index 8bb4012dd2ea7d..1d7361a4aaa405 100644
--- a/Mathlib/Data/Real/Sqrt.lean
+++ b/Mathlib/Data/Real/Sqrt.lean
@@ -431,7 +431,7 @@ theorem sqrt_one_add_le (h : -1 ≤ x) : √(1 + x) ≤ 1 + x / 2 := by
 
 theorem sqrt_prod {ι : Type*} (s : Finset ι) {x : ι → ℝ} (hx : ∀ i ∈ s, 0 ≤ x i) :
     √(∏ i ∈ s, x i) = ∏ i ∈ s, √(x i) := by
-  convert congr_arg NNReal.toReal <| map_prod NNReal.sqrtHom (Real.toNNReal ∘ x) s <;>
+  convert! congr_arg NNReal.toReal <| map_prod NNReal.sqrtHom (Real.toNNReal ∘ x) s <;>
     simp +contextual [-map_prod, NNReal.sqrtHom, hx]
 
 end Real
diff --git a/Mathlib/Data/Seq/Basic.lean b/Mathlib/Data/Seq/Basic.lean
index 9c2de0390ff899..aaed2f9473b5cd 100644
--- a/Mathlib/Data/Seq/Basic.lean
+++ b/Mathlib/Data/Seq/Basic.lean
@@ -495,7 +495,7 @@ theorem drop_get? {n m : ℕ} {s : Seq α} : (s.drop n).get? m = s.get? (n + m)
   | zero => simp [drop]
   | succ k ih =>
     simp only [drop, get?_tail]
-    convert ih using 2
+    convert! ih using 2
     lia
 
 theorem dropn_add (s : Seq α) (m) : ∀ n, drop s (m + n) = drop (drop s m) n
@@ -535,7 +535,7 @@ theorem drop_length' {n : ℕ} {s : Seq α} :
     | nil => simp
     | cons x s =>
       simp only [drop_succ_cons, length'_cons, Nat.cast_add, Nat.cast_one]
-      convert drop_length' using 1
+      convert! drop_length' using 1
       generalize s.length' = m
       enat_to_nat
       lia
@@ -622,12 +622,12 @@ theorem zipWith_map (s₁ : Seq α) (s₂ : Seq β) (f₁ : α → α') (f₂ :
 
 theorem zipWith_map_left (s₁ : Seq α) (s₂ : Seq β) (f : α → α') (g : α' → β → γ) :
     zipWith g (s₁.map f) s₂ = zipWith (fun a b ↦ g (f a) b) s₁ s₂ := by
-  convert zipWith_map _ _ _ (@id β) _
+  convert! zipWith_map _ _ _ (@id β) _
   simp
 
 theorem zipWith_map_right (s₁ : Seq α) (s₂ : Seq β) (f : β → β') (g : α → β' → γ) :
     zipWith g s₁ (s₂.map f) = zipWith (fun a b ↦ g a (f b)) s₁ s₂ := by
-  convert zipWith_map _ _ (@id α) _ _
+  convert! zipWith_map _ _ (@id α) _ _
   simp
 
 theorem zip_map (s₁ : Seq α) (s₂ : Seq β) (f₁ : α → α') (f₂ : β → β') :
@@ -638,12 +638,12 @@ theorem zip_map (s₁ : Seq α) (s₂ : Seq β) (f₁ : α → α') (f₂ : β 
 
 theorem zip_map_left (s₁ : Seq α) (s₂ : Seq β) (f : α → α') :
     (s₁.map f).zip s₂ = (s₁.zip s₂).map (Prod.map f id) := by
-  convert zip_map _ _ _ _
+  convert! zip_map _ _ _ _
   simp
 
 theorem zip_map_right (s₁ : Seq α) (s₂ : Seq β) (f : β → β') :
     s₁.zip (s₂.map f) = (s₁.zip s₂).map (Prod.map id f) := by
-  convert zip_map _ _ _ _
+  convert! zip_map _ _ _ _
   simp
 
 end ZipWith
diff --git a/Mathlib/Data/Set/Card.lean b/Mathlib/Data/Set/Card.lean
index 59cc2f2713652b..cd26ef4f04ab90 100644
--- a/Mathlib/Data/Set/Card.lean
+++ b/Mathlib/Data/Set/Card.lean
@@ -424,7 +424,7 @@ theorem encard_eq_four {α : Type u_1} {s : Set α} :
     encard_singleton] <;> grind
 
 theorem Nat.encard_range (k : ℕ) : {i | i < k}.encard = k := by
-  convert encard_coe_eq_coe_finsetCard (Finset.range k) using 1
+  convert! encard_coe_eq_coe_finsetCard (Finset.range k) using 1
   · rw [Finset.coe_range, Iio_def]
   rw [Finset.card_range]
 
@@ -544,7 +544,7 @@ termination_by encard s
 theorem Finite.exists_bijOn_of_encard_eq [Nonempty β] (hs : s.Finite) (h : s.encard = t.encard) :
     ∃ (f : α → β), BijOn f s t := by
   obtain ⟨f, hf, hinj⟩ := hs.exists_injOn_of_encard_le h.le; use f
-  convert hinj.bijOn_image
+  convert! hinj.bijOn_image
   rw [(hs.image f).eq_of_subset_of_encard_le (image_subset_iff.mpr hf)
     (h.symm.trans hinj.encard_image.symm).le]
 
@@ -733,7 +733,7 @@ theorem ncard_diff_singleton_lt_of_mem {a : α} (h : a ∈ s) (hs : s.Finite :=
 theorem ncard_diff_singleton_le (s : Set α) (a : α) : (s \ {a}).ncard ≤ s.ncard := by
   obtain hs | hs := s.finite_or_infinite
   · apply ncard_le_ncard diff_subset hs
-  convert Nat.zero_le _
+  convert! Nat.zero_le _
   exact (hs.diff (by simp)).ncard
 
 theorem pred_ncard_le_ncard_diff_singleton (s : Set α) (a : α) : s.ncard - 1 ≤ (s \ {a}).ncard := by
@@ -800,7 +800,7 @@ theorem fiber_ncard_ne_zero_iff_mem_image {y : β} (hs : s.Finite := by toFinite
 
 @[simp] theorem ncard_subtype (P : α → Prop) (s : Set α) :
     { x : Subtype P | (x : α) ∈ s }.ncard = (s ∩ setOf P).ncard := by
-  convert (ncard_image_of_injective _ (@Subtype.coe_injective _ P)).symm
+  convert! (ncard_image_of_injective _ (@Subtype.coe_injective _ P)).symm
   ext x
   simp [← and_assoc, exists_eq_right]
 
@@ -917,7 +917,7 @@ theorem surj_on_of_inj_on_of_ncard_le {t : Set β} (f : ∀ a ∈ s, β) (hf : 
   have hft := ht.fintype
   have hft' := Fintype.ofInjective f' finj
   set f'' : ∀ a, a ∈ s.toFinset → β := fun a h ↦ f a (by simpa using h)
-  convert @Finset.surj_on_of_inj_on_of_card_le _ _ _ t.toFinset f'' _ _ _ _ (by simpa) using 1
+  convert! @Finset.surj_on_of_inj_on_of_card_le _ _ _ t.toFinset f'' _ _ _ _ (by simpa) using 1
   · simp [f'']
   · simp [f'', hf]
   · intro a₁ a₂ ha₁ ha₂ h
@@ -1008,7 +1008,7 @@ theorem ncard_le_ncard_diff_add_ncard (s t : Set α) (ht : t.Finite := by toFini
   · to_encard_tac
     rw [ht.cast_ncard_eq, hs.cast_ncard_eq, hs.diff.cast_ncard_eq]
     apply encard_le_encard_diff_add_encard
-  convert Nat.zero_le _
+  convert! Nat.zero_le _
   rw [hs.ncard]
 
 theorem le_ncard_diff (s t : Set α) (hs : s.Finite := by toFinite_tac) :
@@ -1159,7 +1159,7 @@ theorem exists_eq_insert_iff_ncard (hs : s.Finite := by toFinite_tac) :
   rcases t.finite_or_infinite with ht | ht
   · rw [ncard_eq_toFinset_card _ hs, ncard_eq_toFinset_card _ ht,
       ← @Finite.toFinset_subset_toFinset _ _ _ hs ht, ← Finset.exists_eq_insert_iff]
-    convert Iff.rfl using 2; simp only [Finite.mem_toFinset]
+    convert! Iff.rfl using 2; simp only [Finite.mem_toFinset]
     ext x
     simp [Finset.ext_iff, Set.ext_iff]
   simp only [ht.ncard, add_eq_zero, and_false, iff_false, not_exists, not_and,
diff --git a/Mathlib/Data/Set/Countable.lean b/Mathlib/Data/Set/Countable.lean
index 159b4c557c90d1..6b7123b0f8dc27 100644
--- a/Mathlib/Data/Set/Countable.lean
+++ b/Mathlib/Data/Set/Countable.lean
@@ -107,7 +107,7 @@ lemma range_enumerateCountable_of_mem {s : Set α} (h : s.Countable) {default :
 lemma enumerateCountable_mem {s : Set α} (h : s.Countable) {default : α} (h_mem : default ∈ s)
     (n : ℕ) :
     enumerateCountable h default n ∈ s := by
-  convert mem_range_self n
+  convert! mem_range_self n
   exact (range_enumerateCountable_of_mem h h_mem).symm
 
 end Enumerate
diff --git a/Mathlib/Data/Set/Finite/Basic.lean b/Mathlib/Data/Set/Finite/Basic.lean
index f21ac811686ff5..22e20fcdb1c464 100644
--- a/Mathlib/Data/Set/Finite/Basic.lean
+++ b/Mathlib/Data/Set/Finite/Basic.lean
@@ -744,7 +744,7 @@ theorem seq_of_forall_finite_exists {γ : Type*} {P : γ → Set γ → Prop}
   set f : (n : ℕ) → (g : (m : ℕ) → m < n → γ) → γ := fun n g => c (range fun k : Iio n => g k.1 k.2)
   set u : ℕ → γ := fun n => Nat.strongRecOn' n f
   refine ⟨u, fun n => ?_⟩
-  convert hc (u '' Iio n) ((finite_lt_nat _).image _)
+  convert! hc (u '' Iio n) ((finite_lt_nat _).image _)
   rw [image_eq_range]
   exact Nat.strongRecOn'_beta
 
diff --git a/Mathlib/Data/Set/Finite/List.lean b/Mathlib/Data/Set/Finite/List.lean
index be8fbccb43237d..2c876db304d957 100644
--- a/Mathlib/Data/Set/Finite/List.lean
+++ b/Mathlib/Data/Set/Finite/List.lean
@@ -29,7 +29,7 @@ variable (α : Type*) [Finite α] (n : ℕ)
 lemma finite_length_eq : {l : List α | l.length = n}.Finite := List.Vector.finite
 
 lemma finite_length_lt : {l : List α | l.length < n}.Finite := by
-  convert (Finset.range n).finite_toSet.biUnion fun i _ ↦ finite_length_eq α i; ext; simp
+  convert! (Finset.range n).finite_toSet.biUnion fun i _ ↦ finite_length_eq α i; ext; simp
 
 lemma finite_length_le : {l : List α | l.length ≤ n}.Finite := by
   simpa [Nat.lt_succ_iff] using finite_length_lt α (n + 1)
diff --git a/Mathlib/Data/Set/Finite/Powerset.lean b/Mathlib/Data/Set/Finite/Powerset.lean
index a8f20c26fecf65..e35e8dfbe343b6 100644
--- a/Mathlib/Data/Set/Finite/Powerset.lean
+++ b/Mathlib/Data/Set/Finite/Powerset.lean
@@ -46,7 +46,7 @@ section SetFiniteConstructors
 
 /-- There are finitely many subsets of a given finite set -/
 theorem Finite.finite_subsets {α : Type u} {a : Set α} (h : a.Finite) : { b | b ⊆ a }.Finite := by
-  convert ((Finset.powerset h.toFinset).map Finset.coeEmb.1).finite_toSet
+  convert! ((Finset.powerset h.toFinset).map Finset.coeEmb.1).finite_toSet
   ext s
   simpa [← @exists_finite_iff_finset α fun t => t ⊆ a ∧ t = s, Finite.subset_toFinset,
     ← and_assoc, Finset.coeEmb] using h.subset
diff --git a/Mathlib/Data/Set/Function.lean b/Mathlib/Data/Set/Function.lean
index cd97f345ec3ab0..2547fd9e0627c1 100644
--- a/Mathlib/Data/Set/Function.lean
+++ b/Mathlib/Data/Set/Function.lean
@@ -776,7 +776,7 @@ theorem BijOn.insert (h₁ : BijOn f s t) (h₂ : f a ∉ t) :
 
 theorem BijOn.sdiff_singleton (h₁ : BijOn f s t) (h₂ : a ∈ s) :
     BijOn f (s \ {a}) (t \ {f a}) := by
-  convert h₁.subset_left diff_subset
+  convert! h₁.subset_left diff_subset
   simp [h₁.injOn.image_diff, h₁.image_eq, h₂, inter_eq_self_of_subset_right]
 
 end bijOn
diff --git a/Mathlib/Data/Set/Functor.lean b/Mathlib/Data/Set/Functor.lean
index 832006af446848..0f503b76ec6d22 100644
--- a/Mathlib/Data/Set/Functor.lean
+++ b/Mathlib/Data/Set/Functor.lean
@@ -122,10 +122,10 @@ theorem mem_coe_of_mem {a : α} (ha : a ∈ β) (ha' : ⟨a, ha⟩ ∈ γ) : a 
   ⟨_, ⟨⟨_, rfl⟩, _, ⟨ha', rfl⟩, rfl⟩⟩
 
 theorem coe_subset : (γ : Set α) ⊆ β := by
-  intro _ ⟨_, ⟨⟨⟨_, ha⟩, rfl⟩, _, ⟨_, rfl⟩, _⟩⟩; convert ha
+  intro _ ⟨_, ⟨⟨⟨_, ha⟩, rfl⟩, _, ⟨_, rfl⟩, _⟩⟩; convert! ha
 
 theorem mem_of_mem_coe {a : α} (ha : a ∈ (γ : Set α)) : ⟨a, coe_subset ha⟩ ∈ γ := by
-  rcases ha with ⟨_, ⟨_, rfl⟩, _, ⟨ha, rfl⟩, _⟩; convert ha
+  rcases ha with ⟨_, ⟨_, rfl⟩, _, ⟨ha, rfl⟩, _⟩; convert! ha
 
 theorem eq_univ_of_coe_eq (hγ : (γ : Set α) = β) : γ = univ :=
   eq_univ_of_forall fun ⟨_, ha⟩ => mem_of_mem_coe <| hγ.symm ▸ ha
diff --git a/Mathlib/Data/Set/Pairwise/Lattice.lean b/Mathlib/Data/Set/Pairwise/Lattice.lean
index 079baec834fe03..fbf4ab64e45cfb 100644
--- a/Mathlib/Data/Set/Pairwise/Lattice.lean
+++ b/Mathlib/Data/Set/Pairwise/Lattice.lean
@@ -103,11 +103,11 @@ theorem PairwiseDisjoint.prod_left {f : ι × ι' → α}
   rw [mem_prod] at hi hj
   obtain rfl | hij := eq_or_ne i j
   · refine (ht hi.2 hj.2 <| (Prod.mk_right_injective _).ne_iff.1 h).mono ?_ ?_
-    · convert le_iSup₂ (α := α) i hi.1; rfl
-    · convert le_iSup₂ (α := α) i hj.1; rfl
+    · convert! le_iSup₂ (α := α) i hi.1; rfl
+    · convert! le_iSup₂ (α := α) i hj.1; rfl
   · refine (hs hi.1 hj.1 hij).mono ?_ ?_
-    · convert le_iSup₂ (α := α) i' hi.2; rfl
-    · convert le_iSup₂ (α := α) j' hj.2; rfl
+    · convert! le_iSup₂ (α := α) i' hi.2; rfl
+    · convert! le_iSup₂ (α := α) j' hj.2; rfl
 
 end CompleteLattice
 
diff --git a/Mathlib/Data/Set/Prod.lean b/Mathlib/Data/Set/Prod.lean
index 161b9cca4c1660..7d149c0e225d7f 100644
--- a/Mathlib/Data/Set/Prod.lean
+++ b/Mathlib/Data/Set/Prod.lean
@@ -857,7 +857,7 @@ theorem update_preimage_pi [DecidableEq ι] {f : ∀ i, α i} (hi : i ∈ s)
     (hf : ∀ j ∈ s, j ≠ i → f j ∈ t j) : update f i ⁻¹' s.pi t = t i := by
   ext x
   refine ⟨fun h => ?_, fun hx j hj => ?_⟩
-  · convert h i hi
+  · convert! h i hi
     simp
   · obtain rfl | h := eq_or_ne j i
     · simpa
diff --git a/Mathlib/Data/Setoid/Partition.lean b/Mathlib/Data/Setoid/Partition.lean
index cb76177a7c4601..bc60410dd6d3ee 100644
--- a/Mathlib/Data/Setoid/Partition.lean
+++ b/Mathlib/Data/Setoid/Partition.lean
@@ -127,7 +127,7 @@ theorem eqv_class_mem {c : Set (Set α)} (H : ∀ a, ∃! b ∈ c, a ∈ b) {y}
 
 theorem eqv_class_mem' {c : Set (Set α)} (H : ∀ a, ∃! b ∈ c, a ∈ b) {x} :
     { y : α | mkClasses c H x y } ∈ c := by
-  convert @Setoid.eqv_class_mem _ _ H x using 3
+  convert! @Setoid.eqv_class_mem _ _ H x using 3
   rw [Setoid.comm']
 
 /-- Distinct elements of a set of sets partitioning α are disjoint. -/
diff --git a/Mathlib/Data/Sym/Basic.lean b/Mathlib/Data/Sym/Basic.lean
index fc21fbc7ab78bd..df918acd8a60df 100644
--- a/Mathlib/Data/Sym/Basic.lean
+++ b/Mathlib/Data/Sym/Basic.lean
@@ -607,7 +607,7 @@ theorem decode_encode [DecidableEq α] (s : Sym (Option α) n.succ) : decode (en
   · simp [h]
   · simp only [decode, h, not_false_iff, encode_of_none_notMem, Embedding.some_apply, map_map,
       comp_apply, Option.some_get]
-    convert s.attach_map_coe
+    convert! s.attach_map_coe
 
 @[simp]
 theorem encode_decode [DecidableEq α] (s : Sym (Option α) n ⊕ Sym α n.succ) :
diff --git a/Mathlib/Data/Sym/Card.lean b/Mathlib/Data/Sym/Card.lean
index 8d5f7e0fb9eafb..d6146ac7399e49 100644
--- a/Mathlib/Data/Sym/Card.lean
+++ b/Mathlib/Data/Sym/Card.lean
@@ -144,7 +144,7 @@ theorem card_image_offDiag (s : Finset α) :
     Nat.div_eq_of_eq_mul_right Nat.zero_lt_two (two_mul_card_image_offDiag s).symm]
 
 theorem card_subtype_diag [Fintype α] : card { a : Sym2 α // a.IsDiag } = card α := by
-  convert card_image_diag (univ : Finset α)
+  convert! card_image_diag (univ : Finset α)
   rw [← filter_image_mk_isDiag, Fintype.card_of_subtype]
   rintro x
   rw [mem_filter, univ_product_univ, mem_image]
@@ -153,7 +153,7 @@ theorem card_subtype_diag [Fintype α] : card { a : Sym2 α // a.IsDiag } = card
 
 theorem card_subtype_not_diag [Fintype α] :
     card { a : Sym2 α // ¬a.IsDiag } = (card α).choose 2 := by
-  convert card_image_offDiag (univ : Finset α)
+  convert! card_image_offDiag (univ : Finset α)
   rw [← filter_image_mk_not_isDiag, Fintype.card_of_subtype]
   rintro x
   rw [mem_filter, univ_product_univ, mem_image]
diff --git a/Mathlib/Data/Sym/Sym2.lean b/Mathlib/Data/Sym/Sym2.lean
index 9560031b3aadc4..ef739a2f795121 100644
--- a/Mathlib/Data/Sym/Sym2.lean
+++ b/Mathlib/Data/Sym/Sym2.lean
@@ -380,7 +380,7 @@ theorem other_spec {a : α} {z : Sym2 α} (h : a ∈ z) : s(a, Mem.other h) = z
   (Classical.choose_spec h).symm
 
 theorem other_mem {a : α} {z : Sym2 α} (h : a ∈ z) : Mem.other h ∈ z := by
-  convert mem_mk_right a <| Mem.other h
+  convert! mem_mk_right a <| Mem.other h
   rw [other_spec h]
 
 theorem mem_and_mem_iff {x y : α} {z : Sym2 α} (hne : x ≠ y) : x ∈ z ∧ y ∈ z ↔ z = s(x, y) := by
@@ -900,7 +900,7 @@ theorem other_invol {a : α} {z : Sym2 α} (ha : a ∈ z) (hb : Mem.other ha ∈
     Mem.other hb = a := by
   classical
     rw [other_eq_other'] at hb ⊢
-    convert other_invol' ha hb using 2
+    convert! other_invol' ha hb using 2
     apply other_eq_other'
 
 theorem filter_image_mk_isDiag [DecidableEq α] (s : Finset α) :
diff --git a/Mathlib/Data/ZMod/Defs.lean b/Mathlib/Data/ZMod/Defs.lean
index 70625d7130ba48..e1b9832a88d149 100644
--- a/Mathlib/Data/ZMod/Defs.lean
+++ b/Mathlib/Data/ZMod/Defs.lean
@@ -173,7 +173,7 @@ instance infinite : Infinite (ZMod 0) :=
 theorem card (n : ℕ) [Fintype (ZMod n)] : Fintype.card (ZMod n) = n := by
   cases n with
   | zero => exact (not_finite (ZMod 0)).elim
-  | succ n => convert Fintype.card_fin (n + 1) using 2
+  | succ n => convert! Fintype.card_fin (n + 1) using 2
 
 open Fin.CommRing in
 /- We define each field by cases, to ensure that the eta-expanded `ZMod.commRing` is defeq to the
diff --git a/Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean b/Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean
index 19050a9344c7a5..211cc993c968d7 100644
--- a/Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean
+++ b/Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean
@@ -601,7 +601,7 @@ theorem tendsto_translationNumber_of_dist_bounded_aux (x : ℕ → ℝ) (C : ℝ
   · exact fun n => C / 2 ^ n
   · intro n
     have : 0 < (2 ^ n : ℝ) := pow_pos zero_lt_two _
-    convert (div_le_div_iff_of_pos_right this).2 (H (2 ^ n)) using 1
+    convert! (div_le_div_iff_of_pos_right this).2 (H (2 ^ n)) using 1
     rw [transnumAuxSeq, Real.dist_eq, ← sub_div, abs_div, abs_of_pos this, Real.dist_eq]
   · exact mul_zero C ▸ tendsto_const_nhds.mul <| tendsto_inv_atTop_zero.comp <|
       tendsto_pow_atTop_atTop_of_one_lt one_lt_two
diff --git a/Mathlib/Dynamics/Ergodic/AddCircle.lean b/Mathlib/Dynamics/Ergodic/AddCircle.lean
index a28cf4365101ab..18cc7d4d865a22 100644
--- a/Mathlib/Dynamics/Ergodic/AddCircle.lean
+++ b/Mathlib/Dynamics/Ergodic/AddCircle.lean
@@ -77,7 +77,7 @@ theorem ae_empty_or_univ_of_forall_vadd_ae_eq_self {s : Set <| AddCircle T}
       refine tendsto_nhdsWithin_iff.mpr ⟨?_, hδ₀⟩
       replace hu₂ : Tendsto (fun j => T⁻¹ * 2 * n j) l atTop :=
         (tendsto_natCast_atTop_iff.mpr hu₂).const_mul_atTop (by positivity : 0 < T⁻¹ * 2)
-      convert hu₂.inv_tendsto_atTop
+      convert! hu₂.inv_tendsto_atTop
       ext j
       simp only [δ, Pi.inv_apply, mul_inv_rev, inv_inv, div_eq_inv_mul, ← mul_assoc]
     have hw : ∀ᶠ j in l, d ∈ closedBall d (1 * δ j) := hδ₀.mono fun j hj => by
@@ -108,8 +108,8 @@ theorem ergodic_zsmul {n : ℤ} (hn : 1 < |n|) : Ergodic fun y : AddCircle T =>
       let u : ℕ → AddCircle T := fun j => ↑((↑1 : ℝ) / ↑(n.natAbs ^ j) * T)
       replace hn : 1 < n.natAbs := by rwa [Int.abs_eq_natAbs, Nat.one_lt_cast] at hn
       have hu₀ : ∀ j, addOrderOf (u j) = n.natAbs ^ j := fun j => by
-        convert addOrderOf_div_of_gcd_eq_one (p := T) (m := 1)
-          (pow_pos (pos_of_gt hn) j) (gcd_one_left _)
+        convert!
+          addOrderOf_div_of_gcd_eq_one (p := T) (m := 1) (pow_pos (pos_of_gt hn) j) (gcd_one_left _)
         norm_cast
       have hnu : ∀ j, n ^ j • u j = 0 := fun j => by
         rw [← addOrderOf_dvd_iff_zsmul_eq_zero, hu₀, Int.natCast_pow, Int.natCast_natAbs, ← abs_pow,
diff --git a/Mathlib/Dynamics/Ergodic/Conservative.lean b/Mathlib/Dynamics/Ergodic/Conservative.lean
index 49f8e871799643..588beec67d972d 100644
--- a/Mathlib/Dynamics/Ergodic/Conservative.lean
+++ b/Mathlib/Dynamics/Ergodic/Conservative.lean
@@ -111,7 +111,7 @@ theorem frequently_measure_inter_ne_zero (hf : Conservative f μ) (hs : NullMeas
   -- Let `N` be the maximal `n` such that `μ (t n) ≠ 0`.
   obtain ⟨N, hN, hmax⟩ : ∃ N, μ (t N) ≠ 0 ∧ ∀ n > N, μ (t n) = 0 := by
     rw [Nat.frequently_atTop_iff_infinite, not_infinite] at H
-    convert exists_max_image _ (·) H ⟨0, by simpa⟩ using 4
+    convert! exists_max_image _ (·) H ⟨0, by simpa⟩ using 4
     rw [gt_iff_lt, ← not_le, not_imp_comm, mem_setOf]
   have htm {n : ℕ} : NullMeasurableSet (t n) μ :=
     hs.inter <| hs.preimage <| hf.toQuasiMeasurePreserving.iterate n
diff --git a/Mathlib/Dynamics/Ergodic/Extreme.lean b/Mathlib/Dynamics/Ergodic/Extreme.lean
index 2ee079eb31b078..179180aff42be7 100644
--- a/Mathlib/Dynamics/Ergodic/Extreme.lean
+++ b/Mathlib/Dynamics/Ergodic/Extreme.lean
@@ -33,7 +33,7 @@ theorem of_mem_extremePoints_measure_univ_eq {c : ℝ≥0∞} (hc : c ≠ ∞)
     (h : μ ∈ extremePoints ℝ≥0∞ {ν | MeasurePreserving f ν ν ∧ ν univ = c}) : Ergodic f μ := by
   have hf : MeasurePreserving f μ μ := h.1.1
   rcases eq_or_ne c 0 with rfl | hc₀
-  · convert zero_measure hf.measurable
+  · convert! zero_measure hf.measurable
     rw [← measure_univ_eq_zero, h.1.2]
   · refine ⟨hf, ⟨?_⟩⟩
     have : IsFiniteMeasure μ := by
@@ -43,7 +43,7 @@ theorem of_mem_extremePoints_measure_univ_eq {c : ℝ≥0∞} (hc : c ≠ ∞)
     have {s : Set X} (hsm : MeasurableSet s) (hfs : f ⁻¹' s = s) (hμs : μ s ≠ 0) :
         c • μ[|s] ∈ S := by
       refine ⟨.smul_measure (.smul_measure ?_ _) c, ?_⟩
-      · convert hf.restrict_preimage hsm
+      · convert! hf.restrict_preimage hsm
         exact hfs.symm
       · rw [Measure.smul_apply, (cond_isProbabilityMeasure hμs).1, smul_eq_mul, mul_one]
     intro s hsm hfs
diff --git a/Mathlib/Dynamics/Ergodic/MeasurePreserving.lean b/Mathlib/Dynamics/Ergodic/MeasurePreserving.lean
index 9397ca23a5b51e..f032f13e6b867c 100644
--- a/Mathlib/Dynamics/Ergodic/MeasurePreserving.lean
+++ b/Mathlib/Dynamics/Ergodic/MeasurePreserving.lean
@@ -122,13 +122,13 @@ protected theorem trans {e : α ≃ᵐ β} {e' : β ≃ᵐ γ}
 protected theorem comp_left_iff {g : α → β} {e : β ≃ᵐ γ} (h : MeasurePreserving e μb μc) :
     MeasurePreserving (e ∘ g) μa μc ↔ MeasurePreserving g μa μb := by
   refine ⟨fun hg => ?_, fun hg => h.comp hg⟩
-  convert (MeasurePreserving.symm e h).comp hg
+  convert! (MeasurePreserving.symm e h).comp hg
   simp [← Function.comp_assoc e.symm e g]
 
 protected theorem comp_right_iff {g : α → β} {e : γ ≃ᵐ α} (h : MeasurePreserving e μc μa) :
     MeasurePreserving (g ∘ e) μc μb ↔ MeasurePreserving g μa μb := by
   refine ⟨fun hg => ?_, fun hg => hg.comp h⟩
-  convert hg.comp (MeasurePreserving.symm e h)
+  convert! hg.comp (MeasurePreserving.symm e h)
   simp [Function.comp_assoc g e e.symm]
 
 protected theorem sigmaFinite {f : α → β} (hf : MeasurePreserving f μa μb) [SigmaFinite μb] :
diff --git a/Mathlib/Dynamics/Ergodic/RadonNikodym.lean b/Mathlib/Dynamics/Ergodic/RadonNikodym.lean
index 80a8bc36ab3856..e5cd2061fb5d2a 100644
--- a/Mathlib/Dynamics/Ergodic/RadonNikodym.lean
+++ b/Mathlib/Dynamics/Ergodic/RadonNikodym.lean
@@ -39,7 +39,7 @@ protected theorem singularPart [SigmaFinite ν] {f : X → X}
     (hfμ : MeasurePreserving f μ μ) (hfν : MeasurePreserving f ν ν) :
     MeasurePreserving f (μ.singularPart ν) (μ.singularPart ν) := by
   rcases (μ.mutuallySingular_singularPart ν).symm with ⟨s, hsm, hνs, hμs⟩
-  convert hfμ.restrict_preimage hsm using 1
+  convert! hfμ.restrict_preimage hsm using 1
   · refine singularPart_eq_restrict ?_ (hfν.preimage_null hνs)
     rw [← mem_ae_iff, ← Filter.eventuallyEq_univ,
       ae_eq_univ_iff_measure_eq (hfμ.measurable hsm).nullMeasurableSet]
diff --git a/Mathlib/Dynamics/FixedPoints/Basic.lean b/Mathlib/Dynamics/FixedPoints/Basic.lean
index 2a463bb4d6a351..b50d061d690b58 100644
--- a/Mathlib/Dynamics/FixedPoints/Basic.lean
+++ b/Mathlib/Dynamics/FixedPoints/Basic.lean
@@ -64,7 +64,7 @@ protected theorem map {x : α} (hx : IsFixedPt fa x) {g : α → β} (h : Semico
     fb (g x) = g (fa x) := (h.eq x).symm
     _ = g x := congr_arg g hx
 
-protected theorem apply {x : α} (hx : IsFixedPt f x) : IsFixedPt f (f x) := by convert hx
+protected theorem apply {x : α} (hx : IsFixedPt f x) : IsFixedPt f (f x) := by convert! hx
 
 theorem preimage_iterate {s : Set α} (h : IsFixedPt (Set.preimage f) s) (n : ℕ) :
     IsFixedPt (Set.preimage f^[n]) s := by
diff --git a/Mathlib/Dynamics/Newton.lean b/Mathlib/Dynamics/Newton.lean
index 54b4f7eec79b07..3a5a2f1eed579c 100644
--- a/Mathlib/Dynamics/Newton.lean
+++ b/Mathlib/Dynamics/Newton.lean
@@ -92,7 +92,7 @@ theorem aeval_pow_two_pow_dvd_aeval_iterate_newtonMap
     rw [eval_map_algebraMap, eval_map_algebraMap] at hd
     rw [iterate_succ', comp_apply, newtonMap_apply, sub_eq_add_neg, neg_mul_eq_neg_mul, hd]
     refine dvd_add ?_ (dvd_mul_of_dvd_right ?_ _)
-    · convert dvd_zero _
+    · convert! dvd_zero _
       have : IsUnit (aeval (P.newtonMap^[n] x) <| derivative P) :=
         isUnit_aeval_of_isUnit_aeval_of_isNilpotent_sub h' <|
         isNilpotent_iterate_newtonMap_sub_of_isNilpotent h n
diff --git a/Mathlib/Dynamics/PeriodicPts/Defs.lean b/Mathlib/Dynamics/PeriodicPts/Defs.lean
index 53245e2d1fc261..b9f5bcfdb870af 100644
--- a/Mathlib/Dynamics/PeriodicPts/Defs.lean
+++ b/Mathlib/Dynamics/PeriodicPts/Defs.lean
@@ -219,7 +219,7 @@ theorem isPeriodicPt_of_mem_periodicPts_of_isPeriodicPt_iterate (hx : x ∈ peri
   rcases hx with ⟨r, hr, hr'⟩
   suffices n ≤ (n / r + 1) * r by
     unfold IsPeriodicPt IsFixedPt
-    convert (hm.apply_iterate ((n / r + 1) * r - n)).eq <;>
+    convert! (hm.apply_iterate ((n / r + 1) * r - n)).eq <;>
       rw [← iterate_add_apply, Nat.sub_add_cancel this, iterate_mul, (hr'.iterate _).eq]
   rw [Nat.add_mul, one_mul]
   exact (Nat.lt_div_mul_add hr).le
diff --git a/Mathlib/FieldTheory/AxGrothendieck.lean b/Mathlib/FieldTheory/AxGrothendieck.lean
index 8e53ea1d5b9e54..94d369434cca0b 100644
--- a/Mathlib/FieldTheory/AxGrothendieck.lean
+++ b/Mathlib/FieldTheory/AxGrothendieck.lean
@@ -186,7 +186,7 @@ theorem ACF_models_genericPolyMapSurjOnOfInjOn_of_prime_or_zero
   rcases hp with hp | rfl
   · exact ACF_models_genericPolyMapSurjOnOfInjOn_of_prime hp φ mons
   · rw [ACF_zero_realize_iff_infinite_ACF_prime_realize]
-    convert Set.infinite_univ (α := Nat.Primes)
+    convert! Set.infinite_univ (α := Nat.Primes)
     rw [Set.eq_univ_iff_forall]
     intro ⟨p, hp⟩
     exact ACF_models_genericPolyMapSurjOnOfInjOn_of_prime hp φ mons
diff --git a/Mathlib/FieldTheory/ChevalleyWarning.lean b/Mathlib/FieldTheory/ChevalleyWarning.lean
index d82b8e10bcac70..3c677a71b410d5 100644
--- a/Mathlib/FieldTheory/ChevalleyWarning.lean
+++ b/Mathlib/FieldTheory/ChevalleyWarning.lean
@@ -178,7 +178,7 @@ theorem char_dvd_card_solutions {f : MvPolynomial σ K} (h : f.totalDegree < Fin
     p ∣ Fintype.card { x : σ → K // eval x f = 0 } := by
   let F : Unit → MvPolynomial σ K := fun _ => f
   have : (∑ i : Unit, (F i).totalDegree) < Fintype.card σ := h
-  convert char_dvd_card_solutions_of_sum_lt p this
+  convert! char_dvd_card_solutions_of_sum_lt p this
   aesop
 
 /-- The **Chevalley–Warning theorem**, binary version.
diff --git a/Mathlib/FieldTheory/Differential/Liouville.lean b/Mathlib/FieldTheory/Differential/Liouville.lean
index 1dfde8c2da970b..cf3775cc229db0 100644
--- a/Mathlib/FieldTheory/Differential/Liouville.lean
+++ b/Mathlib/FieldTheory/Differential/Liouville.lean
@@ -187,7 +187,7 @@ private local instance isLiouville_of_finiteDimensional_galois [FiniteDimensiona
       · rcongr e
         apply_fun e at h
         simp only [AlgEquiv.commutes, map_add, map_sum, map_mul] at h
-        convert h using 2
+        convert! h using 2
         · rcongr x
           simp [logDeriv, algEquiv_deriv']
         · rw [algEquiv_deriv']
diff --git a/Mathlib/FieldTheory/Extension.lean b/Mathlib/FieldTheory/Extension.lean
index 644fc34de1f01e..7221fe4410be1e 100644
--- a/Mathlib/FieldTheory/Extension.lean
+++ b/Mathlib/FieldTheory/Extension.lean
@@ -244,7 +244,7 @@ private theorem exists_algHom_adjoin_of_splits'' {L : IntermediateField F E}
   have := φ.exists_lift_of_splits' (hK s h).1.tower_top ((hK s h).1.minpoly_splits_tower_top' ?_)
   · obtain ⟨y, h1, h2⟩ := this
     exact (hφ h1).1 h2
-  · convert (hK s h).2; ext; apply hfφ.2
+  · convert! (hK s h).2; ext; apply hfφ.2
 
 variable {L : Type*} [Field L] [Algebra F L] [Algebra L E] [IsScalarTower F L E]
   (f : L →ₐ[F] K) (hK : ∀ s ∈ S, IsIntegral L s ∧ ((minpoly L s).map f.toRingHom).Splits)
@@ -267,7 +267,7 @@ theorem exists_algHom_adjoin_of_splits' :
   letI : Algebra L L' := (AlgEquiv.ofInjectiveField _).toRingHom.toAlgebra
   have : IsScalarTower L L' E := IsScalarTower.of_algebraMap_eq' rfl
   refine ⟨(hK s hs).1.tower_top, (hK s hs).1.minpoly_splits_tower_top' ?_⟩
-  convert (hK s hs).2
+  convert! (hK s hs).2
   ext
   simp only [AlgHom.toRingHom_eq_coe, RingHom.coe_comp, RingHom.coe_coe,
     AlgHom.coe_comp, Function.comp_apply, f']
diff --git a/Mathlib/FieldTheory/Finite/Basic.lean b/Mathlib/FieldTheory/Finite/Basic.lean
index cce31993821d21..16f15d2c985534 100644
--- a/Mathlib/FieldTheory/Finite/Basic.lean
+++ b/Mathlib/FieldTheory/Finite/Basic.lean
@@ -456,7 +456,7 @@ theorem roots_X_pow_card_sub_X : roots (X ^ q - X : K[X]) = Finset.univ.val := b
     rw [← this, Multiset.toFinset_val, eq_comm, Multiset.dedup_eq_self]
     apply nodup_roots
     rw [separable_def]
-    convert isCoprime_one_right.neg_right (R := K[X]) using 1
+    convert! isCoprime_one_right.neg_right (R := K[X]) using 1
     rw [derivative_sub, derivative_X, derivative_X_pow, Nat.cast_card_eq_zero K, C_0,
       zero_mul, zero_sub]
 
diff --git a/Mathlib/FieldTheory/Finite/Extension.lean b/Mathlib/FieldTheory/Finite/Extension.lean
index 8e330e333d1170..299773369de76c 100644
--- a/Mathlib/FieldTheory/Finite/Extension.lean
+++ b/Mathlib/FieldTheory/Finite/Extension.lean
@@ -54,8 +54,9 @@ theorem finrank_zmod_extension [Algebra (ZMod p) k] :
     Module.finrank (ZMod p) (Extension k p n) = Module.finrank (ZMod p) k * n := by
   letI := ZMod.algebra k p
   unfold Extension
-  convert GaloisField.finrank p (n := Module.finrank (ZMod p) k * n) <|
-    mul_ne_zero Module.finrank_pos.ne' <| NeZero.ne n
+  convert!
+    GaloisField.finrank p (n := Module.finrank (ZMod p) k * n) <|
+      mul_ne_zero Module.finrank_pos.ne' <| NeZero.ne n
   subsingleton
 
 theorem nonempty_algHom_extension [Algebra (ZMod p) k] :
@@ -83,7 +84,7 @@ theorem finrank_extension : Module.finrank k (Extension k p n) = n := by
 
 instance : IsSplittingField k (Extension k p n) (X ^ Nat.card k ^ n - X) := by
   have := Fintype.ofFinite (Extension k p n)
-  convert FiniteField.isSplittingField_sub (Extension k p n) k
+  convert! FiniteField.isSplittingField_sub (Extension k p n) k
   · rw [Fintype.card_eq_nat_card, natCard_extension]
 
 example : IsGalois k (Extension k p n) :=
diff --git a/Mathlib/FieldTheory/Finite/GaloisField.lean b/Mathlib/FieldTheory/Finite/GaloisField.lean
index 5cc80830c0e2a2..a3cc93bce9b2e4 100644
--- a/Mathlib/FieldTheory/Finite/GaloisField.lean
+++ b/Mathlib/FieldTheory/Finite/GaloisField.lean
@@ -137,7 +137,7 @@ theorem card (h : n ≠ 0) : Nat.card (GaloisField p n) = p ^ n := by
 theorem splits_zmod_X_pow_sub_X : Splits (X ^ p - X : (ZMod p)[X]) := by
   have hp : 1 < p := h_prime.out.one_lt
   have h1 : roots (X ^ p - X : (ZMod p)[X]) = Finset.univ.val := by
-    convert FiniteField.roots_X_pow_card_sub_X (ZMod p)
+    convert! FiniteField.roots_X_pow_card_sub_X (ZMod p)
     exact (ZMod.card p).symm
   have h2 := FiniteField.X_pow_card_sub_X_natDegree_eq (ZMod p) hp
   -- We discharge the `p = 0` separately, to avoid typeclass issues on `ZMod p`.
@@ -240,9 +240,12 @@ theorem unitsMap_norm_surjective : Function.Surjective (Units.map <| Algebra.nor
     simp_rw [Nat.card_units]
     classical
     have := Fintype.ofFinite K'ˣ
-    convert IsCyclic.card_pow_eq_one_le (α := K'ˣ) <| Nat.div_pos
-      (Nat.sub_le_sub_right (Nat.card_le_card_of_injective _ (algebraMap K K').injective) _) <|
-      Nat.sub_pos_of_lt Finite.one_lt_card
+    convert!
+      IsCyclic.card_pow_eq_one_le (α := K'ˣ) <|
+        Nat.div_pos
+            (Nat.sub_le_sub_right (Nat.card_le_card_of_injective _ (algebraMap K K').injective)
+              _) <|
+          Nat.sub_pos_of_lt Finite.one_lt_card
     rw [← Set.ncard_coe_finset, ← SetLike.coe_sort_coe, Nat.card_coe_set_eq]; congr 1; ext
     simp [Units.ext_iff, ← (algebraMap K K').injective.eq_iff, algebraMap_norm_eq_pow]
 
diff --git a/Mathlib/FieldTheory/Galois/IsGaloisGroup.lean b/Mathlib/FieldTheory/Galois/IsGaloisGroup.lean
index f75a19b0b7735f..54329fa3fe8621 100644
--- a/Mathlib/FieldTheory/Galois/IsGaloisGroup.lean
+++ b/Mathlib/FieldTheory/Galois/IsGaloisGroup.lean
@@ -289,7 +289,7 @@ theorem fixedPoints_of_isGaloisGroup [hGKL : IsGaloisGroup G K L] [hHFL : IsGalo
 theorem of_fixedPoints_eq [hGKL : IsGaloisGroup G K L] (hF : FixedPoints.intermediateField H = F) :
     IsGaloisGroup H F L := by
   rw [eq_comm] at hF
-  convert IsGaloisGroup.subgroup G K L H
+  convert! IsGaloisGroup.subgroup G K L H
 
 variable {G K L H F} in
 theorem subgroup_iff [hGKL : IsGaloisGroup G K L] :
@@ -379,7 +379,7 @@ theorem fixingSubgroup_top : fixingSubgroup G ((⊤ : IntermediateField K L) : S
 @[simp]
 theorem fixedPoints_top :
     (FixedPoints.intermediateField (⊤ : Subgroup G) : IntermediateField K L) = ⊥ := by
-  convert IsGaloisGroup.fixedPoints_eq_bot G K L
+  convert! IsGaloisGroup.fixedPoints_eq_bot G K L
   ext; simp
 
 /-- The Galois correspondence from intermediate fields to subgroups. -/
diff --git a/Mathlib/FieldTheory/Galois/NormalBasis.lean b/Mathlib/FieldTheory/Galois/NormalBasis.lean
index 7f280ac9f671a3..3cb4c04e24d157 100644
--- a/Mathlib/FieldTheory/Galois/NormalBasis.lean
+++ b/Mathlib/FieldTheory/Galois/NormalBasis.lean
@@ -44,7 +44,8 @@ theorem exists_linearIndependent_algEquiv_apply_of_finite [Finite L] :
     .ofBijective _ <| bijective_frobeniusAlgEquivOfAlgebraic_pow K L)]
   /- Therefore, `{Frⁱ | 0 ≤ i < [L : K]}` is linearly independent, which implies that
     `{Frⁱ(x) | 0 ≤ i < [L : K]}` is also linearly independent. -/
-  convert (AdjoinRoot.powerBasis (X_pow_sub_C_ne_zero Module.finrank_pos 1)).basis.linearIndependent
+  convert!
+    (AdjoinRoot.powerBasis (X_pow_sub_C_ne_zero Module.finrank_pos 1)).basis.linearIndependent
     |>.map' ((AEval'.of _).symm.toLinearMap ∘ₗ (liftQ _ _ hx.le).restrictScalars K) <| by
     exact congr($(ker_liftQ_eq_bot' _ _ hx).restrictScalars K)
   ext i
diff --git a/Mathlib/FieldTheory/Galois/Profinite.lean b/Mathlib/FieldTheory/Galois/Profinite.lean
index 61caa2081870fb..303c5161560b10 100644
--- a/Mathlib/FieldTheory/Galois/Profinite.lean
+++ b/Mathlib/FieldTheory/Galois/Profinite.lean
@@ -169,7 +169,7 @@ set_option backward.isDefEq.respectTransparency false in
 lemma algEquivToLimit_continuous : Continuous (algEquivToLimit k K) := by
   rw [continuous_induced_rng]
   refine continuous_pi (fun L ↦ ?_)
-  convert restrictNormalHom_continuous L.unop.1
+  convert! restrictNormalHom_continuous L.unop.1
   exact (DiscreteTopology.eq_bot (α := L.unop ≃ₐ[k] L.unop)).symm
 
 /-- The projection map from `lim Gal(L/k)` to a specific `Gal(L/k)`. -/
diff --git a/Mathlib/FieldTheory/IntermediateField/Adjoin/Algebra.lean b/Mathlib/FieldTheory/IntermediateField/Adjoin/Algebra.lean
index 037a6c723713d1..16ac66b953a997 100644
--- a/Mathlib/FieldTheory/IntermediateField/Adjoin/Algebra.lean
+++ b/Mathlib/FieldTheory/IntermediateField/Adjoin/Algebra.lean
@@ -334,7 +334,7 @@ theorem algHom_fieldRange_eq_of_comp_eq (h : RingHom.comp f (algebraMap A K) = (
     f.fieldRange = IntermediateField.adjoin F g.range := by
   apply IntermediateField.toSubfield_injective
   simp_rw [AlgHom.fieldRange_toSubfield, IntermediateField.adjoin_toSubfield]
-  convert ringHom_fieldRange_eq_of_comp_eq h using 2
+  convert! ringHom_fieldRange_eq_of_comp_eq h using 2
   exact Set.union_eq_self_of_subset_left fun _ ⟨x, hx⟩ ↦ ⟨algebraMap F A x, by simp [← hx]⟩
 
 /-- If `F` is a field, `A` is an `F`-algebra with fraction field `K`, `L` is a field,
diff --git a/Mathlib/FieldTheory/IntermediateField/Adjoin/Basic.lean b/Mathlib/FieldTheory/IntermediateField/Adjoin/Basic.lean
index 97988edea6e63c..3a118004d1cb36 100644
--- a/Mathlib/FieldTheory/IntermediateField/Adjoin/Basic.lean
+++ b/Mathlib/FieldTheory/IntermediateField/Adjoin/Basic.lean
@@ -387,7 +387,7 @@ theorem minpoly_gen (α : E) :
 
 theorem aeval_gen_minpoly (α : E) : aeval (AdjoinSimple.gen F α) (minpoly F α) = 0 := by
   ext
-  convert minpoly.aeval F α
+  convert! minpoly.aeval F α
   conv in aeval α => rw [← AdjoinSimple.algebraMap_gen F α]
   exact (aeval_algebraMap_apply E (AdjoinSimple.gen F α) _).symm
 
@@ -504,8 +504,9 @@ theorem adjoin_minpoly_coeff_of_exists_primitive_element
     simp_all
   refine eq_of_le_of_finrank_le' hsub ?_
   simp_rw [finrank_eq]
-  convert natDegree_le_of_dvd dvd_g
-    ((g.monic_toSubring _ _).mpr <| (minpoly.monic <| .of_finite K α).map _).ne_zero using 1
+  convert!
+    natDegree_le_of_dvd dvd_g
+      ((g.monic_toSubring _ _).mpr <| (minpoly.monic <| .of_finite K α).map _).ne_zero using 1
   rw [natDegree_toSubring, natDegree_map]
 
 instance : Module.Finite F (⊥ : IntermediateField F E) := Subalgebra.finite_bot
diff --git a/Mathlib/FieldTheory/IntermediateField/Adjoin/Defs.lean b/Mathlib/FieldTheory/IntermediateField/Adjoin/Defs.lean
index da6341a6aafb9a..a2f8d2f9e5c6ea 100644
--- a/Mathlib/FieldTheory/IntermediateField/Adjoin/Defs.lean
+++ b/Mathlib/FieldTheory/IntermediateField/Adjoin/Defs.lean
@@ -496,9 +496,9 @@ theorem adjoin_algHom_ext {s : Set E} ⦃φ₁ φ₂ : adjoin F s →ₐ[F] K⦄
     (h : ∀ x hx, φ₁ ⟨x, subset_adjoin _ _ hx⟩ = φ₂ ⟨x, subset_adjoin _ _ hx⟩) :
     φ₁ = φ₂ :=
   AlgHom.ext fun ⟨x, hx⟩ ↦ adjoin_induction _ h (fun _ ↦ φ₂.commutes _ ▸ φ₁.commutes _)
-    (fun _ _ _ _ h₁ h₂ ↦ by convert congr_arg₂ (· + ·) h₁ h₂ <;> rw [← map_add] <;> rfl)
+    (fun _ _ _ _ h₁ h₂ ↦ by convert! congr_arg₂ (· + ·) h₁ h₂ <;> rw [← map_add] <;> rfl)
     (fun _ _ ↦ eq_on_inv₀ _ _)
-    (fun _ _ _ _ h₁ h₂ ↦ by convert congr_arg₂ (· * ·) h₁ h₂ <;> rw [← map_mul] <;> rfl)
+    (fun _ _ _ _ h₁ h₂ ↦ by convert! congr_arg₂ (· * ·) h₁ h₂ <;> rw [← map_mul] <;> rfl)
     hx
 
 theorem algHom_ext_of_eq_adjoin {S : IntermediateField F E} {s : Set E} (hS : S = adjoin F s)
diff --git a/Mathlib/FieldTheory/IsPerfectClosure.lean b/Mathlib/FieldTheory/IsPerfectClosure.lean
index cfbb4f28cb72fd..6f8ac711154e33 100644
--- a/Mathlib/FieldTheory/IsPerfectClosure.lean
+++ b/Mathlib/FieldTheory/IsPerfectClosure.lean
@@ -167,7 +167,7 @@ theorem IsPRadical.comap_pNilradical [IsPRadical i p] :
 variable (K) in
 instance IsPRadical.of_id : IsPRadical (RingHom.id K) p where
   pow_mem' x := ⟨0, x, by simp⟩
-  ker_le' x h := by convert Ideal.zero_mem _
+  ker_le' x h := by convert! Ideal.zero_mem _
 
 /-- Composition of `p`-radical ring homomorphisms is also `p`-radical. -/
 theorem IsPRadical.trans [IsPRadical i p] [IsPRadical f p] :
diff --git a/Mathlib/FieldTheory/JacobsonNoether.lean b/Mathlib/FieldTheory/JacobsonNoether.lean
index 3704c1481f13e3..9bd233c32ef38a 100644
--- a/Mathlib/FieldTheory/JacobsonNoether.lean
+++ b/Mathlib/FieldTheory/JacobsonNoether.lean
@@ -130,7 +130,7 @@ theorem exists_separable_and_not_isCentral (H : k ≠ (⊤ : Subring D)) :
     refine ⟨Nat.find h_exist, ⟨(Nat.find_spec h_exist).1, ?_, (Nat.find_spec h_exist).2⟩⟩
     set t := (Nat.find h_exist - 1 : ℕ) with ht
     by_cases! h_pos : 0 < t
-    · convert (ne_eq _ _) ▸ not_and.mp (Nat.find_min h_exist (m := t) (by lia)) h_pos
+    · convert! (ne_eq _ _) ▸ not_and.mp (Nat.find_min h_exist (m := t) (by lia)) h_pos
       lia
     · suffices h_find : Nat.find h_exist = 1 by
         rwa [h_find]
diff --git a/Mathlib/FieldTheory/KrullTopology.lean b/Mathlib/FieldTheory/KrullTopology.lean
index a353f904b654cc..2388afc6796f00 100644
--- a/Mathlib/FieldTheory/KrullTopology.lean
+++ b/Mathlib/FieldTheory/KrullTopology.lean
@@ -266,7 +266,7 @@ theorem stabilizer_isOpen_of_isIntegral [Algebra.IsIntegral K L] (x : L) :
   open IntermediateField in
   let E := adjoin K {x}
   have hL : FiniteDimensional K E := adjoin.finiteDimensional (Algebra.IsIntegral.isIntegral x)
-  convert fixingSubgroup_isOpen E
+  convert! fixingSubgroup_isOpen E
   ext g
   simpa using (forall_mem_adjoin_smul_eq_self_iff K (S := {x}) g).symm
 
diff --git a/Mathlib/FieldTheory/LinearDisjoint.lean b/Mathlib/FieldTheory/LinearDisjoint.lean
index 2f5378e57a22d1..031d1e1bc37f18 100644
--- a/Mathlib/FieldTheory/LinearDisjoint.lean
+++ b/Mathlib/FieldTheory/LinearDisjoint.lean
@@ -211,7 +211,7 @@ theorem map' (H : A.LinearDisjoint L) (K : Type*) [Field K] [Algebra F K] [Algeb
   rw [linearDisjoint_iff] at H ⊢
   have := H.map (IsScalarTower.toAlgHom F E K) (RingHom.injective _)
   rw [← AlgHom.range_comp] at this
-  convert this
+  convert! this
   ext; exact IsScalarTower.algebraMap_apply L E K _
 
 /-- Linear disjointness is preserved by algebra homomorphism. -/
@@ -225,7 +225,7 @@ theorem map'' {L' : Type*} [Field L'] [Algebra F L'] [Algebra L' E] [IsScalarTow
   have := H.map (IsScalarTower.toAlgHom F E K) (RingHom.injective _)
   simp_rw [AlgHom.fieldRange_toSubalgebra, ← AlgHom.range_comp] at this
   rw [AlgHom.fieldRange_toSubalgebra]
-  convert this <;> (ext; exact IsScalarTower.algebraMap_apply _ E K _)
+  convert! this <;> (ext; exact IsScalarTower.algebraMap_apply _ E K _)
 
 variable (A) in
 theorem self_right : A.LinearDisjoint F := Subalgebra.LinearDisjoint.bot_right _
@@ -370,7 +370,7 @@ theorem of_le_right' (H : A.LinearDisjoint L) (L' : Type*) [Field L']
     [Algebra F L'] [Algebra L' L] [IsScalarTower F L' L]
     [Algebra L' E] [IsScalarTower F L' E] [IsScalarTower L' L E] : A.LinearDisjoint L' := by
   refine Subalgebra.LinearDisjoint.of_le_right_of_flat H ?_
-  convert AlgHom.range_comp_le_range (IsScalarTower.toAlgHom F L' L) (IsScalarTower.toAlgHom F L E)
+  convert! AlgHom.range_comp_le_range (IsScalarTower.toAlgHom F L' L) (IsScalarTower.toAlgHom F L E)
   ext; exact IsScalarTower.algebraMap_apply L' L E _
 
 /-- If `A` and `B` are linearly disjoint, `A'` and `B'` are contained in `A` and `B`,
diff --git a/Mathlib/FieldTheory/Minpoly/Basic.lean b/Mathlib/FieldTheory/Minpoly/Basic.lean
index ab71d551b86685..a1042606580fab 100644
--- a/Mathlib/FieldTheory/Minpoly/Basic.lean
+++ b/Mathlib/FieldTheory/Minpoly/Basic.lean
@@ -194,7 +194,7 @@ theorem natDegree_pos [Nontrivial B] (hx : IsIntegral A x) : 0 < natDegree (minp
   intro ndeg_eq_zero
   have eq_one : minpoly A x = 1 := by
     rw [eq_C_of_natDegree_eq_zero ndeg_eq_zero]
-    convert C_1 (R := A)
+    convert! C_1 (R := A)
     simpa only [ndeg_eq_zero.symm] using (monic hx).leadingCoeff
   simpa only [eq_one, map_one, one_ne_zero] using aeval A x
 
diff --git a/Mathlib/FieldTheory/Minpoly/IsIntegrallyClosed.lean b/Mathlib/FieldTheory/Minpoly/IsIntegrallyClosed.lean
index 0d61f1ce891028..98287a725d13c4 100644
--- a/Mathlib/FieldTheory/Minpoly/IsIntegrallyClosed.lean
+++ b/Mathlib/FieldTheory/Minpoly/IsIntegrallyClosed.lean
@@ -150,10 +150,10 @@ theorem IsIntegrallyClosed.isIntegral_iff_leadingCoeff_dvd {s : S} {p : R[X]} (h
     have ⟨q, hMul⟩ := isIntegrallyClosed_dvd hInt hp
     suffices q.degree ≤ 0 by simp [degree_le_zero_iff.mp this ▸ hMul, minpoly.monic hInt, mul_comm]
     apply WithBot.le_of_add_le_add_left <| Polynomial.degree_ne_bot.mpr <| minpoly.ne_zero hInt
-    convert pmin _ (minpoly.monic hInt) (minpoly.aeval ..)
+    convert! pmin _ (minpoly.monic hInt) (minpoly.aeval ..)
     · rw [hMul, degree_mul]
     · rw [add_zero]
-  · convert right_ne_zero_of_mul <| hMul ▸ h₀
+  · convert! right_ne_zero_of_mul <| hMul ▸ h₀
     refine IsIntegrallyClosed.minpoly.unique ?_ ?_ ?_ |>.symm
     · have := hMul ▸ leadingCoeff_mul .. |>.symm
       simp only [leadingCoeff_C, ne_eq, leadingCoeff_eq_zero, h₀, not_false_eq_true, mul_eq_left₀]
diff --git a/Mathlib/FieldTheory/Normal/Basic.lean b/Mathlib/FieldTheory/Normal/Basic.lean
index c3e5e6b526714e..f6d78c7749aae8 100644
--- a/Mathlib/FieldTheory/Normal/Basic.lean
+++ b/Mathlib/FieldTheory/Normal/Basic.lean
@@ -127,7 +127,7 @@ theorem splits_of_mem_adjoin {L} [Field L] [Algebra F L] {S : Set K}
   have : ∀ x ∈ S, ((minpoly F x).map (algebraMap F E)).Splits := fun x hx ↦ splits_of_splits
     (splits x hx).2 fun y hy ↦ (le_iSup _ ⟨x, hx⟩ : _ ≤ E) (subset_adjoin F _ <| by exact hy)
   obtain ⟨φ⟩ := nonempty_algHom_adjoin_of_splits fun x hx ↦ ⟨(splits x hx).1, this x hx⟩
-  convert (normal.splits <| φ ⟨x, hx⟩).map E.val.toRingHom
+  convert! (normal.splits <| φ ⟨x, hx⟩).map E.val.toRingHom
   simp [minpoly.algHom_eq _ φ.injective, ← minpoly.algHom_eq _ (adjoin F S).val.injective,
     Polynomial.map_map]
 
diff --git a/Mathlib/FieldTheory/Perfect.lean b/Mathlib/FieldTheory/Perfect.lean
index 3e55bcb56a8448..dca92c53e8959b 100644
--- a/Mathlib/FieldTheory/Perfect.lean
+++ b/Mathlib/FieldTheory/Perfect.lean
@@ -362,14 +362,14 @@ theorem roots_expand_pow_map_iterateFrobenius_le :
     simp_rw [count_nsmul, count_roots, ← rootMultiplicity_expand_pow, ← count_roots, count_map,
       count_eq_card_filter_eq]
     exact card_le_card (monotone_filter_right _ fun _ h ↦ iterateFrobenius_inj R p n h)
-  convert Nat.zero_le _
+  convert! Nat.zero_le _
   simp_rw [count_map, card_eq_zero]
   exact ext' fun t ↦ count_zero t ▸ count_filter_of_neg fun h' ↦ h ⟨t, h'⟩
 
 theorem roots_expand_map_frobenius_le :
     (expand R p f).roots.map (frobenius R p) ≤ p • f.roots := by
   rw [← iterateFrobenius_one]
-  convert ← roots_expand_pow_map_iterateFrobenius_le p 1 f <;> apply pow_one
+  convert! ← roots_expand_pow_map_iterateFrobenius_le p 1 f <;> apply pow_one
 
 theorem roots_expand_pow_image_iterateFrobenius_subset [DecidableEq R] :
     (expand R (p ^ n) f).roots.toFinset.image (iterateFrobenius R p n) ⊆ f.roots.toFinset := by
@@ -380,7 +380,7 @@ theorem roots_expand_pow_image_iterateFrobenius_subset [DecidableEq R] :
 theorem roots_expand_image_frobenius_subset [DecidableEq R] :
     (expand R p f).roots.toFinset.image (frobenius R p) ⊆ f.roots.toFinset := by
   rw [← iterateFrobenius_one]
-  convert ← roots_expand_pow_image_iterateFrobenius_subset p 1 f
+  convert! ← roots_expand_pow_image_iterateFrobenius_subset p 1 f
   apply pow_one
 
 section PerfectRing
diff --git a/Mathlib/FieldTheory/PrimitiveElement.lean b/Mathlib/FieldTheory/PrimitiveElement.lean
index 70e72ba48b593d..7808f3e877d094 100644
--- a/Mathlib/FieldTheory/PrimitiveElement.lean
+++ b/Mathlib/FieldTheory/PrimitiveElement.lean
@@ -165,7 +165,7 @@ theorem primitive_element_inf_aux [Algebra.IsSeparable F E] : ∃ γ : E, F⟮α
   rw [← eq_X_sub_C_of_separable_of_root_eq h_sep h_root h_splits h_roots]
   trans EuclideanDomain.gcd (?_ : E[X]) (?_ : E[X])
   · dsimp only [γ]
-    convert (gcd_map (algebraMap F⟮γ⟯ E)).symm
+    convert! (gcd_map (algebraMap F⟮γ⟯ E)).symm
   · simp only [map_comp, Polynomial.map_map, ← IsScalarTower.algebraMap_eq, Polynomial.map_sub,
       map_C, AdjoinSimple.algebraMap_gen, Polynomial.map_mul, map_X]
     congr
@@ -190,7 +190,7 @@ private theorem primitive_element_inf_aux_of_finite_intermediateField
     replace β_in_K := smul_mem _ β_in_K (x := (x - y)⁻¹)
     rw [smul_smul, inv_mul_eq_div, div_self (sub_ne_zero.2 hneq), one_smul] at β_in_K
     have α_in_K : α ∈ F⟮α + x • β⟯ := by
-      convert ← sub_mem αxβ_in_K (smul_mem _ β_in_K)
+      convert! ← sub_mem αxβ_in_K (smul_mem _ β_in_K)
       apply add_sub_cancel_right
     rintro x (rfl | rfl) <;> assumption
   · rw [adjoin_simple_le_iff]
@@ -320,7 +320,7 @@ theorem finite_intermediateField_of_exists_primitive_element [Algebra.IsAlgebrai
   -- which is a monic factor of `f`
   let g : IntermediateField F E → G := fun K ↦
     ⟨(minpoly K α).map (algebraMap K E), (minpoly.monic <| .of_finite K α).map _, by
-      convert Polynomial.map_dvd (algebraMap K E) (minpoly.dvd_map_of_isScalarTower F K α)
+      convert! Polynomial.map_dvd (algebraMap K E) (minpoly.dvd_map_of_isScalarTower F K α)
       rw [Polynomial.map_map]; rfl⟩
   -- The map `K ↦ g` is injective
   have hinj : Function.Injective g := fun K K' heq ↦ by
diff --git a/Mathlib/FieldTheory/PurelyInseparable/PerfectClosure.lean b/Mathlib/FieldTheory/PurelyInseparable/PerfectClosure.lean
index 7a3c681f45009c..41aa640ba2b9ff 100644
--- a/Mathlib/FieldTheory/PurelyInseparable/PerfectClosure.lean
+++ b/Mathlib/FieldTheory/PurelyInseparable/PerfectClosure.lean
@@ -337,7 +337,7 @@ private theorem LinearIndependent.map_pow_expChar_pow_of_fd_isSeparable
     (Field.span_map_pow_expChar_pow_eq_top_of_isSeparable q n b.span_eq).ge
     (Module.finrank_eq_card_basis b).symm
   let f (i : ι) : ι' := ⟨v i, h'.subset_extend _ ⟨i, rfl⟩⟩
-  convert H.comp f fun _ _ heq ↦ h.injective (by simpa only [f, Subtype.mk.injEq] using heq)
+  convert! H.comp f fun _ _ heq ↦ h.injective (by simpa only [f, Subtype.mk.injEq] using heq)
   simp_rw [Function.comp_apply, b]
   rw [Basis.extend_apply_self]
 
diff --git a/Mathlib/FieldTheory/PurelyInseparable/Tower.lean b/Mathlib/FieldTheory/PurelyInseparable/Tower.lean
index 5a785770f2aeda..4c2702c2c0b301 100644
--- a/Mathlib/FieldTheory/PurelyInseparable/Tower.lean
+++ b/Mathlib/FieldTheory/PurelyInseparable/Tower.lean
@@ -73,7 +73,7 @@ theorem LinearIndependent.map_of_isPurelyInseparable_of_isSeparable [IsPurelyIns
   have := (expChar_pow_pos F q n).ne'
   replace hf (i : ι) : l i ^ q ^ n ∈ (algebraMap F E).range := by
     by_cases hs : i ∈ l.support
-    · convert pow_mem (hf i) (q ^ (n - f i)) using 1
+    · convert! pow_mem (hf i) (q ^ (n - f i)) using 1
       rw [← pow_mul, ← pow_add, Nat.add_sub_of_le (Finset.le_sup hs)]
     exact ⟨0, by rw [map_zero, Finsupp.notMem_support_iff.1 hs, zero_pow this]⟩
   choose lF hlF using hf
@@ -89,7 +89,7 @@ theorem LinearIndependent.map_of_isPurelyInseparable_of_isSeparable [IsPurelyIns
     refine Finset.sum_congr rfl fun i _ ↦ ?_
     simp_rw [Algebra.smul_def, mul_pow, IsScalarTower.algebraMap_apply F E K, hlF, map_pow]
   refine eq_zero_of_pow_eq_zero ((hlF _).symm.trans ?_)
-  convert map_zero (algebraMap F E)
+  convert! map_zero (algebraMap F E)
   exact congr($h i)
 
 variable {F K} in
@@ -148,7 +148,7 @@ It is a special case of `Field.lift_sepDegree_mul_lift_sepDegree_of_isAlgebraic`
 intermediate result used to prove it. -/
 lemma sepDegree_eq_of_isPurelyInseparable [IsPurelyInseparable F E] :
     sepDegree F K = sepDegree E K := by
-  convert sepDegree_eq_of_isPurelyInseparable_of_isSeparable F E (separableClosure E K)
+  convert! sepDegree_eq_of_isPurelyInseparable_of_isSeparable F E (separableClosure E K)
   haveI : IsScalarTower F (separableClosure E K) K := IsScalarTower.of_algebraMap_eq (congrFun rfl)
   rw [sepDegree, ← separableClosure.map_eq_of_separableClosure_eq_bot F
     (separableClosure.separableClosure_eq_bot E K)]
diff --git a/Mathlib/FieldTheory/RatFunc/AsPolynomial.lean b/Mathlib/FieldTheory/RatFunc/AsPolynomial.lean
index 73d5d349456068..019416028599ef 100644
--- a/Mathlib/FieldTheory/RatFunc/AsPolynomial.lean
+++ b/Mathlib/FieldTheory/RatFunc/AsPolynomial.lean
@@ -327,7 +327,7 @@ lemma valuation_monomial_eq_valuation_X_pow (n : ℕ) {a : K} (ha : a ≠ 0) :
 Note: The condition `1 < v RatFunc.X` is typically satisfied by the valuation at infinity. -/
 theorem valuation_eq_valuation_X_pow_natDegree_of_one_lt_valuation_X
      (hlt : 1 < v RatFunc.X) {p : K[X]} (hp : p ≠ 0) : v p = v RatFunc.X ^ p.natDegree := by
-  convert valuation_aeval_eq_valuation_X_pow_natDegree_of_one_lt_valuation_X .X hlt hp
+  convert! valuation_aeval_eq_valuation_X_pow_natDegree_of_one_lt_valuation_X .X hlt hp
   ext p
   nth_rw 1 [RatFunc.X, ← aeval_X_left_apply p (R := K)]
   exact (aeval_algebraMap_apply K⟮X⟯ X p).symm
diff --git a/Mathlib/FieldTheory/RatFunc/Basic.lean b/Mathlib/FieldTheory/RatFunc/Basic.lean
index 2b8eb8d1ead150..fb732adde49cc6 100644
--- a/Mathlib/FieldTheory/RatFunc/Basic.lean
+++ b/Mathlib/FieldTheory/RatFunc/Basic.lean
@@ -680,7 +680,7 @@ instance : IsFractionRing K[X] K⟮X⟯ where
     exact fun h ↦ IsLocalization.exists_of_eq ((toFractionRingRingEquiv K).symm.injective h)
   surj := by
     rintro ⟨z⟩
-    convert IsLocalization.surj K[X]⁰ z
+    convert! IsLocalization.surj K[X]⁰ z
     simp only [← ofFractionRing_algebraMap, ← ofFractionRing_mul,
       ofFractionRing.injEq]
 
@@ -899,7 +899,7 @@ private theorem num_div' (p : K[X]) {q : K[X]} (hq : q ≠ 0) :
   rw [num, numDenom_div _ hq]
 
 @[simp]
-theorem num_zero : num (0 : K⟮X⟯) = 0 := by convert num_div' (0 : K[X]) one_ne_zero <;> simp
+theorem num_zero : num (0 : K⟮X⟯) = 0 := by convert! num_div' (0 : K[X]) one_ne_zero <;> simp
 
 open scoped Classical in
 @[simp]
@@ -911,10 +911,10 @@ theorem num_div (p q : K[X]) :
   · exact num_div' p hq
 
 @[simp]
-theorem num_one : num (1 : K⟮X⟯) = 1 := by convert num_div (1 : K[X]) 1 <;> simp
+theorem num_one : num (1 : K⟮X⟯) = 1 := by convert! num_div (1 : K[X]) 1 <;> simp
 
 @[simp]
-theorem num_algebraMap (p : K[X]) : num (algebraMap _ _ p) = p := by convert num_div p 1 <;> simp
+theorem num_algebraMap (p : K[X]) : num (algebraMap _ _ p) = p := by convert! num_div p 1 <;> simp
 
 theorem num_div_dvd (p : K[X]) {q : K[X]} (hq : q ≠ 0) :
     num (algebraMap _ _ p / algebraMap _ _ q) ∣ p := by
@@ -953,15 +953,15 @@ theorem denom_ne_zero (x : K⟮X⟯) : denom x ≠ 0 :=
 
 @[simp]
 theorem denom_zero : denom (0 : K⟮X⟯) = 1 := by
-  convert denom_div (0 : K[X]) one_ne_zero <;> simp
+  convert! denom_div (0 : K[X]) one_ne_zero <;> simp
 
 @[simp]
 theorem denom_one : denom (1 : K⟮X⟯) = 1 := by
-  convert denom_div (1 : K[X]) one_ne_zero <;> simp
+  convert! denom_div (1 : K[X]) one_ne_zero <;> simp
 
 @[simp]
 theorem denom_algebraMap (p : K[X]) : denom (algebraMap _ K⟮X⟯ p) = 1 := by
-  convert denom_div p one_ne_zero <;> simp
+  convert! denom_div p one_ne_zero <;> simp
 
 @[simp]
 theorem denom_div_dvd (p q : K[X]) : denom (algebraMap _ _ p / algebraMap _ _ q) ∣ q := by
@@ -1085,12 +1085,12 @@ theorem denom_inv_dvd {x : K⟮X⟯} (hx : x ≠ 0) : denom x⁻¹ ∣ num x :=
 
 theorem associated_num_inv {x : K⟮X⟯} (hx : x ≠ 0) : Associated (num x⁻¹) (denom x) := by
   apply associated_of_dvd_dvd (num_inv_dvd hx)
-  convert denom_inv_dvd (inv_ne_zero hx)
+  convert! denom_inv_dvd (inv_ne_zero hx)
   rw [inv_inv]
 
 theorem associated_denom_inv {x : K⟮X⟯} (hx : x ≠ 0) : Associated (denom x⁻¹) (num x) := by
   apply Associated.symm
-  convert associated_num_inv (inv_ne_zero hx)
+  convert! associated_num_inv (inv_ne_zero hx)
   rw [inv_inv]
 
 theorem map_denom_ne_zero {L F : Type*} [Zero L] [FunLike F K[X] L] [ZeroHomClass F K[X] L]
diff --git a/Mathlib/FieldTheory/RatFunc/IntermediateField.lean b/Mathlib/FieldTheory/RatFunc/IntermediateField.lean
index 1794002093a788..c91f95b5d33eab 100644
--- a/Mathlib/FieldTheory/RatFunc/IntermediateField.lean
+++ b/Mathlib/FieldTheory/RatFunc/IntermediateField.lean
@@ -141,8 +141,9 @@ theorem irreducible_minpolyX' (hf : ¬∃ c, f = C c) : Irreducible (f.minpolyX
     rw [mul_comm]
     rfl
   rw [this, MulEquiv.irreducible_iff]
-  convert irreducible_C_mul_X_add_C (neg_ne_zero.mpr f.denom_ne_zero)
-    ((IsCoprime.neg_right_iff _ _).mpr f.isCoprime_num_denom).symm.isRelPrime using 1
+  convert!
+    irreducible_C_mul_X_add_C (neg_ne_zero.mpr f.denom_ne_zero)
+      ((IsCoprime.neg_right_iff _ _).mpr f.isCoprime_num_denom).symm.isRelPrime using 1
   rw [add_comm, X_mul_C, map_neg, neg_mul]
   exact sub_eq_add_neg (Polynomial.C f.num) (Polynomial.C f.denom * Polynomial.X)
 
diff --git a/Mathlib/FieldTheory/RatFunc/Luroth.lean b/Mathlib/FieldTheory/RatFunc/Luroth.lean
index 50ecde4d76b852..90ef21134cda3e 100644
--- a/Mathlib/FieldTheory/RatFunc/Luroth.lean
+++ b/Mathlib/FieldTheory/RatFunc/Luroth.lean
@@ -329,7 +329,7 @@ lemma swap_θ : Bivariate.swap (θ E) = -(θ E) := by
   ring
 
 lemma θ_natDegree_le (h : E ≠ ⊥) : (θ E).natDegree ≤ m E := by
-  convert natDegree_sub_le _ _ using 3
+  convert! natDegree_sub_le _ _ using 3
   · rw [natDegree_mul (C_ne_zero.mpr (generator E).denom_ne_zero)
       (Polynomial.map_ne_zero (num_ne_zero (generator_ne_zero h))), natDegree_C, zero_add,
       natDegree_map]
diff --git a/Mathlib/FieldTheory/Separable.lean b/Mathlib/FieldTheory/Separable.lean
index 3acfdbdf55267b..3bdc564024be5b 100644
--- a/Mathlib/FieldTheory/Separable.lean
+++ b/Mathlib/FieldTheory/Separable.lean
@@ -161,7 +161,7 @@ theorem isUnit_of_self_mul_dvd_separable {p q : R[X]} (hp : p.Separable) (hq : q
       (q * (derivative q * p + derivative q * p + q * derivative p)) := by
     simp only [← mul_assoc, mul_add]
     dsimp only [Separable] at hp
-    convert hp using 1
+    convert! hp using 1
     rw [derivative_mul, derivative_mul]
     ring
   exact IsCoprime.of_mul_right_left (IsCoprime.of_mul_left_left this)
diff --git a/Mathlib/FieldTheory/SeparableClosure.lean b/Mathlib/FieldTheory/SeparableClosure.lean
index 6f019bf2a03a7d..abf1b13e81d948 100644
--- a/Mathlib/FieldTheory/SeparableClosure.lean
+++ b/Mathlib/FieldTheory/SeparableClosure.lean
@@ -395,7 +395,7 @@ lemma exists_finset_maximalFor_isTranscendenceBasis_separableClosure
   have : Module.Finite (adjoin F (s : Set E)) E := by
     apply +allowSynthFailures Algebra.finite_of_essFiniteType_of_isAlgebraic
     · exact .of_comp F _ _
-    · convert hs.isAlgebraic_field <;> simp [s]
+    · convert! hs.isAlgebraic_field <;> simp [s]
   have : Module.Finite ((separableClosure (adjoin F (s : Set E)) E).restrictScalars F) E :=
     inferInstanceAs <| Module.Finite (separableClosure (adjoin F (s : Set E)) E) E
   exact d.not_lt_argminOn _ ht (by apply finrank_lt_of_gt H)
diff --git a/Mathlib/FieldTheory/SeparablyGenerated.lean b/Mathlib/FieldTheory/SeparablyGenerated.lean
index 7709e744bdd61f..5cc5321ca4cdb9 100644
--- a/Mathlib/FieldTheory/SeparablyGenerated.lean
+++ b/Mathlib/FieldTheory/SeparablyGenerated.lean
@@ -70,9 +70,10 @@ theorem irreducible_toPolynomialAdjoinImageCompl {F : MvPolynomial ι k} (hF : I
     Irreducible (toPolynomialAdjoinImageCompl F a i) := by
   have : a '' {i}ᶜ = Set.range (fun x : {j | j ≠ i} ↦ a x) := by ext; simp
   delta toPolynomialAdjoinImageCompl
-  convert hF.map (renameEquiv k (Equiv.optionSubtypeNe i).symm) |>.map (optionEquivLeft k _) |>.map
-    (Polynomial.mapAlgEquiv (H.aevalEquiv.trans
-      (Subalgebra.equivOfEq _ _ congr(Algebra.adjoin k $this.symm))))
+  convert!
+    hF.map (renameEquiv k (Equiv.optionSubtypeNe i).symm) |>.map (optionEquivLeft k _) |>.map
+      (Polynomial.mapAlgEquiv
+        (H.aevalEquiv.trans (Subalgebra.equivOfEq _ _ congr(Algebra.adjoin k $this.symm))))
   rw [← AlgEquiv.coe_algHom]
   congr
   aesop
@@ -208,7 +209,7 @@ lemma exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow
     intro h
     refine h.transcendental_adjoin (i := n) (s := {n}ᶜ) (by simp) ?_
     have : a '' {n}ᶜ = Set.range (ι := {i // i ≠ n}) (a ·) := by aesop
-    convert ha'.isAlgebraic.isAlgebraic _
+    convert! ha'.isAlgebraic.isAlgebraic _
   have hFirr : Irreducible F := irreducible_of_forall_totalDegree_le hFmin hF₀ hFa
   obtain ⟨i, σ, hσ, hi⟩ := exists_mem_support_not_dvd_of_forall_totalDegree_le p hp H hFmin hF₀ hFa
   have hσi : σ i ≠ 0 := by aesop
@@ -247,7 +248,7 @@ lemma exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow'
   let e₂ : {j // j ≠ i} ≃ ↥(insert n s \ {i.1}) := ⟨fun x ↦ ⟨x, x.1.2, fun h ↦ x.2 (Subtype.ext h)⟩,
     fun x ↦ ⟨⟨x, x.2.1⟩, fun h ↦ x.2.2 congr($h.1)⟩, fun _ ↦ rfl, fun _ ↦ rfl⟩
   have : a '' (insert n s \ {i.1}) = (a ·.1) '' {i}ᶜ := by ext; aesop
-  refine ⟨i, hi.comp_equiv e₂.symm, by convert hi'⟩
+  refine ⟨i, hi.comp_equiv e₂.symm, by convert! hi'⟩
 
 /--
 Suppose `k` has characteristic `p` and `K/k` is generated by `a₁,...,aₙ₊₁`,
@@ -316,7 +317,7 @@ lemma exists_isTranscendenceBasis_and_isSeparable_of_perfectField
     obtain ⟨t, hts, ht⟩ := exists_isTranscendenceBasis_subset (R := k) (s : Set K)
     lift t to Finset K using s.finite_toSet.subset hts
     have : Algebra.IsAlgebraic (IntermediateField.adjoin k (t : Set K)) K := by
-      convert ht.isAlgebraic_field <;> simp
+      convert! ht.isAlgebraic_field <;> simp
     exact ⟨t, ht, inferInstance⟩
   have : ExpChar k p := .prime hp.out
   have : CharP K p := .of_ringHom_of_ne_zero (algebraMap k K) p hp.out.ne_zero
diff --git a/Mathlib/Geometry/Convex/Cone/Basic.lean b/Mathlib/Geometry/Convex/Cone/Basic.lean
index be11e7599090af..95befafbc1df0f 100644
--- a/Mathlib/Geometry/Convex/Cone/Basic.lean
+++ b/Mathlib/Geometry/Convex/Cone/Basic.lean
@@ -740,7 +740,7 @@ set_option linter.deprecated false in
 @[deprecated "no replacement" (since := "2026-03-30")]
 theorem convexHull_toCone_isLeast (s : Set M) :
     IsLeast { t : ConvexCone 𝕜 M | s ⊆ t } ((convex_convexHull 𝕜 s).toCone _) := by
-  convert (convex_convexHull 𝕜 s).toCone_isLeast using 1
+  convert! (convex_convexHull 𝕜 s).toCone_isLeast using 1
   ext t
   exact ⟨fun h => convexHull_min h t.convex, (subset_convexHull 𝕜 s).trans⟩
 
diff --git a/Mathlib/Geometry/Convex/Cone/Pointed.lean b/Mathlib/Geometry/Convex/Cone/Pointed.lean
index eb5f9d417e8bde..2f5b3b22f6e284 100644
--- a/Mathlib/Geometry/Convex/Cone/Pointed.lean
+++ b/Mathlib/Geometry/Convex/Cone/Pointed.lean
@@ -131,10 +131,10 @@ def _root_.ConvexCone.toPointedCone (C : ConvexCone R E) (hC : C.Pointed) : Poin
     simp_rw [SetLike.mem_coe]
     rcases eq_or_lt_of_le hc with hzero | hpos
     · unfold ConvexCone.Pointed at hC
-      convert hC
+      convert! hC
       simp [← hzero]
     · apply ConvexCone.smul_mem
-      · convert hpos
+      · convert! hpos
       · exact hx
 
 @[simp]
diff --git a/Mathlib/Geometry/Convex/Cone/TensorProduct.lean b/Mathlib/Geometry/Convex/Cone/TensorProduct.lean
index 10aa65f02ed262..aa0498ba0f14f7 100644
--- a/Mathlib/Geometry/Convex/Cone/TensorProduct.lean
+++ b/Mathlib/Geometry/Convex/Cone/TensorProduct.lean
@@ -161,7 +161,7 @@ theorem maxTensorProduct_map_le (f : G →ₗ[R] G') (g : H →ₗ[R] H')
   have h_eq : ((dualDistrib R G' H') (φ ⊗ₜ[R] ψ)).comp (TensorProduct.map f g) =
       ((dualDistrib R G H) ((φ.comp f) ⊗ₜ[R] (ψ.comp g))) :=
     TensorProduct.ext' fun x y ↦ by simp [map_tmul]
-  convert hw (φ.comp f) (fun x hx ↦ hφ ⟨x, hx, rfl⟩) (ψ.comp g) (fun y hy ↦ hψ ⟨y, hy, rfl⟩)
+  convert! hw (φ.comp f) (fun x hx ↦ hφ ⟨x, hx, rfl⟩) (ψ.comp g) (fun y hy ↦ hψ ⟨y, hy, rfl⟩)
   exact DFunLike.congr_fun h_eq w
 
 end PointedCone
diff --git a/Mathlib/Geometry/Diffeology/Basic.lean b/Mathlib/Geometry/Diffeology/Basic.lean
index 38ad8f49f06693..8262d574912185 100644
--- a/Mathlib/Geometry/Diffeology/Basic.lean
+++ b/Mathlib/Geometry/Diffeology/Basic.lean
@@ -336,7 +336,7 @@ def ofCorePlotsOn {X : Type*} (d : DiffeologicalSpace.CorePlotsOn X) :
     refine ⟨_, Metric.isOpen_ball, Metric.mem_ball_self hε, (d.isPlotOn_congr _ ?_).mp h'⟩
     rw [Function.comp_assoc, ← OpenPartialHomeomorph.coe_trans]
     apply Set.EqOn.comp_left
-    convert (OpenPartialHomeomorph.symm_trans_self (OpenPartialHomeomorph.univBall x ε)).2
+    convert! (OpenPartialHomeomorph.symm_trans_self (OpenPartialHomeomorph.univBall x ε)).2
     simp [OpenPartialHomeomorph.univBall_target x hε]
   dTopology := d.dTopology
   isOpen_iff_preimages_plots := d.isOpen_iff_preimages_plots
@@ -356,7 +356,7 @@ protected theorem DSmooth.continuous' {X Y : Type*}
     [TopologicalSpace X] [DiffeologicalSpace X] [IsDTopologyCompatible X]
     [TopologicalSpace Y] [DiffeologicalSpace Y] [IsDTopologyCompatible Y]
     {f : X → Y} (hf : DSmooth f) : Continuous f := by
-  convert hf.continuous
+  convert! hf.continuous
   · rw [IsDTopologyCompatible.dTop_eq X]
   · rw [IsDTopologyCompatible.dTop_eq Y]
 
diff --git a/Mathlib/Geometry/Euclidean/Altitude.lean b/Mathlib/Geometry/Euclidean/Altitude.lean
index 16665c397fb66d..bf6cf086d411e9 100644
--- a/Mathlib/Geometry/Euclidean/Altitude.lean
+++ b/Mathlib/Geometry/Euclidean/Altitude.lean
@@ -100,7 +100,7 @@ lemma altitude_map {n : ℕ} (s : Simplex ℝ P n) (f : P →ᵃⁱ[ℝ] P₂) (
     haveI := Nonempty.map (AffineSubspace.inclusion hS) inferInstance
     ((s.restrict S hS).altitude i).map S.subtype = s.altitude i := by
   rw [eq_comm]
-  convert (s.restrict S hS).altitude_map S.subtypeₐᵢ i
+  convert! (s.restrict S hS).altitude_map S.subtypeₐᵢ i
 
 lemma altitude_restrict_eq_comap_subtype {n : ℕ} (s : Simplex ℝ P n) (S : AffineSubspace ℝ P)
     (hS : affineSpan ℝ (Set.range s.points) ≤ S) (i : Fin (n + 1)) :
@@ -191,7 +191,7 @@ set_option backward.isDefEq.respectTransparency false in
     haveI := Nonempty.map (AffineSubspace.inclusion hS) inferInstance
     (s.restrict S hS).altitudeFoot i = s.altitudeFoot i := by
   rw [eq_comm]
-  convert (s.restrict S hS).altitudeFoot_map S.subtypeₐᵢ i
+  convert! (s.restrict S hS).altitudeFoot_map S.subtypeₐᵢ i
 
 @[simp] lemma ne_altitudeFoot {n : ℕ} [NeZero n] (s : Simplex ℝ P n) (i : Fin (n + 1)) :
     s.points i ≠ s.altitudeFoot i := by
@@ -251,7 +251,7 @@ def height {n : ℕ} [NeZero n] (s : Simplex ℝ P n) (i : Fin (n + 1)) : ℝ :=
     haveI := Nonempty.map (AffineSubspace.inclusion hS) inferInstance
     (s.restrict S hS).height i = s.height i := by
   rw [eq_comm]
-  convert (s.restrict S hS).height_map S.subtypeₐᵢ i
+  convert! (s.restrict S hS).height_map S.subtypeₐᵢ i
 
 @[simp]
 lemma height_pos {n : ℕ} [NeZero n] (s : Simplex ℝ P n) (i : Fin (n + 1)) : 0 < s.height i := by
@@ -315,7 +315,7 @@ lemma abs_inner_vsub_altitudeFoot_lt_mul {i j : Fin (n + 1)} (hij : i ≠ j) :
     |⟪s.points i -ᵥ s.altitudeFoot i, s.points j -ᵥ s.altitudeFoot j⟫|
       < s.height i * s.height j := by
   apply lt_of_le_of_ne
-  · convert abs_real_inner_le_norm _ _ using 1
+  · convert! abs_real_inner_le_norm _ _ using 1
     simp only [dist_eq_norm_vsub, height]
   · simp_rw [height, dist_eq_norm_vsub]
     rw [← Real.norm_eq_abs, ne_eq, norm_inner_eq_norm_iff (by simp) (by simp)]
@@ -348,7 +348,7 @@ lemma abs_inner_vsub_altitudeFoot_lt_mul {i j : Fin (n + 1)} (hij : i ≠ j) :
           simp_rw [← Set.image_univ, ← Set.compl_inter]
           rw [Set.inter_singleton_eq_empty.mpr ?_, Set.compl_empty]
           simpa using hij.symm
-        convert AffineSubspace.vectorSpan_union_of_mem_of_mem ℝ hki' hkj'
+        convert! AffineSubspace.vectorSpan_union_of_mem_of_mem ℝ hki' hkj'
       rw [hs, ← Submodule.inf_orthogonal, Submodule.mem_inf]
       refine ⟨?_, ?_⟩
       · rw [h, ← direction_affineSpan]
diff --git a/Mathlib/Geometry/Euclidean/Angle/Bisector.lean b/Mathlib/Geometry/Euclidean/Angle/Bisector.lean
index 4e6d0a12b779df..a560ad1adffb1b 100644
--- a/Mathlib/Geometry/Euclidean/Angle/Bisector.lean
+++ b/Mathlib/Geometry/Euclidean/Angle/Bisector.lean
@@ -293,14 +293,14 @@ lemma two_zsmul_oangle_eq_of_dist_orthogonalProjection_line_eq {p p₁ p₂ p₃
   · suffices p = p₁ by simp [this]
     have hs := orthogonalProjection_sup_of_orthogonalProjection_eq ho
     have hinf : line[ℝ, p₁, p₂] ⊓ line[ℝ, p₁, p₃] = affineSpan ℝ {p₁} := by
-      convert (ha.inf_affineSpan_eq_affineSpan_inter {0, 1} {0, 2})
+      convert! (ha.inf_affineSpan_eq_affineSpan_inter {0, 1} {0, 2})
       · simp [Set.image_insert_eq]
       · simp [Set.image_insert_eq]
       · suffices {p₁} = ![p₁, p₂, p₃] '' {0} by grind
         simp
     have hsup : line[ℝ, p₁, p₂] ⊔ line[ℝ, p₁, p₃] = ⊤ := by
       rw [← AffineSubspace.span_union]
-      convert ha.affineSpan_eq_top_iff_card_eq_finrank_add_one.2 ?_
+      convert! ha.affineSpan_eq_top_iff_card_eq_finrank_add_one.2 ?_
       · simp
         grind
       · simpa using Fact.out
diff --git a/Mathlib/Geometry/Euclidean/Angle/Incenter.lean b/Mathlib/Geometry/Euclidean/Angle/Incenter.lean
index e140e7869e6d33..b33f20eab32a56 100644
--- a/Mathlib/Geometry/Euclidean/Angle/Incenter.lean
+++ b/Mathlib/Geometry/Euclidean/Angle/Incenter.lean
@@ -90,9 +90,11 @@ lemma dist_orthogonalProjectionSpan_faceOpposite_eq_iff_two_zsmul_oangle_eq {p :
       dist p ((t.faceOpposite i₂).orthogonalProjectionSpan p) ↔
         (2 : ℤ) • ∡ (t.points i₂) (t.points i₁) p = (2 : ℤ) • ∡ p (t.points i₁) (t.points i₃) := by
   have ha : AffineIndependent ℝ ![t.points i₁, t.points i₂, t.points i₃] := by
-    convert t.independent.comp_embedding ⟨![i₁, i₂, i₃], by
-      intro i j hij
-      fin_cases i <;> fin_cases j <;> simp_all⟩
+    convert!
+      t.independent.comp_embedding
+        ⟨![i₁, i₂, i₃], by
+          intro i j hij
+          fin_cases i <;> fin_cases j <;> simp_all⟩
     ext i
     fin_cases i <;> rfl
   rw [orthogonalProjectionSpan, orthogonalProjectionSpan,
@@ -164,7 +166,7 @@ lemma eq_excenter_of_two_zsmul_oangle_eq {p : P}
   rw [← dist_orthogonalProjectionSpan_faceOpposite_eq_iff_two_zsmul_oangle_eq h₂₃ h₁₂.symm h₁₃.symm]
     at h₂
   have hp : p ∈ affineSpan ℝ (Set.range t.points) := by
-    convert AffineSubspace.mem_top ℝ V p
+    convert! AffineSubspace.mem_top ℝ V p
     rw [t.independent.affineSpan_eq_top_iff_card_eq_finrank_add_one]
     simp [hd2.out]
   have hr : ∃ r : ℝ, ∀ i, dist p ((t.faceOpposite i).orthogonalProjectionSpan p) = r := by
diff --git a/Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean b/Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean
index c4fbdcceea09e5..6e11b9084bc6e6 100644
--- a/Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean
+++ b/Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean
@@ -197,7 +197,7 @@ theorem oangle_ne_zero_and_ne_pi_iff_affineIndependent {p₁ p₂ p₃ : P} :
   rw [oangle, o.oangle_ne_zero_and_ne_pi_iff_linearIndependent,
     affineIndependent_iff_linearIndependent_vsub ℝ _ (1 : Fin 3), ←
     linearIndependent_equiv (finSuccAboveEquiv (1 : Fin 3))]
-  convert Iff.rfl
+  convert! Iff.rfl
   ext i
   fin_cases i <;> rfl
 
@@ -317,7 +317,7 @@ theorem oangle_eq_pi_sub_two_zsmul_oangle_of_dist_eq {p₁ p₂ p₃ : P} (hn :
     (h : dist p₁ p₂ = dist p₁ p₃) : ∡ p₃ p₁ p₂ = π - (2 : ℤ) • ∡ p₁ p₂ p₃ := by
   simp_rw [dist_eq_norm_vsub V] at h
   rw [oangle, oangle]
-  convert o.oangle_eq_pi_sub_two_zsmul_oangle_sub_of_norm_eq _ h using 1
+  convert! o.oangle_eq_pi_sub_two_zsmul_oangle_sub_of_norm_eq _ h using 1
   · rw [← neg_vsub_eq_vsub_rev p₁ p₃, ← neg_vsub_eq_vsub_rev p₁ p₂, o.oangle_neg_neg]
   · rw [← o.oangle_sub_eq_oangle_sub_rev_of_norm_eq h]; simp
   · simpa using hn
@@ -356,7 +356,7 @@ theorem angle_eq_abs_oangle_toReal {p p₁ p₂ : P} (hp₁ : p₁ ≠ p) (hp₂
 equals `p` or the unoriented angle is 0 or π. -/
 theorem eq_zero_or_angle_eq_zero_or_pi_of_sign_oangle_eq_zero {p p₁ p₂ : P}
     (h : (∡ p₁ p p₂).sign = 0) : p₁ = p ∨ p₂ = p ∨ ∠ p₁ p p₂ = 0 ∨ ∠ p₁ p p₂ = π := by
-  convert o.eq_zero_or_angle_eq_zero_or_pi_of_sign_oangle_eq_zero h <;> simp
+  convert! o.eq_zero_or_angle_eq_zero_or_pi_of_sign_oangle_eq_zero h <;> simp
 
 /-- If two unoriented angles are equal, and the signs of the corresponding oriented angles are
 equal, then the oriented angles are equal (even in degenerate cases). -/
@@ -748,7 +748,7 @@ theorem _root_.Collinear.oangle_sign_of_sameRay_vsub {p₁ p₂ p₃ p₄ : P} (
         (Set.mem_insert_of_mem _ (Set.mem_insert_of_mem _ (Set.mem_insert _ _))) hp₁p₂⟩, p₄ -ᵥ p₃⟩,
         ⟨hr, vsub_ne_zero.2 hp₃p₄.symm⟩, ?_⟩
       simp
-    convert Real.Angle.sign_eq_of_continuousOn hco hf hsp hp₃p₄s hp₁p₂s
+    convert! Real.Angle.sign_eq_of_continuousOn hco hf hsp hp₃p₄s hp₁p₂s
 
 /-- Given three points in strict order on the same line, and a fourth point, the angles at the
 fourth point between the first and second or second and third points have the same sign. -/
@@ -831,7 +831,7 @@ theorem _root_.AffineSubspace.SSameSide.oangle_sign_eq {s : AffineSubspace ℝ P
   have hp₃ : (p₁, p₃, p₂) ∈ sp :=
     Set.mem_image_of_mem _ (sSameSide_self_iff.2 ⟨hp₃p₄.nonempty, hp₃p₄.2.1⟩)
   have hp₄ : (p₁, p₄, p₂) ∈ sp := Set.mem_image_of_mem _ hp₃p₄
-  convert Real.Angle.sign_eq_of_continuousOn hc hf hsp hp₃ hp₄
+  convert! Real.Angle.sign_eq_of_continuousOn hc hf hsp hp₃ hp₄
 
 /-- Given two points in an affine subspace, the angles between those two points at two other
 points on opposite sides of that subspace have opposite signs. -/
diff --git a/Mathlib/Geometry/Euclidean/Angle/Oriented/Basic.lean b/Mathlib/Geometry/Euclidean/Angle/Oriented/Basic.lean
index 8c58133a6f2806..f68acfd1fd5b5b 100644
--- a/Mathlib/Geometry/Euclidean/Angle/Oriented/Basic.lean
+++ b/Mathlib/Geometry/Euclidean/Angle/Oriented/Basic.lean
@@ -77,7 +77,7 @@ set_option backward.isDefEq.respectTransparency false in
 @[simp]
 theorem oangle_self (x : V) : o.oangle x x = 0 := by
   rw [oangle, kahler_apply_self, ← ofReal_pow]
-  convert QuotientAddGroup.mk_zero (AddSubgroup.zmultiples (2 * π))
+  convert! QuotientAddGroup.mk_zero (AddSubgroup.zmultiples (2 * π))
   apply arg_ofReal_of_nonneg
   positivity
 
@@ -180,14 +180,14 @@ theorem oangle_add_oangle_rev (x y : V) : o.oangle x y + o.oangle y x = 0 := by
 theorem oangle_neg_left {x y : V} (hx : x ≠ 0) (hy : y ≠ 0) :
     o.oangle (-x) y = o.oangle x y + π := by
   simp only [oangle, map_neg]
-  convert Complex.arg_neg_coe_angle _
+  convert! Complex.arg_neg_coe_angle _
   exact o.kahler_ne_zero hx hy
 
 /-- Negating the second vector passed to `oangle` adds `π` to the angle. -/
 theorem oangle_neg_right {x y : V} (hx : x ≠ 0) (hy : y ≠ 0) :
     o.oangle x (-y) = o.oangle x y + π := by
   simp only [oangle, map_neg]
-  convert Complex.arg_neg_coe_angle _
+  convert! Complex.arg_neg_coe_angle _
   exact o.kahler_ne_zero hx hy
 
 /-- Negating the first vector passed to `oangle` does not change twice the angle. -/
@@ -509,7 +509,7 @@ theorem oangle_eq_pi_sub_two_zsmul_oangle_sub_of_norm_eq {x y : V} (hn : x ≠ y
     rw [norm_zero, norm_eq_zero] at h
     exact hn h
   have hx : x ≠ 0 := norm_ne_zero_iff.1 (h.symm ▸ norm_ne_zero_iff.2 hy)
-  convert o.oangle_add_cyc3_neg_right (neg_ne_zero.2 hy) hx (sub_ne_zero_of_ne hn.symm) using 1
+  convert! o.oangle_add_cyc3_neg_right (neg_ne_zero.2 hy) hx (sub_ne_zero_of_ne hn.symm) using 1
   simp
 
 /-- The angle between two vectors, with respect to an orientation given by `Orientation.map`
@@ -715,7 +715,7 @@ theorem eq_zero_or_oangle_eq_iff_inner_eq_zero {x y : V} :
   rw [InnerProductGeometry.inner_eq_zero_iff_angle_eq_pi_div_two, or_iff_right hx, or_iff_right hy]
   refine ⟨fun h => ?_, fun h => ?_⟩
   · rwa [o.angle_eq_abs_oangle_toReal hx hy, Real.Angle.abs_toReal_eq_pi_div_two_iff]
-  · convert o.oangle_eq_angle_or_eq_neg_angle hx hy using 2 <;> rw [h]
+  · convert! o.oangle_eq_angle_or_eq_neg_angle hx hy using 2 <;> rw [h]
     simp only [neg_div, Real.Angle.coe_neg]
 
 /-- If the oriented angle between two vectors is `π / 2`, the inner product of those vectors
@@ -821,10 +821,10 @@ theorem oangle_sign_smul_add_right (x y : V) (r : ℝ) :
     · simpa [hz] using (h' r').1
   have hs : ∀ z : V × V, z ∈ s → o.oangle z.1 z.2 ≠ 0 ∧ o.oangle z.1 z.2 ≠ π := by grind
   have hx : (x, y) ∈ s := by
-    convert Set.mem_image_of_mem (fun r' : ℝ => (x, r' • x + y)) (Set.mem_univ 0)
+    convert! Set.mem_image_of_mem (fun r' : ℝ => (x, r' • x + y)) (Set.mem_univ 0)
     simp
   have hy : (x, r • x + y) ∈ s := Set.mem_image_of_mem _ (Set.mem_univ _)
-  convert Real.Angle.sign_eq_of_continuousOn hc hf hs hx hy
+  convert! Real.Angle.sign_eq_of_continuousOn hc hf hs hx hy
 
 /-- Adding a multiple of the second vector passed to `oangle` to the first vector does not change
 the sign of the angle. -/
diff --git a/Mathlib/Geometry/Euclidean/Angle/Oriented/Rotation.lean b/Mathlib/Geometry/Euclidean/Angle/Oriented/Rotation.lean
index 0def62e379b6aa..7e56474c341b6e 100644
--- a/Mathlib/Geometry/Euclidean/Angle/Oriented/Rotation.lean
+++ b/Mathlib/Geometry/Euclidean/Angle/Oriented/Rotation.lean
@@ -65,7 +65,7 @@ def rotation (θ : Real.Angle) : V ≃ₗᵢ[ℝ] V :=
       Real.Angle.sin θ • (LinearIsometryEquiv.toLinearEquiv J).toLinearMap)
     (by
       ext x
-      convert congr_arg (fun t : ℝ => t • x) θ.cos_sq_add_sin_sq using 1
+      convert! congr_arg (fun t : ℝ => t • x) θ.cos_sq_add_sin_sq using 1
       · simp only [o.rightAngleRotation_rightAngleRotation, o.rotationAux_apply,
           Function.comp_apply, id, LinearEquiv.coe_coe, LinearIsometry.coe_toLinearMap,
           LinearIsometryEquiv.coe_toLinearEquiv, map_smul, map_sub, LinearMap.coe_comp,
@@ -74,7 +74,7 @@ def rotation (θ : Real.Angle) : V ≃ₗᵢ[ℝ] V :=
       · simp)
     (by
       ext x
-      convert congr_arg (fun t : ℝ => t • x) θ.cos_sq_add_sin_sq using 1
+      convert! congr_arg (fun t : ℝ => t • x) θ.cos_sq_add_sin_sq using 1
       · simp only [o.rightAngleRotation_rightAngleRotation, o.rotationAux_apply,
           Function.comp_apply, id, LinearEquiv.coe_coe, LinearIsometry.coe_toLinearMap,
           LinearIsometryEquiv.coe_toLinearEquiv, map_add, map_smul, LinearMap.coe_comp,
diff --git a/Mathlib/Geometry/Euclidean/Angle/Sphere.lean b/Mathlib/Geometry/Euclidean/Angle/Sphere.lean
index 34ba17744df3da..eb8f55b8d8c157 100644
--- a/Mathlib/Geometry/Euclidean/Angle/Sphere.lean
+++ b/Mathlib/Geometry/Euclidean/Angle/Sphere.lean
@@ -263,8 +263,8 @@ theorem inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center {s : Sp
     (hp₂p₃ : p₂ ≠ p₃) :
     ((Real.Angle.tan (∡ p₁ p₂ p₃))⁻¹ / 2) • o.rotation (π / 2 : ℝ) (p₃ -ᵥ p₁) +ᵥ midpoint ℝ p₁ p₃ =
       s.center := by
-  convert tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center hp₁ hp₃ hp₁p₃
-  convert (Real.Angle.tan_eq_inv_of_two_zsmul_add_two_zsmul_eq_pi _).symm
+  convert! tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center hp₁ hp₃ hp₁p₃
+  convert! (Real.Angle.tan_eq_inv_of_two_zsmul_add_two_zsmul_eq_pi _).symm
   rw [add_comm,
     two_zsmul_oangle_center_add_two_zsmul_oangle_eq_pi hp₁ hp₂ hp₃ hp₁p₂.symm hp₂p₃ hp₁p₃]
 
@@ -307,7 +307,7 @@ at the third point (a version of the law of sines or sine rule). -/
 theorem dist_div_sin_oangle_div_two_eq_radius {s : Sphere P} {p₁ p₂ p₃ : P} (hp₁ : p₁ ∈ s)
     (hp₂ : p₂ ∈ s) (hp₃ : p₃ ∈ s) (hp₁p₂ : p₁ ≠ p₂) (hp₁p₃ : p₁ ≠ p₃) (hp₂p₃ : p₂ ≠ p₃) :
     dist p₁ p₃ / |Real.Angle.sin (∡ p₁ p₂ p₃)| / 2 = s.radius := by
-  convert dist_div_cos_oangle_center_div_two_eq_radius hp₁ hp₃ hp₁p₃
+  convert! dist_div_cos_oangle_center_div_two_eq_radius hp₁ hp₃ hp₁p₃
   rw [← Real.Angle.abs_cos_eq_abs_sin_of_two_zsmul_add_two_zsmul_eq_pi
     (two_zsmul_oangle_center_add_two_zsmul_oangle_eq_pi hp₁ hp₂ hp₃ hp₁p₂.symm hp₂p₃ hp₁p₃),
     abs_of_nonneg (Real.Angle.cos_nonneg_iff_abs_toReal_le_pi_div_two.2 _)]
@@ -438,7 +438,7 @@ theorem dist_div_sin_angle_div_two_eq_circumradius (t : Triangle ℝ P) {i₁ i
     simp⟩
   have : Module.Oriented ℝ S.direction (Fin 2) :=
     ⟨Basis.orientation (finBasisOfFinrankEq _ _ hf2.out)⟩
-  convert t'.dist_div_sin_oangle_div_two_eq_circumradius h₁₂ h₁₃ h₂₃ using 3
+  convert! t'.dist_div_sin_oangle_div_two_eq_circumradius h₁₂ h₁₃ h₂₃ using 3
   · rw [← Real.Angle.sin_toReal,
       Real.abs_sin_eq_sin_abs_of_abs_le_pi (Real.Angle.abs_toReal_le_pi _),
       ← angle_eq_abs_oangle_toReal (t'.independent.injective.ne h₁₂)
diff --git a/Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean b/Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean
index 7e688026e00a92..45bf2de5808eef 100644
--- a/Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean
+++ b/Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean
@@ -167,7 +167,7 @@ theorem angle_eq_angle_of_angle_eq_pi (p₁ : P) {p₂ p₃ p₄ : P} (h : ∠ p
   unfold angle at *
   rcases angle_eq_pi_iff.1 h with ⟨_, ⟨r, ⟨hr, hpr⟩⟩⟩
   rw [eq_comm]
-  convert angle_smul_right_of_pos (p₁ -ᵥ p₂) (p₃ -ᵥ p₂) (add_pos (neg_pos_of_neg hr) zero_lt_one)
+  convert! angle_smul_right_of_pos (p₁ -ᵥ p₂) (p₃ -ᵥ p₂) (add_pos (neg_pos_of_neg hr) zero_lt_one)
   rw [add_smul, ← neg_vsub_eq_vsub_rev p₂ p₃, smul_neg, neg_smul, ← hpr]
   simp
 
@@ -288,7 +288,7 @@ theorem angle_eq_pi_iff_sbtw {p₁ p₂ p₃ : P} : ∠ p₁ p₂ p₃ = π ↔
   · rw [← eq_vadd_iff_vsub_eq] at hp₃p₂
     rw [AffineMap.lineMap_apply, hp₃p₂, vadd_vsub_assoc, ← neg_vsub_eq_vsub_rev p₂ p₁, smul_neg, ←
       neg_smul, smul_add, smul_smul, ← add_smul, eq_comm, eq_vadd_iff_vsub_eq]
-    convert (one_smul ℝ (p₂ -ᵥ p₁)).symm
+    convert! (one_smul ℝ (p₂ -ᵥ p₁)).symm
     field [(sub_pos.2 (hr.trans zero_lt_one)).ne.symm]
   · rw [ne_comm, ← @vsub_ne_zero V, hp₃p₂, smul_ne_zero_iff]
     exact ⟨hr.ne, hp₁p₂⟩
diff --git a/Mathlib/Geometry/Euclidean/Circumcenter.lean b/Mathlib/Geometry/Euclidean/Circumcenter.lean
index b857463b403a24..21f56505cee09f 100644
--- a/Mathlib/Geometry/Euclidean/Circumcenter.lean
+++ b/Mathlib/Geometry/Euclidean/Circumcenter.lean
@@ -173,7 +173,7 @@ theorem _root_.AffineIndependent.existsUnique_dist_eq {ι : Type*} [hne : Nonemp
         simp [Classical.em]
       rw [hr, ← affineSpan_insert_affineSpan]
       refine existsUnique_dist_eq_of_insert (Set.range_nonempty _) (subset_affineSpan ℝ _) ?_ hm
-      convert ha.notMem_affineSpan_diff i Set.univ
+      convert! ha.notMem_affineSpan_diff i Set.univ
       change (Set.range fun i2 : { x | x ≠ i } => p i2) = _
       rw [← Set.image_eq_range]
       congr 1 with j
@@ -489,7 +489,7 @@ def pointWeightsWithCircumcenter {n : ℕ} (i : Fin (n + 1)) : PointsWithCircumc
 theorem sum_pointWeightsWithCircumcenter {n : ℕ} (i : Fin (n + 1)) :
     ∑ j, pointWeightsWithCircumcenter i j = 1 := by
   classical
-  convert sum_ite_eq' univ (pointIndex i) (Function.const _ (1 : ℝ)) with j
+  convert! sum_ite_eq' univ (pointIndex i) (Function.const _ (1 : ℝ)) with j
   · cases j <;> simp [pointWeightsWithCircumcenter]
   · simp
 
@@ -550,7 +550,7 @@ def circumcenterWeightsWithCircumcenter (n : ℕ) : PointsWithCircumcenterIndex
 theorem sum_circumcenterWeightsWithCircumcenter (n : ℕ) :
     ∑ i, circumcenterWeightsWithCircumcenter n i = 1 := by
   classical
-  convert sum_ite_eq' univ circumcenterIndex (Function.const _ (1 : ℝ)) with j
+  convert! sum_ite_eq' univ circumcenterIndex (Function.const _ (1 : ℝ)) with j
   · cases j <;> simp [circumcenterWeightsWithCircumcenter]
   · simp
 
@@ -606,7 +606,7 @@ theorem reflection_circumcenter_eq_affineCombination_of_pointsWithCircumcenter {
     centroidWeightsWithCircumcenter, circumcenterWeightsWithCircumcenter,
     reflectionCircumcenterWeightsWithCircumcenter, ite_smul, zero_smul, sub_zero,
     apply_ite₂ (· + ·), add_zero, ← add_smul, hc, zero_sub, neg_smul, sub_self, add_zero]
-  convert sum_const_zero
+  convert! sum_const_zero
   norm_num
 
 end Simplex
diff --git a/Mathlib/Geometry/Euclidean/Incenter.lean b/Mathlib/Geometry/Euclidean/Incenter.lean
index e1a96658ecfe25..2d2c443c690725 100644
--- a/Mathlib/Geometry/Euclidean/Incenter.lean
+++ b/Mathlib/Geometry/Euclidean/Incenter.lean
@@ -229,10 +229,10 @@ lemma sum_inv_height_sq_smul_vsub_eq_zero :
   intro i hi
   rw [← Finset.add_sum_erase _ _ (Finset.mem_univ 0),
     ← Finset.add_sum_erase _ _ (Finset.mem_erase.2 ⟨hi, Finset.mem_univ _⟩), ← add_assoc]
-  convert add_zero _
-  · convert Finset.sum_const_zero with j hj
+  convert! add_zero _
+  · convert! Finset.sum_const_zero with j hj
     rw [real_inner_smul_right]
-    convert mul_zero _
+    convert! mul_zero _
     rw [← Submodule.mem_orthogonal_singleton_iff_inner_right]
     refine SetLike.le_def.1 (Submodule.orthogonal_le ?_)
       (vsub_orthogonalProjection_mem_direction_orthogonal _ _)
@@ -270,7 +270,7 @@ lemma inv_height_eq_sum_mul_inv_dist (i : Fin (n + 1)) :
   apply_fun fun v ↦ (s.height i)⁻¹ * ⟪s.points i -ᵥ s.altitudeFoot i, v⟫ at h
   rw [inner_sum, Finset.mul_sum] at h
   simp only [inner_zero_right, mul_zero, inner_smul_right, height] at h
-  convert h using 2 with j
+  convert! h using 2 with j
   ring
 
 /-- The inverse of the distance from one vertex to the opposite face is less than the sum of that
@@ -296,7 +296,7 @@ lemma sum_excenterWeightsUnnorm_singleton_pos [Nat.AtLeastTwo n] (i : Fin (n + 1
   rw [← Finset.sum_add_sum_compl {i}, Finset.sum_singleton]
   nth_rw 1 [excenterWeightsUnnorm]
   simp only [Finset.mem_singleton, ↓reduceIte, neg_mul, one_mul, lt_neg_add_iff_add_lt, add_zero]
-  convert s.inv_height_lt_sum_inv_height i using 2 with j h
+  convert! s.inv_height_lt_sum_inv_height i using 2 with j h
   · ext j
     simp
   · rw [Finset.mem_filter_univ] at h
@@ -305,7 +305,7 @@ lemma sum_excenterWeightsUnnorm_singleton_pos [Nat.AtLeastTwo n] (i : Fin (n + 1
 lemma sign_excenterWeights_singleton_neg [Nat.AtLeastTwo n] (i : Fin (n + 1)) :
     SignType.sign (s.excenterWeights {i} i) = -1 := by
   simp_rw [excenterWeights, Pi.smul_apply, smul_eq_mul, sign_mul]
-  convert one_mul _
+  convert! one_mul _
   · rw [sign_eq_one_iff, inv_pos]
     exact s.sum_excenterWeightsUnnorm_singleton_pos i
   · simp [excenterWeightsUnnorm]
@@ -313,7 +313,7 @@ lemma sign_excenterWeights_singleton_neg [Nat.AtLeastTwo n] (i : Fin (n + 1)) :
 lemma sign_excenterWeights_singleton_pos [Nat.AtLeastTwo n] {i j : Fin (n + 1)} (h : i ≠ j) :
     SignType.sign (s.excenterWeights {i} j) = 1 := by
   simp_rw [excenterWeights, Pi.smul_apply, smul_eq_mul, sign_mul]
-  convert one_mul _
+  convert! one_mul _
   · rw [sign_eq_one_iff, inv_pos]
     exact s.sum_excenterWeightsUnnorm_singleton_pos i
   · simp [excenterWeightsUnnorm, h.symm]
@@ -336,7 +336,7 @@ lemma excenterWeights_empty_lt_inv_two [n.AtLeastTwo] (i : Fin (n + 1)) :
     rwa [two_mul, sum_singleton]
   replace h : (s.height i)⁻¹ / ∑ i, (s.height i)⁻¹ < 2⁻¹ := by
     rwa [sum_add_sum_compl, ← lt_inv_mul_iff₀ zero_lt_two, ← div_lt_iff₀ (by positivity)] at h
-  convert h
+  convert! h
   simp [excenterWeights, excenterWeightsUnnorm, div_eq_inv_mul]
 
 /-- The exsphere with signs determined by the given set of indices (for the empty set, this is
@@ -567,13 +567,13 @@ lemma ExcenterExists.sign_signedInfDist_excenter {signs : Finset (Fin (n + 1))}
       SignType.sign (s.excenterWeights signs i) := by
   rw [excenter_eq_affineCombination,
     signedInfDist_affineCombination _ _ h.sum_excenterWeights_eq_one, sign_mul]
-  convert mul_one _
+  convert! mul_one _
   rw [sign_eq_one_iff, ← dist_eq_norm_vsub]
   exact s.height_pos _
 
 lemma sign_signedInfDist_incenter (i : Fin (n + 1)) :
     SignType.sign (s.signedInfDist i s.incenter) = 1 := by
-  convert s.excenterExists_empty.sign_signedInfDist_excenter i
+  convert! s.excenterExists_empty.sign_signedInfDist_excenter i
   simp
 
 variable {s} in
@@ -639,7 +639,8 @@ lemma ExcenterExists.excenter_notMem_affineSpan_pair [Nat.AtLeastTwo n]
   · simp only [hij, Set.mem_singleton_iff, Set.insert_eq_of_mem,
       AffineSubspace.mem_affineSpan_singleton]
     exact h.excenter_ne_point j
-  · convert h.excenter_notMem_affineSpan_face (fs := {i, j}) (m := 1) (by simp_all)
+  · convert!
+    h.excenter_notMem_affineSpan_face (fs := { i, j }) (m := 1) (by simp_all)
       Nat.AtLeastTwo.ne_one.symm
     simp [Set.image_insert_eq]
 
@@ -959,7 +960,7 @@ lemma exists_forall_signedInfDist_eq_iff_excenterExists_and_eq_excenter {p : P}
 lemma exists_forall_signedInfDist_eq_iff_eq_incenter {p : P}
     (hp : p ∈ affineSpan ℝ (Set.range s.points)) :
     (∃ r : ℝ, ∀ i, s.signedInfDist i p = r) ↔ p = s.incenter := by
-  convert s.exists_forall_signedInfDist_eq_iff_excenterExists_and_eq_excenter hp (signs := ∅)
+  convert! s.exists_forall_signedInfDist_eq_iff_excenterExists_and_eq_excenter hp (signs := ∅)
   · simp
   · simp [excenterExists_empty]
 
@@ -991,7 +992,7 @@ lemma ExcenterExists.touchpoint_injective {signs : Finset (Fin (n + 1))}
   · subst hn1
     rw [s.touchpoint_eq_point_rev signs i, s.touchpoint_eq_point_rev signs j] at hij
     apply s.independent.injective.ne hne
-    convert hij.symm <;> clear hij <;> decide +revert
+    convert! hij.symm <;> clear hij <;> decide +revert
   · suffices s.excenter signs -ᵥ s.touchpoint signs i ∈ (vectorSpan ℝ (Set.range s.points))ᗮ by
       have h' : s.excenter signs -ᵥ s.touchpoint signs i ∈ (vectorSpan ℝ (Set.range s.points)) := by
         rw [← direction_affineSpan]
@@ -1007,7 +1008,7 @@ lemma ExcenterExists.touchpoint_injective {signs : Finset (Fin (n + 1))}
     have hu : Set.range s.points =
         Set.range (s.faceOpposite i).points ∪ Set.range (s.faceOpposite j).points := by
       simp only [range_faceOpposite_points, ← Set.image_union, ← Set.compl_inter]
-      convert Set.image_univ.symm
+      convert! Set.image_univ.symm
       simp [Ne.symm hne]
     rw [hu, range_faceOpposite_points, range_faceOpposite_points,
       AffineSubspace.vectorSpan_union_of_mem_of_mem ℝ (p := s.points k)
@@ -1064,7 +1065,7 @@ lemma ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint {signs : Fin
       exact ContinuousAffineMap.cont _
   refine ((isConnected_Icc zero_le_one).image _ hc).isPreconnected.subsingleton
     (Set.mem_image_of_mem _ hr) ?_
-  convert Set.mem_image_of_mem _ (Set.left_mem_Icc.2 (zero_le_one' ℝ))
+  convert! Set.mem_image_of_mem _ (Set.left_mem_Icc.2 (zero_le_one' ℝ))
   simp
 
 lemma sign_signedInfDist_lineMap_incenter_touchpoint {i j : Fin (n + 1)} (hne : i ≠ j) {r : ℝ}
@@ -1156,7 +1157,7 @@ lemma ExcenterExists.sign_touchpointWeights {signs : Finset (Fin (n + 1))}
   rw [← s.affineCombination_touchpointWeights signs i, h.sign_signedInfDist_excenter,
     s.signedInfDist_affineCombination j (by simp)] at hs
   rw [← hs, sign_mul]
-  convert (mul_one _).symm
+  convert! (mul_one _).symm
   rw [sign_eq_one_iff, ← dist_eq_norm_vsub]
   exact s.height_pos _
 
@@ -1172,7 +1173,7 @@ variable {s} in
     (s.sum_touchpointWeights signs i) ?_ (Finset.mem_univ _)
     (Set.notMem_compl_iff.2 (Set.mem_singleton _))
   rw [s.affineCombination_touchpointWeights]
-  convert s.touchpoint_mem_affineSpan _ _
+  convert! s.touchpoint_mem_affineSpan _ _
   simp
 
 lemma touchpointWeights_empty_pos {i j : Fin (n + 1)} (hne : i ≠ j) :
@@ -1282,42 +1283,42 @@ lemma excenter_eq_incenter_or_excenter_singleton_of_ne (signs : Finset (Fin 3))
 lemma sSameSide_affineSpan_pair_incenter_point {i₁ i₂ i₃ : Fin 3} (h₁₂ : i₁ ≠ i₂) (h₁₃ : i₁ ≠ i₃)
     (h₂₃ : i₂ ≠ i₃) :
     line[ℝ, t.points i₂, t.points i₃].SSameSide t.incenter (t.points i₁) := by
-  convert t.sSameSide_incenter_point i₁
+  convert! t.sSameSide_incenter_point i₁
   simp
   grind
 
 lemma sSameSide_affineSpan_pair_point_incenter {i₁ i₂ i₃ : Fin 3} (h₁₂ : i₁ ≠ i₂) (h₁₃ : i₁ ≠ i₃)
     (h₂₃ : i₂ ≠ i₃) :
     line[ℝ, t.points i₂, t.points i₃].SSameSide (t.points i₁) t.incenter := by
-  convert t.sSameSide_point_incenter i₁
+  convert! t.sSameSide_point_incenter i₁
   simp
   grind
 
 lemma sOppSide_affineSpan_pair_excenter_singleton_point {i₁ i₂ i₃ : Fin 3} (h₁₂ : i₁ ≠ i₂)
     (h₁₃ : i₁ ≠ i₃) (h₂₃ : i₂ ≠ i₃) :
     line[ℝ, t.points i₂, t.points i₃].SOppSide (t.excenter {i₁}) (t.points i₁) := by
-  convert t.sOppSide_excenter_singleton_point i₁
+  convert! t.sOppSide_excenter_singleton_point i₁
   simp
   grind
 
 lemma sOppSide_affineSpan_pair_point_excenter_singleton {i₁ i₂ i₃ : Fin 3} (h₁₂ : i₁ ≠ i₂)
     (h₁₃ : i₁ ≠ i₃) (h₂₃ : i₂ ≠ i₃) :
     line[ℝ, t.points i₂, t.points i₃].SOppSide (t.points i₁) (t.excenter {i₁}) := by
-  convert t.sOppSide_point_excenter_singleton i₁
+  convert! t.sOppSide_point_excenter_singleton i₁
   simp
   grind
 
 lemma sSameSide_affineSpan_pair_excenter_singleton_point {i₁ i₂ i₃ : Fin 3} (h₁₂ : i₁ ≠ i₂)
     (h₁₃ : i₁ ≠ i₃) (h₂₃ : i₂ ≠ i₃) :
     line[ℝ, t.points i₂, t.points i₃].SSameSide (t.excenter {i₂}) (t.points i₁) := by
-  convert t.sSameSide_excenter_singleton_point h₁₂
+  convert! t.sSameSide_excenter_singleton_point h₁₂
   simp
   grind
 
 lemma sSameSide_affineSpan_pair_point_excenter_singleton {i₁ i₂ i₃ : Fin 3} (h₁₂ : i₁ ≠ i₂)
     (h₁₃ : i₁ ≠ i₃) (h₂₃ : i₂ ≠ i₃) :
     line[ℝ, t.points i₂, t.points i₃].SSameSide (t.points i₁) (t.excenter {i₂}) := by
-  convert t.sSameSide_point_excenter_singleton h₁₂
+  convert! t.sSameSide_point_excenter_singleton h₁₂
   simp
   grind
 
@@ -1325,7 +1326,7 @@ lemma affineSpan_pair_eq_orthRadius [Fact (Module.finrank ℝ V = 2)] (signs : F
     {i₁ i₂ i₃ : Fin 3} (h₁₂ : i₁ ≠ i₂) (h₁₃ : i₁ ≠ i₃) (h₂₃ : i₂ ≠ i₃) :
     line[ℝ, t.points i₂, t.points i₃] =
       (t.exsphere signs).orthRadius (t.touchpoint signs i₁) := by
-  convert (t.excenterExists signs).affineSpan_faceOpposite_eq_orthRadius i₁
+  convert! (t.excenterExists signs).affineSpan_faceOpposite_eq_orthRadius i₁
   have hc : {i₁}ᶜ = ({i₂, i₃} : Set (Fin 3)) := by grind
   simp [Simplex.range_faceOpposite_points, hc, Set.image_insert_eq]
 
@@ -1337,17 +1338,17 @@ lemma affineSpan_pair_eq_orthRadius_insphere [Fact (Module.finrank ℝ V = 2)]
 lemma sbtw_touchpoint_empty {i₁ i₂ i₃ : Fin 3} (h₁₂ : i₁ ≠ i₂) (h₁₃ : i₁ ≠ i₃) (h₂₃ : i₂ ≠ i₃) :
     Sbtw ℝ (t.points i₁) (t.touchpoint ∅ i₂) (t.points i₃) := by
   rw [← t.mem_interior_face_iff_sbtw h₁₃]
-  convert t.touchpoint_empty_mem_interior_faceOpposite i₂
+  convert! t.touchpoint_empty_mem_interior_faceOpposite i₂
   rw [Affine.Simplex.faceOpposite]
-  convert rfl using 2
+  convert! rfl using 2
   decide +revert
 
 lemma sbtw_touchpoint_singleton {i₁ i₂ i₃ : Fin 3} (h₁₂ : i₁ ≠ i₂) (h₁₃ : i₁ ≠ i₃) (h₂₃ : i₂ ≠ i₃) :
     Sbtw ℝ (t.points i₁) (t.touchpoint {i₂} i₂) (t.points i₃) := by
   rw [← t.mem_interior_face_iff_sbtw h₁₃]
-  convert t.touchpoint_singleton_mem_interior_faceOpposite i₂
+  convert! t.touchpoint_singleton_mem_interior_faceOpposite i₂
   rw [Affine.Simplex.faceOpposite]
-  convert rfl using 2
+  convert! rfl using 2
   decide +revert
 
 lemma touchpoint_singleton_sbtw {i₁ i₂ i₃ : Fin 3} (h₁₂ : i₁ ≠ i₂) (h₁₃ : i₁ ≠ i₃) (h₂₃ : i₂ ≠ i₃) :
diff --git a/Mathlib/Geometry/Euclidean/Inversion/Basic.lean b/Mathlib/Geometry/Euclidean/Inversion/Basic.lean
index 4bbea59cb89e6a..257a3c57a22969 100644
--- a/Mathlib/Geometry/Euclidean/Inversion/Basic.lean
+++ b/Mathlib/Geometry/Euclidean/Inversion/Basic.lean
@@ -192,7 +192,7 @@ theorem mul_dist_le_mul_dist_add_mul_dist (a b c d : P) :
     dist_inversion_inversion hc hd, one_pow] at H
   rw [← dist_pos] at hb hc hd
   rw [← div_le_div_iff_of_pos_right (mul_pos hb (mul_pos hc hd))]
-  convert H using 1 <;> simp [field, dist_comm a]; ring
+  convert! H using 1 <;> simp [field, dist_comm a]; ring
 
 end EuclideanGeometry
 
diff --git a/Mathlib/Geometry/Euclidean/MongePoint.lean b/Mathlib/Geometry/Euclidean/MongePoint.lean
index 6a3f9b9a1b9e89..e75eae0305c8d2 100644
--- a/Mathlib/Geometry/Euclidean/MongePoint.lean
+++ b/Mathlib/Geometry/Euclidean/MongePoint.lean
@@ -91,7 +91,7 @@ theorem mongePoint_eq_smul_vsub_vadd_circumcenter {n : ℕ} (s : Simplex ℝ P n
   simp_rw [mongePoint, circumcenter_reindex, centroid_def, reindex]
   obtain rfl : n = m := by simpa using Fintype.card_eq.2 ⟨e⟩
   congr 3
-  convert Finset.univ.affineCombination_map e.toEmbedding _ _ <;> simp [Function.comp_assoc]
+  convert! Finset.univ.affineCombination_map e.toEmbedding _ _ <;> simp [Function.comp_assoc]
 
 @[simp]
 theorem mongePoint_map {V₂ P₂ : Type*} [NormedAddCommGroup V₂] [InnerProductSpace ℝ V₂]
@@ -280,7 +280,7 @@ lemma mongePlane_reindex {m n : ℕ} (s : Simplex ℝ P (n + 2)) (e : Fin (n + 3
   simp_rw [mongePlane, reindex_points, reindex_range_points, Function.comp_apply, centroid_def,
     reindex]
   congr 2
-  convert Finset.affineCombination_map {e.symm i₁, e.symm i₂}ᶜ e.toEmbedding _ _ using 3
+  convert! Finset.affineCombination_map {e.symm i₁, e.symm i₂}ᶜ e.toEmbedding _ _ using 3
   · ext i
     simp
   · simp [Function.comp_assoc]
@@ -614,7 +614,7 @@ theorem exists_dist_eq_circumradius_of_subset_insert_orthocenter {t : Triangle 
     rcases hp₁ with ⟨i, rfl⟩
     have h₁₂₃ := h₁₂₃ i
     repeat' rcases h₁₂₃ with h₁₂₃ | h₁₂₃
-    · convert Triangle.dist_orthocenter_reflection_circumcenter t hj₂₃
+    · convert! Triangle.dist_orthocenter_reflection_circumcenter t hj₂₃
     · rw [← h₂, dist_reflection_eq_of_mem _
        (mem_affineSpan ℝ (Set.mem_image_of_mem _ (Set.mem_insert _ _)))]
       exact t.dist_circumcenter_eq_circumradius _
@@ -695,7 +695,7 @@ theorem OrthocentricSystem.eq_insert_orthocenter {s : Set P} (ho : OrthocentricS
       (Triangle.orthocenter_replace_orthocenter_eq_point hj₁₂ hj₁₃ hj₂₃ h₁₂ h₁₃ h₂₃ h₁ h₂.symm
           h₃.symm).symm
   · rw [hs]
-    convert ht₀s using 2
+    convert! ht₀s using 2
     exact Triangle.orthocenter_eq_of_range_eq hs
 
 end EuclideanGeometry
diff --git a/Mathlib/Geometry/Euclidean/NinePointCircle.lean b/Mathlib/Geometry/Euclidean/NinePointCircle.lean
index f34245a633be17..3bd274ff36de7d 100644
--- a/Mathlib/Geometry/Euclidean/NinePointCircle.lean
+++ b/Mathlib/Geometry/Euclidean/NinePointCircle.lean
@@ -216,7 +216,7 @@ theorem eulerPoint_eq_midpoint (s : Triangle ℝ P) (i : Fin 3) :
 
 theorem altitudeFoot_mem_ninePointCircle (s : Triangle ℝ P) (i : Fin 3) :
     s.altitudeFoot i ∈ s.ninePointCircle := by
-  convert s.orthogonalProjectionSpan_eulerPoint_mem_ninePointCircle i
+  convert! s.orthogonalProjectionSpan_eulerPoint_mem_ninePointCircle i
   rw [Simplex.altitudeFoot]
   unfold Simplex.orthogonalProjectionSpan
   congr 1
diff --git a/Mathlib/Geometry/Euclidean/Projection.lean b/Mathlib/Geometry/Euclidean/Projection.lean
index da214a27239471..19e26e3b6cfc28 100644
--- a/Mathlib/Geometry/Euclidean/Projection.lean
+++ b/Mathlib/Geometry/Euclidean/Projection.lean
@@ -495,7 +495,7 @@ theorem dist_reflection_eq_of_mem (s : AffineSubspace 𝕜 P) [Nonempty s]
     [s.direction.HasOrthogonalProjection] {p₁ : P} (hp₁ : p₁ ∈ s) (p₂ : P) :
     dist p₁ (reflection s p₂) = dist p₁ p₂ := by
   rw [← reflection_eq_self_iff p₁] at hp₁
-  convert (reflection s).dist_map p₁ p₂
+  convert! (reflection s).dist_map p₁ p₂
   rw [hp₁]
 
 /-- The reflection of a point in a subspace is contained in any larger
@@ -551,7 +551,7 @@ lemma orthogonalProjection_subtype (s : AffineSubspace 𝕜 P) [Nonempty s] (s'
   have : (s'.map s.subtypeₐᵢ.toAffineMap).direction.HasOrthogonalProjection := by
     rw [subtypeₐᵢ_toAffineMap]
     infer_instance
-  convert orthogonalProjection_map s' s.subtypeₐᵢ p
+  convert! orthogonalProjection_map s' s.subtypeₐᵢ p
 
 @[simp] lemma reflection_map (s : AffineSubspace 𝕜 P) [Nonempty s]
     [s.direction.HasOrthogonalProjection] (f : P →ᵃⁱ[𝕜] P₂)
@@ -619,7 +619,7 @@ theorem dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq
 lemma orthogonalProjectionSpan_eq_point (s : Simplex 𝕜 P 0) (p : P) :
     s.orthogonalProjectionSpan p = s.points 0 := by
   rw [orthogonalProjectionSpan]
-  convert orthogonalProjection_affineSpan_singleton _ _
+  convert! orthogonalProjection_affineSpan_singleton _ _
   simp [Fin.fin_one_eq_zero]
 
 lemma orthogonalProjectionSpan_faceOpposite_eq_point_rev (s : Simplex 𝕜 P 1) (i : Fin 2)
@@ -632,7 +632,7 @@ lemma orthogonalProjectionSpan_map {n : ℕ} (s : Simplex 𝕜 P n) (f : P →
     (s.map f.toAffineMap f.injective).orthogonalProjectionSpan (f p) =
       f (s.orthogonalProjectionSpan p) := by
   simp_rw [orthogonalProjectionSpan]
-  convert orthogonalProjection_map (affineSpan 𝕜 (Set.range s.points)) f p
+  convert! orthogonalProjection_map (affineSpan 𝕜 (Set.range s.points)) f p
   simp [AffineSubspace.map_span, Set.range_comp]
 
 @[simp] lemma orthogonalProjectionSpan_restrict {n : ℕ} (s : Simplex 𝕜 P n)
@@ -640,7 +640,7 @@ lemma orthogonalProjectionSpan_map {n : ℕ} (s : Simplex 𝕜 P n) (f : P →
     haveI := Nonempty.map (AffineSubspace.inclusion hS) inferInstance
     ((s.restrict S hS).orthogonalProjectionSpan p : P) = s.orthogonalProjectionSpan p := by
   rw [eq_comm]
-  convert (s.restrict S hS).orthogonalProjectionSpan_map S.subtypeₐᵢ p
+  convert! (s.restrict S hS).orthogonalProjectionSpan_map S.subtypeₐᵢ p
 
 end Simplex
 
diff --git a/Mathlib/Geometry/Euclidean/SignedDist.lean b/Mathlib/Geometry/Euclidean/SignedDist.lean
index 7b12d3a68e54d6..37621c1f735dee 100644
--- a/Mathlib/Geometry/Euclidean/SignedDist.lean
+++ b/Mathlib/Geometry/Euclidean/SignedDist.lean
@@ -338,7 +338,7 @@ lemma abs_signedInfDist_eq_dist_of_mem_affineSpan_range {p : P}
     orthogonalProjectionSpan]
   · simp_rw [range_faceOpposite_points]
   rw [affineSpan_insert_affineSpan]
-  convert h
+  convert! h
   exact Set.insert_image_compl_eq_range s.points i
 
 end Simplex
diff --git a/Mathlib/Geometry/Euclidean/Simplex.lean b/Mathlib/Geometry/Euclidean/Simplex.lean
index 01e862976979c4..7ccbcfba69441d 100644
--- a/Mathlib/Geometry/Euclidean/Simplex.lean
+++ b/Mathlib/Geometry/Euclidean/Simplex.lean
@@ -59,8 +59,8 @@ def AcuteAngled (s : Simplex ℝ P n) : Prop :=
 @[simp] lemma acuteAngled_reindex_iff {s : Simplex ℝ P m} (e : Fin (m + 1) ≃ Fin (n + 1)) :
     (s.reindex e).AcuteAngled ↔ s.AcuteAngled := by
   refine ⟨fun h {i₁ i₂ i₃} h₁₂ h₁₃ h₂₃ ↦ ?_, fun h {i₁ i₂ i₃} h₁₂ h₁₃ h₂₃ ↦ ?_⟩
-  · convert h (i₁ := e i₁) (i₂ := e i₂) (i₃ := e i₃) ?_ ?_ ?_ using 1 <;> simp [*]
-  · convert h (i₁ := e.symm i₁) (i₂ := e.symm i₂) (i₃ := e.symm i₃) ?_ ?_ ?_ using 1 <;> simp [*]
+  · convert! h (i₁ := e i₁) (i₂ := e i₂) (i₃ := e i₃) ?_ ?_ ?_ using 1 <;> simp [*]
+  · convert! h (i₁ := e.symm i₁) (i₂ := e.symm i₂) (i₃ := e.symm i₃) ?_ ?_ ?_ using 1 <;> simp [*]
 
 lemma Equilateral.acuteAngled {s : Simplex ℝ P n} (he : s.Equilateral) : s.AcuteAngled := by
   intro i₁ i₂ i₃ h₁₂ h₁₃ h₂₃
diff --git a/Mathlib/Geometry/Euclidean/Sphere/OrthRadius.lean b/Mathlib/Geometry/Euclidean/Sphere/OrthRadius.lean
index 5634c5cb25300e..11c7b29162be66 100644
--- a/Mathlib/Geometry/Euclidean/Sphere/OrthRadius.lean
+++ b/Mathlib/Geometry/Euclidean/Sphere/OrthRadius.lean
@@ -119,14 +119,14 @@ lemma orthRadius_injective (s : Sphere P) : Injective s.orthRadius :=
 lemma finrank_orthRadius [FiniteDimensional ℝ V] {s : Sphere P} {p : P} (hp : p ≠ s.center) :
     Module.finrank ℝ (s.orthRadius p).direction + 1 = Module.finrank ℝ V := by
   rw [orthRadius, add_comm, direction_mk']
-  convert (ℝ ∙ (p -ᵥ s.center)).finrank_add_finrank_orthogonal
+  convert! (ℝ ∙ (p -ᵥ s.center)).finrank_add_finrank_orthogonal
   exact (finrank_span_singleton (vsub_ne_zero.2 hp)).symm
 
 lemma orthRadius_map {s : Sphere P} (p : P) {f : P ≃ᵃⁱ[ℝ] P} (h : f s.center = s.center) :
     (s.orthRadius p).map f.toAffineMap = s.orthRadius (f p) := by
   rw [orthRadius, map_mk', orthRadius]
-  convert rfl using 2
-  convert (Submodule.map_orthogonal_equiv (ℝ ∙ (p -ᵥ s.center)) f.linearIsometryEquiv).symm
+  convert! rfl using 2
+  convert! (Submodule.map_orthogonal_equiv (ℝ ∙ (p -ᵥ s.center)) f.linearIsometryEquiv).symm
   simp [Submodule.map_span, Set.image_singleton, h]
 
 lemma direction_orthRadius_le_iff {s : Sphere P} {p q : P} :
@@ -350,8 +350,9 @@ lemma inter_orthRadius_eq_of_dist_le_radius [hf2 : Fact (Module.finrank ℝ V =
     (hv : v ∈ (ℝ ∙ (p -ᵥ s.center))ᗮ) (hv0 : v ≠ 0) :
     (s ∩ s.orthRadius p : Set P) = {(√(s.radius ^ 2 - (dist p s.center) ^ 2) / ‖v‖) • v +ᵥ p,
       -(√(s.radius ^ 2 - (dist p s.center) ^ 2) / ‖v‖) • v +ᵥ p} := by
-  convert inter_orthRadius_eq_of_dist_le_radius_of_norm_eq_one hp hpc (v := ‖v‖⁻¹ • v)
-    (Submodule.smul_mem _ _ hv) ?_ using 2
+  convert!
+    inter_orthRadius_eq_of_dist_le_radius_of_norm_eq_one hp hpc (v := ‖v‖⁻¹ • v)
+      (Submodule.smul_mem _ _ hv) ?_ using 2
   · simp [div_eq_mul_inv, smul_smul]
   · simp [div_eq_mul_inv, smul_smul]
   · simp [norm_smul, norm_ne_zero_iff.2 hv0]
diff --git a/Mathlib/Geometry/Euclidean/Sphere/Power.lean b/Mathlib/Geometry/Euclidean/Sphere/Power.lean
index 96899bc1fdbccd..c1fc4fbcd7aa5c 100644
--- a/Mathlib/Geometry/Euclidean/Sphere/Power.lean
+++ b/Mathlib/Geometry/Euclidean/Sphere/Power.lean
@@ -203,7 +203,7 @@ theorem cospherical_of_mul_dist_eq_mul_dist_of_angle_eq_pi {p₁ p₂ p₃ p₄
   have hncol : ¬ Collinear ℝ {p₁', p', p₃'} := by
     rw [← affineIndependent_iff_not_collinear_set,
       ← s_isom.toAffineMap.affineIndependent_iff s_isom.injective]
-    convert hindep
+    convert! hindep
     ext i; fin_cases i <;> rfl
   exact cospherical_of_mul_dist_eq_mul_dist_of_angle_eq_pi_aux h_dist' hp₁'p₂' hp₃'p₄' hncol
 
diff --git a/Mathlib/Geometry/Euclidean/Sphere/SecondInter.lean b/Mathlib/Geometry/Euclidean/Sphere/SecondInter.lean
index 10fc2ecb820cfe..8b4dbdca401b76 100644
--- a/Mathlib/Geometry/Euclidean/Sphere/SecondInter.lean
+++ b/Mathlib/Geometry/Euclidean/Sphere/SecondInter.lean
@@ -110,8 +110,8 @@ theorem Sphere.eq_or_eq_secondInter_of_mem_mk'_span_singleton_iff_mem {s : Spher
 lemma Sphere.eq_or_eq_secondInter_iff_mem_of_mem_affineSpan_pair {s : Sphere P} {p q : P}
     (hp : p ∈ s) {p' : P} (hp' : p' ∈ line[ℝ, p, q]) :
     p' = p ∨ p' = s.secondInter p (q -ᵥ p) ↔ p' ∈ s := by
-  convert s.eq_or_eq_secondInter_of_mem_mk'_span_singleton_iff_mem hp ?_
-  convert hp'
+  convert! s.eq_or_eq_secondInter_of_mem_mk'_span_singleton_iff_mem hp ?_
+  convert! hp'
   rw [AffineSubspace.eq_iff_direction_eq_of_mem (AffineSubspace.self_mem_mk' p _)
     (left_mem_affineSpan_pair _ _ _)]
   simp [direction_affineSpan, vectorSpan_pair_rev]
@@ -140,8 +140,8 @@ theorem Sphere.secondInter_secondInter (s : Sphere P) (p : P) (v : V) :
   simp only [Sphere.secondInter, vadd_vsub_assoc, vadd_vadd, inner_add_right, inner_smul_right,
     div_mul_cancel₀ _ hv']
   rw [← @vsub_eq_zero_iff_eq V, vadd_vsub, ← add_smul, ← add_div]
-  convert zero_smul ℝ _
-  convert zero_div (G₀ := ℝ) _
+  convert! zero_smul ℝ _
+  convert! zero_div (G₀ := ℝ) _
   ring
 
 /-- If the vector passed to `secondInter` is given by a subtraction involving the point in
diff --git a/Mathlib/Geometry/Euclidean/Sphere/Tangent.lean b/Mathlib/Geometry/Euclidean/Sphere/Tangent.lean
index ba25a2110435cd..44141b8669e0c3 100644
--- a/Mathlib/Geometry/Euclidean/Sphere/Tangent.lean
+++ b/Mathlib/Geometry/Euclidean/Sphere/Tangent.lean
@@ -178,7 +178,7 @@ lemma IsTangent.infDist_eq_radius {s : Sphere P} {as : AffineSubspace ℝ P} (h
     Metric.infDist s.center as = s.radius := by
   obtain ⟨p, h⟩ := h
   refine le_antisymm ?_ ?_
-  · convert Metric.infDist_le_dist_of_mem h.mem_space
+  · convert! Metric.infDist_le_dist_of_mem h.mem_space
     rw [mem_sphere'.1 h.mem_sphere]
   · rw [Metric.infDist_eq_iInf]
     have : Nonempty as := ⟨⟨p, h.mem_space⟩⟩
@@ -246,7 +246,7 @@ lemma IsTangent.eq_orthRadius_or_eq_orthRadius_pointReflection_of_parallel_orthR
     rcases eq_or_eq_neg_of_abs_eq hr' with rfl | rfl
     · simp_all
     · right
-      convert rfl
+      convert! rfl
       rw [← eq_vadd_iff_vsub_eq] at hr
       rw [hr]
       simp [Equiv.pointReflection_apply]
diff --git a/Mathlib/Geometry/Euclidean/Triangle.lean b/Mathlib/Geometry/Euclidean/Triangle.lean
index 6b989cbc41a5b0..bc6702b17b5361 100644
--- a/Mathlib/Geometry/Euclidean/Triangle.lean
+++ b/Mathlib/Geometry/Euclidean/Triangle.lean
@@ -244,8 +244,9 @@ theorem dist_sq_eq_dist_sq_add_dist_sq_sub_two_mul_dist_mul_dist_mul_cos_angle (
       2 * dist p₁ p₂ * dist p₃ p₂ * Real.cos (∠ p₁ p₂ p₃) := by
   rw [dist_eq_norm_vsub V p₁ p₃, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub V p₃ p₂]
   unfold angle
-  convert norm_sub_sq_eq_norm_sq_add_norm_sq_sub_two_mul_norm_mul_norm_mul_cos_angle
-    (p₁ -ᵥ p₂ : V) (p₃ -ᵥ p₂ : V)
+  convert!
+    norm_sub_sq_eq_norm_sq_add_norm_sq_sub_two_mul_norm_mul_norm_mul_cos_angle (p₁ -ᵥ p₂ : V)
+      (p₃ -ᵥ p₂ : V)
   · exact (vsub_sub_vsub_cancel_right p₁ p₃ p₂).symm
   · exact (vsub_sub_vsub_cancel_right p₁ p₃ p₂).symm
 
@@ -285,7 +286,7 @@ theorem angle_eq_angle_of_dist_eq {p₁ p₂ p₃ : P} (h : dist p₁ p₂ = dis
     ∠ p₁ p₂ p₃ = ∠ p₁ p₃ p₂ := by
   rw [dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub V p₁ p₃] at h
   unfold angle
-  convert angle_sub_eq_angle_sub_rev_of_norm_eq h
+  convert! angle_sub_eq_angle_sub_rev_of_norm_eq h
   · exact (vsub_sub_vsub_cancel_left p₃ p₂ p₁).symm
   · exact (vsub_sub_vsub_cancel_left p₂ p₃ p₁).symm
 
@@ -302,15 +303,16 @@ theorem dist_eq_of_angle_eq_angle_of_angle_ne_pi {p₁ p₂ p₃ : P} (h : ∠ p
 theorem dist_eq_of_two_zsmul_oangle_eq [Module.Oriented ℝ V (Fin 2)]
     [Fact (Module.finrank ℝ V = 2)] {p₁ p₂ p₃ : P} (h : (2 : ℤ) • ∡ p₁ p₂ p₃ = (2 : ℤ) • ∡ p₂ p₃ p₁)
     (h0 : ∡ p₃ p₁ p₂ ≠ 0) (hpi : ∡ p₃ p₁ p₂ ≠ π) : dist p₁ p₂ = dist p₁ p₃ := by
-  convert (Orientation.norm_eq_of_two_zsmul_oangle_sub_eq (x := p₃ -ᵥ p₁) (y := p₂ -ᵥ p₁) ?_ ?_
-    h0 hpi).symm
+  convert!
+    (Orientation.norm_eq_of_two_zsmul_oangle_sub_eq (x := p₃ -ᵥ p₁) (y := p₂ -ᵥ p₁) ?_ ?_ h0
+        hpi).symm
   · rw [dist_eq_norm_vsub']
   · rw [dist_eq_norm_vsub']
   · rw [eq_comm, o.oangle_rev, ← o.oangle_neg_neg]
     nth_rw 2 [o.oangle_rev, ← o.oangle_neg_neg]
     simp_rw [smul_neg, neg_inj]
     simp_rw [oangle] at h
-    convert h <;> simp
+    convert! h <;> simp
 
 /-- The **sum of the angles of a triangle** (possibly degenerate, where two
 given vertices are distinct), angle-at-point. -/
diff --git a/Mathlib/Geometry/Manifold/ChartedSpace.lean b/Mathlib/Geometry/Manifold/ChartedSpace.lean
index 645371fd38bd5d..fedf3dbb18ef85 100644
--- a/Mathlib/Geometry/Manifold/ChartedSpace.lean
+++ b/Mathlib/Geometry/Manifold/ChartedSpace.lean
@@ -313,7 +313,7 @@ theorem ChartedSpace.discreteTopology [DiscreteTopology H] : DiscreteTopology M
   apply discreteTopology_iff_isOpen_singleton.2 (fun x ↦ ?_)
   have : IsOpen ((chartAt H x).source ∩ (chartAt H x) ⁻¹' {chartAt H x x}) :=
     isOpen_inter_preimage _ (isOpen_discrete _)
-  convert this
+  convert! this
   refine Subset.antisymm (by simp) ?_
   simp only [subset_singleton_iff, mem_inter_iff, mem_preimage, mem_singleton_iff, and_imp]
   intro y hy h'y
@@ -644,8 +644,8 @@ protected def openPartialHomeomorph (e : PartialEquiv M H) (he : e ∈ c.atlas)
     @OpenPartialHomeomorph M H c.toTopologicalSpace _ :=
   { __ := c.toTopologicalSpace
     __ := e
-    open_source := by convert c.open_source' he
-    open_target := by convert c.open_target he
+    open_source := by convert! c.open_source' he
+    open_target := by convert! c.open_target he
     continuousOn_toFun := by
       letI : TopologicalSpace M := c.toTopologicalSpace
       rw [continuousOn_open_iff (c.open_source' he)]
diff --git a/Mathlib/Geometry/Manifold/Complex.lean b/Mathlib/Geometry/Manifold/Complex.lean
index 3281bf3890f95c..09ab464a5fd039 100644
--- a/Mathlib/Geometry/Manifold/Complex.lean
+++ b/Mathlib/Geometry/Manifold/Complex.lean
@@ -73,7 +73,7 @@ theorem Complex.norm_eventually_eq_of_mdifferentiableAt_of_isLocalMax {f : M →
     rw [mdifferentiableAt_iff_of_mem_source hys hfy, hI, differentiableWithinAt_univ,
       e.right_inv hyt] at hy₂
     exact hy₂.2
-  convert norm_eventually_eq_of_isLocalMax hd _
+  convert! norm_eventually_eq_of_isLocalMax hd _
   · exact congr_arg f (extChartAt_to_inv _).symm
   · simpa only [e, IsLocalMax, IsMaxFilter, ← H₂, (· ∘ ·), extChartAt_to_inv] using hc
 
diff --git a/Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean b/Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
index 6c32f1ec3ebd97..d27801c0c92d47 100644
--- a/Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
+++ b/Mathlib/Geometry/Manifold/ContMDiff/Atlas.lean
@@ -117,7 +117,7 @@ theorem contMDiffOn_extend_symm (he : e ∈ maximalAtlas I n M) :
 
 theorem contMDiffOn_extChartAt_symm (x : M) :
     ContMDiffOn 𝓘(𝕜, E) I n (extChartAt I x).symm (extChartAt I x).target := by
-  convert contMDiffOn_extend_symm (chart_mem_maximalAtlas (I := I) x)
+  convert! contMDiffOn_extend_symm (chart_mem_maximalAtlas (I := I) x)
   · rw [extChartAt_target, I.image_eq]
   · infer_instance
   · infer_instance
@@ -143,7 +143,7 @@ theorem contMDiffWithinAt_extChartAt_symm_target_self (x : M) :
     apply ContinuousAt.comp _ I.continuousAt_symm
     exact (chartAt H x).symm.continuousAt (by simp)
   · apply contMDiffWithinAt_id.congr_of_mem (fun y hy ↦ ?_) (by simp)
-    convert PartialEquiv.right_inv (extChartAt I x) hy
+    convert! PartialEquiv.right_inv (extChartAt I x) hy
     simp
 
 omit [IsManifold I n M] in
@@ -282,7 +282,7 @@ theorem isLocalStructomorphOn_contDiffGroupoid_iff (f : OpenPartialHomeomorph M
       have hy'' : f ((extChartAt I x).symm y) ∈ c'.source := by
         simp only [c, hy, mfld_simps]
       rw [contMDiffWithinAt_iff_of_mem_source hy' hy''] at H
-      convert H.2.mono _
+      convert! H.2.mono _
       · simp only [c, hy, mfld_simps]
       · dsimp [c, c']; mfld_set_tac
     · -- regularity of the candidate local structomorphism in the reverse direction
@@ -297,7 +297,7 @@ theorem isLocalStructomorphOn_contDiffGroupoid_iff (f : OpenPartialHomeomorph M
       have hy'' : f.symm ((extChartAt I (f x)).symm y) ∈ c.source := by
         simp only [c', hy, mfld_simps]
       rw [contMDiffWithinAt_iff_of_mem_source hy' hy''] at H
-      convert H.2.mono _
+      convert! H.2.mono _
       · simp only [c', hy, mfld_simps]
       · dsimp [c, c']; mfld_set_tac
     -- now check the candidate local structomorphism agrees with `f` where it is supposed to
diff --git a/Mathlib/Geometry/Manifold/ContMDiff/Constructions.lean b/Mathlib/Geometry/Manifold/ContMDiff/Constructions.lean
index fe13581917f544..f991b3f1e20250 100644
--- a/Mathlib/Geometry/Manifold/ContMDiff/Constructions.lean
+++ b/Mathlib/Geometry/Manifold/ContMDiff/Constructions.lean
@@ -207,7 +207,7 @@ theorem contMDiffOn_prod_module_iff (f : M → F₁ × F₂) :
 theorem contMDiff_prod_iff (f : M → M' × N') :
     ContMDiff I (I'.prod J') n f ↔
       ContMDiff I I' n (Prod.fst ∘ f) ∧ ContMDiff I J' n (Prod.snd ∘ f) :=
-  ⟨fun h => ⟨h.fst, h.snd⟩, fun h => by convert h.1.prodMk h.2⟩
+  ⟨fun h => ⟨h.fst, h.snd⟩, fun h => by convert! h.1.prodMk h.2⟩
 
 theorem contMDiff_prod_module_iff (f : M → F₁ × F₂) :
     ContMDiff I 𝓘(𝕜, F₁ × F₂) n f ↔
diff --git a/Mathlib/Geometry/Manifold/ContMDiff/Defs.lean b/Mathlib/Geometry/Manifold/ContMDiff/Defs.lean
index c6d9e419099402..224c9ebd3782a3 100644
--- a/Mathlib/Geometry/Manifold/ContMDiff/Defs.lean
+++ b/Mathlib/Geometry/Manifold/ContMDiff/Defs.lean
@@ -117,8 +117,7 @@ theorem contDiffWithinAt_localInvariantProp_of_le (n m : ℕ∞ω) (hmn : m ≤
     rw [this] at h
     have : I (e x) ∈ I.symm ⁻¹' e.target ∩ range I := by simp only [hx, mfld_simps]
     have := (mem_groupoid_of_pregroupoid.2 he).2.contDiffWithinAt this
-    convert (h.comp_inter _ (this.of_le hmn)).mono_of_mem_nhdsWithin _
-      using 1
+    convert! (h.comp_inter _ (this.of_le hmn)).mono_of_mem_nhdsWithin _ using 1
     · ext y; simp only [mfld_simps]
     refine mem_nhdsWithin.mpr
       ⟨I.symm ⁻¹' e.target, e.open_target.preimage I.continuous_symm, by
@@ -135,7 +134,7 @@ theorem contDiffWithinAt_localInvariantProp_of_le (n m : ℕ∞ω) (hmn : m ≤
     have A : (I' ∘ f ∘ I.symm) (I x) ∈ I'.symm ⁻¹' e'.source ∩ range I' := by
       simp only [hx, mfld_simps]
     have := (mem_groupoid_of_pregroupoid.2 he').1.contDiffWithinAt A
-    convert (this.of_le hmn).comp _ h _
+    convert! (this.of_le hmn).comp _ h _
     · ext y; simp only [mfld_simps]
     · intro y hy; simp only [mfld_simps] at hy; simpa only [hy, mfld_simps] using hs hy.1
 
@@ -491,14 +490,14 @@ theorem contMDiffOn_iff :
     specialize h w this
     have w1 : w ∈ (chartAt H x).source := by simp only [w, hz, mfld_simps]
     have w2 : f w ∈ (chartAt H' y).source := by simp only [w, hz, mfld_simps]
-    convert ((contMDiffWithinAt_iff_of_mem_source w1 w2).mp h).2.mono _
+    convert! ((contMDiffWithinAt_iff_of_mem_source w1 w2).mp h).2.mono _
     · simp only [w, hz, mfld_simps]
     · mfld_set_tac
   · rintro ⟨hcont, hdiff⟩ x hx
     refine (contDiffWithinAt_localInvariantProp n).liftPropWithinAt_iff.mpr ?_
     refine ⟨hcont x hx, ?_⟩
     dsimp [ContDiffWithinAtProp]
-    convert hdiff x (f x) (extChartAt I x x) (by simp only [hx, mfld_simps]) using 1
+    convert! hdiff x (f x) (extChartAt I x x) (by simp only [hx, mfld_simps]) using 1
     mfld_set_tac
 
 /-- zero-smoothness on a set is equivalent to continuity on this set. -/
@@ -530,7 +529,7 @@ theorem contMDiffOn_iff_target :
   constructor
   · refine fun h' y => ⟨?_, fun x _ => h' x y⟩
     have h'' : ContinuousOn _ univ := (ModelWithCorners.continuous I').continuousOn
-    convert (h''.comp_inter (chartAt H' y).continuousOn_toFun).comp_inter h
+    convert! (h''.comp_inter (chartAt H' y).continuousOn_toFun).comp_inter h
     simp
   · exact fun h' x y => (h' y).2 x 0
 
diff --git a/Mathlib/Geometry/Manifold/ContMDiffMFDeriv.lean b/Mathlib/Geometry/Manifold/ContMDiffMFDeriv.lean
index be9e7382dec0f6..126498eec36f50 100644
--- a/Mathlib/Geometry/Manifold/ContMDiffMFDeriv.lean
+++ b/Mathlib/Geometry/Manifold/ContMDiffMFDeriv.lean
@@ -127,7 +127,7 @@ protected theorem ContMDiffWithinAt.mfderivWithin {x₀ : N} {f : N → M → M'
             ∩ range J ×ˢ range I) := by
         apply inter_subset_inter_right
         exact Set.prod_mono_right (extChartAt_target_subset_range (g x₀))
-      convert hf'.2.mono this
+      convert! hf'.2.mono this
       · ext y; simp; tauto
       · simp
     · exact hg'.2
@@ -167,7 +167,7 @@ protected theorem ContMDiffWithinAt.mfderivWithin {x₀ : N} {f : N → M → M'
   · exact mfderivWithin_eq_fderivWithin
   · exact mdifferentiableAt_extChartAt (by simpa using h'x)
   · apply MDifferentiableWithinAt.comp (I' := I) (u := u) _ _ _ inter_subset_right
-    · convert hx.mdifferentiableWithinAt one_ne_zero
+    · convert! hx.mdifferentiableWithinAt one_ne_zero
       exact PartialEquiv.left_inv (extChartAt I (g x₀)) h2
     · apply (mdifferentiableWithinAt_extChartAt_symm _).mono
       · exact inter_subset_left.trans (extChartAt_target_subset_range (g x₀))
@@ -308,7 +308,7 @@ theorem ContMDiffOn.continuousOn_tangentMapWithin (hf : CMDiff[s] n f) (hmn : 1
 theorem ContMDiff.contMDiff_tangentMap (hf : CMDiff n f) (hmn : m + 1 ≤ n) :
     CMDiff m (tangentMap I I' f) := by
   rw [← contMDiffOn_univ] at hf ⊢
-  convert hf.contMDiffOn_tangentMapWithin hmn uniqueMDiffOn_univ
+  convert! hf.contMDiffOn_tangentMapWithin hmn uniqueMDiffOn_univ
   rw [tangentMapWithin_univ]
 
 /-- If a function is `C^n`, with `1 ≤ n`, then its bundled derivative is continuous. -/
@@ -316,7 +316,7 @@ theorem ContMDiff.continuous_tangentMap (hf : CMDiff n f) (hmn : 1 ≤ n) :
     Continuous (tangentMap I I' f) := by
   rw [← contMDiffOn_univ] at hf
   rw [← continuousOn_univ]
-  convert hf.continuousOn_tangentMapWithin hmn uniqueMDiffOn_univ
+  convert! hf.continuousOn_tangentMapWithin hmn uniqueMDiffOn_univ
   rw [tangentMapWithin_univ]
 
 end tangentMap
diff --git a/Mathlib/Geometry/Manifold/Diffeomorph.lean b/Mathlib/Geometry/Manifold/Diffeomorph.lean
index cd9fc59ede9a9a..0e6e6e8fc38027 100644
--- a/Mathlib/Geometry/Manifold/Diffeomorph.lean
+++ b/Mathlib/Geometry/Manifold/Diffeomorph.lean
@@ -339,7 +339,7 @@ theorem toOpenPartialHomeomorph_mdifferentiable (h : M ≃ₘ^n⟮I, J⟯ N) (hn
 
 theorem uniqueMDiffOn_image_aux (h : M ≃ₘ^n⟮I, J⟯ N) (hn : n ≠ 0) {s : Set M}
     (hs : UniqueMDiffOn I s) : UniqueMDiffOn J (h '' s) := by
-  convert hs.uniqueMDiffOn_preimage (h.toOpenPartialHomeomorph_mdifferentiable hn)
+  convert! hs.uniqueMDiffOn_preimage (h.toOpenPartialHomeomorph_mdifferentiable hn)
   simp [h.image_eq_preimage_symm]
 
 @[simp]
diff --git a/Mathlib/Geometry/Manifold/GroupLieAlgebra.lean b/Mathlib/Geometry/Manifold/GroupLieAlgebra.lean
index 70016c7a63bb7d..c41b803c69865a 100644
--- a/Mathlib/Geometry/Manifold/GroupLieAlgebra.lean
+++ b/Mathlib/Geometry/Manifold/GroupLieAlgebra.lean
@@ -176,7 +176,7 @@ theorem contMDiff_mulInvariantVectorField (v : GroupLieAlgebra I G) :
     rw [A]
     exact contMDiff_mul I (minSmoothness 𝕜 3)
   let S := (S₃.comp S₂).comp S₁
-  convert S with g
+  convert! S with g
   · simp [F₁, F₂, F₃, fg, fv]
   · simp only [comp_apply, tangentMap, F₃, F₂, F₁, fg, fv]
     rw [mfderiv_prod_eq_add_apply ((contMDiff_mul I (minSmoothness 𝕜 3)).mdifferentiableAt M)]
diff --git a/Mathlib/Geometry/Manifold/HasGroupoid.lean b/Mathlib/Geometry/Manifold/HasGroupoid.lean
index 9b79a770952ead..3a379fc2555dab 100644
--- a/Mathlib/Geometry/Manifold/HasGroupoid.lean
+++ b/Mathlib/Geometry/Manifold/HasGroupoid.lean
@@ -282,7 +282,7 @@ of some chart on `M`. -/
 lemma chart_eq {s : Opens M} (hs : Nonempty s) {e : OpenPartialHomeomorph s H}
     (he : e ∈ atlas H s) : ∃ x : s, e = (chartAt H (x : M)).subtypeRestr hs := by
   rcases he with ⟨xset, ⟨x, hx⟩, he⟩
-  exact ⟨x, mem_singleton_iff.mp (by convert he)⟩
+  exact ⟨x, mem_singleton_iff.mp (by convert! he)⟩
 
 /-- If `t` is a non-empty open subset of `H`,
 every chart of `t` is the restriction of some chart on `H`. -/
@@ -468,7 +468,7 @@ def OpenPartialHomeomorph.toStructomorph {e : OpenPartialHomeomorph M H} (he : e
         fun c c' hc hc' ↦ G.compatible_of_mem_maximalAtlas (G.subset_maximalAtlas hc)
           (G.restriction_mem_maximalAtlas_subtype he h c' hc') }
   · have : IsEmpty t := isEmpty_coe_sort.mpr
-      (by convert e.image_source_eq_target ▸ image_eq_empty.mpr (isEmpty_coe_sort.mp h))
+      (by convert! e.image_source_eq_target ▸ image_eq_empty.mpr (isEmpty_coe_sort.mp h))
     exact { Homeomorph.empty with
       -- `c'` cannot exist: it would be the restriction of `chartAt H x` at some `x ∈ t`.
       mem_groupoid := fun _ c' _ ⟨_, ⟨x, _⟩, _⟩ ↦ (this.false x).elim }
diff --git a/Mathlib/Geometry/Manifold/Instances/Icc.lean b/Mathlib/Geometry/Manifold/Instances/Icc.lean
index c4a4d3a74709ce..ac1cf5c733ae4a 100644
--- a/Mathlib/Geometry/Manifold/Instances/Icc.lean
+++ b/Mathlib/Geometry/Manifold/Instances/Icc.lean
@@ -143,7 +143,7 @@ lemma contMDiffOn_projIcc : CMDiff[Icc x y] n (Set.projIcc x y h.out.le) := by
 lemma contMDiffOn_comp_projIcc_iff {f : Icc x y → M} :
     CMDiff[Icc x y] n (f ∘ (Set.projIcc x y h.out.le)) ↔ CMDiff n f := by
   refine ⟨fun hf ↦ ?_, fun hf ↦ hf.comp_contMDiffOn contMDiffOn_projIcc⟩
-  convert hf.comp_contMDiff (contMDiff_subtype_coe_Icc (x := x) (y := y)) (fun z ↦ z.2)
+  convert! hf.comp_contMDiff (contMDiff_subtype_coe_Icc (x := x) (y := y)) (fun z ↦ z.2)
   ext z
   simp
 
@@ -153,7 +153,7 @@ lemma contMDiffWithinAt_comp_projIcc_iff {f : Icc x y → M} {w : Icc x y} :
     fun hf ↦ hf.comp_contMDiffWithinAt_of_eq (contMDiffOn_projIcc w w.2) (by simp)⟩
   have A := contMDiff_subtype_coe_Icc (x := x) (y := y) (n := n) w
   rw [← contMDiffWithinAt_univ] at A ⊢
-  convert hf.comp _ A (fun z hz ↦ z.2)
+  convert! hf.comp _ A (fun z hz ↦ z.2)
   ext z
   simp
 
@@ -162,7 +162,7 @@ lemma mdifferentiableWithinAt_comp_projIcc_iff {f : Icc x y → M} {w : Icc x y}
   refine ⟨fun hf ↦ ?_, fun hf ↦ ?_⟩
   · have A := (contMDiff_subtype_coe_Icc (x := x) (y := y) w).mdifferentiableAt one_ne_zero
     rw [← mdifferentiableWithinAt_univ] at A ⊢
-    convert hf.comp _ A (fun z hz ↦ z.2)
+    convert! hf.comp _ A (fun z hz ↦ z.2)
     ext z
     simp
   · have := (contMDiffOn_projIcc (x := x) (y := y) w w.2).mdifferentiableWithinAt one_ne_zero
@@ -190,7 +190,7 @@ lemma mfderivWithin_comp_projIcc_one {f : Icc x y → M} {w : Icc x y} :
   have : w = projIcc x y h.out.le (w : ℝ) := by rw [projIcc_of_mem]
   rw [projIcc_of_mem _ w.2]
   congr 1
-  convert mfderivWithin_projIcc_one w.2
+  convert! mfderivWithin_projIcc_one w.2
 
 lemma mfderiv_subtype_coe_Icc_one (z : Icc x y) :
     mfderiv (𝓡∂ 1) 𝓘(ℝ) (Subtype.val : Icc x y → ℝ) z 1 = 1 := by
diff --git a/Mathlib/Geometry/Manifold/Instances/Sphere.lean b/Mathlib/Geometry/Manifold/Instances/Sphere.lean
index 0d727ce4bc721d..e4a64c4977d88e 100644
--- a/Mathlib/Geometry/Manifold/Instances/Sphere.lean
+++ b/Mathlib/Geometry/Manifold/Instances/Sphere.lean
@@ -140,17 +140,18 @@ theorem stereoInvFunAux_mem (hv : ‖v‖ = 1) {w : E} (hw : w ∈ (ℝ ∙ v)
 theorem hasFDerivAt_stereoInvFunAux (v : E) :
     HasFDerivAt (stereoInvFunAux v) (ContinuousLinearMap.id ℝ E) 0 := by
   have h₀ : HasFDerivAt (fun w : E => ‖w‖ ^ 2) (0 : StrongDual ℝ E) 0 := by
-    convert (hasStrictFDerivAt_norm_sq (0 : E)).hasFDerivAt
+    convert! (hasStrictFDerivAt_norm_sq (0 : E)).hasFDerivAt
     simp only [map_zero, smul_zero]
   have h₁ : HasFDerivAt (fun w : E => (‖w‖ ^ 2 + 4)⁻¹) (0 : StrongDual ℝ E) 0 := by
-    convert (hasFDerivAt_inv _).comp _ (h₀.add (hasFDerivAt_const 4 0)) <;> simp
+    convert! (hasFDerivAt_inv _).comp _ (h₀.add (hasFDerivAt_const 4 0)) <;> simp
   have h₂ : HasFDerivAt (fun w => (4 : ℝ) • w + (‖w‖ ^ 2 - 4) • v)
       ((4 : ℝ) • ContinuousLinearMap.id ℝ E) 0 := by
-    convert ((hasFDerivAt_const (4 : ℝ) 0).smul (hasFDerivAt_id 0)).add
-      ((h₀.sub (hasFDerivAt_const (4 : ℝ) 0)).smul (hasFDerivAt_const v 0)) using 1
+    convert!
+      ((hasFDerivAt_const (4 : ℝ) 0).smul (hasFDerivAt_id 0)).add
+        ((h₀.sub (hasFDerivAt_const (4 : ℝ) 0)).smul (hasFDerivAt_const v 0)) using 1
     ext w
     simp
-  convert h₁.smul h₂ using 1
+  convert! h₁.smul h₂ using 1
   ext w
   simp
 
@@ -215,7 +216,7 @@ theorem stereo_left_inv (hv : ‖v‖ = 1) {x : sphere (0 : E) 1} (hx : (x : E)
   have hvy : ⟪v, y⟫_ℝ = 0 := Submodule.mem_orthogonal_singleton_iff_inner_right.mp y.2
   have pythag : 1 = a ^ 2 + ‖y‖ ^ 2 := by
     have hvy' : ⟪a • v, y⟫_ℝ = 0 := by simp only [inner_smul_left, hvy, mul_zero]
-    convert norm_add_sq_eq_norm_sq_add_norm_sq_of_inner_eq_zero _ _ hvy' using 2
+    convert! norm_add_sq_eq_norm_sq_add_norm_sq_of_inner_eq_zero _ _ hvy' using 2
     · simp [← split]
     · simp [norm_smul, hv, ← sq, sq_abs]
     · exact sq _
@@ -287,7 +288,7 @@ theorem stereographic_apply_neg (v : sphere (0 : E) 1) :
 @[simp]
 theorem stereographic_neg_apply (v : sphere (0 : E) 1) :
     stereographic (norm_eq_of_mem_sphere (-v)) v = 0 := by
-  convert stereographic_apply_neg (-v)
+  convert! stereographic_apply_neg (-v)
   ext1
   simp
 
@@ -401,7 +402,9 @@ instance EuclideanSpace.instIsManifoldSphere
       -- Porting note: need to help with implicit variables again
       have H₂ := (contDiff_stereoInvFunAux (m := ω) (v := v.val) |>.comp
         (ℝ ∙ (v : E))ᗮ.subtypeL.contDiff).comp U.symm.contDiff
-      convert H₁.comp_inter (H₂.contDiffOn : ContDiffOn ℝ ω _ Set.univ) using 1
+      convert! H₁.comp_inter (H₂.contDiffOn : ContDiffOn ℝ ω _ Set.univ) using 1
+        -- -- squeezed from `ext, simp [sphere_ext_iff, stereographic'_symm_apply, real_inner_comm]`
+
       -- -- squeezed from `ext, simp [sphere_ext_iff, stereographic'_symm_apply, real_inner_comm]`
       simp only [OpenPartialHomeomorph.trans_toPartialEquiv,
         OpenPartialHomeomorph.symm_toPartialEquiv, PartialEquiv.trans_source,
@@ -450,7 +453,7 @@ theorem ContMDiff.codRestrict_sphere {n : ℕ} [Fact (finrank ℝ E = n + 1)] {f
   have h : ContDiffOn ℝ ω _ Set.univ := U.contDiff.contDiffOn
   have H₁ := (h.comp_inter contDiffOn_stereoToFun).contMDiffOn
   have H₂ : CMDiff[Set.univ] m f := hf.contMDiffOn
-  convert (H₁.of_le le_top).comp' H₂ using 1
+  convert! (H₁.of_le le_top).comp' H₂ using 1
   ext x
   have hfxv : f x = -↑v ↔ ⟪f x, -↑v⟫_ℝ = 1 := by
     have hfx : ‖f x‖ = 1 := by simpa using hf' x
@@ -491,16 +494,16 @@ theorem range_mfderiv_coe_sphere {n : ℕ} [Fact (finrank ℝ E = n + 1)] (v : s
     (ne_zero_of_mem_unit_sphere (-v))).repr
   suffices
       (fderiv ℝ ((stereoInvFunAux (-v : E) ∘ (↑)) ∘ U.symm) 0).range = (ℝ ∙ (v : E))ᗮ by
-    convert this using 4
+    convert! this using 4
     apply stereographic'_neg
   have :
     HasFDerivAt (stereoInvFunAux (-v : E) ∘ (Subtype.val : (ℝ ∙ (↑(-v) : E))ᗮ → E))
       (ℝ ∙ (↑(-v) : E))ᗮ.subtypeL (U.symm 0) := by
-    convert hasFDerivAt_stereoInvFunAux_comp_coe (-v : E)
+    convert! hasFDerivAt_stereoInvFunAux_comp_coe (-v : E)
     simp
-  convert congr($((this.comp 0 U.symm.toContinuousLinearEquiv.hasFDerivAt).fderiv).range)
+  convert! congr($((this.comp 0 U.symm.toContinuousLinearEquiv.hasFDerivAt).fderiv).range)
   symm
-  convert
+  convert!
     (U.symm : EuclideanSpace ℝ (Fin n) ≃ₗᵢ[ℝ] (ℝ ∙ (↑(-v) : E))ᗮ).range_comp
       (ℝ ∙ (↑(-v) : E))ᗮ.subtype using 1
   simp only [Submodule.range_subtype, coe_neg_sphere]
@@ -524,11 +527,11 @@ theorem mfderiv_coe_sphere_injective {n : ℕ} [Fact (finrank ℝ E = n + 1)] (v
   let U := (OrthonormalBasis.fromOrthogonalSpanSingleton
       (𝕜 := ℝ) n (ne_zero_of_mem_unit_sphere (-v))).repr
   suffices Injective (fderiv ℝ ((stereoInvFunAux (-v : E) ∘ (↑)) ∘ U.symm) 0) by
-    convert this using 3
+    convert! this using 3
     apply stereographic'_neg
   have : HasFDerivAt (stereoInvFunAux (-v : E) ∘ (Subtype.val : (ℝ ∙ (↑(-v) : E))ᗮ → E))
       (ℝ ∙ (↑(-v) : E))ᗮ.subtypeL (U.symm 0) := by
-    convert hasFDerivAt_stereoInvFunAux_comp_coe (-v : E)
+    convert! hasFDerivAt_stereoInvFunAux_comp_coe (-v : E)
     simp
   have := congr_arg DFunLike.coe <| (this.comp 0 U.symm.toContinuousLinearEquiv.hasFDerivAt).fderiv
   refine Eq.subst this.symm ?_
diff --git a/Mathlib/Geometry/Manifold/IntegralCurve/Transform.lean b/Mathlib/Geometry/Manifold/IntegralCurve/Transform.lean
index b5401ab42f2c51..629c1472014882 100644
--- a/Mathlib/Geometry/Manifold/IntegralCurve/Transform.lean
+++ b/Mathlib/Geometry/Manifold/IntegralCurve/Transform.lean
@@ -50,7 +50,7 @@ lemma IsMIntegralCurveOn.comp_add (hγ : IsMIntegralCurveOn γ v s) (dt : ℝ) :
 lemma isMIntegralCurveOn_comp_add {dt : ℝ} :
     IsMIntegralCurveOn (γ ∘ (· + dt)) v { t | t + dt ∈ s } ↔ IsMIntegralCurveOn γ v s := by
   refine ⟨fun hγ ↦ ?_, fun hγ ↦ hγ.comp_add _⟩
-  convert hγ.comp_add (-dt)
+  convert! hγ.comp_add (-dt)
   · ext t
     simp
   · simp
@@ -64,14 +64,14 @@ lemma IsMIntegralCurveAt.comp_add (hγ : IsMIntegralCurveAt γ v t₀) (dt : ℝ
   rw [isMIntegralCurveAt_iff'] at *
   obtain ⟨ε, hε, h⟩ := hγ
   refine ⟨ε, hε, ?_⟩
-  convert h.comp_add dt
+  convert! h.comp_add dt
   rw [Metric.ball]
   simp_rw [Metric.mem_ball, Real.dist_eq, ← sub_add, add_sub_right_comm]
 
 lemma isMIntegralCurveAt_comp_add {dt : ℝ} :
     IsMIntegralCurveAt (γ ∘ (· + dt)) v (t₀ - dt) ↔ IsMIntegralCurveAt γ v t₀ := by
   refine ⟨fun hγ ↦ ?_, fun hγ ↦ hγ.comp_add _⟩
-  convert hγ.comp_add (-dt)
+  convert! hγ.comp_add (-dt)
   · ext t
     simp only [Function.comp_apply, neg_add_cancel_right]
   · simp only [sub_neg_eq_add, sub_add_cancel]
@@ -88,7 +88,7 @@ lemma IsMIntegralCurve.comp_add (hγ : IsMIntegralCurve γ v) (dt : ℝ) :
 lemma isMIntegralCurve_comp_add {dt : ℝ} :
     IsMIntegralCurve (γ ∘ (· + dt)) v ↔ IsMIntegralCurve γ v := by
   refine ⟨fun hγ ↦ ?_, fun hγ ↦ hγ.comp_add _⟩
-  convert hγ.comp_add (-dt)
+  convert! hγ.comp_add (-dt)
   ext t
   simp only [Function.comp_apply, neg_add_cancel_right]
 
@@ -115,7 +115,7 @@ lemma IsMIntegralCurveOn.comp_mul (hγ : IsMIntegralCurveOn γ v s) (a : ℝ) :
 lemma isMIntegralCurveOn_comp_mul_ne_zero {a : ℝ} (ha : a ≠ 0) :
     IsMIntegralCurveOn (γ ∘ (· * a)) (a • v) { t | t * a ∈ s } ↔ IsMIntegralCurveOn γ v s := by
   refine ⟨fun hγ ↦ ?_, fun hγ ↦ hγ.comp_mul a⟩
-  convert hγ.comp_mul a⁻¹
+  convert! hγ.comp_mul a⁻¹
   · ext t
     simp only [Function.comp_apply, mul_assoc, inv_mul_eq_div, div_self ha, mul_one]
   · simp only [smul_smul, inv_mul_eq_div, div_self ha, one_smul]
@@ -126,7 +126,7 @@ lemma IsMIntegralCurveAt.comp_mul_ne_zero (hγ : IsMIntegralCurveAt γ v t₀) {
   rw [isMIntegralCurveAt_iff'] at *
   obtain ⟨ε, hε, h⟩ := hγ
   refine ⟨ε / |a|, by positivity, ?_⟩
-  convert h.comp_mul a
+  convert! h.comp_mul a
   ext t
   rw [mem_setOf_eq, Metric.mem_ball, Metric.mem_ball, Real.dist_eq, Real.dist_eq,
     lt_div_iff₀ (abs_pos.mpr ha), ← abs_mul, sub_mul, div_mul_cancel₀ _ ha]
@@ -134,7 +134,7 @@ lemma IsMIntegralCurveAt.comp_mul_ne_zero (hγ : IsMIntegralCurveAt γ v t₀) {
 lemma isMIntegralCurveAt_comp_mul_ne_zero {a : ℝ} (ha : a ≠ 0) :
     IsMIntegralCurveAt (γ ∘ (· * a)) (a • v) (t₀ / a) ↔ IsMIntegralCurveAt γ v t₀ := by
   refine ⟨fun hγ ↦ ?_, fun hγ ↦ hγ.comp_mul_ne_zero ha⟩
-  convert hγ.comp_mul_ne_zero (inv_ne_zero ha)
+  convert! hγ.comp_mul_ne_zero (inv_ne_zero ha)
   · ext t
     simp only [Function.comp_apply, mul_assoc, inv_mul_eq_div, div_self ha, mul_one]
   · simp only [smul_smul, inv_mul_eq_div, div_self ha, one_smul]
@@ -148,7 +148,7 @@ lemma IsMIntegralCurve.comp_mul (hγ : IsMIntegralCurve γ v) (a : ℝ) :
 lemma isMIntegralCurve_comp_mul_ne_zero {a : ℝ} (ha : a ≠ 0) :
     IsMIntegralCurve (γ ∘ (· * a)) (a • v) ↔ IsMIntegralCurve γ v := by
   refine ⟨fun hγ ↦ ?_, fun hγ ↦ hγ.comp_mul _⟩
-  convert hγ.comp_mul a⁻¹
+  convert! hγ.comp_mul a⁻¹
   · ext t
     simp only [Function.comp_apply, mul_assoc, inv_mul_eq_div, div_self ha, mul_one]
   · simp only [smul_smul, inv_mul_eq_div, div_self ha, one_smul]
diff --git a/Mathlib/Geometry/Manifold/IsManifold/Basic.lean b/Mathlib/Geometry/Manifold/IsManifold/Basic.lean
index 06326309b3964c..b3a41ea3b8d56c 100644
--- a/Mathlib/Geometry/Manifold/IsManifold/Basic.lean
+++ b/Mathlib/Geometry/Manifold/IsManifold/Basic.lean
@@ -314,7 +314,7 @@ lemma _root_.Convex.convex_isRCLikeNormedField [NormedSpace ℝ E] [h : IsRCLike
   letI := NormedSpace.restrictScalars ℝ 𝕜 E
   simp only [Convex, StarConvex] at hs ⊢
   intro u hu v hv a b ha hb hab
-  convert hs hu hv ha hb hab using 2
+  convert! hs hu hv ha hb hab using 2
   · rw [← @algebraMap_smul (R := ℝ) (A := 𝕜), ← @algebraMap_smul (R := ℝ) (A := 𝕜)]
   · rw [← @algebraMap_smul (R := ℝ) (A := 𝕜), ← @algebraMap_smul (R := ℝ) (A := 𝕜)]
 
@@ -344,7 +344,7 @@ theorem convex_range [NormedSpace ℝ E] : Convex ℝ (range I) := by
     simp only [h, ↓reduceDIte, toPartialEquiv_coe] at W
     simp only [Convex, StarConvex] at W ⊢
     intro u hu v hv a b ha hb hab
-    convert W hu hv ha hb hab using 2
+    convert! W hu hv ha hb hab using 2
     · rw [← @algebraMap_smul (R := ℝ) (A := 𝕜)]
       rfl
     · rw [← @algebraMap_smul (R := ℝ) (A := 𝕜)]
diff --git a/Mathlib/Geometry/Manifold/IsManifold/ExtChartAt.lean b/Mathlib/Geometry/Manifold/IsManifold/ExtChartAt.lean
index d8d869830ddd27..b2581f57d9c419 100644
--- a/Mathlib/Geometry/Manifold/IsManifold/ExtChartAt.lean
+++ b/Mathlib/Geometry/Manifold/IsManifold/ExtChartAt.lean
@@ -569,7 +569,7 @@ theorem isOpen_extChartAt_target [I.Boundaryless] (x : M) : IsOpen (extChartAt I
 /-- If we're boundaryless, `(extChartAt I x).target` is a neighborhood of the key point -/
 theorem extChartAt_target_mem_nhds [I.Boundaryless] (x : M) :
     (extChartAt I x).target ∈ 𝓝 (extChartAt I x x) := by
-  convert extChartAt_target_mem_nhdsWithin x
+  convert! extChartAt_target_mem_nhdsWithin x
   simp only [I.range_eq_univ, nhdsWithin_univ]
 
 /-- If we're boundaryless, `(extChartAt I x).target` is a neighborhood of any of its points -/
diff --git a/Mathlib/Geometry/Manifold/LocalInvariantProperties.lean b/Mathlib/Geometry/Manifold/LocalInvariantProperties.lean
index 4603690ac742ba..7549d6ab48b275 100644
--- a/Mathlib/Geometry/Manifold/LocalInvariantProperties.lean
+++ b/Mathlib/Geometry/Manifold/LocalInvariantProperties.lean
@@ -337,7 +337,7 @@ theorem liftPropOn_indep_chart [HasGroupoid M G] [HasGroupoid M' G'] (he : e ∈
     (hf : f ∈ G'.maximalAtlas M') (h : LiftPropOn P g s) {y : H}
     (hy : y ∈ e.target ∩ e.symm ⁻¹' (s ∩ g ⁻¹' f.source)) :
     P (f ∘ g ∘ e.symm) (e.symm ⁻¹' s) y := by
-  convert ((hG.liftPropWithinAt_indep_chart he (e.symm_mapsTo hy.1) hf hy.2.2).1 (h _ hy.2.1)).2
+  convert! ((hG.liftPropWithinAt_indep_chart he (e.symm_mapsTo hy.1) hf hy.2.2).1 (h _ hy.2.1)).2
   rw [e.right_inv hy.1]
 
 theorem liftPropWithinAt_inter' (ht : t ∈ 𝓝[s] x) :
diff --git a/Mathlib/Geometry/Manifold/MFDeriv/Atlas.lean b/Mathlib/Geometry/Manifold/MFDeriv/Atlas.lean
index da0ee8ee88c2f2..513b957f83acff 100644
--- a/Mathlib/Geometry/Manifold/MFDeriv/Atlas.lean
+++ b/Mathlib/Geometry/Manifold/MFDeriv/Atlas.lean
@@ -293,7 +293,7 @@ lemma mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm' {x : M}
     (mfderiv% (extChartAt I x) y) ∘L (mfderiv[range I] (extChartAt I x).symm (extChartAt I x y))
     = ContinuousLinearMap.id _ _ := by
   have : y = (extChartAt I x).symm (extChartAt I x y) := ((extChartAt I x).left_inv hy).symm
-  convert mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm ((extChartAt I x).map_source hy)
+  convert! mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm ((extChartAt I x).map_source hy)
 
 /-- The composition of the derivative of the inverse of `extChartAt` with the derivative of
 `extChartAt` gives the identity.
@@ -335,7 +335,7 @@ lemma mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt'
     (mfderiv[range I] (extChartAt I x).symm (extChartAt I x y)) ∘L (mfderiv% (extChartAt I x) y)
       = ContinuousLinearMap.id _ _ := by
   have : y = (extChartAt I x).symm (extChartAt I x y) := ((extChartAt I x).left_inv hy).symm
-  convert mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt ((extChartAt I x).map_source hy)
+  convert! mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt ((extChartAt I x).map_source hy)
 
 lemma isInvertible_mfderivWithin_extChartAt_symm {y : E} (hy : y ∈ (extChartAt I x).target) :
     (mfderiv[range I] (extChartAt I x).symm y).IsInvertible :=
diff --git a/Mathlib/Geometry/Manifold/MFDeriv/Basic.lean b/Mathlib/Geometry/Manifold/MFDeriv/Basic.lean
index d5975adcbf83fb..46457b61c6de9b 100644
--- a/Mathlib/Geometry/Manifold/MFDeriv/Basic.lean
+++ b/Mathlib/Geometry/Manifold/MFDeriv/Basic.lean
@@ -413,14 +413,14 @@ theorem mdifferentiableOn_iff :
     specialize h w this
     have w1 : w ∈ (chartAt H x).source := by simp only [w, hz, mfld_simps]
     have w2 : f w ∈ (chartAt H' y).source := by simp only [w, hz, mfld_simps]
-    convert ((mdifferentiableWithinAt_iff_of_mem_source w1 w2).mp h).2.mono _
+    convert! ((mdifferentiableWithinAt_iff_of_mem_source w1 w2).mp h).2.mono _
     · simp only [w, hz, mfld_simps]
     · mfld_set_tac
   · rintro ⟨hcont, hdiff⟩ x hx
     refine differentiableWithinAt_localInvariantProp.liftPropWithinAt_iff.mpr ?_
     refine ⟨hcont x hx, ?_⟩
     dsimp [DifferentiableWithinAtProp]
-    convert hdiff x (f x) (extChartAt I x x) (by simp only [hx, mfld_simps]) using 1
+    convert! hdiff x (f x) (extChartAt I x x) (by simp only [hx, mfld_simps]) using 1
     mfld_set_tac
 
 /-- One can reformulate smoothness on a set as continuity on this set, and smoothness in any
@@ -437,7 +437,7 @@ theorem mdifferentiableOn_iff_target :
   constructor
   · refine fun h' y => ⟨?_, fun x _ => h' x y⟩
     have h'' : ContinuousOn _ univ := (ModelWithCorners.continuous I').continuousOn
-    convert (h''.comp_inter (chartAt H' y).continuousOn_toFun).comp_inter h
+    convert! (h''.comp_inter (chartAt H' y).continuousOn_toFun).comp_inter h
     simp
   · exact fun h' x y => (h' y).2 x 0
 
@@ -625,7 +625,7 @@ theorem HasMFDerivWithinAt.union (hs : HasMFDerivWithinAt I I' f s x f')
     (ht : HasMFDerivWithinAt I I' f t x f') : HasMFDerivWithinAt I I' f (s ∪ t) x f' := by
   constructor
   · exact ContinuousWithinAt.union hs.1 ht.1
-  · convert HasFDerivWithinAt.union hs.2 ht.2 using 1
+  · convert! HasFDerivWithinAt.union hs.2 ht.2 using 1
     simp only [union_inter_distrib_right, preimage_union]
 
 theorem HasMFDerivWithinAt.mono_of_mem_nhdsWithin
diff --git a/Mathlib/Geometry/Manifold/MFDeriv/Defs.lean b/Mathlib/Geometry/Manifold/MFDeriv/Defs.lean
index da0fe2816a112d..f7e08d8e323f6f 100644
--- a/Mathlib/Geometry/Manifold/MFDeriv/Defs.lean
+++ b/Mathlib/Geometry/Manifold/MFDeriv/Defs.lean
@@ -171,7 +171,7 @@ theorem differentiableWithinAt_localInvariantProp :
       rw [this] at h
       have : I (e x) ∈ I.symm ⁻¹' e.target ∩ Set.range I := by simp only [hx, mfld_simps]
       have := (mem_groupoid_of_pregroupoid.2 he).2.contDiffWithinAt this
-      convert (h.comp' _ (this.differentiableWithinAt one_ne_zero)).mono_of_mem_nhdsWithin _
+      convert! (h.comp' _ (this.differentiableWithinAt one_ne_zero)).mono_of_mem_nhdsWithin _
         using 1
       · ext y; simp only [mfld_simps]
       refine
@@ -192,7 +192,7 @@ theorem differentiableWithinAt_localInvariantProp :
       have A : (I' ∘ f ∘ I.symm) (I x) ∈ I'.symm ⁻¹' e'.source ∩ Set.range I' := by
         simp only [hx, mfld_simps]
       have := (mem_groupoid_of_pregroupoid.2 he').1.contDiffWithinAt A
-      convert (this.differentiableWithinAt one_ne_zero).comp _ h _
+      convert! (this.differentiableWithinAt one_ne_zero).comp _ h _
       · ext y; simp only [mfld_simps]
       · intro y hy; simp only [mfld_simps] at hy; simpa only [hy, mfld_simps] using hs hy.1 }
 
diff --git a/Mathlib/Geometry/Manifold/MFDeriv/SpecificFunctions.lean b/Mathlib/Geometry/Manifold/MFDeriv/SpecificFunctions.lean
index 7f4ad4775d421d..0695cec8e71f2c 100644
--- a/Mathlib/Geometry/Manifold/MFDeriv/SpecificFunctions.lean
+++ b/Mathlib/Geometry/Manifold/MFDeriv/SpecificFunctions.lean
@@ -435,7 +435,7 @@ theorem mdifferentiableOn_prod_module_iff (f : M → F₁ × F₂) :
 
 theorem mdifferentiable_prod_iff (f : M → M' × N') :
     MDiff f ↔ MDiff (Prod.fst ∘ f) ∧ MDiff (Prod.snd ∘ f) :=
-  ⟨fun h ↦ ⟨h.fst, h.snd⟩, fun h ↦ by convert h.1.prodMk h.2⟩
+  ⟨fun h ↦ ⟨h.fst, h.snd⟩, fun h ↦ by convert! h.1.prodMk h.2⟩
 
 theorem mdifferentiable_prod_module_iff (f : M → F₁ × F₂) :
     MDifferentiable I 𝓘(𝕜, F₁ × F₂) f ↔ MDiff (Prod.fst ∘ f) ∧ MDiff (Prod.snd ∘ f) := by
@@ -462,7 +462,7 @@ theorem MDifferentiableWithinAt.prodMap (hf : MDiffAt[s] f x) (hg : MDiffAt[r] g
 theorem MDifferentiableAt.prodMap (hf : MDiffAt f x) (hg : MDiffAt g y) :
     MDiffAt (Prod.map f g) (x, y) := by
   rw [← mdifferentiableWithinAt_univ] at *
-  convert hf.prodMap hg
+  convert! hf.prodMap hg
   exact univ_prod_univ.symm
 
 /-- Variant of `MDifferentiableAt.prod_map` in which the point in the product is given as `p`
@@ -506,7 +506,7 @@ lemma HasMFDerivAt.prodMap {p : M × M'} {f : M → N} {g : M' → N'}
     HasMFDerivAt% (Prod.map f g) p
       ((mfderiv% f p.1).prodMap (mfderiv% g p.2)) := by
   simp_rw [← hasMFDerivWithinAt_univ, ← mfderivWithin_univ, ← univ_prod_univ]
-  convert hf.hasMFDerivWithinAt.prodMap hg.hasMFDerivWithinAt
+  convert! hf.hasMFDerivWithinAt.prodMap hg.hasMFDerivWithinAt
   · rw [mfderivWithin_univ]; exact hf.mfderiv
   · rw [mfderivWithin_univ]; exact hg.mfderiv
 
@@ -587,7 +587,7 @@ theorem mfderiv_prod_eq_add {f : M × M' → M''} {p : M × M'}
     mdifferentiableAt_const.mfderiv_prod mdifferentiableAt_snd, mfderiv_fst,
     mfderiv_snd, mfderiv_const, mfderiv_const]
   symm
-  convert ContinuousLinearMap.comp_id <| mfderiv% f (p.1, p.2)
+  convert! ContinuousLinearMap.comp_id <| mfderiv% f (p.1, p.2)
   exact ContinuousLinearMap.coprod_inl_inr
 
 /-- The total derivative of a function in two variables is the sum of the partial derivatives.
@@ -858,7 +858,7 @@ theorem HasMFDerivAt.neg (hf : HasMFDerivAt% f z f') : HasMFDerivAt% (-f) z (-f'
   ⟨hf.1.neg, hf.2.neg⟩
 
 theorem hasMFDerivAt_neg : HasMFDerivAt% (-f) z (-f') ↔ HasMFDerivAt% f z f' :=
-  ⟨fun hf ↦ by convert hf.neg <;> rw [neg_neg], fun hf ↦ hf.neg⟩
+  ⟨fun hf ↦ by convert! hf.neg <;> rw [neg_neg], fun hf ↦ hf.neg⟩
 
 theorem MDifferentiableWithinAt.neg {s : Set M} (hf : MDiffAt[s] f z) : MDiffAt[s] (-f) z :=
   (hf.hasMFDerivWithinAt.neg).mdifferentiableWithinAt
@@ -873,7 +873,7 @@ theorem mdifferentiableWithinAt_neg : MDiffAt[s] (-f) z ↔ MDiffAt[s] f z :=
   ⟨fun hf ↦ by convert hf.neg; rw [neg_neg], fun hf ↦ hf.neg⟩
 
 theorem mdifferentiableAt_neg : MDiffAt (-f) z ↔ MDiffAt f z :=
-  ⟨fun hf ↦ by convert hf.neg; rw [neg_neg], fun hf ↦ hf.neg⟩
+  ⟨fun hf ↦ by convert! hf.neg; rw [neg_neg], fun hf ↦ hf.neg⟩
 
 theorem MDifferentiable.neg (hf : MDiff f) : MDiff (-f) := fun x ↦ (hf x).neg
 
@@ -983,7 +983,7 @@ set_option backward.isDefEq.respectTransparency false in
 theorem HasMFDerivWithinAt.mul (hp : HasMFDerivWithinAt I 𝓘(𝕜, F') p s z p')
     (hq : HasMFDerivWithinAt I 𝓘(𝕜, F') q s z q') :
     HasMFDerivWithinAt I 𝓘(𝕜, F') (p * q) s z (p z • q' + q z • p' : E →L[𝕜] F') := by
-  convert hp.mul' hq; ext _; apply mul_comm
+  convert! hp.mul' hq; ext _; apply mul_comm
 
 theorem HasMFDerivAt.mul (hp : HasMFDerivAt I 𝓘(𝕜, F') p z p')
     (hq : HasMFDerivAt I 𝓘(𝕜, F') q z q') :
@@ -1004,7 +1004,7 @@ lemma HasMFDerivWithinAt.prod [DecidableEq ι]
   | insert i t hi IH =>
     rw [t.sum_insert hi, t.erase_insert hi, t.prod_insert hi, add_comm]
     rw [t.forall_mem_insert] at hf
-    convert hf.1.mul (IH hf.2) using 2
+    convert! hf.1.mul (IH hf.2) using 2
     · simp only [t.smul_sum, ← mul_smul]
       refine t.sum_congr rfl (fun j hj ↦ ?_)
       rw [t.erase_insert_of_ne (by grind), Finset.prod_insert (by grind)]
@@ -1099,7 +1099,7 @@ variable {z : M} {F' : Type*} [NormedField F'] [NormedAlgebra 𝕜 F'] {p q : M
 
 lemma HasMFDerivWithinAt.inv (hp : HasMFDerivWithinAt I 𝓘(𝕜, F') p s z p') (hp_ne : p z ≠ 0) :
     HasMFDerivWithinAt I 𝓘(𝕜, F') (p⁻¹) s z (-(p z ^ 2)⁻¹ • p' : E →L[𝕜] F') := by
-  convert hp.inv' hp_ne
+  convert! hp.inv' hp_ne
   ext
   simp
   ring_nf
@@ -1112,7 +1112,7 @@ lemma HasMFDerivWithinAt.div (hp : HasMFDerivWithinAt I 𝓘(𝕜, F') p s z p')
     (hq : HasMFDerivWithinAt I 𝓘(𝕜, F') q s z q') (hq_ne : q z ≠ 0) :
     HasMFDerivWithinAt I 𝓘(𝕜, F') (p / q) s z
       ((1 / q z) • p' - (p z / q z ^ 2) • q' : E →L[𝕜] F') := by
-  convert hp.mul (hq.inv hq_ne) using 1
+  convert! hp.mul (hq.inv hq_ne) using 1
   · simp [div_eq_mul_inv]
   · ext
     simp [div_eq_mul_inv]
diff --git a/Mathlib/Geometry/Manifold/MFDeriv/UniqueDifferential.lean b/Mathlib/Geometry/Manifold/MFDeriv/UniqueDifferential.lean
index d66c40bcd3c8d9..87483b86150d63 100644
--- a/Mathlib/Geometry/Manifold/MFDeriv/UniqueDifferential.lean
+++ b/Mathlib/Geometry/Manifold/MFDeriv/UniqueDifferential.lean
@@ -161,7 +161,7 @@ private lemma UniqueMDiffWithinAt.bundle_preimage_aux {p : TotalSpace F Z}
       ModelWithCorners.toPartialEquiv_coe_symm, PartialEquiv.refl_coe,
       OpenPartialHomeomorph.prod_symm, OpenPartialHomeomorph.refl_symm,
       OpenPartialHomeomorph.prod_apply, OpenPartialHomeomorph.refl_apply]
-    convert hz.1
+    convert! hz.1
     apply Trivialization.proj_symm_apply'
     exact h's hz.1
   · rcases hz.2 with ⟨u, rfl⟩
diff --git a/Mathlib/Geometry/Manifold/Riemannian/Basic.lean b/Mathlib/Geometry/Manifold/Riemannian/Basic.lean
index 635fe49139f4cb..05cc1140d768f4 100644
--- a/Mathlib/Geometry/Manifold/Riemannian/Basic.lean
+++ b/Mathlib/Geometry/Manifold/Riemannian/Basic.lean
@@ -119,7 +119,7 @@ noncomputable def riemannianMetricVectorSpace :
   contMDiff := by
     intro x
     rw [contMDiffAt_section]
-    convert contMDiffAt_const (c := innerSL ℝ)
+    convert! contMDiffAt_const (c := innerSL ℝ)
     ext v w
     simp [hom_trivializationAt_apply, ContinuousLinearMap.inCoordinates, TangentSpace]
 
@@ -267,7 +267,7 @@ lemma eventually_norm_mfderivWithin_symm_extChartAt_comp_lt (x : M) :
   rw [TangentBundle.symmL_trivializationAt h'y] at hy
   have A : (extChartAt I x).symm (extChartAt I x y) = y :=
     (extChartAt I x).left_inv (by simpa using h'y)
-  convert hy using 3 <;> congr
+  convert! hy using 3 <;> congr
 
 lemma eventually_norm_mfderivWithin_symm_extChartAt_lt (x : M) :
     ∃ C > 0, ∀ᶠ y in 𝓝[range I] (extChartAt I x x),
@@ -281,7 +281,7 @@ lemma eventually_norm_mfderivWithin_symm_extChartAt_lt (x : M) :
     extChartAt_target_mem_nhdsWithin x] with y hy h'y
   have : y = (extChartAt I x) ((extChartAt I x).symm y) := by simp [-extChartAt, h'y]
   simp only [preimage_setOf_eq, mem_setOf_eq] at hy
-  convert hy
+  convert! hy
 
 lemma eventually_enorm_mfderivWithin_symm_extChartAt_lt (x : M) :
     ∃ C > (0 : ℝ≥0), ∀ᶠ y in 𝓝[range I] (extChartAt I x x),
@@ -484,9 +484,9 @@ lemma setOf_riemannianEDist_lt_subset_nhds [RegularSpace M] {x : M} {s : Set M}
   have : γ' t₁ ∈ (extChartAt I x).symm ⁻¹' v := by
     apply hr
     rw [← Metric.eball_coe, Metric.mem_eball, edist_eq_enorm_sub]
-    convert this
+    convert! this
     simp [γ', hγx]
-  convert mem_preimage.1 this
+  convert! mem_preimage.1 this
   simp only [Function.comp_apply, γ', (extChartAt I x).left_inv <| uc <| t₁_mem
     (right_mem_Icc.mpr ht₁0)]
 
diff --git a/Mathlib/Geometry/Manifold/Riemannian/PathELength.lean b/Mathlib/Geometry/Manifold/Riemannian/PathELength.lean
index 07db9fb67a9f40..0d2359fcea513b 100644
--- a/Mathlib/Geometry/Manifold/Riemannian/PathELength.lean
+++ b/Mathlib/Geometry/Manifold/Riemannian/PathELength.lean
@@ -292,7 +292,7 @@ lemma exists_lt_locally_constant_of_riemannianEDist_lt
       fun_prop
     · intro t ht
       exact ⟨Real.smoothTransition.nonneg _, Real.smoothTransition.le_one _⟩
-  · convert hγ using 1
+  · convert! hγ using 1
     rw [← A a haa', ← B b hb'b]
     apply pathELength_comp_of_monotoneOn hab.le
     · apply Monotone.monotoneOn
@@ -331,7 +331,7 @@ lemma riemannianEDist_comm : riemannianEDist I x y = riemannianEDist I y x := by
   · exact differentiableOn_neg _
   · exact h_smooth.contMDiffOn.mdifferentiableOn one_ne_zero
   apply this.trans_lt
-  convert hγ
+  convert! hγ
   ext t
   simp [η]
 
@@ -355,11 +355,11 @@ lemma riemannianEDist_triangle :
   apply this.trans_lt (lt_trans ?_ huv)
   rw [← pathELength_add zero_le_one one_le_two]
   gcongr
-  · convert hγ₁ using 1
+  · convert! hγ₁ using 1
     apply pathELength_congr
     intro t ht
     simp [γ, ht.2]
-  · convert hγ₂ using 1
+  · convert! hγ₂ using 1
     apply pathELength_congr_Ioo
     intro t ht
     simp [γ, ht.1]
diff --git a/Mathlib/Geometry/Manifold/Sheaf/Basic.lean b/Mathlib/Geometry/Manifold/Sheaf/Basic.lean
index db74d6a484e841..81d13fd9a85cef 100644
--- a/Mathlib/Geometry/Manifold/Sheaf/Basic.lean
+++ b/Mathlib/Geometry/Manifold/Sheaf/Basic.lean
@@ -70,7 +70,7 @@ def StructureGroupoid.LocalInvariantProp.localPredicate (hG : LocalInvariantProp
     have : ChartedSpace.LiftPropAt P f (Opens.inclusion hUV x') := by
       rw [hG.liftPropAt_iff_comp_inclusion hUV]
       exact hU x'
-    convert this
+    convert! this
 
 /-- Let `P` be a `LocalInvariantProp` for functions between spaces with the groupoids `G`, `G'`
 and let `M`, `M'` be charted spaces modelled on the model spaces of those groupoids.  Then there is
diff --git a/Mathlib/Geometry/Manifold/Sheaf/LocallyRingedSpace.lean b/Mathlib/Geometry/Manifold/Sheaf/LocallyRingedSpace.lean
index e79bf2999cef62..31a4874663c1bd 100644
--- a/Mathlib/Geometry/Manifold/Sheaf/LocallyRingedSpace.lean
+++ b/Mathlib/Geometry/Manifold/Sheaf/LocallyRingedSpace.lean
@@ -66,7 +66,7 @@ theorem smoothSheafCommRing.isUnit_stalk_iff {x : M}
     -- `x`, which is nonzero at `x`
     obtain ⟨U : Opens M, hxU, f : C^∞⟮IM, U; 𝓘(𝕜), 𝕜⟯, rfl⟩ := S.exists_germ_eq f
     have hf' : f ⟨x, hxU⟩ ≠ 0 := by
-      convert hf
+      convert! hf
       exact (smoothSheafCommRing.eval_germ U x hxU f).symm
     -- In fact, by continuity, `f` is nonzero on a neighbourhood `V` of `x`
     have H : ∀ᶠ (z : U) in 𝓝 ⟨x, hxU⟩, f z ≠ 0 := f.2.continuous.continuousAt.eventually_ne hf'
@@ -75,7 +75,7 @@ theorem smoothSheafCommRing.isUnit_stalk_iff {x : M}
     let V : Opens M := ⟨Subtype.val '' V₀, U.2.isOpenMap_subtype_val V₀ hV₀⟩
     have hUV : V ≤ U := Subtype.coe_image_subset (U : Set M) V₀
     have hV : V₀ = Set.range (Set.inclusion hUV) := by
-      convert (Set.range_inclusion hUV).symm
+      convert! (Set.range_inclusion hUV).symm
       ext y
       change _ ↔ y ∈ Subtype.val ⁻¹' Subtype.val '' V₀
       rw [Set.preimage_image_eq _ Subtype.coe_injective]
@@ -83,7 +83,7 @@ theorem smoothSheafCommRing.isUnit_stalk_iff {x : M}
     subst hV
     have hxV : x ∈ (V : Set M) := by
       obtain ⟨x₀, hxx₀⟩ := hxV₀
-      convert x₀.2
+      convert! x₀.2
       exact congr_arg Subtype.val hxx₀.symm
     have hVf : ∀ y : V, f (Set.inclusion hUV y) ≠ 0 :=
       fun y ↦ hV₀f (Set.inclusion hUV y) (Set.mem_range_self y)
@@ -94,14 +94,14 @@ theorem smoothSheafCommRing.isUnit_stalk_iff {x : M}
         ?_, ?_⟩, S.germ_res_apply hUV.hom x hxV f⟩
       · rw [← map_mul]
         -- Qualified the name to avoid Lean not finding a `OneHomClass` https://github.com/leanprover-community/mathlib4/pull/8386
-        convert RingHom.map_one _
+        convert! RingHom.map_one _
         apply Subtype.ext
         ext y
         apply mul_inv_cancel₀
         exact hVf y
       · rw [← map_mul]
         -- Qualified the name to avoid Lean not finding a `OneHomClass` https://github.com/leanprover-community/mathlib4/pull/8386
-        convert RingHom.map_one _
+        convert! RingHom.map_one _
         apply Subtype.ext
         ext y
         apply inv_mul_cancel₀
@@ -172,7 +172,7 @@ def ChartedSpace.locallyRingedSpaceMap (f : M → N) (hf : ContMDiff IM IN ∞ f
   prop x := by
     refine ⟨fun a ha ↦ ?_⟩
     rw [smoothSheafCommRing.isUnit_stalk_iff, RingHom.mem_ker] at ha ⊢
-    convert ha
+    convert! ha
     exact (congr($(stalkMap_locallyRingedSpaceMapAux f hf x) a)).symm
 
 @[reassoc (attr := simp)]
@@ -213,7 +213,7 @@ instance (U : Opens M) :
       refine ⟨⟨g ∘ b.symm, ContMDiff.comp hg ?_⟩, Subtype.ext <| funext fun _ ↦ ?_⟩
       · refine (ContMDiff.subtypeVal_comp_iff V' _).mp ?_
         rw [← ContMDiff.subtypeVal_comp_iff]
-        convert contMDiff_subtype_val
+        convert! contMDiff_subtype_val
         ext x
         exact congr($(b.apply_symm_apply x).1)
       · change g _ = _
diff --git a/Mathlib/Geometry/Manifold/StructureGroupoid.lean b/Mathlib/Geometry/Manifold/StructureGroupoid.lean
index ef946c8dbdbfd0..31f9f8ab53e866 100644
--- a/Mathlib/Geometry/Manifold/StructureGroupoid.lean
+++ b/Mathlib/Geometry/Manifold/StructureGroupoid.lean
@@ -303,7 +303,7 @@ def Pregroupoid.groupoid (PG : Pregroupoid H) : StructureGroupoid H where
     · refine PG.locality e.open_source fun x xu ↦ ?_
       rcases he x xu with ⟨s, s_open, xs, hs⟩
       refine ⟨s, s_open, xs, ?_⟩
-      convert hs.1 using 1
+      convert! hs.1 using 1
       dsimp [OpenPartialHomeomorph.restr]
       rw [s_open.interior_eq]
     · refine PG.locality e.open_target fun x xu ↦ ?_
@@ -311,7 +311,7 @@ def Pregroupoid.groupoid (PG : Pregroupoid H) : StructureGroupoid H where
       refine ⟨e.target ∩ e.symm ⁻¹' s, ?_, ⟨xu, xs⟩, ?_⟩
       · exact ContinuousOn.isOpen_inter_preimage e.continuousOn_invFun e.open_target s_open
       · rw [← inter_assoc, inter_self]
-        convert hs.2 using 1
+        convert! hs.2 using 1
         dsimp [OpenPartialHomeomorph.restr]
         rw [s_open.interior_eq]
   mem_of_eqOnSource' e e' he ee' := by
@@ -320,7 +320,7 @@ def Pregroupoid.groupoid (PG : Pregroupoid H) : StructureGroupoid H where
       simp only [ee'.1, he.1]
     · have A := EqOnSource.symm' ee'
       apply PG.congr e'.symm.open_source A.2
-      convert he.2 using 1
+      convert! he.2 using 1
       rw [A.1, symm_toPartialEquiv, PartialEquiv.symm_source]
 
 theorem mem_groupoid_of_pregroupoid {PG : Pregroupoid H} {e : OpenPartialHomeomorph H H} :
@@ -434,7 +434,7 @@ theorem closedUnderRestriction_iff_id_le (G : StructureGroupoid H) :
     rw [StructureGroupoid.le_iff]
     rintro e ⟨s, hs, hes⟩
     refine G.mem_of_eqOnSource ?_ hes
-    convert closedUnderRestriction' G.id_mem hs
+    convert! closedUnderRestriction' G.id_mem hs
     ext <;> simp [hs.interior_eq]
   · intro h
     constructor
diff --git a/Mathlib/Geometry/Manifold/VectorBundle/LocalFrame.lean b/Mathlib/Geometry/Manifold/VectorBundle/LocalFrame.lean
index ecff97d02c97fe..3983316d6b7853 100644
--- a/Mathlib/Geometry/Manifold/VectorBundle/LocalFrame.lean
+++ b/Mathlib/Geometry/Manifold/VectorBundle/LocalFrame.lean
@@ -367,11 +367,11 @@ lemma isLocalFrameOn_localFrame_baseSet : IsLocalFrameOn I F n (e.localFrame b)
   contMDiffOn i := e.contMDiffOn_localFrame_baseSet _ b i
   linearIndependent := by
     intro x hx
-    convert (e.basisAt b hx).linearIndependent
+    convert! (e.basisAt b hx).linearIndependent
     simp [hx, basisAt]
   generating := by
     intro x hx
-    convert (e.basisAt b hx).span_eq.ge
+    convert! (e.basisAt b hx).span_eq.ge
     simp [hx, basisAt]
 
 lemma _root_.contMDiffAt_localFrame_of_mem (i : ι) (hx : x ∈ e.baseSet) :
diff --git a/Mathlib/Geometry/Manifold/VectorBundle/Riemannian.lean b/Mathlib/Geometry/Manifold/VectorBundle/Riemannian.lean
index 40e4f332dd4b50..02befed8d77f10 100644
--- a/Mathlib/Geometry/Manifold/VectorBundle/Riemannian.lean
+++ b/Mathlib/Geometry/Manifold/VectorBundle/Riemannian.lean
@@ -101,7 +101,7 @@ is a Riemannian bundle. -/
 instance : IsContMDiffRiemannianBundle IB n F₁ (Bundle.Trivial B F₁) := by
   refine ⟨fun x ↦ innerSL ℝ, fun x ↦ ?_, fun x v w ↦ rfl⟩
   simp only [contMDiffAt_section]
-  convert contMDiffAt_const (c := innerSL ℝ)
+  convert! contMDiffAt_const (c := innerSL ℝ)
   ext v w
   simp [hom_trivializationAt_apply, inCoordinates]
 
diff --git a/Mathlib/Geometry/Manifold/VectorBundle/Tangent.lean b/Mathlib/Geometry/Manifold/VectorBundle/Tangent.lean
index 2031dd86ca2713..b52f954aa8e8b2 100644
--- a/Mathlib/Geometry/Manifold/VectorBundle/Tangent.lean
+++ b/Mathlib/Geometry/Manifold/VectorBundle/Tangent.lean
@@ -170,7 +170,7 @@ lemma hasFDerivWithinAt_tangentCoordChange {x y z : M}
 
 lemma continuousOn_tangentCoordChange (x y : M) : ContinuousOn (tangentCoordChange I x y)
     ((extChartAt I x).source ∩ (extChartAt I y).source) := by
-  convert (tangentBundleCore I M).continuousOn_coordChange (achart H x) (achart H y) <;>
+  convert! (tangentBundleCore I M).continuousOn_coordChange (achart H x) (achart H y) <;>
   simp only [tangentBundleCore_baseSet, coe_achart, ← extChartAt_source I]
 
 end tangentCoordChange
@@ -401,14 +401,14 @@ def tangentBundleModelSpaceHomeomorph : TangentBundle I H ≃ₜ ModelProd H E :
       let p : TangentBundle I H := ⟨I.symm (0 : E), (0 : E)⟩
       have : Continuous (chartAt (ModelProd H E) p) := by
         rw [← continuousOn_univ]
-        convert (chartAt (ModelProd H E) p).continuousOn
+        convert! (chartAt (ModelProd H E) p).continuousOn
         simp only [mfld_simps]
       simpa only [mfld_simps] using this
     continuous_invFun := by
       let p : TangentBundle I H := ⟨I.symm (0 : E), (0 : E)⟩
       have : Continuous (chartAt (ModelProd H E) p).symm := by
         rw [← continuousOn_univ]
-        convert (chartAt (ModelProd H E) p).symm.continuousOn
+        convert! (chartAt (ModelProd H E) p).symm.continuousOn
         simp only [mfld_simps]
       simpa only [mfld_simps] using this }
 
@@ -454,7 +454,7 @@ lemma contMDiff_snd_tangentBundle_modelSpace :
   change ContMDiff I.tangent 𝓘(𝕜, E) n
     ((id Prod.snd : ModelProd H E → E) ∘ (tangentBundleModelSpaceHomeomorph I))
   apply ContMDiff.comp (I' := I.prod 𝓘(𝕜, E))
-  · convert contMDiff_snd
+  · convert! contMDiff_snd
     rw [chartedSpaceSelf_prod]
     rfl
   · exact contMDiff_tangentBundleModelSpaceHomeomorph
@@ -469,7 +469,7 @@ lemma contMDiffWithinAt_vectorSpace_iff_contDiffWithinAt
       (contMDiff_snd_tangentBundle_modelSpace E 𝓘(𝕜, E)).contMDiffAt.comp_contMDiffWithinAt _ h
   · apply Bundle.contMDiffWithinAt_totalSpace.2
     refine ⟨contMDiffWithinAt_id, ?_⟩
-    convert h.contMDiffWithinAt with y
+    convert! h.contMDiffWithinAt with y
     simp
 
 /-- A vector field on a vector space is `C^n` in the manifold sense iff it is `C^n` in the vector
diff --git a/Mathlib/Geometry/Manifold/VectorField/LieBracket.lean b/Mathlib/Geometry/Manifold/VectorField/LieBracket.lean
index 2417b2491888a0..759a3854f98317 100644
--- a/Mathlib/Geometry/Manifold/VectorField/LieBracket.lean
+++ b/Mathlib/Geometry/Manifold/VectorField/LieBracket.lean
@@ -224,7 +224,7 @@ theorem _root_.Filter.EventuallyEq.mlieBracketWithin_vectorField_eq
     congr 1
   · simp only [mpullbackWithin_apply]
     congr 1
-    convert hxV <;> exact extChartAt_to_inv x
+    convert! hxV <;> exact extChartAt_to_inv x
   · apply nhdsWithin_mono _ inter_subset_left
     filter_upwards [(continuousAt_extChartAt_symm x).continuousWithinAt.preimage_mem_nhdsWithin''
       hW (by simp)] with y hy
@@ -232,7 +232,7 @@ theorem _root_.Filter.EventuallyEq.mlieBracketWithin_vectorField_eq
     congr 1
   · simp only [mpullbackWithin_apply]
     congr 1
-    convert hxW <;> exact extChartAt_to_inv x
+    convert! hxW <;> exact extChartAt_to_inv x
 
 theorem _root_.Filter.EventuallyEq.mlieBracketWithin_vectorField_eq_of_mem
     (hV : V₁ =ᶠ[𝓝[s] x] V) (hW : W₁ =ᶠ[𝓝[s] x] W) (hx : x ∈ s) :
@@ -538,10 +538,12 @@ private lemma mpullbackWithin_mlieBracketWithin_aux [CompleteSpace E']
   have : (mfderiv[range I] (extChartAt I x₀).symm (extChartAt I x₀ x₀)).inverse =
       mfderiv% (extChartAt I x₀) x₀ := by
     apply ContinuousLinearMap.inverse_eq
-    · convert mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt (I := I) (x := x₀)
-        (y := extChartAt I x₀ x₀) (by simp)
-    · convert mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm (I := I) (x := x₀)
-        (y := extChartAt I x₀ x₀) (by simp)
+    · convert!
+      mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt (I := I) (x := x₀) (y :=
+        extChartAt I x₀ x₀) (by simp)
+    · convert!
+      mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm (I := I) (x := x₀) (y :=
+        extChartAt I x₀ x₀) (by simp)
   rw [← this, ← ContinuousLinearMap.IsInvertible.inverse_comp_apply_of_right]; swap
   · exact isInvertible_mfderivWithin_extChartAt_symm (mem_extChartAt_target x₀)
   have : mfderiv[range I] (extChartAt I x₀).symm (extChartAt I x₀ x₀) =
@@ -605,8 +607,8 @@ private lemma mpullbackWithin_mlieBracketWithin_aux [CompleteSpace E']
         (extChartAt I' (f x₀) (f ((extChartAt I x₀).symm y)))) ∘L
         (mfderiv% (extChartAt I' (f x₀)) (f ((extChartAt I x₀).symm y))) =
         ContinuousLinearMap.id _ _ := by
-      convert mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt
-        ((PartialEquiv.map_source _ h'y))
+      convert!
+        mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt ((PartialEquiv.map_source _ h'y))
     simp only [← ContinuousLinearMap.comp_assoc, this, ContinuousLinearMap.id_comp]
     congr 1
     exact ((mdifferentiableWithinAt_extChartAt_symm h'''y).mfderivWithin_mono huy
@@ -637,7 +639,7 @@ private lemma mpullbackWithin_mlieBracketWithin_aux [CompleteSpace E']
   · intro z hz
     simp only [comp_apply, mem_inter_iff, mem_preimage, mem_range, F]
     refine ⟨?_, mem_range_self _⟩
-    convert hst hz.1
+    convert! hst hz.1
     exact PartialEquiv.left_inv (extChartAt I' (f x₀)) (ht (hst hz.1))
   · rw [← nhdsWithin_eq_iff_eventuallyEq]
     apply le_antisymm
diff --git a/Mathlib/Geometry/Manifold/VectorField/Pullback.lean b/Mathlib/Geometry/Manifold/VectorField/Pullback.lean
index 650a2bab25910d..8194db30ba9664 100644
--- a/Mathlib/Geometry/Manifold/VectorField/Pullback.lean
+++ b/Mathlib/Geometry/Manifold/VectorField/Pullback.lean
@@ -514,7 +514,7 @@ protected lemma _root_.ContMDiffWithinAt.mpullbackWithin_vectorField' {u : Set M
     CMDiffAt[s] m (T% (mpullbackWithin I I' f V u)) x₀ := by
   have hn : 1 ≤ n := le_trans (by simp) hmn
   have hh : (mfderiv[s] f x₀).IsInvertible := by
-    convert hf' using 1
+    convert! hf' using 1
     exact (hf.mdifferentiableWithinAt <| by positivity).mfderivWithin_mono (hs _ hx₀) hu
   apply (hV.mpullbackWithin_vectorField_of_mem (hf.mono hu) hh hx₀ hs hmn
     hst).congr_of_eventuallyEq_of_mem _ hx₀
diff --git a/Mathlib/Geometry/Manifold/WhitneyEmbedding.lean b/Mathlib/Geometry/Manifold/WhitneyEmbedding.lean
index c60acf0777322d..a1b2751b430118 100644
--- a/Mathlib/Geometry/Manifold/WhitneyEmbedding.lean
+++ b/Mathlib/Geometry/Manifold/WhitneyEmbedding.lean
@@ -89,7 +89,7 @@ theorem comp_embeddingPiTangent_mfderiv (x : M) (hx : x ∈ s) :
       (@ContinuousLinearMap.proj ℝ _ ι (fun _ => E × ℝ) _ _ (fun _ => inferInstance) (f.ind x hx))
   have := L.hasMFDerivAt.comp x
     (f.embeddingPiTangent.contMDiff.mdifferentiableAt (by simp)).hasMFDerivAt
-  convert hasMFDerivAt_unique this _
+  convert! hasMFDerivAt_unique this _
   refine (hasMFDerivAt_extChartAt (f.mem_chartAt_ind_source x hx)).congr_of_eventuallyEq ?_
   refine (f.eventuallyEq_one x hx).mono fun y hy => ?_
   simp only [L, embeddingPiTangent_coe, ContinuousLinearMap.coe_comp', (· ∘ ·),
diff --git a/Mathlib/Geometry/RingedSpace/Basic.lean b/Mathlib/Geometry/RingedSpace/Basic.lean
index 1d5b76e45947d3..ce4c5879fe072e 100644
--- a/Mathlib/Geometry/RingedSpace/Basic.lean
+++ b/Mathlib/Geometry/RingedSpace/Basic.lean
@@ -136,7 +136,7 @@ def basicOpen {U : Opens X} (f : X.presheaf.obj (op U)) : Opens X where
     refine ⟨?_, V.2, hxV⟩
     intro y hy
     use i.le hy
-    convert RingHom.isUnit_map (X.presheaf.germ _ y hy).hom hf
+    convert! RingHom.isUnit_map (X.presheaf.germ _ y hy).hom hf
     exact (X.presheaf.germ_res_apply i y hy f).symm
 
 theorem mem_basicOpen {U : Opens X} (f : X.presheaf.obj (op U)) (x : X) (hx : x ∈ U) :
@@ -162,7 +162,7 @@ theorem isUnit_res_basicOpen {U : Opens X} (f : X.presheaf.obj (op U)) :
     IsUnit (X.presheaf.map (@homOfLE (Opens X) _ _ _ (X.basicOpen_le f)).op f) := by
   apply isUnit_of_isUnit_germ
   rintro x ⟨hxU, hx⟩
-  convert hx
+  convert! hx
   exact X.presheaf.germ_res_apply _ _ _ _
 
 @[simp]
diff --git a/Mathlib/Geometry/RingedSpace/LocallyRingedSpace/HasColimits.lean b/Mathlib/Geometry/RingedSpace/LocallyRingedSpace/HasColimits.lean
index 419c4f8cb04ae7..d48b644c04ed42 100644
--- a/Mathlib/Geometry/RingedSpace/LocallyRingedSpace/HasColimits.lean
+++ b/Mathlib/Geometry/RingedSpace/LocallyRingedSpace/HasColimits.lean
@@ -245,7 +245,8 @@ theorem coequalizer_π_stalk_isLocalHom (x : Y) :
     ← isUnit_map_iff (Y.presheaf.map (eqToHom hV').op).hom]
   -- Porting note (https://github.com/leanprover-community/mathlib4/issues/11224): change `rw` to `erw`
   erw [← CommRingCat.comp_apply, ← CommRingCat.comp_apply, ← Y.presheaf.map_comp]
-  convert @RingedSpace.isUnit_res_basicOpen Y.toRingedSpace (unop _)
+  convert!
+    @RingedSpace.isUnit_res_basicOpen Y.toRingedSpace (unop _)
       (((coequalizer.π f.toShHom g.toShHom).hom.c.app (op U)) s)
 
 end HasCoequalizer
diff --git a/Mathlib/Geometry/RingedSpace/OpenImmersion.lean b/Mathlib/Geometry/RingedSpace/OpenImmersion.lean
index 1d2f27e67ad6cc..9be5f196d7d814 100644
--- a/Mathlib/Geometry/RingedSpace/OpenImmersion.lean
+++ b/Mathlib/Geometry/RingedSpace/OpenImmersion.lean
@@ -283,7 +283,7 @@ theorem to_iso [h' : Epi f.base] : IsIso f := by
       dsimp only [Functor.op, Opens.map]
       congr
       exact (Set.image_preimage_eq _ ((TopCat.epi_iff_surjective _).mp h')).symm
-    convert H.c_iso (Opens.map f.base |>.obj <| unop U)
+    convert! H.c_iso (Opens.map f.base |>.obj <| unop U)
   have : IsIso f.c := NatIso.isIso_of_isIso_app _
   apply +allowSynthFailures isIso_of_components
   let t : X ≃ₜ Y := H.base_open.isEmbedding.toHomeomorph.trans
@@ -618,7 +618,7 @@ theorem isIso_of_subset {X Y : PresheafedSpace C} (f : X ⟶ Y)
   have : U = H.base_open.functor.obj ((Opens.map f.base).obj U) := by
     ext1
     exact (Set.inter_eq_left.mpr hU).symm.trans Set.image_preimage_eq_inter_range.symm
-  convert H.c_iso ((Opens.map f.base).obj U)
+  convert! H.c_iso ((Opens.map f.base).obj U)
 
 end PresheafedSpace.IsOpenImmersion
 
@@ -907,7 +907,7 @@ theorem image_preimage_is_empty (j : Discrete ι) (h : i ≠ j) (U : Opens (F.ob
   rw [ι_preservesColimitIso_hom_assoc, ι_preservesColimitIso_hom_assoc,
     HasColimit.isoOfNatIso_ι_hom_assoc, HasColimit.isoOfNatIso_ι_hom_assoc,
     TopCat.sigmaIsoSigma_hom_ι, TopCat.sigmaIsoSigma_hom_ι] at eq
-  convert h (congr_arg Discrete.mk (congr_arg Sigma.fst eq))
+  convert! h (congr_arg Discrete.mk (congr_arg Sigma.fst eq))
 
 set_option backward.isDefEq.respectTransparency false in
 instance sigma_ι_isOpenImmersion_aux [HasStrictTerminalObjects C] :
@@ -924,11 +924,11 @@ instance sigma_ι_isOpenImmersion_aux [HasStrictTerminalObjects C] :
         (colimit.ι (F ⋙ SheafedSpace.forgetToPresheafedSpace) i ≫
             (preservesColimitIso SheafedSpace.forgetToPresheafedSpace F).inv).base := by
       have := h₁.symm
-      convert sigma_ι_isOpenEmbedding F i
+      convert! sigma_ι_isOpenEmbedding F i
     suffices IsIso <| (colimit.ι (F ⋙ SheafedSpace.forgetToPresheafedSpace) i ≫
         (preservesColimitIso SheafedSpace.forgetToPresheafedSpace F).inv).c.app <|
       op (H.functor.obj U) by
-      convert this
+      convert! this
     rw [PresheafedSpace.comp_c_app,
       ← PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_hom_π]
     -- Porting note: this instance created manually to make the `inferInstance` below work
@@ -940,8 +940,8 @@ instance sigma_ι_isOpenImmersion_aux [HasStrictTerminalObjects C] :
     apply limit_π_isIso_of_is_strict_terminal
     rintro ⟨j⟩ hj
     dsimp
-    convert (F.obj j).sheaf.isTerminalOfEmpty using 3
-    convert image_preimage_is_empty F i j (fun h => hj (congr_arg op h.symm)) U using 6
+    convert! (F.obj j).sheaf.isTerminalOfEmpty using 3
+    convert! image_preimage_is_empty F i j (fun h => hj (congr_arg op h.symm)) U using 6
     exact congr_arg PresheafedSpace.Hom.base h₁
 
 set_option backward.isDefEq.respectTransparency false in
diff --git a/Mathlib/Geometry/RingedSpace/PresheafedSpace/Gluing.lean b/Mathlib/Geometry/RingedSpace/PresheafedSpace/Gluing.lean
index 9ab7b6f40b6d4f..ccf902adb37af0 100644
--- a/Mathlib/Geometry/RingedSpace/PresheafedSpace/Gluing.lean
+++ b/Mathlib/Geometry/RingedSpace/PresheafedSpace/Gluing.lean
@@ -163,7 +163,7 @@ theorem f_invApp_f_app (i j k : D.J) (U : Opens (D.V (i, j)).carrier) :
   erw [(π₁ i, j, k).c.naturality_assoc, reassoc_of% this, ← Functor.map_comp_assoc,
     IsOpenImmersion.inv_naturality_assoc, IsOpenImmersion.app_invApp_assoc, ←
     (D.V (i, k)).presheaf.map_comp, ← (D.V (i, k)).presheaf.map_comp]
-  convert (Category.comp_id _).symm
+  convert! (Category.comp_id _).symm
   erw [(D.V (i, k)).presheaf.map_id]
   rfl
 
@@ -395,7 +395,7 @@ theorem ιInvApp_π {i : D.J} (U : Opens (D.U i).carrier) :
     simp only [SetLike.mem_coe, unop_op, Set.mem_preimage, Set.mem_image]
     refine ⟨fun h => ⟨_, h, rfl⟩, ?_⟩
     rintro ⟨y, h1, h2⟩
-    convert h1 using 1
+    convert! h1 using 1
     delta ι Multicoequalizer.π at h2
     apply_fun (D.ι _).base
     · exact h2.symm
@@ -444,7 +444,7 @@ theorem π_ιInvApp_π (i j : D.J) (U : Opens (D.U i).carrier) :
     iterate 3 rw [← Functor.map_comp_assoc]
     rw [NatTrans.naturality_assoc]
     erw [← (D.V (i, j)).presheaf.map_comp]
-    convert
+    convert!
       limit.w (componentwiseDiagram 𝖣.diagram.multispan _)
         (Quiver.Hom.op (WalkingMultispan.Hom.fst (i, j)))
   · rw [Category.comp_id]
diff --git a/Mathlib/GroupTheory/ArchimedeanDensely.lean b/Mathlib/GroupTheory/ArchimedeanDensely.lean
index bb5164b750ff67..33f0079d4fc41e 100644
--- a/Mathlib/GroupTheory/ArchimedeanDensely.lean
+++ b/Mathlib/GroupTheory/ArchimedeanDensely.lean
@@ -166,7 +166,7 @@ lemma Subgroup.isLeast_of_closure_iff_eq_mabs {a b : G} :
     rcases key with ⟨rfl, rfl⟩ | ⟨rfl, rfl⟩ <;>
     simp [this.right.le, this.right, mabs]
   · wlog ha : 1 ≤ a generalizing a
-    · convert @this (a⁻¹) ?_ (by simpa using le_of_not_ge ha) using 4
+    · convert! @this (a⁻¹) ?_ (by simpa using le_of_not_ge ha) using 4
       · simp
       · rwa [mabs_inv]
     rw [mabs, sup_eq_left.mpr ((inv_le_one'.mpr ha).trans ha)] at h
diff --git a/Mathlib/GroupTheory/ClassEquation.lean b/Mathlib/GroupTheory/ClassEquation.lean
index cde16a2e95a5de..feb3494aeb895b 100644
--- a/Mathlib/GroupTheory/ClassEquation.lean
+++ b/Mathlib/GroupTheory/ClassEquation.lean
@@ -56,7 +56,7 @@ theorem Group.nat_card_center_add_sum_card_noncenter_eq_card [Finite G] :
   simp only [Nat.card_eq_fintype_card, Set.toFinset_card]
   congr 1
   swap
-  · convert finsum_cond_eq_sum_of_cond_iff _ _
+  · convert! finsum_cond_eq_sum_of_cond_iff _ _
     simp [Set.mem_toFinset]
   calc
     Fintype.card (Subgroup.center G) = Fintype.card ((noncenter G)ᶜ : Set _) :=
@@ -76,7 +76,7 @@ theorem Group.card_center_add_sum_card_noncenter_eq_card (G) [Group G]
     [∀ x : ConjClasses G, Fintype x.carrier] [Fintype G] [Fintype <| Subgroup.center G]
     [Fintype <| noncenter G] : Fintype.card (Subgroup.center G) +
     ∑ x ∈ (noncenter G).toFinset, x.carrier.toFinset.card = Fintype.card G := by
-  convert Group.nat_card_center_add_sum_card_noncenter_eq_card G using 2
+  convert! Group.nat_card_center_add_sum_card_noncenter_eq_card G using 2
   · simp
   · rw [← finsum_set_coe_eq_finsum_mem (noncenter G), finsum_eq_sum_of_fintype,
       ← Finset.sum_set_coe]
diff --git a/Mathlib/GroupTheory/Complement.lean b/Mathlib/GroupTheory/Complement.lean
index cc978efcf9a40c..1a64cb08eb93a1 100644
--- a/Mathlib/GroupTheory/Complement.lean
+++ b/Mathlib/GroupTheory/Complement.lean
@@ -196,7 +196,7 @@ theorem isComplement'_top_right : IsComplement' H ⊤ ↔ H = ⊥ :=
 @[to_additive]
 lemma isComplement_iff_existsUnique_inv_mul_mem :
     IsComplement S T ↔ ∀ g, ∃! s : S, (s : G)⁻¹ * g ∈ T := by
-  convert isComplement_iff_existsUnique with g
+  convert! isComplement_iff_existsUnique with g
   constructor <;> rintro ⟨x, hx, hx'⟩
   · exact ⟨(x, ⟨_, hx⟩), by simp, by aesop⟩
   · exact ⟨x.1, by simp [← hx], fun y hy ↦ (Prod.ext_iff.1 <| by simpa using hx' (y, ⟨_, hy⟩)).1⟩
@@ -204,7 +204,7 @@ lemma isComplement_iff_existsUnique_inv_mul_mem :
 @[to_additive]
 lemma isComplement_iff_existsUnique_mul_inv_mem :
     IsComplement S T ↔ ∀ g, ∃! t : T, g * (t : G)⁻¹ ∈ S := by
-  convert isComplement_iff_existsUnique with g
+  convert! isComplement_iff_existsUnique with g
   constructor <;> rintro ⟨x, hx, hx'⟩
   · exact ⟨(⟨_, hx⟩, x), by simp, by aesop⟩
   · exact ⟨x.2, by simp [← hx], fun y hy ↦ (Prod.ext_iff.1 <| by simpa using hx' (⟨_, hy⟩, y)).2⟩
diff --git a/Mathlib/GroupTheory/Coset/Basic.lean b/Mathlib/GroupTheory/Coset/Basic.lean
index 0437c2e2a3084d..fbfae8c16c679c 100644
--- a/Mathlib/GroupTheory/Coset/Basic.lean
+++ b/Mathlib/GroupTheory/Coset/Basic.lean
@@ -285,7 +285,7 @@ theorem strictMono_comap_prod_image :
   refine fun t₁ t₂ h ↦ ⟨⟨Subgroup.comap_mono h.1, Set.image_mono h.1⟩,
     mt (fun ⟨le1, le2⟩ a ha ↦ ?_) h.2⟩
   obtain ⟨a', h', eq⟩ := le2 ⟨_, ha, rfl⟩
-  convert ← t₁.mul_mem h' (@le1 ⟨_, QuotientGroup.eq.1 eq⟩ <| t₂.mul_mem (t₂.inv_mem <| h.1 h') ha)
+  convert! ← t₁.mul_mem h' (@le1 ⟨_, QuotientGroup.eq.1 eq⟩ <| t₂.mul_mem (t₂.inv_mem <| h.1 h') ha)
   apply mul_inv_cancel_left
 
 variable {s} {a b : α}
diff --git a/Mathlib/GroupTheory/Coset/Card.lean b/Mathlib/GroupTheory/Coset/Card.lean
index cc0791975027ad..56fd7b146f712a 100644
--- a/Mathlib/GroupTheory/Coset/Card.lean
+++ b/Mathlib/GroupTheory/Coset/Card.lean
@@ -60,7 +60,7 @@ lemma card_mul_eq_card_subgroup_mul_card_quotient (s : Subgroup α) (t : Set α)
   rw [← Nat.card_prod, Nat.card_congr]
   apply Equiv.trans _ (QuotientGroup.preimageMkEquivSubgroupProdSet _ _)
   rw [QuotientGroup.preimage_image_mk]
-  convert Equiv.refl ↑(t * s)
+  convert! Equiv.refl ↑(t * s)
   aesop (add simp [Set.mem_mul])
 
 /-- **Lagrange's Theorem**: The order of a subgroup divides the order of its ambient group. -/
diff --git a/Mathlib/GroupTheory/Coxeter/Inversion.lean b/Mathlib/GroupTheory/Coxeter/Inversion.lean
index 89718224b961a6..43ab142b541a9a 100644
--- a/Mathlib/GroupTheory/Coxeter/Inversion.lean
+++ b/Mathlib/GroupTheory/Coxeter/Inversion.lean
@@ -138,7 +138,7 @@ theorem isRightInversion_inv_iff {w t : W} :
 
 theorem isLeftInversion_inv_iff {w t : W} :
     cs.IsLeftInversion w⁻¹ t ↔ cs.IsRightInversion w t := by
-  convert cs.isRightInversion_inv_iff.symm
+  convert! cs.isRightInversion_inv_iff.symm
   simp
 
 namespace IsReflection
diff --git a/Mathlib/GroupTheory/DivisibleHull.lean b/Mathlib/GroupTheory/DivisibleHull.lean
index 21eaebe088f68c..478bdce543d11d 100644
--- a/Mathlib/GroupTheory/DivisibleHull.lean
+++ b/Mathlib/GroupTheory/DivisibleHull.lean
@@ -143,7 +143,7 @@ theorem nsmul_mk (a : ℕ) (m : M) (s : ℕ+) : a • mk m s = mk (a • m) s :=
 
 theorem nnqsmul_mk (a : ℚ≥0) (m : M) (s : ℕ+) :
     a • mk m s = mk (a.num • m) (⟨a.den, a.den_pos⟩ * s) := by
-  convert LocalizedModule.mk'_smul_mk ℚ≥0 a.num m ⟨a.den, by simp⟩ (↑ⁿ s)
+  convert! LocalizedModule.mk'_smul_mk ℚ≥0 a.num m ⟨a.den, by simp⟩ (↑ⁿ s)
   simp [IsLocalization.eq_mk'_iff_mul_eq]
 
 section TorsionFree
@@ -223,7 +223,7 @@ instance : Module ℚ (DivisibleHull M) where
     use 1
     suffices ((a + b).num * a.den * b.den * (s * s)) • m =
         ((a.num * b.den + b.num * a.den) * (a + b).den * (s * s)) • m by
-      convert this using 1
+      convert! this using 1
       all_goals
       simp [← natCast_zsmul, smul_smul, ← add_smul]
       ring_nf
@@ -233,7 +233,7 @@ instance : Module ℚ (DivisibleHull M) where
     simp_rw [qsmul_mk, mk_eq_mk]
     use 1
     suffices ((a * b).num * a.den * b.den * s) • m = (a.num * b.num * (a * b).den * s) • m by
-      convert this using 1
+      convert! this using 1
       all_goals
       simp [← natCast_zsmul, smul_smul]
       ring_nf
@@ -253,7 +253,7 @@ private theorem lift_aux (m n m' n' : M) (s t s' t' : ℕ+)
     (t.val • m ≤ s.val • n) = (t'.val • m' ≤ s'.val • n') := by
   rw [mk_eq_mk_iff_smul_eq_smul] at h h'
   rw [propext_iff, ← nsmul_le_nsmul_iff_right (mul_ne_zero s'.ne_zero t'.ne_zero)]
-  convert (nsmul_le_nsmul_iff_right (M := M) (mul_ne_zero s.ne_zero t.ne_zero)) using 2
+  convert! (nsmul_le_nsmul_iff_right (M := M) (mul_ne_zero s.ne_zero t.ne_zero)) using 2
   · simp_rw [smul_smul, mul_rotate s'.val, ← smul_smul, h, smul_smul]
     ring_nf
   · simp_rw [smul_smul, ← mul_rotate s'.val, ← smul_smul, ← h', smul_smul]
@@ -310,7 +310,7 @@ instance : IsOrderedCancelAddMonoid (DivisibleHull M) :=
     simp_rw [PNat.mul_coe, mul_smul, smul_add, smul_smul]
     have := add_lt_add_right (nsmul_lt_nsmul_right (sa * sa).ne_zero h) ((sa * sb * sc.val) • ma)
     simp_rw [PNat.mul_coe, smul_smul] at this
-    convert this using 3 <;> ring)
+    convert! this using 3 <;> ring)
 
 instance : IsStrictOrderedModule ℚ≥0 (DivisibleHull M) where
   smul_lt_smul_of_pos_left a ha b c h := by
@@ -324,7 +324,7 @@ instance : IsStrictOrderedModule ℚ≥0 (DivisibleHull M) where
     induction a with | mk m s
     simp_rw [nnqsmul_mk, mk_lt_mk, smul_smul, PNat.mul_coe, PNat.mk_coe]
     refine smul_lt_smul_of_pos_right ?_ ?_
-    · convert mul_lt_mul_of_pos_right (NNRat.lt_def.mp h) (show 0 < s.val by simp) using 1 <;> ring
+    · convert! mul_lt_mul_of_pos_right (NNRat.lt_def.mp h) (show 0 < s.val by simp) using 1 <;> ring
     · rw [← mk_zero 1, mk_lt_mk] at ha
       simpa using ha
 
diff --git a/Mathlib/GroupTheory/Finiteness.lean b/Mathlib/GroupTheory/Finiteness.lean
index 9d59e20a9f5827..b23c7420082cfc 100644
--- a/Mathlib/GroupTheory/Finiteness.lean
+++ b/Mathlib/GroupTheory/Finiteness.lean
@@ -75,7 +75,7 @@ theorem Submonoid.fg_iff_add_fg (P : Submonoid M) : P.FG ↔ P.toAddSubmonoid.FG
 
 theorem AddSubmonoid.fg_iff_mul_fg {M : Type*} [AddMonoid M] (P : AddSubmonoid M) :
     P.FG ↔ P.toSubmonoid.FG := by
-  convert (Submonoid.fg_iff_add_fg (toSubmonoid P)).symm
+  convert! (Submonoid.fg_iff_add_fg (toSubmonoid P)).symm
 
 @[to_additive]
 theorem Submonoid.FG.bot : FG (⊥ : Submonoid M) :=
diff --git a/Mathlib/GroupTheory/FreeAbelianGroup.lean b/Mathlib/GroupTheory/FreeAbelianGroup.lean
index 86c2d955ee513e..fbbabf07e4941e 100644
--- a/Mathlib/GroupTheory/FreeAbelianGroup.lean
+++ b/Mathlib/GroupTheory/FreeAbelianGroup.lean
@@ -122,8 +122,7 @@ open FreeAbelianGroup
 -- Porting note: needed to add `(β := Multiplicative β)`
 @[simp]
 theorem lift_apply_of (x : α) : lift f (of x) = f x := by
-  convert Abelianization.lift_apply_of
-     (FreeGroup.lift f (β := Multiplicative β)) (FreeGroup.of x)
+  convert! Abelianization.lift_apply_of (FreeGroup.lift f (β := Multiplicative β)) (FreeGroup.of x)
   exact (FreeGroup.lift_apply_of (β := Multiplicative β)).symm
 
 theorem lift_unique (g : FreeAbelianGroup α →+ β) (hg : ∀ x, g (of x) = f x) {x} :
diff --git a/Mathlib/GroupTheory/FreeGroup/NielsenSchreier.lean b/Mathlib/GroupTheory/FreeGroup/NielsenSchreier.lean
index 23ac03c96b7442..9f238a21620d71 100644
--- a/Mathlib/GroupTheory/FreeGroup/NielsenSchreier.lean
+++ b/Mathlib/GroupTheory/FreeGroup/NielsenSchreier.lean
@@ -128,7 +128,7 @@ instance actionGroupoidIsFree {G A : Type u} [Group G] [IsFreeGroup G] [MulActio
         apply uF'
         intro e
         ext
-        · convert hE _ _ _
+        · convert! hE _ _ _
           rfl
         · rfl
       apply Functor.hext
diff --git a/Mathlib/GroupTheory/Goursat.lean b/Mathlib/GroupTheory/Goursat.lean
index 42bf3ae9057a16..1a630276856a2a 100644
--- a/Mathlib/GroupTheory/Goursat.lean
+++ b/Mathlib/GroupTheory/Goursat.lean
@@ -168,7 +168,7 @@ lemma goursat :
       rintro h₁ hgh₁ g₁ hg₁h g₂ h₂ hg₂h₂ hP hQ
       simp only [Subtype.ext_iff] at hP hQ
       rwa [← hP, ← hQ]
-  · convert goursatFst_prod_goursatSnd_le (P.prod Q).range
+  · convert! goursatFst_prod_goursatSnd_le (P.prod Q).range
     ext ⟨g, h⟩
     simp_rw [G', H', MonoidHom.mem_ker, MonoidHom.coe_prodMap, Prod.map_apply, Subgroup.mem_prod,
       Prod.one_eq_mk, Prod.ext_iff, ← MonoidHom.mem_ker, QuotientGroup.ker_mk']
diff --git a/Mathlib/GroupTheory/GroupAction/Blocks.lean b/Mathlib/GroupTheory/GroupAction/Blocks.lean
index a7927e318bb7bb..7fc7ad60625867 100644
--- a/Mathlib/GroupTheory/GroupAction/Blocks.lean
+++ b/Mathlib/GroupTheory/GroupAction/Blocks.lean
@@ -158,7 +158,7 @@ theorem IsTrivialBlock.smul_iff {B : Set α} (g : M) :
     IsTrivialBlock (g • B) ↔ IsTrivialBlock B := by
   constructor
   · intro H
-    convert IsTrivialBlock.smul H g⁻¹
+    convert! IsTrivialBlock.smul H g⁻¹
     simp only [inv_smul_smul]
   · intro H
     exact IsTrivialBlock.smul H g
diff --git a/Mathlib/GroupTheory/GroupAction/Defs.lean b/Mathlib/GroupTheory/GroupAction/Defs.lean
index 99992783736e57..f3764ac6821cee 100644
--- a/Mathlib/GroupTheory/GroupAction/Defs.lean
+++ b/Mathlib/GroupTheory/GroupAction/Defs.lean
@@ -308,7 +308,7 @@ theorem quotient_preimage_image_eq_union_mul (U : Set α) :
     rw [Set.mem_preimage, Set.mem_image]
     refine ⟨g⁻¹ • a, ?_, by simp +instances [f, orbitRel, Quotient.eq']⟩
     rw [← hu₂]
-    convert hu₁
+    convert! hu₁
     simp only [inv_smul_smul]
 
 @[to_additive]
@@ -439,13 +439,13 @@ lemma orbitRel.Quotient.mem_subgroup_orbit_iff' {H : Subgroup G} {x : orbitRel.Q
     {a b : x.orbit} {c : α} (h : (⟦a⟧ : orbitRel.Quotient H x.orbit) = ⟦b⟧) :
     (a : α) ∈ MulAction.orbit H c ↔ (b : α) ∈ MulAction.orbit H c := by
   simp_rw [mem_orbit_symm (a₂ := c)]
-  convert Iff.rfl using 2
+  convert! Iff.rfl using 2
   rw [orbit_eq_iff]
   suffices hb : ↑b ∈ orbitRel.Quotient.orbit (⟦a⟧ : orbitRel.Quotient H x.orbit) by
     rw [orbitRel.Quotient.orbit_eq_orbit_out (⟦a⟧ : orbitRel.Quotient H x.orbit) Quotient.out_eq']
        at hb
     rw [orbitRel.Quotient.mem_subgroup_orbit_iff]
-    convert hb using 1
+    convert! hb using 1
     rw [orbit_eq_iff, ← orbitRel_apply, ← Quotient.eq'', Quotient.out_eq', @Quotient.mk''_eq_mk]
   rw [orbitRel.Quotient.mem_orbit, h, @Quotient.mk''_eq_mk]
 
diff --git a/Mathlib/GroupTheory/GroupAction/Jordan.lean b/Mathlib/GroupTheory/GroupAction/Jordan.lean
index d114e849b6d444..c22dcadf933ecf 100644
--- a/Mathlib/GroupTheory/GroupAction/Jordan.lean
+++ b/Mathlib/GroupTheory/GroupAction/Jordan.lean
@@ -414,7 +414,7 @@ theorem subgroup_eq_top_of_isPreprimitive_of_isSwap_mem
   · rw [hn]; apply Nat.lt_add_one
   have := isPretransitive_of_isCycle_mem h2g.isCycle hg
   apply IsPreprimitive.of_prime_card
-  convert Nat.prime_two
+  convert! Nat.prime_two
   rw [Nat.card_eq_fintype_card, Fintype.card_subtype, ← card_support_eq_two.mpr h2g]
   simp [SubMulAction.mem_ofFixingSubgroup_iff, support]
 
@@ -451,7 +451,7 @@ theorem alternatingGroup_le_of_isPreprimitive_of_isThreeCycle_mem
   · grind
   have := isPretransitive_of_isCycle_mem h3g.isCycle hg
   apply IsPreprimitive.of_prime_card
-  convert Nat.prime_three
+  convert! Nat.prime_three
   rw [Nat.card_eq_fintype_card, Fintype.card_subtype, ← h3g.card_support]
   apply congr_arg
   ext x
diff --git a/Mathlib/GroupTheory/GroupAction/MultipleTransitivity.lean b/Mathlib/GroupTheory/GroupAction/MultipleTransitivity.lean
index 7f93eefe06c2ca..f7a6d09eefbdfd 100644
--- a/Mathlib/GroupTheory/GroupAction/MultipleTransitivity.lean
+++ b/Mathlib/GroupTheory/GroupAction/MultipleTransitivity.lean
@@ -358,7 +358,7 @@ theorem isMultiplyPretransitive [IsPretransitive G α] {n : ℕ} {a : α} :
   · obtain ⟨g, hgxy⟩ := exists_smul_eq G (ofStabilizer.snoc x) (ofStabilizer.snoc y)
     have hg : g ∈ stabilizer G a := by
       rw [DFunLike.ext_iff] at hgxy
-      convert hgxy (last n)
+      convert! hgxy (last n)
       simp [ofStabilizer.snoc_last]
     use ⟨g, hg⟩
     ext i
@@ -476,7 +476,7 @@ theorem IsMultiplyPretransitive.index_of_fixingSubgroup_mul
     have htcard : t.ncard = k := by
       rw [← Nat.succ_inj, Nat.succ_eq_add_one, Nat.succ_eq_add_one, ← hs, hat', eq_comm]
       suffices ¬ a ∈ (Subtype.val '' t) by
-        convert Set.ncard_insert_of_notMem this ?_
+        convert! Set.ncard_insert_of_notMem this ?_
         · rw [Set.ncard_image_of_injective _ Subtype.coe_injective]
         apply Set.toFinite
       intro h
@@ -489,7 +489,7 @@ theorem IsMultiplyPretransitive.index_of_fixingSubgroup_mul
       rw [add_comm k, Nat.mul_right_comm, ← Nat.sub_sub, this, mul_comm,
         index_stabilizer_of_transitive G a]
       exact Nat.mul_factorial_pred (card_ne_zero.mpr ⟨⟨a⟩, inferInstance⟩)
-    convert hrec (ofStabilizer.isMultiplyPretransitive.mp Hk) htcard
+    convert! hrec (ofStabilizer.isMultiplyPretransitive.mp Hk) htcard
     all_goals { rw [nat_card_ofStabilizer_eq G a] }
 
 /-- For a multiply pretransitive action,
diff --git a/Mathlib/GroupTheory/GroupAction/Quotient.lean b/Mathlib/GroupTheory/GroupAction/Quotient.lean
index ebdc6fb14b39ed..083893be40f6ab 100644
--- a/Mathlib/GroupTheory/GroupAction/Quotient.lean
+++ b/Mathlib/GroupTheory/GroupAction/Quotient.lean
@@ -167,7 +167,7 @@ theorem injective_ofQuotientStabilizer : Function.Injective (ofQuotientStabilize
 noncomputable def orbitEquivQuotientStabilizer (b : β) : orbit α b ≃ α ⧸ stabilizer α b :=
   Equiv.symm <|
     Equiv.ofBijective (fun g => ⟨ofQuotientStabilizer α b g, ofQuotientStabilizer_mem_orbit α b g⟩)
-      ⟨fun x y hxy => injective_ofQuotientStabilizer α b (by convert congr_arg Subtype.val hxy),
+      ⟨fun x y hxy => injective_ofQuotientStabilizer α b (by convert! congr_arg Subtype.val hxy),
         fun ⟨_, ⟨g, hgb⟩⟩ => ⟨g, Subtype.ext hgb⟩⟩
 
 /-- Orbit-stabilizer theorem. -/
@@ -369,14 +369,14 @@ noncomputable def equivSubgroupOrbitsQuotientGroup [IsPretransitive α β]
     cases y using Quotient.inductionOn'
     simp only [Quotient.liftOn'_mk'']
     rw [← @Quotient.mk''_eq_mk, Quotient.eq'', orbitRel_apply]
-    convert mem_orbit_self _
+    convert! mem_orbit_self _
     rw [inv_smul_eq_iff, (exists_smul_eq α _ x).choose_spec]
   right_inv := fun g ↦ by
     cases g using Quotient.inductionOn' with | _ g
     simp only [Quotient.liftOn'_mk'', QuotientGroup.mk]
     rw [Quotient.eq'', leftRel_eq]
     simp only
-    convert one_mem H
+    convert! one_mem H
     rw [inv_mul_eq_one, eq_comm, ← inv_mul_eq_one, ← Subgroup.mem_bot,
         ← IsCancelSMul.stabilizer_eq_bot (g⁻¹ • x), mem_stabilizer_iff, mul_smul,
         (exists_smul_eq α (g⁻¹ • x) x).choose_spec]
diff --git a/Mathlib/GroupTheory/GroupAction/SubMulAction/OfStabilizer.lean b/Mathlib/GroupTheory/GroupAction/SubMulAction/OfStabilizer.lean
index adb60ed349d257..8ddb6a714c3d43 100644
--- a/Mathlib/GroupTheory/GroupAction/SubMulAction/OfStabilizer.lean
+++ b/Mathlib/GroupTheory/GroupAction/SubMulAction/OfStabilizer.lean
@@ -232,7 +232,7 @@ variable (G : Type*) [Group G] (α : Type*) [MulAction G α]
 instance _root_.SMul.ofStabilizer (s : Set α) :
     SMul (stabilizer G s) s where
   smul g x := ⟨g • ↑x, by
-    convert Set.smul_mem_smul_set x.prop
+    convert! Set.smul_mem_smul_set x.prop
     exact (mem_stabilizer_iff.mp g.prop).symm⟩
 
 @[simp]
diff --git a/Mathlib/GroupTheory/HNNExtension.lean b/Mathlib/GroupTheory/HNNExtension.lean
index f6bcb03ab30f49..c9d218788c3fa2 100644
--- a/Mathlib/GroupTheory/HNNExtension.lean
+++ b/Mathlib/GroupTheory/HNNExtension.lean
@@ -160,7 +160,7 @@ and `toSubgroupEquiv` is the group isomorphism from `toSubgroup A B u` to `toSub
 It is defined to be `φ` when `u = 1` and `φ⁻¹` when `u = -1`. -/
 def toSubgroupEquiv (u : ℤˣ) : toSubgroup A B u ≃* toSubgroup A B (-u) :=
   if hu : u = 1 then hu ▸ φ else by
-    convert φ.symm <;>
+    convert! φ.symm <;>
     cases Int.units_eq_one_or u <;> simp_all
 
 @[simp]
@@ -449,7 +449,7 @@ noncomputable def unitsSMulEquiv : NormalWord d ≃ NormalWord d :=
   { toFun := unitsSMul φ 1
     invFun := unitsSMul φ (-1),
     left_inv := fun _ => by rw [unitsSMul_neg]
-    right_inv := fun w => by convert unitsSMul_neg _ _ w; simp }
+    right_inv := fun w => by convert! unitsSMul_neg _ _ w; simp }
 
 set_option backward.isDefEq.respectTransparency false in
 theorem unitsSMul_one_group_smul (g : A) (w : NormalWord d) :
diff --git a/Mathlib/GroupTheory/Index.lean b/Mathlib/GroupTheory/Index.lean
index df318f9dc7fd78..a0bf0a289123cc 100644
--- a/Mathlib/GroupTheory/Index.lean
+++ b/Mathlib/GroupTheory/Index.lean
@@ -566,7 +566,7 @@ lemma exists_pow_mem_of_index_ne_zero (h : H.index ≠ 0) (a : G) :
     rw [eq_comm, QuotientGroup.eq, ← zpow_natCast, ← zpow_natCast, ← zpow_neg, ← zpow_add,
         add_comm] at he
     rw [← zpow_natCast]
-    convert he
+    convert! he
     lia
   suffices ∃ n₁ n₂, n₁ ≠ n₂ ∧ n₁ ≤ H.index ∧ n₂ ≤ H.index ∧
       ((a ^ n₂ : G) : G ⧸ H) = ((a ^ n₁ : G) : G ⧸ H) by
@@ -604,7 +604,7 @@ lemma pow_mem_of_index_ne_zero_of_dvd (h : H.index ≠ 0) (a : G) {n : ℕ}
 @[to_additive]
 lemma pow_mem_of_relIndex_ne_zero_of_dvd (h : H.relIndex K ≠ 0) {a : G} (ha : a ∈ K) {n : ℕ}
     (hn : ∀ m, 0 < m → m ≤ H.relIndex K → m ∣ n) : a ^ n ∈ H ⊓ K := by
-  convert pow_mem_of_index_ne_zero_of_dvd h ⟨a, ha⟩ hn
+  convert! pow_mem_of_index_ne_zero_of_dvd h ⟨a, ha⟩ hn
   simp [pow_mem ha, mem_subgroupOf]
 
 @[to_additive (attr := simp) index_prod]
diff --git a/Mathlib/GroupTheory/IndexNormal.lean b/Mathlib/GroupTheory/IndexNormal.lean
index 15d5a65affcf7e..ca0bb1d7e3db47 100644
--- a/Mathlib/GroupTheory/IndexNormal.lean
+++ b/Mathlib/GroupTheory/IndexNormal.lean
@@ -51,7 +51,7 @@ theorem normal_of_index_eq_minFac_card (hHp : H.index = (Nat.card G).minFac) :
   · rw [hG1, minFac_one] at hHp
     exact normal_of_index_eq_one hHp
   suffices H.normalCore.relIndex H = 1 by
-    convert H.normalCore_normal
+    convert! H.normalCore_normal
     exact le_antisymm (relIndex_eq_one.mp this) (normalCore_le H)
   have : Finite G := finite_of_card_ne_zero hG0
   have index_ne_zero : H.index ≠ 0 := index_ne_zero_of_finite
diff --git a/Mathlib/GroupTheory/MonoidLocalization/Basic.lean b/Mathlib/GroupTheory/MonoidLocalization/Basic.lean
index 0b4b4875036959..240ed345434169 100644
--- a/Mathlib/GroupTheory/MonoidLocalization/Basic.lean
+++ b/Mathlib/GroupTheory/MonoidLocalization/Basic.lean
@@ -181,7 +181,7 @@ theorem r_eq_r' : r S = r' S :=
     le_sInf fun b H ⟨p, q⟩ ⟨x, y⟩ ⟨t, ht⟩ ↦ by
       rw [← one_mul (p, q), ← one_mul (x, y)]
       refine b.trans (b.mul (H (t * y)) (b.refl _)) ?_
-      convert b.symm (b.mul (H (t * q)) (b.refl (x, y))) using 1
+      convert! b.symm (b.mul (H (t * q)) (b.refl (x, y))) using 1
       dsimp only [Prod.mk_mul_mk, Submonoid.coe_mul] at ht ⊢
       simp_rw [mul_assoc, ht, mul_comm y q]
 
diff --git a/Mathlib/GroupTheory/MonoidLocalization/GrothendieckGroup.lean b/Mathlib/GroupTheory/MonoidLocalization/GrothendieckGroup.lean
index 80dafe76c8b08b..4fe295b7bccc1a 100644
--- a/Mathlib/GroupTheory/MonoidLocalization/GrothendieckGroup.lean
+++ b/Mathlib/GroupTheory/MonoidLocalization/GrothendieckGroup.lean
@@ -65,7 +65,7 @@ instance instCommGroup : CommGroup (GrothendieckGroup M) where
   inv_mul_cancel a := by
     cases a using ind
     rw [inv_mk, mk_eq_monoidOf_mk', ← Submonoid.LocalizationMap.mk'_mul]
-    convert Submonoid.LocalizationMap.mk'_self' _ _
+    convert! Submonoid.LocalizationMap.mk'_self' _ _
     rw [mul_comm, Submonoid.coe_mul]
 
 @[to_additive (attr := simp)]
diff --git a/Mathlib/GroupTheory/Nilpotent.lean b/Mathlib/GroupTheory/Nilpotent.lean
index 1411471484b394..f0207360983e20 100644
--- a/Mathlib/GroupTheory/Nilpotent.lean
+++ b/Mathlib/GroupTheory/Nilpotent.lean
@@ -98,7 +98,7 @@ def upperCentralSeriesStep : Subgroup G where
   carrier := { x : G | ∀ y : G, ⁅x, y⁆ ∈ H }
   one_mem' y := by simp
   mul_mem' {a b} ha hb y := by
-    convert Subgroup.mul_mem _ (ha (b * y * b⁻¹)) (hb y) using 1
+    convert! Subgroup.mul_mem _ (ha (b * y * b⁻¹)) (hb y) using 1
     group
   inv_mem' {x} hx y := by
     specialize hx y⁻¹
@@ -343,7 +343,7 @@ theorem is_descending_rev_series_of_is_ascending {H : ℕ → Subgroup G} {n : 
     rw [commutatorElement_one_left]
     exact Subgroup.one_mem _
   · apply hH
-    convert hx using 1
+    convert! hx using 1
     rw [tsub_add_eq_add_tsub (Nat.succ_le_of_lt hm), Nat.succ_eq_add_one, Nat.add_sub_add_right]
 
 @[to_additive]
@@ -356,7 +356,7 @@ theorem is_ascending_rev_series_of_is_descending {H : ℕ → Subgroup G} {n : 
   · have hnm : n - m = 0 := tsub_eq_zero_iff_le.mpr hm
     rw [hnm, h0]
     exact mem_top _
-  · convert hH x _ hx g using 1
+  · convert! hH x _ hx g using 1
     rw [tsub_add_eq_add_tsub (Nat.succ_le_of_lt hm), Nat.succ_eq_add_one, Nat.add_sub_add_right]
 
 /-- A group `G` is nilpotent iff there exists a descending central series which reaches the
diff --git a/Mathlib/GroupTheory/NoncommPiCoprod.lean b/Mathlib/GroupTheory/NoncommPiCoprod.lean
index 54d36addcd1b4f..bf213e8c34802c 100644
--- a/Mathlib/GroupTheory/NoncommPiCoprod.lean
+++ b/Mathlib/GroupTheory/NoncommPiCoprod.lean
@@ -108,7 +108,7 @@ def noncommPiCoprod : (∀ i : ι, N i) →* M where
     simp
   map_mul' f g := by
     classical
-    convert @Finset.noncommProd_mul_distrib _ _ _ _ (fun i => ϕ i (f i)) (fun i => ϕ i (g i)) _ _ _
+    convert! @Finset.noncommProd_mul_distrib _ _ _ _ (fun i => ϕ i (f i)) (fun i => ϕ i (g i)) _ _ _
     · exact map_mul _ _ _
     · rintro i - j - h
       exact hcomm h _ _
diff --git a/Mathlib/GroupTheory/OrderOfElement.lean b/Mathlib/GroupTheory/OrderOfElement.lean
index b6f9f4d027381f..23bbec6f425dd4 100644
--- a/Mathlib/GroupTheory/OrderOfElement.lean
+++ b/Mathlib/GroupTheory/OrderOfElement.lean
@@ -198,7 +198,7 @@ protected lemma IsOfFinOrder.orderOf_pos (h : IsOfFinOrder x) : 0 < orderOf x :=
 
 @[to_additive (attr := simp) addOrderOf_nsmul_eq_zero]
 theorem pow_orderOf_eq_one (x : G) : x ^ orderOf x = 1 := by
-  convert Eq.trans _ (isPeriodicPt_minimalPeriod (x * ·) 1)
+  convert! Eq.trans _ (isPeriodicPt_minimalPeriod (x * ·) 1)
   rw [orderOf, mul_left_iterate_apply_one]
 
 @[to_additive]
diff --git a/Mathlib/GroupTheory/OreLocalization/Cardinality.lean b/Mathlib/GroupTheory/OreLocalization/Cardinality.lean
index 24ba3f64e12da4..92d6feb5aa44ce 100644
--- a/Mathlib/GroupTheory/OreLocalization/Cardinality.lean
+++ b/Mathlib/GroupTheory/OreLocalization/Cardinality.lean
@@ -75,14 +75,14 @@ theorem cardinalMk_le_max : #(OreLocalization S X) ≤ max (lift.{v} #S) (lift.{
   · have := lift_mk_le_lift_mk_of_surjective (oreDiv_one_surjective_of_finite_left S X)
     rw [lift_umax.{v, u}, lift_id'] at this
     exact le_max_of_le_right this
-  convert ← mk_le_of_surjective (show Surjective fun x : X × S ↦ x.1 /ₒ x.2 from
-    Quotient.mk''_surjective)
+  convert! ←
+    mk_le_of_surjective (show Surjective fun x : X × S ↦ x.1 /ₒ x.2 from Quotient.mk''_surjective)
   rw [mk_prod, mul_comm]
   refine mul_eq_max ?_ ?_ <;> simp
 
 @[to_additive]
 theorem cardinalMk_le : #(OreLocalization S R) ≤ #R := by
-  convert ← cardinalMk_le_max S R
+  convert! ← cardinalMk_le_max S R
   simp_rw [lift_id, max_eq_right_iff, mk_subtype_le]
 
 -- TODO: remove the `Commute` assumption
diff --git a/Mathlib/GroupTheory/Perm/Centralizer.lean b/Mathlib/GroupTheory/Perm/Centralizer.lean
index 79bc10e7a6dc0d..170e2579f1fa8e 100644
--- a/Mathlib/GroupTheory/Perm/Centralizer.lean
+++ b/Mathlib/GroupTheory/Perm/Centralizer.lean
@@ -646,7 +646,7 @@ theorem card_isConj_mul_eq :
   classical
   rw [Nat.card_eq_fintype_card, ← nat_card_centralizer g]
   rw [Subgroup.nat_card_centralizer_nat_card_stabilizer, Nat.card_eq_fintype_card]
-  convert MulAction.card_orbit_mul_card_stabilizer_eq_card_group (ConjAct (Perm α)) g
+  convert! MulAction.card_orbit_mul_card_stabilizer_eq_card_group (ConjAct (Perm α)) g
   · ext h
     simp only [Set.mem_setOf_eq, ConjAct.mem_orbit_conjAct, isConj_comm]
   · rw [ConjAct.card, Fintype.card_perm]
@@ -681,7 +681,7 @@ theorem card_of_cycleType_mul_eq (m : Multiset ℕ) :
   · -- nonempty case
     classical
     obtain ⟨g, rfl⟩ := (exists_with_cycleType_iff α).mpr hm
-    convert card_isConj_mul_eq g
+    convert! card_isConj_mul_eq g
     simp_rw [Set.coe_setOf, Nat.card_eq_fintype_card, ← Fintype.card_coe, Finset.mem_filter,
       Finset.mem_univ, true_and, ← isConj_iff_cycleType_eq, isConj_comm (g := g)]
   · -- empty case
diff --git a/Mathlib/GroupTheory/Perm/Closure.lean b/Mathlib/GroupTheory/Perm/Closure.lean
index 6ae430ba90da64..7d3158643c5ff5 100644
--- a/Mathlib/GroupTheory/Perm/Closure.lean
+++ b/Mathlib/GroupTheory/Perm/Closure.lean
@@ -53,14 +53,14 @@ theorem closure_cycle_adjacent_swap {σ : Perm α} (h1 : IsCycle σ) (h2 : σ.su
     induction n with
     | zero => exact subset_closure (Set.mem_insert_of_mem _ (Set.mem_singleton _))
     | succ n ih =>
-      convert H.mul_mem (H.mul_mem h3 ih) (H.inv_mem h3)
+      convert! H.mul_mem (H.mul_mem h3 ih) (H.inv_mem h3)
       simp_rw [mul_swap_eq_swap_mul, mul_inv_cancel_right, pow_succ', coe_mul, comp_apply]
   have step2 : ∀ n : ℕ, swap x ((σ ^ n) x) ∈ H := by
     intro n
     induction n with
     | zero =>
       simp only [pow_zero, coe_one, id_eq, swap_self]
-      convert H.one_mem
+      convert! H.one_mem
     | succ n ih =>
       by_cases h5 : x = (σ ^ n) x
       · rw [pow_succ', mul_apply, ← h5]
diff --git a/Mathlib/GroupTheory/Perm/ClosureSwap.lean b/Mathlib/GroupTheory/Perm/ClosureSwap.lean
index 295a60aefc331e..78204cfa163147 100644
--- a/Mathlib/GroupTheory/Perm/ClosureSwap.lean
+++ b/Mathlib/GroupTheory/Perm/ClosureSwap.lean
@@ -107,7 +107,7 @@ theorem mem_closure_isSwap {S : Set (Perm α)} (hS : ∀ f ∈ S, f.IsSwap) {f :
   suffices h : (fixedBy α f)ᶜ ⊆ supp → f ∈ closure S from h supp_eq.symm.subset
   clear_value supp; clear supp_eq; revert f
   apply fin.induction_on ..
-  · rintro f - emp; convert (closure S).one_mem; ext; by_contra h; exact emp h
+  · rintro f - emp; convert! (closure S).one_mem; ext; by_contra h; exact emp h
   rintro a s - - ih f hf supp_subset
   refine (mul_mem_cancel_left ((swap_mem_closure_isSwap hS).2 (hf a))).1
     (ih (fun b ↦ ?_) fun b hb ↦ ?_)
diff --git a/Mathlib/GroupTheory/Perm/Cycle/Basic.lean b/Mathlib/GroupTheory/Perm/Cycle/Basic.lean
index 32d0ab199b8011..312d420e8cd10a 100644
--- a/Mathlib/GroupTheory/Perm/Cycle/Basic.lean
+++ b/Mathlib/GroupTheory/Perm/Cycle/Basic.lean
@@ -363,7 +363,7 @@ theorem IsCycle.zpowersEquivSupport_symm_apply {σ : Perm α} (hσ : IsCycle σ)
 
 protected theorem IsCycle.orderOf (hf : IsCycle f) : orderOf f = #f.support := by
   rw [← Fintype.card_zpowers, ← Fintype.card_coe]
-  convert Fintype.card_congr (IsCycle.zpowersEquivSupport hf)
+  convert! Fintype.card_congr (IsCycle.zpowersEquivSupport hf)
 
 theorem isCycle_swap_mul_aux₁ {α : Type*} [DecidableEq α] :
     ∀ (n : ℕ) {b x : α} {f : Perm α} (_ : (swap x (f x) * f) b ≠ b) (_ : (f ^ n) (f x) = b),
@@ -398,7 +398,7 @@ theorem isCycle_swap_mul_aux₂ {α : Type*} [DecidableEq α] :
     obtain ⟨i, hi⟩ := isCycle_swap_mul_aux₁ n hb <| by
       rw [← mul_apply, ← pow_succ]; simpa [pow_succ', eq_symm_apply] using h
     refine ⟨-i, (swap x (f⁻¹ x) * f⁻¹).injective ?_⟩
-    convert hi using 1
+    convert! hi using 1
     · rw [zpow_neg, ← inv_zpow, ← mul_apply, mul_inv_rev, swap_inv, mul_swap_eq_swap_mul]
       simp [swap_comm _ x, ← mul_apply, -coe_mul, ← inv_def, -coe_inv, ← inv_def, mul_assoc _ f⁻¹,
         ← mul_zpow_mul, mul_assoc _ _ f]
@@ -688,7 +688,7 @@ alias ⟨IsCycleOn.of_inv, IsCycleOn.inv⟩ := isCycleOn_inv
 theorem IsCycleOn.conj (h : f.IsCycleOn s) : (g * f * g⁻¹).IsCycleOn ((g : Perm α) '' s) :=
   ⟨(g.bijOn_image.comp h.1).comp g.bijOn_symm_image, fun x hx y hy => by
     rw [Equiv.image_eq_preimage_symm] at hx hy
-    convert Equiv.Perm.SameCycle.conj (h.2 hx hy) (g := g) <;> simp⟩
+    convert! Equiv.Perm.SameCycle.conj (h.2 hx hy) (g := g) <;> simp⟩
 
 theorem isCycleOn_swap [DecidableEq α] (hab : a ≠ b) : (swap a b).IsCycleOn {a, b} :=
   ⟨bijOn_swap (by simp) (by simp), fun x hx y hy => by
@@ -736,7 +736,7 @@ protected theorem IsCycleOn.subtypePerm (hf : f.IsCycleOn s) :
   obtain hs | hs := s.subsingleton_or_nontrivial
   · haveI := hs.coe_sort
     exact isCycleOn_of_subsingleton _ _
-  convert (hf.isCycle_subtypePerm hs).isCycleOn
+  convert! (hf.isCycle_subtypePerm hs).isCycleOn
   rw [eq_comm, Set.eq_univ_iff_forall]
   exact fun x => ne_of_apply_ne ((↑) : s → α) (hf.apply_ne hs x.2)
 
@@ -855,7 +855,7 @@ theorem exists_cycleOn (s : Finset α) :
     ∃ f : Perm α, f.IsCycleOn s ∧ f.support ⊆ s := by
   refine ⟨s.toList.formPerm, ?_, fun x hx => by
     simpa using List.mem_of_formPerm_apply_ne (Perm.mem_support.1 hx)⟩
-  convert s.nodup_toList.isCycleOn_formPerm
+  convert! s.nodup_toList.isCycleOn_formPerm
   simp
 
 end Finset
@@ -870,14 +870,14 @@ theorem Countable.exists_cycleOn (hs : s.Countable) :
   obtain hs' | hs' := s.finite_or_infinite
   · refine ⟨hs'.toFinset.toList.formPerm, ?_, fun x hx => by
       simpa using List.mem_of_formPerm_apply_ne hx⟩
-    convert hs'.toFinset.nodup_toList.isCycleOn_formPerm
+    convert! hs'.toFinset.nodup_toList.isCycleOn_formPerm
     simp
   · haveI := hs.to_subtype
     haveI := hs'.to_subtype
     obtain ⟨f⟩ : Nonempty (ℤ ≃ s) := inferInstance
     refine ⟨(Equiv.addRight 1).extendDomain f, ?_, fun x hx =>
       of_not_not fun h => hx <| Perm.extendDomain_apply_not_subtype _ _ h⟩
-    convert Int.addRight_one_isCycle.isCycleOn.extendDomain f
+    convert! Int.addRight_one_isCycle.isCycleOn.extendDomain f
     rw [Set.image_comp, Equiv.image_eq_preimage_symm]
     ext
     simp
diff --git a/Mathlib/GroupTheory/Perm/Cycle/Factors.lean b/Mathlib/GroupTheory/Perm/Cycle/Factors.lean
index 4f0a76b60ed3af..96cf6d1f99a917 100644
--- a/Mathlib/GroupTheory/Perm/Cycle/Factors.lean
+++ b/Mathlib/GroupTheory/Perm/Cycle/Factors.lean
@@ -101,12 +101,12 @@ theorem cycleOf_apply_apply_zpow_self (f : Perm α) [DecidableRel f.SameCycle] (
 @[simp]
 theorem cycleOf_apply_apply_pow_self (f : Perm α) [DecidableRel f.SameCycle] (x : α) (k : ℕ) :
     cycleOf f x ((f ^ k) x) = (f ^ (k + 1) : Perm α) x := by
-  convert cycleOf_apply_apply_zpow_self f x k using 1
+  convert! cycleOf_apply_apply_zpow_self f x k using 1
 
 @[simp]
 theorem cycleOf_apply_apply_self (f : Perm α) [DecidableRel f.SameCycle] (x : α) :
     cycleOf f x (f x) = f (f x) := by
-  convert cycleOf_apply_apply_pow_self f x 1 using 1
+  convert! cycleOf_apply_apply_pow_self f x 1 using 1
 
 @[simp]
 theorem cycleOf_apply_self (f : Perm α) [DecidableRel f.SameCycle] (x : α) : cycleOf f x x = f x :=
@@ -438,7 +438,7 @@ theorem mem_list_cycles_iff {α : Type*} [Finite α] {l : List (Perm α)}
       have key : ∀ x ∈ σ.support ∩ τ.support, σ x = τ x := by
         intro x hx
         rw [h x (mem_support.mp (mem_of_mem_inter_left hx)), hτl x (mem_of_mem_inter_right hx)]
-      convert hτ
+      convert! hτ
       refine h3.eq_on_support_inter_nonempty_congr (h1 _ hτ) key ?_ ha
       exact key a (mem_inter_of_mem ha hτa)
 
diff --git a/Mathlib/GroupTheory/Perm/Cycle/Type.lean b/Mathlib/GroupTheory/Perm/Cycle/Type.lean
index 5e459c0700bb44..58cf7430a724ec 100644
--- a/Mathlib/GroupTheory/Perm/Cycle/Type.lean
+++ b/Mathlib/GroupTheory/Perm/Cycle/Type.lean
@@ -530,7 +530,7 @@ theorem _root_.exists_prime_orderOf_dvd_card {G : Type*} [Group G] [Fintype G] (
 order `p` in `G`. This is the additive version of Cauchy's theorem. -/
 theorem _root_.exists_prime_addOrderOf_dvd_card {G : Type*} [AddGroup G] [Fintype G] (p : ℕ)
     [Fact p.Prime] (hdvd : p ∣ Fintype.card G) : ∃ x : G, addOrderOf x = p :=
-  @exists_prime_orderOf_dvd_card (Multiplicative G) _ _ _ _ (by convert hdvd)
+  @exists_prime_orderOf_dvd_card (Multiplicative G) _ _ _ _ (by convert! hdvd)
 
 attribute [to_additive existing] exists_prime_orderOf_dvd_card
 
diff --git a/Mathlib/GroupTheory/Perm/Fin.lean b/Mathlib/GroupTheory/Perm/Fin.lean
index 7081d03fd025c0..e13b1af86ec985 100644
--- a/Mathlib/GroupTheory/Perm/Fin.lean
+++ b/Mathlib/GroupTheory/Perm/Fin.lean
@@ -490,7 +490,7 @@ theorem Equiv.Perm.sign_eq_prod_prod_Iio (σ : Equiv.Perm (Fin n)) :
     σ.sign = ∏ j, ∏ i ∈ Finset.Iio j, (if σ i < σ j then 1 else -1) := by
   suffices h : σ.sign = σ.signAux by
     rw [h, Finset.prod_sigma', Equiv.Perm.signAux]
-    convert rfl using 2 with x hx
+    convert! rfl using 2 with x hx
     · simp [Finset.ext_iff, Equiv.Perm.mem_finPairsLT]
     simp [← ite_not (p := _ ≤ _)]
   refine σ.swap_induction_on (by simp) fun π i j hne h_eq ↦ ?_
@@ -528,9 +528,9 @@ theorem Equiv.Perm.prod_Iio_comp_eq_sign_mul_prod {R : Type*} [CommRing R]
 theorem Equiv.Perm.prod_Ioi_comp_eq_sign_mul_prod {R : Type*} [CommRing R]
     (σ : Equiv.Perm (Fin n)) {f : Fin n → Fin n → R} (hf : ∀ i j, f i j = -f j i) :
     ∏ i, ∏ j ∈ Finset.Ioi i, f (σ i) (σ j) = σ.sign * ∏ i, ∏ j ∈ Finset.Ioi i, f i j := by
-  convert σ.prod_Iio_comp_eq_sign_mul_prod hf using 1
+  convert! σ.prod_Iio_comp_eq_sign_mul_prod hf using 1
   · apply Finset.prod_comm' (by simp)
-  convert rfl using 2
+  convert! rfl using 2
   apply Finset.prod_comm' (by simp)
 
 end Sign
diff --git a/Mathlib/GroupTheory/Perm/List.lean b/Mathlib/GroupTheory/Perm/List.lean
index b75975a38624e4..3fb752b7a901e8 100644
--- a/Mathlib/GroupTheory/Perm/List.lean
+++ b/Mathlib/GroupTheory/Perm/List.lean
@@ -211,7 +211,7 @@ theorem support_formPerm_of_nodup' (l : List α) (h : Nodup l) (h' : ∀ x : α,
 theorem support_formPerm_of_nodup [Fintype α] (l : List α) (h : Nodup l) (h' : ∀ x : α, l ≠ [x]) :
     support (formPerm l) = l.toFinset := by
   rw [← Finset.coe_inj]
-  convert support_formPerm_of_nodup' _ h h'
+  convert! support_formPerm_of_nodup' _ h h'
   simp [Set.ext_iff]
 
 theorem formPerm_rotate_one (l : List α) (h : Nodup l) : formPerm (l.rotate 1) = formPerm l := by
@@ -263,7 +263,7 @@ theorem formPerm_pow_apply_getElem (l : List α) (w : Nodup l) (n : ℕ) (i : 
 theorem formPerm_pow_apply_head (x : α) (l : List α) (h : Nodup (x :: l)) (n : ℕ) :
     (formPerm (x :: l) ^ n) x =
       (x :: l)[(n % (x :: l).length)]'(Nat.mod_lt _ (Nat.zero_lt_succ _)) := by
-  convert formPerm_pow_apply_getElem _ h n 0 (Nat.succ_pos _)
+  convert! formPerm_pow_apply_getElem _ h n 0 (Nat.succ_pos _)
   simp
 
 theorem formPerm_ext_iff {x y x' y' : α} {l l' : List α} (hd : Nodup (x :: y :: l))
diff --git a/Mathlib/GroupTheory/Perm/MaximalSubgroups.lean b/Mathlib/GroupTheory/Perm/MaximalSubgroups.lean
index 171d6255bc18ac..3516919c0eb728 100644
--- a/Mathlib/GroupTheory/Perm/MaximalSubgroups.lean
+++ b/Mathlib/GroupTheory/Perm/MaximalSubgroups.lean
@@ -178,7 +178,7 @@ theorem has_swap_mem_of_lt_stabilizer [DecidableEq α]
   have hα : Set.encard (_root_.Set.univ : Set α) = 2 := by
     rw [← Set.encard_add_encard_compl s]
     have : (1 + 1 : ENat) = 2 := by norm_num
-    convert this <;>
+    convert! this <;>
     · apply le_antisymm
       · assumption
       rw [one_le_encard_iff_nonempty, Set.nonempty_iff_ne_empty]
diff --git a/Mathlib/GroupTheory/Perm/Support.lean b/Mathlib/GroupTheory/Perm/Support.lean
index ed19e262463d4d..0f670d4667e4ac 100644
--- a/Mathlib/GroupTheory/Perm/Support.lean
+++ b/Mathlib/GroupTheory/Perm/Support.lean
@@ -95,7 +95,7 @@ theorem Disjoint.inv_right (h : Disjoint f g) : Disjoint f g⁻¹ :=
 @[simp]
 theorem disjoint_inv_left_iff : Disjoint f⁻¹ g ↔ Disjoint f g := by
   refine ⟨fun h => ?_, Disjoint.inv_left⟩
-  convert h.inv_left
+  convert! h.inv_left
 
 @[simp]
 theorem disjoint_inv_right_iff : Disjoint f g⁻¹ ↔ Disjoint f g := by
@@ -451,7 +451,7 @@ theorem support_swap_mul_swap {x y z : α} (h : List.Nodup [x, y, z]) :
     and_self_iff, List.nodup_nil] at h
   push Not at h
   apply le_antisymm
-  · convert support_mul_le (swap x y) (swap y z) using 1
+  · convert! support_mul_le (swap x y) (swap y z) using 1
     rw [support_swap h.left.left, support_swap h.right.left]
     simp [-Finset.union_singleton]
   · intro
diff --git a/Mathlib/GroupTheory/PushoutI.lean b/Mathlib/GroupTheory/PushoutI.lean
index 0b298dd2b8a19f..31d04e07702548 100644
--- a/Mathlib/GroupTheory/PushoutI.lean
+++ b/Mathlib/GroupTheory/PushoutI.lean
@@ -496,14 +496,14 @@ noncomputable def consRecOn {motive : NormalWord d → Sort _} (w : NormalWord d
     (base : ∀ (h : H) (w : NormalWord d), w.head = 1 → motive w → motive
       (base φ h • w)) : motive w := by
   rcases w with ⟨w, head, h3⟩
-  convert base head ⟨w, 1, h3⟩ rfl ?_
+  convert! base head ⟨w, 1, h3⟩ rfl ?_
   · simp [base_smul_def]
   · induction w using Word.consRecOn with
     | empty => exact empty
     | cons i g w h1 hg1 ih =>
-      convert cons i g ⟨w, 1, fun _ _ h => h3 _ _ (List.mem_cons_of_mem _ h)⟩
-        h1 (h3 _ _ List.mem_cons_self) ?_ rfl
-        (ih ?_)
+      convert!
+        cons i g ⟨w, 1, fun _ _ h => h3 _ _ (List.mem_cons_of_mem _ h)⟩ h1
+          (h3 _ _ List.mem_cons_self) ?_ rfl (ih ?_)
       · simp only [Word.cons, NormalWord.cons, map_one, mul_one,
           (equiv_snd_eq_self_iff_mem (d.compl i) (one_mem _)).2
           (h3 _ _ List.mem_cons_self)]
diff --git a/Mathlib/GroupTheory/SpecificGroups/Alternating/Centralizer.lean b/Mathlib/GroupTheory/SpecificGroups/Alternating/Centralizer.lean
index abecfd5f776ff1..0814180e5da1c6 100644
--- a/Mathlib/GroupTheory/SpecificGroups/Alternating/Centralizer.lean
+++ b/Mathlib/GroupTheory/SpecificGroups/Alternating/Centralizer.lean
@@ -177,7 +177,7 @@ theorem count_le_one_of_centralizer_le_alternating
   have hk_cT : k.val.cycleType = Multiset.replicate k.val.cycleType.card 2 := by
     rw [Multiset.eq_replicate_card, ← pow_prime_eq_one_iff, ← Subgroup.coe_pow,
       ← Subgroup.coe_one, Subtype.coe_inj, hk, ← map_pow]
-    convert MonoidHom.map_one _
+    convert! MonoidHom.map_one _
     rw [← Subtype.coe_inj]
     apply Equiv.swap_mul_self
   rw [sign_of_cycleType, hk_cT]
@@ -228,12 +228,12 @@ theorem centralizer_le_alternating_iff :
     rw [← kerParam_range_eq_centralizer_of_count_le_one h_count] at hx
     obtain ⟨⟨y, uv⟩, rfl⟩ := MonoidHom.mem_range.mp hx
     rw [mem_alternatingGroup, sign_kerParam_apply_apply (g := g) y uv]
-    convert mul_one _
+    convert! mul_one _
     · apply Finset.prod_eq_one
       rintro ⟨c, hc⟩ _
       obtain ⟨k, hk⟩ := (uv _).prop
       rw [← hk, map_zpow]
-      convert one_zpow k
+      convert! one_zpow k
       rw [IsCycle.sign, Odd.neg_one_pow, neg_neg]
       · apply h_odd
         rw [cycleType_def, Multiset.mem_map]
diff --git a/Mathlib/GroupTheory/SpecificGroups/Alternating/KleinFour.lean b/Mathlib/GroupTheory/SpecificGroups/Alternating/KleinFour.lean
index bb01d92291dbb8..38f32ea1732143 100644
--- a/Mathlib/GroupTheory/SpecificGroups/Alternating/KleinFour.lean
+++ b/Mathlib/GroupTheory/SpecificGroups/Alternating/KleinFour.lean
@@ -118,7 +118,7 @@ theorem coe_two_sylow_of_card_eq_four
   · -- inclusion S ⊆ {1} ∪ {g |  cycleType g = { 2, 2 }}
     obtain ⟨n, hn⟩ := (IsPGroup.iff_orderOf.mp S.isPGroup') ⟨k, hk⟩
     replace hn : (orderOf (k : Perm α)) = 2 ^ n := by simpa using hn
-    convert mem_kleinFour_of_order_two_pow hα4 k.2 hn.dvd
+    convert! mem_kleinFour_of_order_two_pow hα4 k.2 hn.dvd
     simp
   · -- card (kleinFour α) ≤ card S
     simp_rw [← Nat.card_eq_fintype_card]
@@ -173,9 +173,9 @@ theorem exponent_kleinFour_of_card_eq_four (hα4 : Nat.card α = 4) :
     simp only [Subgroup.orderOf_mk, orderOf_dvd_iff_pow_eq_one]
     rw [← SetLike.mem_coe, coe_kleinFour_of_card_eq_four hα4] at hg'
     rcases hg' with hg' | hg'
-    · convert one_pow _
+    · convert! one_pow _
       simpa only [Set.mem_singleton_iff, Subgroup.mk_eq_one] using hg'
-    · convert pow_orderOf_eq_one g
+    · convert! pow_orderOf_eq_one g
       rw [← Equiv.Perm.lcm_cycleType, hg']
       simp
   rw [Nat.dvd_prime Nat.prime_two] at this
diff --git a/Mathlib/GroupTheory/SpecificGroups/Alternating/MaximalSubgroups.lean b/Mathlib/GroupTheory/SpecificGroups/Alternating/MaximalSubgroups.lean
index a203be1f7287b8..f53c195d6d9c20 100644
--- a/Mathlib/GroupTheory/SpecificGroups/Alternating/MaximalSubgroups.lean
+++ b/Mathlib/GroupTheory/SpecificGroups/Alternating/MaximalSubgroups.lean
@@ -92,7 +92,7 @@ theorem stabilizer.surjective_toPerm {s : Set α} (hs : sᶜ.Nontrivial) :
     intro _
     simp only [mem_smul_set]
     rintro ⟨x, hx, rfl⟩
-    convert hx
+    convert! hx
     rw [Perm.smul_def, ← Perm.notMem_support]
     exact (Set.disjoint_left.mp hk_support) hx
   intro g
diff --git a/Mathlib/GroupTheory/SpecificGroups/Alternating/Simple.lean b/Mathlib/GroupTheory/SpecificGroups/Alternating/Simple.lean
index b9717035c55abd..47abda9765ffbc 100644
--- a/Mathlib/GroupTheory/SpecificGroups/Alternating/Simple.lean
+++ b/Mathlib/GroupTheory/SpecificGroups/Alternating/Simple.lean
@@ -75,7 +75,7 @@ def iwasawaStructure_two [∀ s : Set α, DecidablePred fun x ↦ x ∈ s] :
     have : IsMulCommutative (Perm s) := isMulCommutative_iff_card_le_two.mpr (by simp)
     infer_instance
   is_conj g s := by
-    convert (conj_smul_range_ofSubtype g s).symm
+    convert! (conj_smul_range_ofSubtype g s).symm
   is_generator := by
     rw [eq_top_iff, ← Equiv.Perm.closure_isSwap, Subgroup.closure_le]
     rintro g ⟨a, b, hab, rfl⟩
diff --git a/Mathlib/GroupTheory/SpecificGroups/Cyclic/Basic.lean b/Mathlib/GroupTheory/SpecificGroups/Cyclic/Basic.lean
index 585a96d9494533..cfd567da7754a6 100644
--- a/Mathlib/GroupTheory/SpecificGroups/Cyclic/Basic.lean
+++ b/Mathlib/GroupTheory/SpecificGroups/Cyclic/Basic.lean
@@ -220,7 +220,7 @@ theorem exists_pow_ne_one_of_isCyclic [G_cyclic : IsCyclic G]
   rcases G_cyclic with ⟨a, ha⟩
   use a
   contrapose! k_lt_card_G
-  convert orderOf_le_of_pow_eq_one k_pos.bot_lt k_lt_card_G
+  convert! orderOf_le_of_pow_eq_one k_pos.bot_lt k_lt_card_G
   rw [← Nat.card_zpowers, eq_comm, card_eq_iff_eq_top, eq_top_iff]
   exact fun x _ ↦ ha x
 
diff --git a/Mathlib/GroupTheory/SpecificGroups/Dihedral.lean b/Mathlib/GroupTheory/SpecificGroups/Dihedral.lean
index 43572ba856ee1c..abea98a604b6d9 100644
--- a/Mathlib/GroupTheory/SpecificGroups/Dihedral.lean
+++ b/Mathlib/GroupTheory/SpecificGroups/Dihedral.lean
@@ -220,9 +220,9 @@ theorem exponent : Monoid.exponent (DihedralGroup n) = lcm n 2 := by
     · rw [← orderOf_dvd_iff_pow_eq_one, orderOf_sr]
       exact dvd_lcm_right n 2
   · apply lcm_dvd
-    · convert Monoid.order_dvd_exponent (r (1 : ZMod n))
+    · convert! Monoid.order_dvd_exponent (r (1 : ZMod n))
       exact orderOf_r_one.symm
-    · convert Monoid.order_dvd_exponent (sr (0 : ZMod n))
+    · convert! Monoid.order_dvd_exponent (sr (0 : ZMod n))
       exact (orderOf_sr 0).symm
 
 lemma not_commutative : ∀ {n : ℕ}, n ≠ 1 → n ≠ 2 → ¬IsMulCommutative (DihedralGroup n)
diff --git a/Mathlib/GroupTheory/SpecificGroups/Quaternion.lean b/Mathlib/GroupTheory/SpecificGroups/Quaternion.lean
index 42b73e2c582a4a..cf44529992f105 100644
--- a/Mathlib/GroupTheory/SpecificGroups/Quaternion.lean
+++ b/Mathlib/GroupTheory/SpecificGroups/Quaternion.lean
@@ -262,9 +262,9 @@ theorem exponent : Monoid.exponent (QuaternionGroup n) = 2 * lcm n 2 := by
     · rw [← orderOf_dvd_iff_pow_eq_one, orderOf_xa]
       exact dvd_lcm_right (2 * n) 4
   · apply lcm_dvd
-    · convert Monoid.order_dvd_exponent (a 1)
+    · convert! Monoid.order_dvd_exponent (a 1)
       exact orderOf_a_one.symm
-    · convert Monoid.order_dvd_exponent (xa (0 : ZMod (2 * n)))
+    · convert! Monoid.order_dvd_exponent (xa (0 : ZMod (2 * n)))
       exact (orderOf_xa 0).symm
 
 end QuaternionGroup
diff --git a/Mathlib/GroupTheory/Subgroup/Centralizer.lean b/Mathlib/GroupTheory/Subgroup/Centralizer.lean
index 64cf7478c6198c..dd2a87b9c066a8 100644
--- a/Mathlib/GroupTheory/Subgroup/Centralizer.lean
+++ b/Mathlib/GroupTheory/Subgroup/Centralizer.lean
@@ -157,7 +157,7 @@ instance instIsMulCommutative_closure {S : Type*} [SetLike S G] [MulMemClass S G
 theorem centralizer_le_normalizer (s : Set G) : centralizer s ≤ normalizer s := by
   refine fun g hg h ↦ ⟨fun hh ↦ ?_, fun hh ↦ ?_⟩
   · simpa [← hg h hh]
-  · convert hh
+  · convert! hh
     simpa using hg _ hh
 
 @[to_additive]
diff --git a/Mathlib/GroupTheory/Submonoid/Inverses.lean b/Mathlib/GroupTheory/Submonoid/Inverses.lean
index a9fbba3d794619..be217e8b138c79 100644
--- a/Mathlib/GroupTheory/Submonoid/Inverses.lean
+++ b/Mathlib/GroupTheory/Submonoid/Inverses.lean
@@ -47,7 +47,7 @@ noncomputable instance [Monoid M] : Group (IsUnit.submonoid M) :=
 @[to_additive]
 noncomputable instance [CommMonoid M] : CommGroup (IsUnit.submonoid M) :=
   { (inferInstance : Group (IsUnit.submonoid M)) with
-    mul_comm := fun a b ↦ by convert mul_comm a b }
+    mul_comm := fun a b ↦ by convert! mul_comm a b }
 
 @[to_additive]
 theorem IsUnit.Submonoid.coe_inv [Monoid M] (x : IsUnit.submonoid M) :
@@ -70,7 +70,7 @@ def leftInv : Submonoid M where
 @[to_additive]
 theorem leftInv_leftInv_le : S.leftInv.leftInv ≤ S := by
   rintro x ⟨⟨y, z, h₁⟩, h₂ : x * y = 1⟩
-  convert z.prop
+  convert! z.prop
   rw [← mul_one x, ← h₁, ← mul_assoc, h₂, one_mul]
 
 @[to_additive]
@@ -168,12 +168,12 @@ theorem mul_leftInvEquiv (x : S.leftInv) : (x : M) * S.leftInvEquiv hS x = 1 :=
 
 @[to_additive (attr := simp)]
 theorem leftInvEquiv_symm_mul (x : S) : ((S.leftInvEquiv hS).symm x : M) * x = 1 := by
-  convert S.mul_leftInvEquiv hS ((S.leftInvEquiv hS).symm x)
+  convert! S.mul_leftInvEquiv hS ((S.leftInvEquiv hS).symm x)
   simp
 
 @[to_additive (attr := simp)]
 theorem mul_leftInvEquiv_symm (x : S) : (x : M) * (S.leftInvEquiv hS).symm x = 1 := by
-  convert S.leftInvEquiv_mul hS ((S.leftInvEquiv hS).symm x)
+  convert! S.leftInvEquiv_mul hS ((S.leftInvEquiv hS).symm x)
   simp
 
 end CommMonoid
diff --git a/Mathlib/GroupTheory/Sylow.lean b/Mathlib/GroupTheory/Sylow.lean
index 2f705d30131a95..c726ff3cd679ee 100644
--- a/Mathlib/GroupTheory/Sylow.lean
+++ b/Mathlib/GroupTheory/Sylow.lean
@@ -522,7 +522,7 @@ theorem mem_fixedPoints_mul_left_cosets_iff_mem_normalizer {H : Subgroup G} [Fin
         have : (n⁻¹ * x)⁻¹ * x ∈ H := QuotientGroup.eq.1 (ha ⟨⟨n⁻¹, inv_mem hn⟩, rfl⟩)
         show _ ∈ H by
           rw [mul_inv_rev, inv_inv] at this
-          convert this
+          convert! this
           rw [inv_inv]),
     fun hx : ∀ n : G, n ∈ H ↔ x * n * x⁻¹ ∈ H =>
     mem_fixedPoints'.2 fun y =>
@@ -614,7 +614,7 @@ theorem exists_subgroup_card_pow_succ [Finite G] {p : ℕ} {n : ℕ} [hp : Fact
       (comap (mk' (H.subgroupOf (normalizer H))) (Subgroup.zpowers x))) = p ^ (n + 1)
     suffices Nat.card (Subtype.val ''
       ((zpowers x).comap (mk' (H.subgroupOf (normalizer H))) : Set (normalizer H))) = p ^ (n + 1)
-      by convert this using 2
+      by convert! this using 2
     rw [Nat.card_image_of_injective Subtype.val_injective
         ((zpowers x).comap (mk' (H.subgroupOf (normalizer H))) : Set (normalizer (H : Set G))),
       pow_succ, ← hH, Nat.card_congr hequiv, ← hx, ← Nat.card_zpowers, ← Nat.card_prod]
diff --git a/Mathlib/InformationTheory/KullbackLeibler/Basic.lean b/Mathlib/InformationTheory/KullbackLeibler/Basic.lean
index e3318363356624..783b5d96721160 100644
--- a/Mathlib/InformationTheory/KullbackLeibler/Basic.lean
+++ b/Mathlib/InformationTheory/KullbackLeibler/Basic.lean
@@ -84,7 +84,7 @@ lemma klDiv_self (μ : Measure α) [SigmaFinite μ] : klDiv μ μ = 0 := by
 
 @[simp]
 lemma klDiv_zero_left [IsFiniteMeasure ν] : klDiv 0 ν = ν univ := by
-  convert klDiv_of_ac_of_integrable (Measure.AbsolutelyContinuous.zero _) integrable_zero_measure
+  convert! klDiv_of_ac_of_integrable (Measure.AbsolutelyContinuous.zero _) integrable_zero_measure
   simp
 
 @[simp]
diff --git a/Mathlib/InformationTheory/KullbackLeibler/KLFun.lean b/Mathlib/InformationTheory/KullbackLeibler/KLFun.lean
index 9cc926ea638db8..4f0487fc8c7be9 100644
--- a/Mathlib/InformationTheory/KullbackLeibler/KLFun.lean
+++ b/Mathlib/InformationTheory/KullbackLeibler/KLFun.lean
@@ -87,7 +87,7 @@ section Derivatives
 
 /-- The derivative of `klFun` at `x ≠ 0` is `log x`. -/
 lemma hasDerivAt_klFun (hx : x ≠ 0) : HasDerivAt klFun (log x) x := by
-  convert ((hasDerivAt_mul_log hx).add (hasDerivAt_const x 1)).sub (hasDerivAt_id x) using 1
+  convert! ((hasDerivAt_mul_log hx).add (hasDerivAt_const x 1)).sub (hasDerivAt_id x) using 1
   ring
 
 lemma not_differentiableAt_klFun_zero : ¬ DifferentiableAt ℝ klFun 0 := by
@@ -170,7 +170,7 @@ lemma integrable_klFun_rnDeriv_iff (hμν : μ ≪ ν) :
     Integrable (fun x ↦ klFun (μ.rnDeriv ν x).toReal) ν ↔ Integrable (llr μ ν) μ := by
   suffices Integrable (fun x ↦ (μ.rnDeriv ν x).toReal * log (μ.rnDeriv ν x).toReal
       + (1 - (μ.rnDeriv ν x).toReal)) ν ↔ Integrable (llr μ ν) μ by
-    convert this using 3 with x
+    convert! this using 3 with x
     rw [klFun, add_sub_assoc]
   rw [integrable_add_iff_integrable_left', integrable_rnDeriv_mul_log_iff hμν]
   fun_prop
diff --git a/Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean b/Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean
index 63be48109f2d6d..1fc8959ff57ebb 100644
--- a/Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean
+++ b/Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean
@@ -804,7 +804,7 @@ note [partially-applied ext lemmas]. Analogous to `LinearMap.pi_ext'` -/
 theorem pi_ext_nonempty' [Nonempty ι] (h : ∀ i, f.comp (LinearMap.single _ _ i).toAffineMap =
     g.comp (LinearMap.single _ _ i).toAffineMap) : f = g := by
   refine pi_ext_nonempty fun i x => ?_
-  convert AffineMap.congr_fun (h i) x
+  convert! AffineMap.congr_fun (h i) x
 
 end Ext
 
diff --git a/Mathlib/LinearAlgebra/AffineSpace/AffineSubspace/Basic.lean b/Mathlib/LinearAlgebra/AffineSpace/AffineSubspace/Basic.lean
index 58bf073a40daab..57492f70f5b998 100644
--- a/Mathlib/LinearAlgebra/AffineSpace/AffineSubspace/Basic.lean
+++ b/Mathlib/LinearAlgebra/AffineSpace/AffineSubspace/Basic.lean
@@ -330,7 +330,8 @@ spans `P`. -/
 theorem affineSpan_singleton_union_vadd_eq_top_of_span_eq_top {s : Set V} (p : P)
     (h : Submodule.span k (Set.range ((↑) : s → V)) = ⊤) :
     affineSpan k ({p} ∪ (fun v => v +ᵥ p) '' s) = ⊤ := by
-  convert ext_of_direction_eq _
+  convert!
+    ext_of_direction_eq _
       ⟨p, mem_affineSpan k (Set.mem_union_left _ (Set.mem_singleton _)), mem_top k V p⟩
   rw [direction_affineSpan, direction_top,
     vectorSpan_eq_span_vsub_set_right k (Set.mem_union_left _ (Set.mem_singleton _) : p ∈ _),
@@ -954,9 +955,9 @@ lemma affineSpan_pair_eq_of_mem_of_mem_of_ne {p₁ p₂ p₃ p₄ : P} (hp₁ :
     simp [sub_smul, hp₁, hp₂]
   rw [← eq_inv_smul_iff₀ hr₀] at hr
   refine affineSpan_pair_le_of_mem_of_mem ?_ ?_
-  · convert smul_vsub_vadd_mem_affineSpan_pair (-r₁ * (r₂ - r₁)⁻¹) p₁ p₂
+  · convert! smul_vsub_vadd_mem_affineSpan_pair (-r₁ * (r₂ - r₁)⁻¹) p₁ p₂
     simp [mul_smul, ← hr, hp₁]
-  · convert smul_vsub_vadd_mem_affineSpan_pair ((1 - r₁) * (r₂ - r₁)⁻¹) p₁ p₂
+  · convert! smul_vsub_vadd_mem_affineSpan_pair ((1 - r₁) * (r₂ - r₁)⁻¹) p₁ p₂
     simp [mul_smul, ← hr, sub_smul, hp₁]
 
 /-- One line equals another differing in the first point if the first point of the first line is
diff --git a/Mathlib/LinearAlgebra/AffineSpace/AffineSubspace/Defs.lean b/Mathlib/LinearAlgebra/AffineSpace/AffineSubspace/Defs.lean
index b74ea673f23960..5d3837877fba84 100644
--- a/Mathlib/LinearAlgebra/AffineSpace/AffineSubspace/Defs.lean
+++ b/Mathlib/LinearAlgebra/AffineSpace/AffineSubspace/Defs.lean
@@ -206,7 +206,7 @@ def directionOfNonempty {s : AffineSubspace k P} (h : (s : Set P).Nonempty) : Su
     rintro _ _ ⟨p₁, hp₁, p₂, hp₂, rfl⟩ ⟨p₃, hp₃, p₄, hp₄, rfl⟩
     rw [← vadd_vsub_assoc]
     refine vsub_mem_vsub ?_ hp₄
-    convert s.smul_vsub_vadd_mem 1 hp₁ hp₂ hp₃
+    convert! s.smul_vsub_vadd_mem 1 hp₁ hp₂ hp₃
     rw [one_smul]
   smul_mem' := by
     rintro c _ ⟨p₁, hp₁, p₂, hp₂, rfl⟩
@@ -241,7 +241,7 @@ theorem vadd_mem_of_mem_direction {s : AffineSubspace k P} {v : V} (hv : v ∈ s
   rw [mem_direction_iff_eq_vsub ⟨p, hp⟩] at hv
   rcases hv with ⟨p₁, hp₁, p₂, hp₂, hv⟩
   rw [hv]
-  convert s.smul_vsub_vadd_mem 1 hp₁ hp₂ hp
+  convert! s.smul_vsub_vadd_mem 1 hp₁ hp₂ hp
   rw [one_smul]
 
 /-- Subtracting two points in the subspace produces a vector in the direction. -/
@@ -260,7 +260,7 @@ the original point is in the subspace. -/
 theorem vadd_mem_iff_mem_of_mem_direction {s : AffineSubspace k P} {v : V} (hv : v ∈ s.direction)
     {p : P} : v +ᵥ p ∈ s ↔ p ∈ s := by
   refine ⟨fun h => ?_, fun h => vadd_mem_of_mem_direction hv h⟩
-  convert vadd_mem_of_mem_direction (Submodule.neg_mem _ hv) h
+  convert! vadd_mem_of_mem_direction (Submodule.neg_mem _ hv) h
   simp
 
 /-- Given a point in an affine subspace, the set of vectors in its direction equals the set of
diff --git a/Mathlib/LinearAlgebra/AffineSpace/Basis.lean b/Mathlib/LinearAlgebra/AffineSpace/Basis.lean
index 3b73839f1305da..5b78567a33ba69 100644
--- a/Mathlib/LinearAlgebra/AffineSpace/Basis.lean
+++ b/Mathlib/LinearAlgebra/AffineSpace/Basis.lean
@@ -219,7 +219,7 @@ theorem sum_coord_apply_eq_one [Fintype ι] (q : P) : ∑ i, b.coord i q = 1 :=
     rw [b.tot]
     exact AffineSubspace.mem_top k V q
   obtain ⟨w, hw, rfl⟩ := eq_affineCombination_of_mem_affineSpan_of_fintype hq
-  convert hw
+  convert! hw
   exact b.coord_apply_combination_of_mem (Finset.mem_univ _) hw
 
 @[simp]
diff --git a/Mathlib/LinearAlgebra/AffineSpace/Centroid.lean b/Mathlib/LinearAlgebra/AffineSpace/Centroid.lean
index ecd3e30bc7f9cc..56fcb32ad7744f 100644
--- a/Mathlib/LinearAlgebra/AffineSpace/Centroid.lean
+++ b/Mathlib/LinearAlgebra/AffineSpace/Centroid.lean
@@ -113,7 +113,7 @@ as adding a vector to the first point. -/
 theorem centroid_pair_fin [Invertible (2 : k)] (p : Fin 2 → P) :
     univ.centroid k p = (2⁻¹ : k) • (p 1 -ᵥ p 0) +ᵥ p 0 := by
   rw [univ_fin2]
-  convert centroid_pair k p 0 1
+  convert! centroid_pair k p 0 1
 
 /-- A centroid, over the image of an embedding, equals a centroid with
 the same points and weights over the original `Finset`. -/
diff --git a/Mathlib/LinearAlgebra/AffineSpace/Ceva.lean b/Mathlib/LinearAlgebra/AffineSpace/Ceva.lean
index 47605d401651ae..535f636e0a744e 100644
--- a/Mathlib/LinearAlgebra/AffineSpace/Ceva.lean
+++ b/Mathlib/LinearAlgebra/AffineSpace/Ceva.lean
@@ -60,7 +60,7 @@ private lemma exists_affineCombination_eq_smul_eq_aux {p : ι → P} (hp : Affin
       by_cases hj : j = i
       · simp [hj]
       replace hind := congr_fun hind j
-      convert hind using 1
+      convert! hind using 1
       · simp [Set.indicator_apply, hj]
       · simp [Set.indicator_apply, hj, w', AffineMap.lineMap_apply_module]
     · simp [Finset.sum_add_distrib, ← Finset.mul_sum, hw, hfs]
@@ -86,14 +86,14 @@ lemma exists_affineCombination_eq_smul_eq {p : ι → P} (hp : AffineIndependent
     by_cases hi : (i : ι) ∈ fs i <;> simpa [hi] using Finset.sum_congr rfl (by aesop)
   have hp'x : ∀ i : s, p' ∈ line[k, p i, (fsx i).affineCombination k p (wx i)] := by
     intro i
-    convert hp' i using 4
+    convert! hp' i using 4
     simp_rw [fsx, wx]
     exact (Finset.affineCombination_indicator_subset _ _ (by simp)).symm
   obtain ⟨w', fs', h⟩ := hp.exists_affineCombination_eq_smul_eq_aux hs hfsx hwx hp'x
   refine ⟨w', fs', h.1, h.2.1, fun i ↦ ?_⟩
   obtain ⟨r, hr⟩ := h.2.2 i
   refine ⟨r, fun j ↦ ?_⟩
-  convert hr j using 2
+  convert! hr j using 2
   simp only [Set.indicator_apply, Set.mem_diff, SetLike.mem_coe, Set.mem_singleton_iff,
     Finset.coe_insert, Set.insert_diff_of_mem, fsx, wx]
   grind
@@ -119,7 +119,7 @@ lemma exists_affineCombination_eq_smul_eq_of_fintype [Fintype ι] {p : ι → P}
   · intro i
     obtain ⟨r, hr⟩ := hi i
     refine ⟨r, fun j ↦ ?_⟩
-    convert hr j using 1
+    convert! hr j using 1
     · simp [Set.indicator_apply]
     · by_cases hj : j = (i : ι) <;> simp [Set.indicator_apply, hj]
 
diff --git a/Mathlib/LinearAlgebra/AffineSpace/Combination.lean b/Mathlib/LinearAlgebra/AffineSpace/Combination.lean
index a4e6ab208bc281..78843dcbb221d9 100644
--- a/Mathlib/LinearAlgebra/AffineSpace/Combination.lean
+++ b/Mathlib/LinearAlgebra/AffineSpace/Combination.lean
@@ -432,7 +432,7 @@ theorem affineCombination_of_eq_one_of_eq_zero (w : ι → k) (p : ι → P) {i
   have h1 : ∑ i ∈ s, w i = 1 := hwi ▸ sum_eq_single i hw0 fun h => False.elim (h his)
   rw [s.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one w p h1 (p i),
     weightedVSubOfPoint_apply]
-  convert zero_vadd V (p i)
+  convert! zero_vadd V (p i)
   refine sum_eq_zero ?_
   intro i2 hi2
   by_cases h : i2 = i
@@ -588,8 +588,8 @@ lemma affineCombination_apply_eq_lineMap_sum [DecidableEq ι] (w : ι → k) (p
   rw [s.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one w p h p₁,
     weightedVSubOfPoint_apply, ← s.sum_inter_add_sum_diff s', AffineMap.lineMap_apply,
     vadd_right_cancel_iff, sum_smul]
-  convert add_zero _ with i hi
-  · convert Finset.sum_const_zero with i hi
+  convert! add_zero _ with i hi
+  · convert! Finset.sum_const_zero with i hi
     simp [hp₁ i hi]
   · exact (hp₂ i hi).symm
 
@@ -906,7 +906,7 @@ lemma affineCombination_mem_affineSpan_image [Nontrivial k] {s : Finset ι} {w :
     simp only [Finset.mem_sdiff, Finset.mem_filter, not_and] at hi
     exact hs' i hi.1 (hi.2 hi.1)
   rw [← Finset.sum_subtype_eq_sum_filter] at h'
-  convert affineCombination_mem_affineSpan h' (fun x ↦ p x)
+  convert! affineCombination_mem_affineSpan h' (fun x ↦ p x)
   rw [Finset.affineCombination_subtype_eq_filter, Finset.affineCombination_indicator_subset w p
     (Finset.filter_subset _ _)]
   refine Finset.affineCombination_congr _ (fun i hi ↦ ?_) (fun _ _ ↦ rfl)
diff --git a/Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean b/Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean
index b118fc3ce80573..5890ae57f58b85 100644
--- a/Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean
+++ b/Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean
@@ -366,7 +366,7 @@ instance finiteDimensional_vectorSpan_insert (s : AffineSubspace k P)
   rcases (s : Set P).eq_empty_or_nonempty with (hs | ⟨p₀, hp₀⟩)
   · rw [coe_eq_bot_iff] at hs
     rw [hs, bot_coe, span_empty, bot_coe, direction_affineSpan]
-    convert finiteDimensional_bot k V <;> simp
+    convert! finiteDimensional_bot k V <;> simp
   · rw [affineSpan_coe, direction_affineSpan_insert hp₀]
     infer_instance
 
@@ -666,7 +666,7 @@ theorem affineIndependent_iff_affineIndependent_collinear_ne {p₁ p₂ p₃ p :
     AffineIndependent k ![p₁, p₂, p] ↔ AffineIndependent k ![p₁, p₂, p₃] := by
   refine ⟨fun h ↦ affineIndependent_of_affineIndependent_collinear_ne h hcol hne2,
     fun h ↦ affineIndependent_of_affineIndependent_collinear_ne h ?_ hne1⟩
-  convert hcol using 1
+  convert! hcol using 1
   aesop
 
 variable (k) in
@@ -753,9 +753,9 @@ theorem finrank_vectorSpan_insert_le (s : AffineSubspace k P) (p : P) :
   · rw [coe_eq_bot_iff] at hs
     rw [hs, bot_coe, span_empty, bot_coe, direction_affineSpan, direction_bot, finrank_bot,
       zero_add]
-    convert zero_le_one' ℕ
+    convert! zero_le_one' ℕ
     rw [← finrank_bot k V]
-    convert rfl <;> simp
+    convert! rfl <;> simp
   · rw [affineSpan_coe, direction_affineSpan_insert hp₀, add_comm]
     refine (Submodule.finrank_add_le_finrank_add_finrank _ _).trans ?_
     gcongr
diff --git a/Mathlib/LinearAlgebra/AffineSpace/Independent.lean b/Mathlib/LinearAlgebra/AffineSpace/Independent.lean
index cf95dacc26c436..0f6fc3f0c4e20a 100644
--- a/Mathlib/LinearAlgebra/AffineSpace/Independent.lean
+++ b/Mathlib/LinearAlgebra/AffineSpace/Independent.lean
@@ -130,7 +130,7 @@ theorem affineIndependent_iff_linearIndependent_vsub (p : ι → P) (i1 : ι) :
       let f : ι → V := fun i => w i • (p i -ᵥ p i1)
       have hs2 : (∑ i ∈ (s.erase i1).subtype fun i => i ≠ i1, f i) = 0 := by
         rw [← hs]
-        convert Finset.sum_subtype_of_mem f fun x => Finset.ne_of_mem_erase
+        convert! Finset.sum_subtype_of_mem f fun x => Finset.ne_of_mem_erase
       have h2 := h ((s.erase i1).subtype fun i => i ≠ i1) (fun x => w x) hs2
       simp_rw [Finset.mem_subtype] at h2
       have h2b : ∀ i ∈ s, i ≠ i1 → w i = 0 := fun i his hi =>
@@ -150,15 +150,16 @@ theorem affineIndependent_set_iff_linearIndependent_vsub {s : Set P} {p₁ : P}
     let f : (fun p : P => (p -ᵥ p₁ : V)) '' (s \ {p₁}) → { x : s // x ≠ ⟨p₁, hp₁⟩ } := fun x =>
       ⟨⟨(x : V) +ᵥ p₁, Set.mem_of_mem_diff (hv x)⟩, fun hx =>
         Set.notMem_of_mem_diff (hv x) (Subtype.ext_iff.1 hx)⟩
-    convert h.comp f fun x1 x2 hx =>
+    convert!
+      h.comp f fun x1 x2 hx =>
         Subtype.ext (vadd_right_cancel p₁ (Subtype.ext_iff.1 (Subtype.ext_iff.1 hx)))
     ext v
     exact (vadd_vsub (v : V) p₁).symm
   · intro h
     let f : { x : s // x ≠ ⟨p₁, hp₁⟩ } → (fun p : P => (p -ᵥ p₁ : V)) '' (s \ {p₁}) := fun x =>
       ⟨((x : s) : P) -ᵥ p₁, ⟨x, ⟨⟨(x : s).property, fun hx => x.property (Subtype.ext hx)⟩, rfl⟩⟩⟩
-    convert h.comp f fun x1 x2 hx =>
-        Subtype.ext (Subtype.ext (vsub_left_cancel (Subtype.ext_iff.1 hx)))
+    convert!
+      h.comp f fun x1 x2 hx => Subtype.ext (Subtype.ext (vsub_left_cancel (Subtype.ext_iff.1 hx)))
 
 /-- A set of nonzero vectors is linearly independent if and only if,
 given a point `p₁`, the vectors added to `p₁` and `p₁` itself are
@@ -321,7 +322,7 @@ protected theorem AffineIndependent.range {p : ι → P} (ha : AffineIndependent
   let f : Set.range p → ι := fun x => x.property.choose
   have hf : ∀ x, p (f x) = x := fun x => x.property.choose_spec
   let fe : Set.range p ↪ ι := ⟨f, fun x₁ x₂ he => Subtype.ext (hf x₁ ▸ hf x₂ ▸ he ▸ rfl)⟩
-  convert ha.comp_embedding fe
+  convert! ha.comp_embedding fe
   ext
   simp [fe, hf]
 
@@ -339,7 +340,7 @@ theorem affineIndependent_equiv {ι' : Type*} (e : ι ≃ ι') {p : ι' → P} :
 theorem AffineIndependent.comm_left {p₁ p₂ p₃ : P} (h : AffineIndependent k ![p₁, p₂, p₃]) :
     AffineIndependent k ![p₂, p₁, p₃] := by
   rw [← affineIndependent_equiv (Equiv.swap 0 1)]
-  convert h using 1
+  convert! h using 1
   ext x
   fin_cases x <;> rfl
 
@@ -347,7 +348,7 @@ theorem AffineIndependent.comm_left {p₁ p₂ p₃ : P} (h : AffineIndependent
 theorem AffineIndependent.comm_right {p₁ p₂ p₃ : P} (h : AffineIndependent k ![p₁, p₂, p₃]) :
     AffineIndependent k ![p₁, p₃, p₂] := by
   rw [← affineIndependent_equiv (Equiv.swap 1 2)]
-  convert h using 1
+  convert! h using 1
   ext x
   fin_cases x <;> rfl
 
@@ -355,7 +356,7 @@ theorem AffineIndependent.comm_right {p₁ p₂ p₃ : P} (h : AffineIndependent
 theorem AffineIndependent.reverse_of_three {p₁ p₂ p₃ : P} (h : AffineIndependent k ![p₁, p₂, p₃]) :
     AffineIndependent k ![p₃, p₂, p₁] := by
   rw [← affineIndependent_equiv (Equiv.swap 0 2)]
-  convert h using 1
+  convert! h using 1
   ext x
   fin_cases x <;> rfl
 
@@ -396,7 +397,7 @@ lemma AffineIndependent.indicator_extend_eq_of_affineCombination_comp_embedding_
   rw [← hw₂e, ← affineCombination_map] at h
   refine (ha.indicator_eq_of_affineCombination_eq s₁ (s₂.map e) _ _ hw₁ ?_ h.symm).symm
   rw [sum_map]
-  convert hw₂ with i hi
+  convert! hw₂ with i hi
   exact e.injective.extend_apply _ _ _
 
 lemma AffineIndependent.indicator_extend_eq_of_affineCombination_comp_embedding_eq_of_fintype
@@ -470,7 +471,7 @@ lemma AffineIndependent.inf_affineSpan_eq_affineSpan_inter [Nontrivial k] {p : 
     replace ha := ha fs₁ fs₂ w₁ w₂ hw₁ hw₂ hw₁₂
     refine ⟨fs₁ ∩ fs₂, by grind, w₁, ?_, ?_⟩
     · rw [← hw₁, ← fs₁.sum_inter_add_sum_diff fs₂, eq_comm]
-      convert add_zero _
+      convert! add_zero _
       refine Finset.sum_eq_zero ?_
       intro i hi
       rw [← Set.indicator_of_mem (s := ↑fs₁) (by grind) w₁, ha, Set.indicator_of_notMem (by grind)]
@@ -619,7 +620,7 @@ theorem exists_nontrivial_relation_sum_zero_of_not_affine_ind {t : Finset V}
     refine ⟨fun x => if hx : x ∈ t then f x hx else (0 : k), ?_, ?_, by use i; simp [f, hi]⟩
     on_goal 1 =>
       suffices (∑ e ∈ t, dite (e ∈ t) (fun hx => f e hx • e) fun _ => 0) = 0 by
-        convert this
+        convert! this
         rename V => x
         by_cases hx : x ∈ t <;> simp [hx]
     all_goals
@@ -850,7 +851,7 @@ theorem affineIndependent_of_ne_of_mem_of_mem_of_notMem {s : AffineSubspace k P}
     AffineIndependent k ![p₁, p₂, p₃] := by
   have ha : AffineIndependent k fun x : { x : Fin 3 // x ≠ 2 } => ![p₁, p₂, p₃] x := by
     rw [← affineIndependent_equiv (finSuccAboveEquiv (2 : Fin 3))]
-    convert affineIndependent_of_ne k hp₁p₂
+    convert! affineIndependent_of_ne k hp₁p₂
     ext x
     fin_cases x <;> rfl
   refine ha.affineIndependent_of_notMem_span ?_
@@ -866,7 +867,7 @@ theorem affineIndependent_of_ne_of_mem_of_notMem_of_mem {s : AffineSubspace k P}
     (hp₁p₃ : p₁ ≠ p₃) (hp₁ : p₁ ∈ s) (hp₂ : p₂ ∉ s) (hp₃ : p₃ ∈ s) :
     AffineIndependent k ![p₁, p₂, p₃] := by
   rw [← affineIndependent_equiv (Equiv.swap (1 : Fin 3) 2)]
-  convert affineIndependent_of_ne_of_mem_of_mem_of_notMem hp₁p₃ hp₁ hp₃ hp₂ using 1
+  convert! affineIndependent_of_ne_of_mem_of_mem_of_notMem hp₁p₃ hp₁ hp₃ hp₂ using 1
   ext x
   fin_cases x <;> rfl
 
@@ -876,7 +877,7 @@ theorem affineIndependent_of_ne_of_notMem_of_mem_of_mem {s : AffineSubspace k P}
     (hp₂p₃ : p₂ ≠ p₃) (hp₁ : p₁ ∉ s) (hp₂ : p₂ ∈ s) (hp₃ : p₃ ∈ s) :
     AffineIndependent k ![p₁, p₂, p₃] := by
   rw [← affineIndependent_equiv (Equiv.swap (0 : Fin 3) 2)]
-  convert affineIndependent_of_ne_of_mem_of_mem_of_notMem hp₂p₃.symm hp₃ hp₂ hp₁ using 1
+  convert! affineIndependent_of_ne_of_mem_of_mem_of_notMem hp₂p₃.symm hp₃ hp₂ hp₁ using 1
   ext x
   fin_cases x <;> rfl
 
diff --git a/Mathlib/LinearAlgebra/AffineSpace/Simplex/Basic.lean b/Mathlib/LinearAlgebra/AffineSpace/Simplex/Basic.lean
index 0f6150d39387b8..d7d4745575b921 100644
--- a/Mathlib/LinearAlgebra/AffineSpace/Simplex/Basic.lean
+++ b/Mathlib/LinearAlgebra/AffineSpace/Simplex/Basic.lean
@@ -551,8 +551,8 @@ lemma affineCombination_mem_setInterior_face_iff_mem (I : Set k) {n : ℕ} (s :
         (fun i hi ↦ hi0 _ (by simpa using hi)) (fun _ ↦ rfl), hw]
     have hw'01 (i) : w' i ∈ I := hii (fs.orderEmbOfFin h i) (by simp)
     rw [← (s.face h).affineCombination_mem_setInterior_iff hw'] at hw'01
-    convert hw'01
-    convert Finset.univ.affineCombination_map (fs.orderEmbOfFin h).toEmbedding w s.points using 1
+    convert! hw'01
+    convert! Finset.univ.affineCombination_map (fs.orderEmbOfFin h).toEmbedding w s.points using 1
     simp only [map_orderEmbOfFin_univ, Finset.affineCombination_indicator_subset _ _ fs.subset_univ]
     congr
     grind [Set.indicator_eq_self, support_subset_iff]
diff --git a/Mathlib/LinearAlgebra/AffineSpace/Simplex/Centroid.lean b/Mathlib/LinearAlgebra/AffineSpace/Simplex/Centroid.lean
index 12f3b1bb8d5120..2856c6aba0432c 100644
--- a/Mathlib/LinearAlgebra/AffineSpace/Simplex/Centroid.lean
+++ b/Mathlib/LinearAlgebra/AffineSpace/Simplex/Centroid.lean
@@ -138,7 +138,7 @@ theorem eq_centroid_iff_sum_vsub_eq_zero [CharZero k] {s : Simplex k P n} {p : P
 the points. -/
 theorem face_centroid_eq_centroid {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ}
     (h : #fs = m + 1) : Finset.univ.centroid k (s.face h).points = fs.centroid k s.points := by
-  convert (Finset.univ.centroid_map k (fs.orderEmbOfFin h).toEmbedding s.points).symm
+  convert! (Finset.univ.centroid_map k (fs.orderEmbOfFin h).toEmbedding s.points).symm
   rw [← Finset.coe_inj, Finset.coe_map, Finset.coe_univ, Set.image_univ]
   simp
 
@@ -213,7 +213,7 @@ theorem centroid_reindex {m n : ℕ} (s : Simplex k P m)
   simp only [reindex]
   have h_eq : m = n := by simpa using Fintype.card_eq.2 ⟨e⟩
   subst h_eq
-  convert Finset.univ.affineCombination_map e.toEmbedding _ _ <;> simp [Function.comp_assoc]
+  convert! Finset.univ.affineCombination_map e.toEmbedding _ _ <;> simp [Function.comp_assoc]
 
 theorem centroid_restrict [CharZero k] {n : ℕ} (s : Simplex k P n) (S : AffineSubspace k P)
     (hS : affineSpan k (Set.range s.points) ≤ S) :
@@ -515,7 +515,7 @@ theorem eq_centroid_of_forall_mem_median [CharZero k] (s : Simplex k P n) {hn :
       fun x => ⟨x.val, h x⟩
     have f_inj : Function.Injective f := by intro x y hxy; grind
     have h2 := h1.comp f f_inj
-    convert h2 using 1
+    convert! h2 using 1
     grind only [mem_compl, Finset.notMem_singleton]
   have he : ∃ i j : s', i ≠ j := by
     simp only [ne_eq, Subtype.exists, Subtype.mk.injEq, exists_prop]
@@ -539,7 +539,7 @@ def medial [CharZero k] (s : Simplex k P n) : Simplex k P n where
     obtain h := s.independent
     rw [affineIndependent_iff_linearIndependent_vsub k _ 0] at h ⊢
     simp_rw [faceOppositeCentroid_vsub_faceOppositeCentroid]
-    convert h.units_smul fun _ ↦ Units.mk0 (-n)⁻¹ (by simpa using NeZero.ne n) with i
+    convert! h.units_smul fun _ ↦ Units.mk0 (-n)⁻¹ (by simpa using NeZero.ne n) with i
     simp [← smul_neg]
 
 theorem medial_points [CharZero k] (s : Simplex k P n) (i : Fin (n + 1)) :
diff --git a/Mathlib/LinearAlgebra/AffineSpace/Slope.lean b/Mathlib/LinearAlgebra/AffineSpace/Slope.lean
index ea43e7c24d3bb4..e000e52df3486c 100644
--- a/Mathlib/LinearAlgebra/AffineSpace/Slope.lean
+++ b/Mathlib/LinearAlgebra/AffineSpace/Slope.lean
@@ -127,7 +127,7 @@ theorem lineMap_slope_lineMap_slope_lineMap (f : k → PE) (a b r : k) :
     lineMap (slope f (lineMap a b r) b) (slope f a (lineMap a b r)) r = slope f a b := by
   obtain rfl | hab : a = b ∨ a ≠ b := Classical.em _; · simp
   rw [slope_comm _ a, slope_comm _ a, slope_comm _ _ b]
-  convert lineMap_slope_slope_sub_div_sub f b (lineMap a b r) a hab.symm using 2
+  convert! lineMap_slope_slope_sub_div_sub f b (lineMap a b r) a hab.symm using 2
   rw [lineMap_apply_ring, eq_div_iff (sub_ne_zero.2 hab), sub_mul, one_mul, mul_sub, ← sub_sub,
     sub_sub_cancel]
 
diff --git a/Mathlib/LinearAlgebra/Alternating/Basic.lean b/Mathlib/LinearAlgebra/Alternating/Basic.lean
index 0dd6c8d60bcf89..b94d11f9bc47a2 100644
--- a/Mathlib/LinearAlgebra/Alternating/Basic.lean
+++ b/Mathlib/LinearAlgebra/Alternating/Basic.lean
@@ -657,7 +657,7 @@ theorem map_update_update [DecidableEq ι] {i j : ι} (hij : i ≠ j) (m : M) :
 theorem map_swap_add [DecidableEq ι] {i j : ι} (hij : i ≠ j) :
     f (v ∘ Equiv.swap i j) + f v = 0 := by
   rw [Equiv.comp_swap_eq_update]
-  convert f.map_update_update v hij (v i + v j)
+  convert! f.map_update_update v hij (v i + v j)
   simp [f.map_update_self _ hij, f.map_update_self _ hij.symm,
     Function.update_comm hij (v i + v j) (v _) v, Function.update_comm hij.symm (v i) (v i) v]
 
diff --git a/Mathlib/LinearAlgebra/Alternating/DomCoprod.lean b/Mathlib/LinearAlgebra/Alternating/DomCoprod.lean
index 2475c505a79254..78db36d5a3094b 100644
--- a/Mathlib/LinearAlgebra/Alternating/DomCoprod.lean
+++ b/Mathlib/LinearAlgebra/Alternating/DomCoprod.lean
@@ -84,7 +84,7 @@ theorem domCoprod.summand_add_swap_smul_eq_zero (a : Mᵢ [⋀^ιa]→ₗ[R'] N
   simp only [one_mul, neg_mul, Function.comp_apply, Units.neg_smul, Perm.coe_mul,
     MultilinearMap.smul_apply, MultilinearMap.neg_apply, MultilinearMap.domDomCongr_apply,
     MultilinearMap.domCoprod_apply]
-  convert add_neg_cancel (G := N₁ ⊗[R'] N₂) _ using 6 <;>
+  convert! add_neg_cancel (G := N₁ ⊗[R'] N₂) _ using 6 <;>
     · ext k
       rw [Equiv.apply_swap_eq_self hv]
 
diff --git a/Mathlib/LinearAlgebra/Basis/Submodule.lean b/Mathlib/LinearAlgebra/Basis/Submodule.lean
index e627a3f168126f..aa9d6ba203ab18 100644
--- a/Mathlib/LinearAlgebra/Basis/Submodule.lean
+++ b/Mathlib/LinearAlgebra/Basis/Submodule.lean
@@ -66,7 +66,7 @@ theorem Basis.eq_bot_of_rank_eq_zero [IsDomain R] (b : Basis ι R M) (N : Submod
   rintro g sum_eq i
   simp only [Fin.default_eq_zero, Finset.univ_unique,
     Finset.sum_singleton] at sum_eq
-  convert (b.smul_eq_zero.mp sum_eq).resolve_right x_ne
+  convert! (b.smul_eq_zero.mp sum_eq).resolve_right x_ne
 
 end Module
 
@@ -100,7 +100,7 @@ def Submodule.inductionOnRankAux (b : Basis ι R M) (P : Submodule R M → Sort*
     apply rank_ih
     intro m v hli
     refine Nat.succ_le_succ_iff.mp (rank_le (Fin.cons ⟨x, x_mem⟩ fun i => ⟨v i, N'_le (v i).2⟩) ?_)
-    convert hli.finCons' x _ ?_
+    convert! hli.finCons' x _ ?_
     · ext i
       refine Fin.cases ?_ ?_ i <;> simp
     · intro c y hy hc
diff --git a/Mathlib/LinearAlgebra/Basis/VectorSpace.lean b/Mathlib/LinearAlgebra/Basis/VectorSpace.lean
index b9e1cea57f2518..3f58c0a4c43c26 100644
--- a/Mathlib/LinearAlgebra/Basis/VectorSpace.lean
+++ b/Mathlib/LinearAlgebra/Basis/VectorSpace.lean
@@ -164,7 +164,7 @@ theorem coe_ofVectorSpace : ⇑(ofVectorSpace K V) = ((↑) : _ → _) :=
 
 theorem ofVectorSpaceIndex.linearIndependent :
     LinearIndependent K ((↑) : ofVectorSpaceIndex K V → V) := by
-  convert (ofVectorSpace K V).linearIndependent
+  convert! (ofVectorSpace K V).linearIndependent
   ext x
   rw [ofVectorSpace_apply_self]
 
diff --git a/Mathlib/LinearAlgebra/BilinearForm/DualLattice.lean b/Mathlib/LinearAlgebra/BilinearForm/DualLattice.lean
index 495ad4187a5b99..628935e785ca77 100644
--- a/Mathlib/LinearAlgebra/BilinearForm/DualLattice.lean
+++ b/Mathlib/LinearAlgebra/BilinearForm/DualLattice.lean
@@ -39,7 +39,7 @@ def dualSubmodule (N : Submodule R M) : Submodule R M where
   add_mem' {a b} ha hb y hy := by simpa using add_mem (ha y hy) (hb y hy)
   zero_mem' y _ := by rw [B.zero_left]; exact zero_mem _
   smul_mem' r a ha y hy := by
-    convert (1 : Submodule R S).smul_mem r (ha y hy)
+    convert! (1 : Submodule R S).smul_mem r (ha y hy)
     rw [← IsScalarTower.algebraMap_smul S r a]
     simp only [algebraMap_smul, map_smul_of_tower, LinearMap.smul_apply]
 
diff --git a/Mathlib/LinearAlgebra/BilinearForm/Properties.lean b/Mathlib/LinearAlgebra/BilinearForm/Properties.lean
index 444f35f423d906..5f791c917facf3 100644
--- a/Mathlib/LinearAlgebra/BilinearForm/Properties.lean
+++ b/Mathlib/LinearAlgebra/BilinearForm/Properties.lean
@@ -316,7 +316,7 @@ theorem Nondegenerate.congr {B : BilinForm R M} (e : M ≃ₗ[R] M') (h : B.Nond
 theorem nondegenerate_congr_iff {B : BilinForm R M} (e : M ≃ₗ[R] M') :
     (congr e B).Nondegenerate ↔ B.Nondegenerate :=
   ⟨fun h => by
-    convert h.congr e.symm
+    convert! h.congr e.symm
     rw [congr_congr, e.self_trans_symm, congr_refl, LinearEquiv.refl_apply], Nondegenerate.congr e⟩
 
 theorem Nondegenerate.ker_eq_bot {B : BilinForm R M} (h : B.Nondegenerate) :
@@ -412,7 +412,7 @@ lemma dualBasis_flip_dualBasis (hB : B.Nondegenerate) (b : Basis ι K V) :
 lemma dualBasis_dualBasis (hB : B.Nondegenerate) (hB' : B.IsSymm)
     (b : Basis ι K V) :
     B.dualBasis hB (B.dualBasis hB b) = b := by
-  convert dualBasis_dualBasis_flip hB.flip b
+  convert! dualBasis_dualBasis_flip hB.flip b
   rwa [eq_comm, ← isSymm_iff_flip]
 
 lemma dualBasis_involutive (hB : B.Nondegenerate) (hB' : B.IsSymm) :
diff --git a/Mathlib/LinearAlgebra/BilinearMap.lean b/Mathlib/LinearAlgebra/BilinearMap.lean
index 1c69ebe4f2f03a..275e57109ee607 100644
--- a/Mathlib/LinearAlgebra/BilinearMap.lean
+++ b/Mathlib/LinearAlgebra/BilinearMap.lean
@@ -365,7 +365,7 @@ theorem compl₁₂_inj [SMulCommClass R₂ R₁ Pₗ]
     ext x y
     obtain ⟨x', rfl⟩ := hₗ x
     obtain ⟨y', rfl⟩ := hᵣ y
-    convert LinearMap.congr_fun₂ h x' y' using 0
+    convert! LinearMap.congr_fun₂ h x' y' using 0
   · -- B₁ = B₂ → B₁.comp l r = B₂.comp l r
     subst h; rfl
 
diff --git a/Mathlib/LinearAlgebra/CliffordAlgebra/Basic.lean b/Mathlib/LinearAlgebra/CliffordAlgebra/Basic.lean
index f9295fc40db4aa..51f80547faaf2a 100644
--- a/Mathlib/LinearAlgebra/CliffordAlgebra/Basic.lean
+++ b/Mathlib/LinearAlgebra/CliffordAlgebra/Basic.lean
@@ -155,7 +155,7 @@ theorem lift_ι_apply (f : M →ₗ[R] A) (cond : ∀ m, f m * f m = algebraMap
 @[simp]
 theorem lift_unique (f : M →ₗ[R] A) (cond : ∀ m : M, f m * f m = algebraMap _ _ (Q m))
     (g : CliffordAlgebra Q →ₐ[R] A) : g.toLinearMap.comp (ι Q) = f ↔ g = lift Q ⟨f, cond⟩ := by
-  convert (lift Q : _ ≃ (CliffordAlgebra Q →ₐ[R] A)).symm_apply_eq
+  convert! (lift Q : _ ≃ (CliffordAlgebra Q →ₐ[R] A)).symm_apply_eq
   rw [lift_symm_apply, Subtype.mk_eq_mk]
 
 @[simp]
@@ -367,11 +367,11 @@ equivalent. -/
 def equivOfIsometry (e : Q₁.IsometryEquiv Q₂) : CliffordAlgebra Q₁ ≃ₐ[R] CliffordAlgebra Q₂ :=
   AlgEquiv.ofAlgHom (map e.toIsometry) (map e.symm.toIsometry)
     ((map_comp_map _ _).trans <| by
-      convert map_id Q₂ using 2
+      convert! map_id Q₂ using 2
       ext m
       exact e.toLinearEquiv.apply_symm_apply m)
     ((map_comp_map _ _).trans <| by
-      convert map_id Q₁ using 2
+      convert! map_id Q₁ using 2
       ext m
       exact e.toLinearEquiv.symm_apply_apply m)
 
diff --git a/Mathlib/LinearAlgebra/CliffordAlgebra/Inversion.lean b/Mathlib/LinearAlgebra/CliffordAlgebra/Inversion.lean
index d32b0bd48cfd06..c9dfc7c666d345 100644
--- a/Mathlib/LinearAlgebra/CliffordAlgebra/Inversion.lean
+++ b/Mathlib/LinearAlgebra/CliffordAlgebra/Inversion.lean
@@ -35,7 +35,7 @@ def invertibleιOfInvertible (m : M) [Invertible (Q m)] : Invertible (ι Q m) wh
 theorem invOf_ι (m : M) [Invertible (Q m)] [Invertible (ι Q m)] :
     ⅟(ι Q m) = ι Q (⅟(Q m) • m) := by
   letI := invertibleιOfInvertible Q m
-  convert (rfl : ⅟(ι Q m) = _)
+  convert! (rfl : ⅟(ι Q m) = _)
 
 theorem isUnit_ι_of_isUnit {m : M} (h : IsUnit (Q m)) : IsUnit (ι Q m) := by
   cases h.nonempty_invertible
diff --git a/Mathlib/LinearAlgebra/CliffordAlgebra/SpinGroup.lean b/Mathlib/LinearAlgebra/CliffordAlgebra/SpinGroup.lean
index 9917233aedbacd..f5a2f3c2fffd58 100644
--- a/Mathlib/LinearAlgebra/CliffordAlgebra/SpinGroup.lean
+++ b/Mathlib/LinearAlgebra/CliffordAlgebra/SpinGroup.lean
@@ -226,7 +226,7 @@ See `star_mem` for only one direction. -/
 theorem star_mem_iff {x : CliffordAlgebra Q} : star x ∈ pinGroup Q ↔ x ∈ pinGroup Q := by
   refine ⟨?_, star_mem⟩
   intro hx
-  convert star_mem hx
+  convert! star_mem hx
   exact (star_star x).symm
 
 instance : Star (pinGroup Q) where
@@ -357,7 +357,7 @@ See `star_mem` for only one direction.
 theorem star_mem_iff {x : CliffordAlgebra Q} : star x ∈ spinGroup Q ↔ x ∈ spinGroup Q := by
   refine ⟨?_, star_mem⟩
   intro hx
-  convert star_mem hx
+  convert! star_mem hx
   exact (star_star x).symm
 
 instance : Star (spinGroup Q) where
diff --git a/Mathlib/LinearAlgebra/Determinant.lean b/Mathlib/LinearAlgebra/Determinant.lean
index 8b475bc7aed35c..4e0b7b9fb3ea2f 100644
--- a/Mathlib/LinearAlgebra/Determinant.lean
+++ b/Mathlib/LinearAlgebra/Determinant.lean
@@ -572,7 +572,7 @@ abbrev LinearMap.equivOfDetNeZero {𝕜 : Type*} [Field 𝕜] {M : Type*} [AddCo
 theorem LinearMap.associated_det_of_eq_comp (e : M ≃ₗ[R] M) (f f' : M →ₗ[R] M)
     (h : ∀ x, f x = f' (e x)) : Associated (LinearMap.det f) (LinearMap.det f') := by
   suffices Associated (LinearMap.det (f' ∘ₗ ↑e)) (LinearMap.det f') by
-    convert this using 2
+    convert! this using 2
     ext x
     exact h x
   rw [← mul_one (LinearMap.det f'), LinearMap.det_comp]
@@ -630,7 +630,7 @@ theorem is_basis_iff_det {v : ι → M} :
   · rintro ⟨hli, hspan⟩
     set v' := Basis.mk hli hspan.ge
     rw [e.det_apply]
-    convert LinearEquiv.isUnit_det (LinearEquiv.refl R M) v' e using 2
+    convert! LinearEquiv.isUnit_det (LinearEquiv.refl R M) v' e using 2
     ext i j
     simp [v']
   · intro h
@@ -763,7 +763,7 @@ theorem det_unitsSMul (e : Basis ι R M) (w : ι → Rˣ) :
     (Matrix.det fun i j => (e.unitsSMul w).repr (f j) i) =
       (↑(∏ i, w i)⁻¹ : R) • Matrix.det fun i j => e.repr (f j) i
   simp only [e.repr_unitsSMul]
-  convert Matrix.det_mul_column (fun i => (↑(w i)⁻¹ : R)) fun i j => e.repr (f j) i
+  convert! Matrix.det_mul_column (fun i => (↑(w i)⁻¹ : R)) fun i j => e.repr (f j) i
   simp [← Finset.prod_inv_distrib]
 
 /-- The determinant of a basis constructed by `unitsSMul` is the product of the given units. -/
diff --git a/Mathlib/LinearAlgebra/Dimension/Basic.lean b/Mathlib/LinearAlgebra/Dimension/Basic.lean
index 645d360414038d..824dc4f9b01d3a 100644
--- a/Mathlib/LinearAlgebra/Dimension/Basic.lean
+++ b/Mathlib/LinearAlgebra/Dimension/Basic.lean
@@ -381,7 +381,7 @@ theorem lift_rank_range_le (f : M →ₗ[R] M') : Cardinal.lift.{v}
   · apply Cardinal.lift_le.mpr
     refine le_ciSup Cardinal.bddAbove_of_small ⟨rangeSplitting f '' s, ?_⟩
     apply LinearIndependent.of_comp f.rangeRestrict
-    convert li.comp (Equiv.Set.rangeSplittingImageEquiv f s) (Equiv.injective _) using 1
+    convert! li.comp (Equiv.Set.rangeSplittingImageEquiv f s) (Equiv.injective _) using 1
   · exact (Cardinal.lift_mk_eq'.mpr ⟨Equiv.Set.rangeSplittingImageEquiv f s⟩).ge
 
 theorem rank_range_le (f : M →ₗ[R] M₁) : Module.rank R (LinearMap.range f) ≤ Module.rank R M := by
diff --git a/Mathlib/LinearAlgebra/Dimension/Constructions.lean b/Mathlib/LinearAlgebra/Dimension/Constructions.lean
index 3f20a79eaade79..46fa52812f084a 100644
--- a/Mathlib/LinearAlgebra/Dimension/Constructions.lean
+++ b/Mathlib/LinearAlgebra/Dimension/Constructions.lean
@@ -62,7 +62,7 @@ theorem LinearIndependent.sumElim_of_quotient
 theorem LinearIndepOn.union_of_quotient {s t : Set ι} {f : ι → M} (hs : LinearIndepOn R f s)
     (ht : LinearIndepOn R (mkQ (span R (f '' s)) ∘ f) t) : LinearIndepOn R f (s ∪ t) := by
   apply hs.union ht.of_comp
-  convert (Submodule.range_ker_disjoint ht).symm
+  convert! (Submodule.range_ker_disjoint ht).symm
   · simp
   aesop
 
@@ -475,7 +475,7 @@ theorem finrank_span_set_eq_card {s : Set M} [Fintype s] (hs : LinearIndepOn R i
 
 theorem finrank_span_finset_eq_card {s : Finset M} (hs : LinearIndepOn R id (s : Set M)) :
     finrank R (span R (s : Set M)) = s.card := by
-  convert finrank_span_set_eq_card (s := (s : Set M)) hs
+  convert! finrank_span_set_eq_card (s := (s : Set M)) hs
   ext
   simp
 
@@ -492,7 +492,7 @@ lemma finrank_le_of_span_eq_top {ι : Type*} [Fintype ι] {v : ι → M}
     (hv : Submodule.span R (Set.range v) = ⊤) : finrank R M ≤ Fintype.card ι := by
   classical
   rw [← finrank_top, ← hv]
-  exact (finrank_span_le_card _).trans (by convert Fintype.card_range_le v; rw [Set.toFinset_card])
+  exact (finrank_span_le_card _).trans (by convert! Fintype.card_range_le v; rw [Set.toFinset_card])
 
 @[simp]
 lemma Pi.dim_spanSubset [Finite ι] [Nontrivial R] {s : Set ι} :
@@ -579,7 +579,7 @@ noncomputable def sumQuot :
   apply Basis.mk (v := b)
   · apply LinearIndependent.sumElim_of_quotient
     · exact bW.linearIndependent
-    · convert bQ.linearIndependent
+    · convert! bQ.linearIndependent
   · unfold b
     rw [Set.Sum.elim_range, Submodule.span_union,
       show Set.range (fun i ↦ (bW i : V)) = W.subtype '' (Set.range (fun i ↦ bW i)) by aesop,
diff --git a/Mathlib/LinearAlgebra/Dimension/ErdosKaplansky.lean b/Mathlib/LinearAlgebra/Dimension/ErdosKaplansky.lean
index bde5ae08d101b2..0f9db109afca68 100644
--- a/Mathlib/LinearAlgebra/Dimension/ErdosKaplansky.lean
+++ b/Mathlib/LinearAlgebra/Dimension/ErdosKaplansky.lean
@@ -136,10 +136,10 @@ theorem lift_rank_lt_rank_dual {K : Type u} {V : Type v} [Field K] [AddCommGroup
 
 theorem rank_lt_rank_dual' {V : Type u} [AddCommGroup V] [Module K V] (h : ℵ₀ ≤ Module.rank K V) :
     Module.rank K V < Module.rank Kᵐᵒᵖ (V →ₗ[K] K) := by
-  convert lift_rank_lt_rank_dual' h; rw [lift_id]
+  convert! lift_rank_lt_rank_dual' h; rw [lift_id]
 
 theorem rank_lt_rank_dual {K V : Type u} [Field K] [AddCommGroup V] [Module K V]
     (h : ℵ₀ ≤ Module.rank K V) : Module.rank K V < Module.rank K (V →ₗ[K] K) := by
-  convert lift_rank_lt_rank_dual h; rw [lift_id]
+  convert! lift_rank_lt_rank_dual h; rw [lift_id]
 
 end Cardinal
diff --git a/Mathlib/LinearAlgebra/Dimension/Finite.lean b/Mathlib/LinearAlgebra/Dimension/Finite.lean
index 0ffa7cd3a87e2c..d08c8e0cf7ff44 100644
--- a/Mathlib/LinearAlgebra/Dimension/Finite.lean
+++ b/Mathlib/LinearAlgebra/Dimension/Finite.lean
@@ -223,7 +223,7 @@ lemma exists_finset_linearIndependent_of_le_finrank {n : ℕ} (hn : n ≤ finran
     ∃ s : Finset M, s.card = n ∧ LinearIndependent R ((↑) : s → M) := by
   by_cases h : finrank R M = 0
   · rw [le_zero_iff.mp (hn.trans_eq h)]
-    exact ⟨∅, rfl, by convert linearIndependent_empty R M using 2 <;> aesop⟩
+    exact ⟨∅, rfl, by convert! linearIndependent_empty R M using 2 <;> aesop⟩
   exact exists_finset_linearIndependent_of_le_rank
     ((Nat.cast_le.mpr hn).trans_eq (cast_toNat_of_lt_aleph0 (toNat_ne_zero.mp h).2))
 
@@ -301,7 +301,7 @@ theorem Module.exists_nontrivial_relation_of_finrank_lt_card {t : Finset M}
   obtain ⟨g, sum, z, nonzero⟩ := Fintype.not_linearIndependent_iff.mp
     (mt LinearIndependent.finset_card_le_finrank h.not_ge)
   refine ⟨Subtype.val.extend g 0, ?_, z, z.2, by rwa [Subtype.val_injective.extend_apply]⟩
-  rw [← Finset.sum_finset_coe]; convert sum; apply Subtype.val_injective.extend_apply
+  rw [← Finset.sum_finset_coe]; convert! sum; apply Subtype.val_injective.extend_apply
 
 /-- If a finset has cardinality larger than `finrank + 1`,
 then there is a nontrivial linear relation amongst its elements,
@@ -476,7 +476,7 @@ theorem finrank_eq_zero_of_basis_imp_false (h : ∀ s : Finset M, Basis.{v} (s :
   finrank_eq_zero_of_basis_imp_not_finite fun s b hs =>
     h hs.toFinset
       (by
-        convert b
+        convert! b
         simp)
 
 theorem finrank_eq_zero_of_not_exists_basis
diff --git a/Mathlib/LinearAlgebra/Dimension/Free.lean b/Mathlib/LinearAlgebra/Dimension/Free.lean
index 1b4235a7c1a7f7..9a6ff3562f240a 100644
--- a/Mathlib/LinearAlgebra/Dimension/Free.lean
+++ b/Mathlib/LinearAlgebra/Dimension/Free.lean
@@ -58,7 +58,7 @@ This is a simpler version of `lift_rank_mul_lift_rank` with `K` and `A` in the s
 theorem rank_mul_rank (A : Type v) [AddCommMonoid A]
     [Module K A] [Module F A] [IsScalarTower F K A] [Module.Free K A] :
     Module.rank F K * Module.rank K A = Module.rank F A := by
-  convert lift_rank_mul_lift_rank F K A <;> rw [lift_id]
+  convert! lift_rank_mul_lift_rank F K A <;> rw [lift_id]
 
 /-- Tower law: if `A` is a `K`-module and `K` is an extension of `F` then
 $\operatorname{rank}_F(A) = \operatorname{rank}_F(K) * \operatorname{rank}_K(A)$. -/
diff --git a/Mathlib/LinearAlgebra/Dimension/FreeAndStrongRankCondition.lean b/Mathlib/LinearAlgebra/Dimension/FreeAndStrongRankCondition.lean
index f2ad8180f7cbc6..8907719c5773e6 100644
--- a/Mathlib/LinearAlgebra/Dimension/FreeAndStrongRankCondition.lean
+++ b/Mathlib/LinearAlgebra/Dimension/FreeAndStrongRankCondition.lean
@@ -53,7 +53,7 @@ theorem le_rank_iff_exists_linearIndependent [Module.Free K V] {c : Cardinal} :
     obtain ⟨κ, t'⟩ := Module.Free.exists_basis (R := K) (M := V)
     let t := t'.reindexRange
     have : LinearIndepOn K id (Set.range t') := by
-      convert t.linearIndependent.linearIndepOn_id
+      convert! t.linearIndependent.linearIndepOn_id
       ext
       simp [t]
     rw [← t.mk_eq_rank'', le_mk_iff_exists_subset] at h
diff --git a/Mathlib/LinearAlgebra/Dimension/LinearMap.lean b/Mathlib/LinearAlgebra/Dimension/LinearMap.lean
index a1f49c0143aecd..4ab815f8bdfc0f 100644
--- a/Mathlib/LinearAlgebra/Dimension/LinearMap.lean
+++ b/Mathlib/LinearAlgebra/Dimension/LinearMap.lean
@@ -110,14 +110,14 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'}
     refine ⟨g '' s, Cardinal.mk_image_eq_lift _ _ fg.injective, ?_⟩
     replace fg : ∀ x, f (g x) = x := by
       intro x
-      convert congr_arg Subtype.val (fg x)
+      convert! congr_arg Subtype.val (fg x)
     replace si : LinearIndepOn K (fun x => f (g x)) s := by
       simpa only [fg] using si.map' _ (ker_subtype _)
     exact si.image_of_comp
   · rintro ⟨s, hsc, si⟩
     have : LinearIndepOn K f.rangeRestrict s :=
-      LinearIndependent.of_comp (LinearMap.range f).subtype (by convert si)
-    convert this.id_image.cardinal_le_rank
+      LinearIndependent.of_comp (LinearMap.range f).subtype (by convert! si)
+    convert! this.id_image.cardinal_le_rank
     rw [← Cardinal.lift_inj, ← hsc, Cardinal.mk_image_eq_of_injOn_lift]
     exact injOn_iff_injective.2 this.injective
 
diff --git a/Mathlib/LinearAlgebra/Dimension/StrongRankCondition.lean b/Mathlib/LinearAlgebra/Dimension/StrongRankCondition.lean
index 1cd53f73f250a8..368c32cb3e9fed 100644
--- a/Mathlib/LinearAlgebra/Dimension/StrongRankCondition.lean
+++ b/Mathlib/LinearAlgebra/Dimension/StrongRankCondition.lean
@@ -147,7 +147,7 @@ theorem Module.Basis.le_span {J : Set M} (v : Basis ι R M) (hJ : span R J = ⊤
   haveI := nontrivial_of_invariantBasisNumber R
   cases fintypeOrInfinite J
   · rw [← Cardinal.lift_le, Cardinal.mk_range_eq_of_injective v.injective, Cardinal.mk_fintype J]
-    convert Cardinal.lift_le.{v}.2 (basis_le_span' v hJ)
+    convert! Cardinal.lift_le.{v}.2 (basis_le_span' v hJ)
     simp
   · let S : J → Set ι := fun j => ↑(v.repr j).support
     let S' : J → Set M := fun j => v '' S j
@@ -330,7 +330,7 @@ theorem Module.Basis.mk_eq_rank'' {ι : Type v} (v : Basis ι R M) : #ι = Modul
       exact
         ⟨Set.range v, by
           rw [LinearIndepOn]
-          convert v.reindexRange.linearIndependent
+          convert! v.reindexRange.linearIndependent
           simp⟩
     · exact (Cardinal.mk_range_eq v v.injective).ge
   · apply ciSup_le'
@@ -601,7 +601,7 @@ theorem strongRankCondition_iff_forall_rank_lt_aleph0 [Nontrivial R] :
     refine ⟨fun ⟨n, f, inj⟩ ↦ ⟨n, ?_⟩, fun ⟨n, le⟩ ↦
       ⟨n, le_rank_iff_exists_linearMap.mp (natCast_le_aleph0.trans le)⟩⟩
     have ⟨g, hg⟩ := f.exists_finsupp_nat_of_fin_fun_injective inj
-    convert (Finsupp.basisSingleOne.linearIndependent.map_injOn _ hg.injOn).cardinal_lift_le_rank
+    convert! (Finsupp.basisSingleOne.linearIndependent.map_injOn _ hg.injOn).cardinal_lift_le_rank
     simp
 
 theorem strongRankCondition_iff_forall_zero_lt_finrank [Nontrivial R] :
diff --git a/Mathlib/LinearAlgebra/Dual/Basis.lean b/Mathlib/LinearAlgebra/Dual/Basis.lean
index 96feeb0126d692..8c652b22e163be 100644
--- a/Mathlib/LinearAlgebra/Dual/Basis.lean
+++ b/Mathlib/LinearAlgebra/Dual/Basis.lean
@@ -135,7 +135,7 @@ def dualBasis : Basis ι R (Dual R M) :=
 -- We use `j = i` to match `Basis.repr_self`
 theorem dualBasis_apply_self (i j : ι) : b.dualBasis i (b j) =
     if j = i then 1 else 0 := by
-  convert b.toDual_apply i j using 2
+  convert! b.toDual_apply i j using 2
   rw [@eq_comm _ j i]
 
 theorem linearCombination_dualBasis (f : ι →₀ R) (i : ι) :
diff --git a/Mathlib/LinearAlgebra/Dual/Lemmas.lean b/Mathlib/LinearAlgebra/Dual/Lemmas.lean
index 29c42d49de56d2..b7dee15231048a 100644
--- a/Mathlib/LinearAlgebra/Dual/Lemmas.lean
+++ b/Mathlib/LinearAlgebra/Dual/Lemmas.lean
@@ -295,7 +295,7 @@ instance instFiniteDimensionalOfIsReflexive (K V : Type*)
     exact lt_irrefl _ this
   have h₁ : lift (Module.rank K V) < Module.rank K (Dual K V) := lift_rank_lt_rank_dual contra
   have h₂ : Module.rank K (Dual K V) < Module.rank K (Dual K (Dual K V)) := by
-    convert lift_rank_lt_rank_dual <| le_trans (by simpa) h₁.le
+    convert! lift_rank_lt_rank_dual <| le_trans (by simpa) h₁.le
     rw [lift_id']
   exact lt_trans h₁ h₂
 
@@ -383,7 +383,7 @@ theorem _root_.mem_span_of_iInf_ker_le_ker [Finite ι] {L : ι → E →ₗ[𝕜
   conv_lhs => enter [2]; intro i; rw [← p.liftQ_mkQ (L i) (iInf_le _ i)]
   rw [← p.liftQ_mkQ K h]
   ext x
-  convert LinearMap.congr_fun hK' (p.mkQ x)
+  convert! LinearMap.congr_fun hK' (p.mkQ x)
   simp only [L', LinearMap.coe_sum, Finset.sum_apply, smul_apply, coe_comp, Function.comp_apply,
     smul_eq_mul]
 
@@ -701,7 +701,7 @@ theorem range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjective (f : M
   have rr_surj : Function.Surjective f.rangeRestrict := by
     rw [← range_eq_top, range_rangeRestrict]
   have := range_dualMap_eq_dualAnnihilator_ker_of_surjective f.rangeRestrict rr_surj
-  convert this using 1
+  convert! this using 1
   · calc
       _ = range ((range f).subtype.comp f.rangeRestrict).dualMap := by simp
       _ = _ := ?_
diff --git a/Mathlib/LinearAlgebra/Eigenspace/Basic.lean b/Mathlib/LinearAlgebra/Eigenspace/Basic.lean
index ae75420493bb31..7dc1121ef6347e 100644
--- a/Mathlib/LinearAlgebra/Eigenspace/Basic.lean
+++ b/Mathlib/LinearAlgebra/Eigenspace/Basic.lean
@@ -280,7 +280,7 @@ lemma genEigenspace_top_eq_maxUnifEigenspaceIndex [IsNoetherian R M] (f : End R
     genEigenspace f μ ⊤ = f.genEigenspace μ (maxUnifEigenspaceIndex f μ) := by
   have := WellFoundedGT.iSup_eq_monotonicSequenceLimit <|
     (f.genEigenspace μ).comp <| WithTop.coeOrderHom.toOrderHom
-  convert this using 1
+  convert! this using 1
   simp only [genEigenspace, OrderHom.coe_mk, le_top, iSup_pos, OrderHom.comp_coe,
     Function.comp_def]
   rw [iSup_prod', iSup_subtype', ← sSup_range, ← sSup_range]
diff --git a/Mathlib/LinearAlgebra/Eigenspace/Minpoly.lean b/Mathlib/LinearAlgebra/Eigenspace/Minpoly.lean
index 81d19c7a1eefb6..e3e6ed43a718f9 100644
--- a/Mathlib/LinearAlgebra/Eigenspace/Minpoly.lean
+++ b/Mathlib/LinearAlgebra/Eigenspace/Minpoly.lean
@@ -99,7 +99,7 @@ variable (f)
 
 lemma finite_hasEigenvalue : Set.Finite f.HasEigenvalue := by
   have h : minpoly R f ≠ 0 := minpoly.ne_zero (Algebra.IsIntegral.isIntegral (R := R) f)
-  convert (minpoly R f).rootSet_finite R
+  convert! (minpoly R f).rootSet_finite R
   ext μ
   change f.HasEigenvalue μ ↔ _
   rw [hasEigenvalue_iff_isRoot, mem_rootSet_of_ne h, IsRoot, coe_aeval_eq_eval]
@@ -140,7 +140,7 @@ section FiniteSpectrum
 theorem Module.End.finite_spectrum {K : Type v} {V : Type w} [Field K] [AddCommGroup V]
     [Module K V] [FiniteDimensional K V] (f : Module.End K V) :
     Set.Finite (spectrum K f) := by
-  convert f.finite_hasEigenvalue
+  convert! f.finite_hasEigenvalue
   ext f x
   exact Module.End.hasEigenvalue_iff_mem_spectrum.symm
 
diff --git a/Mathlib/LinearAlgebra/ExteriorAlgebra/Basic.lean b/Mathlib/LinearAlgebra/ExteriorAlgebra/Basic.lean
index 1ebc16ae040f93..35dcdd716096a7 100644
--- a/Mathlib/LinearAlgebra/ExteriorAlgebra/Basic.lean
+++ b/Mathlib/LinearAlgebra/ExteriorAlgebra/Basic.lean
@@ -285,7 +285,7 @@ def ιMulti (n : ℕ) : M [⋀^Fin n]→ₗ[R] ExteriorAlgebra R M :=
           rw [hfxy, ← Fin.succ_pred y (ne_of_lt h).symm]
           exact ι_mul_prod_list (f ∘ Fin.succ) _
         -- ignore the left-most term and induct on the remaining ones, decrementing indices
-        · convert mul_zero (ι R (f 0))
+        · convert! mul_zero (ι R (f 0))
           refine
             hn
               (fun i => f <| Fin.succ i) (x.pred hx)
diff --git a/Mathlib/LinearAlgebra/ExteriorPower/Basic.lean b/Mathlib/LinearAlgebra/ExteriorPower/Basic.lean
index beb5809e99aa93..98aee3cf78eee7 100644
--- a/Mathlib/LinearAlgebra/ExteriorPower/Basic.lean
+++ b/Mathlib/LinearAlgebra/ExteriorPower/Basic.lean
@@ -160,14 +160,14 @@ noncomputable def relationsSolutionEquiv {ι : Type*} [DecidableEq ι] {M : Type
         rw [map_sub, map_add, Finsupp.linearCombination_single, one_smul,
           Finsupp.linearCombination_single, one_smul,
           Finsupp.linearCombination_single, one_smul, sub_eq_zero] at this
-        convert this.symm -- `convert` is necessary due to the implementation of `MultilinearMap`
+        convert! this.symm -- `convert` is necessary due to the implementation of `MultilinearMap`
       map_update_smul' := fun m i r x ↦ by
         have := s.linearCombination_var_relation (.smul m i r x)
         dsimp at this ⊢
         rw [Finsupp.smul_single, smul_eq_mul, mul_one, map_sub,
           Finsupp.linearCombination_single, one_smul,
           Finsupp.linearCombination_single, sub_eq_zero] at this
-        convert this
+        convert! this
       map_eq_zero_of_eq' := fun v i j hm hij ↦
         by simpa using s.linearCombination_var_relation (.alt v i j hm hij) }
   invFun f :=
diff --git a/Mathlib/LinearAlgebra/FiniteDimensional/Lemmas.lean b/Mathlib/LinearAlgebra/FiniteDimensional/Lemmas.lean
index 4f217eaa1ecfa2..8b507723c38860 100644
--- a/Mathlib/LinearAlgebra/FiniteDimensional/Lemmas.lean
+++ b/Mathlib/LinearAlgebra/FiniteDimensional/Lemmas.lean
@@ -78,7 +78,7 @@ theorem eq_top_of_disjoint [FiniteDimensional K V] (s t : Submodule K V)
   replace hdim : finrank K V = finrank K s + finrank K t :=
     le_antisymm hdim (finrank_add_finrank_le_of_disjoint hdisjoint)
   rw [hdim]
-  convert s.finrank_sup_add_finrank_inf_eq t
+  convert! s.finrank_sup_add_finrank_inf_eq t
   rw [h_finrank_inf, add_zero]
 
 theorem isCompl_iff_disjoint [FiniteDimensional K V] (s t : Submodule K V)
diff --git a/Mathlib/LinearAlgebra/Finsupp/Span.lean b/Mathlib/LinearAlgebra/Finsupp/Span.lean
index 9b363336f7e7d6..42f2508aaa93a8 100644
--- a/Mathlib/LinearAlgebra/Finsupp/Span.lean
+++ b/Mathlib/LinearAlgebra/Finsupp/Span.lean
@@ -128,7 +128,7 @@ theorem mem_sSup_iff_exists_finset {S : Set (Submodule R M)} {m : M} :
   · simp
   · suffices m ∈ ⨆ (i) (hi : i ∈ S) (_ : ⟨i, hi⟩ ∈ s), i by simpa
     rwa [iSup_subtype']
-  · have : ⨆ (i) (_ : i ∈ S ∧ i ∈ s), i = ⨆ (i) (_ : i ∈ s), i := by convert rfl; grind
+  · have : ⨆ (i) (_ : i ∈ S ∧ i ∈ s), i = ⨆ (i) (_ : i ∈ s), i := by convert! rfl; grind
     simpa only [Finset.mem_preimage, iSup_subtype, iSup_and', this]
 
 end Semiring
diff --git a/Mathlib/LinearAlgebra/Finsupp/Supported.lean b/Mathlib/LinearAlgebra/Finsupp/Supported.lean
index 2ffbe608c3fe4b..a774d2ba9954e7 100644
--- a/Mathlib/LinearAlgebra/Finsupp/Supported.lean
+++ b/Mathlib/LinearAlgebra/Finsupp/Supported.lean
@@ -204,7 +204,7 @@ lemma codisjoint_supported_supported_iff [Nontrivial M] {s t : Set α} :
 
 @[simp] theorem supportedEquivFinsupp_symm_apply_coe (s : Set α) [DecidablePred (· ∈ s)]
     (f : s →₀ M) : (supportedEquivFinsupp (R := R) s).symm f = f.extendDomain := by
-  convert restrictSupportEquiv_symm_apply_coe ..
+  convert! restrictSupportEquiv_symm_apply_coe ..
 
 @[simp] theorem supportedEquivFinsupp_symm_single (s : Set α) (i : s) (a : M) :
     ((supportedEquivFinsupp (R := R) s).symm (single i a) : α →₀ M) = single ↑i a := by
diff --git a/Mathlib/LinearAlgebra/Finsupp/VectorSpace.lean b/Mathlib/LinearAlgebra/Finsupp/VectorSpace.lean
index 03c4579274e72c..5193b3d60d253c 100644
--- a/Mathlib/LinearAlgebra/Finsupp/VectorSpace.lean
+++ b/Mathlib/LinearAlgebra/Finsupp/VectorSpace.lean
@@ -79,8 +79,9 @@ theorem linearIndependent_single {φ : ι → Type*} (f : ∀ i, φ i → M)
     (hf : ∀ i, LinearIndependent R (f i)) :
     LinearIndependent R fun ix : Σ i, φ i ↦ single ix.1 (f ix.1 ix.2) := by
   classical
-  convert (DFinsupp.linearIndependent_single _ hf).map_injOn
-    _ (finsuppLequivDFinsupp R).symm.injective.injOn
+  convert!
+    (DFinsupp.linearIndependent_single _ hf).map_injOn _
+      (finsuppLequivDFinsupp R).symm.injective.injOn
   simp
 
 lemma linearIndependent_single_iff {φ : ι → Type*} {f : ∀ i, φ i → M} :
diff --git a/Mathlib/LinearAlgebra/FreeModule/Finite/Matrix.lean b/Mathlib/LinearAlgebra/FreeModule/Finite/Matrix.lean
index afbe5d1d20c242..faacd6dc147ce3 100644
--- a/Mathlib/LinearAlgebra/FreeModule/Finite/Matrix.lean
+++ b/Mathlib/LinearAlgebra/FreeModule/Finite/Matrix.lean
@@ -82,14 +82,14 @@ instance Finite.algHom : Finite (M →ₐ[K] L) :=
 open Cardinal
 
 theorem cardinalMk_algHom_le_rank : #(M →ₐ[K] L) ≤ lift.{v} (Module.rank K M) := by
-  convert (linearIndependent_algHom_toLinearMap K M L).cardinal_lift_le_rank
+  convert! (linearIndependent_algHom_toLinearMap K M L).cardinal_lift_le_rank
   · rw [lift_id]
   · have := Module.nontrivial K L
     rw [lift_id, Module.rank_linearMap_self]
 
 @[stacks 09HS]
 theorem card_algHom_le_finrank : Nat.card (M →ₐ[K] L) ≤ finrank K M := by
-  convert toNat_le_toNat (cardinalMk_algHom_le_rank K M L) ?_
+  convert! toNat_le_toNat (cardinalMk_algHom_le_rank K M L) ?_
   · rw [toNat_lift, finrank]
   · rw [lift_lt_aleph0]; have := Module.nontrivial K L; apply Module.rank_lt_aleph0
 
diff --git a/Mathlib/LinearAlgebra/FreeModule/Int.lean b/Mathlib/LinearAlgebra/FreeModule/Int.lean
index 5e3683fbf59b0a..f48d41c34c3581 100644
--- a/Mathlib/LinearAlgebra/FreeModule/Int.lean
+++ b/Mathlib/LinearAlgebra/FreeModule/Int.lean
@@ -49,7 +49,7 @@ lemma toAddSubgroup_index_eq_pow_mul_prod [Module R M] {N : Submodule R M}
     set e : (ι → R) ≃+ M := ↑bM.equivFun.symm with he
     let e' : (ι → R) →+ M := e
     have he' : Function.Surjective e' := e.surjective
-    convert (AddSubgroup.index_comap_of_surjective N.toAddSubgroup he').symm using 2
+    convert! (AddSubgroup.index_comap_of_surjective N.toAddSubgroup he').symm using 2
     rw [AddSubgroup.comap_equiv_eq_map_symm, he, hN', LinearEquiv.coe_toAddEquiv_symm,
     AddEquiv.symm_symm]
     exact Submodule.map_toAddSubgroup ..
@@ -64,7 +64,7 @@ lemma toAddSubgroup_index_eq_pow_mul_prod [Module R M] {N : Submodule R M}
       intro i
       simp only [Finset.sum_apply, Pi.smul_apply, Pi.single_apply]
       split_ifs with h
-      · convert dvd_mul_left (a h.choose) (c h.choose)
+      · convert! dvd_mul_left (a h.choose) (c h.choose)
         calc ∑ x : Fin n, _ = c h.choose * if i = f h.choose then a h.choose else 0 := by
               refine Finset.sum_eq_single h.choose ?_ (by simp)
               rintro j - hj
@@ -72,8 +72,8 @@ lemma toAddSubgroup_index_eq_pow_mul_prod [Module R M] {N : Submodule R M}
               rw [h.choose_spec] at hinj
               simp [hinj.symm]
           _ = c h.choose * a h.choose := by simp [h.choose_spec]
-      · convert dvd_refl (0 : R)
-        convert Finset.sum_const_zero with j
+      · convert! dvd_refl (0 : R)
+        convert! Finset.sum_const_zero with j
         rw [not_exists] at h
         specialize h j
         rw [eq_comm] at h
@@ -86,7 +86,7 @@ lemma toAddSubgroup_index_eq_pow_mul_prod [Module R M] {N : Submodule R M}
       by_cases! hj : ∃ j, f j = i
       · calc ∑ x : Fin n, _ =
             if i = f hj.choose then (h (f hj.choose)).choose * a hj.choose else 0 := by
-              convert Finset.sum_eq_single (M := R) hj.choose ?_ ?_
+              convert! Finset.sum_eq_single (M := R) hj.choose ?_ ?_
               · simp
               · rintro j - h
                 have hinj := f.injective.ne h
@@ -102,21 +102,21 @@ lemma toAddSubgroup_index_eq_pow_mul_prod [Module R M] {N : Submodule R M}
               congr!
               · exact hj.choose_spec.symm
               · simp [hj]
-      · convert Finset.sum_const_zero with x
+      · convert! Finset.sum_const_zero with x
         · specialize hj x
           rw [ne_comm] at hj
           simp [hj]
         · rw [← zero_dvd_iff]
-          convert h i
+          convert! h i
           simp [hj]
   simp only [hN', AddSubgroup.index_pi, apply_dite, Finset.prod_dite, Set.singleton_zero,
     Ideal.span_zero, Submodule.bot_toAddSubgroup, AddSubgroup.index_pi, AddSubgroup.index_bot,
     Finset.prod_const, Finset.univ_eq_attach, Finset.card_attach]
   rw [mul_comm]
   congr
-  · convert Finset.card_compl {x | ∃ j, f j = x} using 2
+  · convert! Finset.card_compl {x | ∃ j, f j = x} using 2
     · exact (Finset.compl_filter _).symm
-    · convert (Finset.card_image_of_injective Finset.univ f.injective).symm <;> simp
+    · convert! (Finset.card_image_of_injective Finset.univ f.injective).symm <;> simp
   · rw [Finset.attach_eq_univ]
     let f' : Fin n → { x // x ∈ Finset.filter (fun x ↦ ∃ j, f j = x) Finset.univ } :=
       fun i ↦ ⟨f i, by simp⟩
@@ -194,7 +194,7 @@ lemma submodule_toAddSubgroup_index_ne_zero_iff {N : Submodule ℤ (ι → ℤ)}
 
 lemma addSubgroup_index_ne_zero_iff {H : AddSubgroup (ι → ℤ)} :
     H.index ≠ 0 ↔ Nonempty (H ≃+ (ι → ℤ)) := by
-  convert submodule_toAddSubgroup_index_ne_zero_iff (N := AddSubgroup.toIntSubmodule H) using 1
+  convert! submodule_toAddSubgroup_index_ne_zero_iff (N := AddSubgroup.toIntSubmodule H) using 1
   exact ⟨fun ⟨e⟩ ↦ ⟨e.toIntLinearEquiv⟩, fun ⟨e⟩ ↦ ⟨e.toAddEquiv⟩⟩
 
 set_option backward.isDefEq.respectTransparency false in
diff --git a/Mathlib/LinearAlgebra/FreeProduct/Basic.lean b/Mathlib/LinearAlgebra/FreeProduct/Basic.lean
index 59c4dca4926b09..e916dbecd9b492 100644
--- a/Mathlib/LinearAlgebra/FreeProduct/Basic.lean
+++ b/Mathlib/LinearAlgebra/FreeProduct/Basic.lean
@@ -189,7 +189,7 @@ the same `i` is just the injection of multiplication `aᵢ * aᵢ'` in `A i`. -/
 theorem mul_injections (a₁ a₂ : A i) :
     ι' R A (DirectSum.lof R I A i a₁) * ι' R A (DirectSum.lof R I A i a₂)
       = ι' R A (DirectSum.lof R I A i (a₁ * a₂)) := by
-  convert RingQuot.mkAlgHom_rel R <| rel.prod
+  convert! RingQuot.mkAlgHom_rel R <| rel.prod
   simp
 
 /-- The `i`th canonical injection, from `A i` to the free product, as
diff --git a/Mathlib/LinearAlgebra/Goursat.lean b/Mathlib/LinearAlgebra/Goursat.lean
index b39c302ba97412..6c60553745f33d 100644
--- a/Mathlib/LinearAlgebra/Goursat.lean
+++ b/Mathlib/LinearAlgebra/Goursat.lean
@@ -90,7 +90,7 @@ lemma goursat_surjective : ∃ e : (M ⧸ L.goursatFst) ≃ₗ[R] N ⧸ L.goursa
   -- define the map as an R-linear equiv
   use { e with map_smul' := this }
   rw [← toAddSubgroup_injective.eq_iff]
-  convert he using 1
+  convert! he using 1
   ext v
   rw [mem_toAddSubgroup, mem_graph_iff, Eq.comm]
   rfl
@@ -131,7 +131,7 @@ lemma goursat : ∃ (M' : Submodule R M) (N' : Submodule R N) (M'' : Submodule R
       Subtype.exists, Prod.exists, LinearMap.prodMap_apply, subtype_apply, Prod.mk.injEq,
       snd_apply, fst_apply, Subtype.ext_iff, submoduleMap_coe_apply]
       grind
-  · convert goursatFst_prod_goursatSnd_le (range <| P.prod Q)
+  · convert! goursatFst_prod_goursatSnd_le (range <| P.prod Q)
     simp only [ker_prodMap, ker_mkQ, Submodule.ext_iff]
     grind
 
diff --git a/Mathlib/LinearAlgebra/Lagrange.lean b/Mathlib/LinearAlgebra/Lagrange.lean
index 275b424e2e2ff3..0a7fcc873a46ba 100644
--- a/Mathlib/LinearAlgebra/Lagrange.lean
+++ b/Mathlib/LinearAlgebra/Lagrange.lean
@@ -244,7 +244,7 @@ theorem natDegree_basis (hvs : Set.InjOn v s) (hi : i ∈ s) :
     simp_rw [Ne, mem_erase, basisDivisor_eq_zero_iff]
     exact fun j ⟨hij₁, hj⟩ hij₂ => hij₁ (hvs hj hi hij₂.symm)
   rw [← card_erase_of_mem hi, card_eq_sum_ones]
-  convert natDegree_prod _ _ H using 1
+  convert! natDegree_prod _ _ H using 1
   refine sum_congr rfl fun j hj => (natDegree_basisDivisor_of_ne ?_).symm
   rw [Ne, ← basisDivisor_eq_zero_iff]
   exact H _ hj
@@ -414,7 +414,8 @@ theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs :
         Nat.succ_add_sub_one, zero_add]
     rw [degree_basis (Set.InjOn.mono hst hvt) hi, H, WithBot.coe_add, Nat.cast_withBot,
       WithBot.add_lt_add_iff_right (@WithBot.coe_ne_bot _ (#s - 1))]
-    convert degree_interpolate_lt _
+    convert!
+      degree_interpolate_lt _
         (hvt.mono (coe_subset.mpr (insert_subset_iff.mpr ⟨hst hi, sdiff_subset⟩)))
     rw [card_insert_of_notMem (notMem_sdiff_of_mem_right hi), card_sdiff_of_subset hst, add_comm]
   · simp_rw [eval_finsetSum, eval_mul]
diff --git a/Mathlib/LinearAlgebra/LinearDisjoint.lean b/Mathlib/LinearAlgebra/LinearDisjoint.lean
index 74b1ae128c5357..92b016cadf3c42 100644
--- a/Mathlib/LinearAlgebra/LinearDisjoint.lean
+++ b/Mathlib/LinearAlgebra/LinearDisjoint.lean
@@ -542,7 +542,7 @@ theorem rank_inf_le_one_of_commute_of_flat (hf : Module.Flat R M ∨ Module.Flat
     · simp [hab] at hij
     · simp [hab.symm] at hij
     · rfl
-  convert this
+  convert! this
   ext i
   fin_cases i <;> simp
 
diff --git a/Mathlib/LinearAlgebra/LinearIndependent/Basic.lean b/Mathlib/LinearAlgebra/LinearIndependent/Basic.lean
index ae6ab85be8021e..130045217cd615 100644
--- a/Mathlib/LinearAlgebra/LinearIndependent/Basic.lean
+++ b/Mathlib/LinearAlgebra/LinearIndependent/Basic.lean
@@ -161,7 +161,7 @@ theorem LinearIndepOn_iff_linearIndepOn_image_injOn [Nontrivial R] :
 theorem linearIndepOn_congr {w : ι → M} (h : EqOn v w s) :
     LinearIndepOn R v s ↔ LinearIndepOn R w s := by
   rw [LinearIndepOn, LinearIndepOn]
-  convert Iff.rfl using 2
+  convert! Iff.rfl using 2
   ext x
   exact h.symm x.2
 
@@ -184,7 +184,7 @@ theorem LinearIndependent.group_smul_iff {G : Type*} [hG : Group G] [MulAction G
     [MulAction G M] [IsScalarTower G R M] [SMulCommClass G R M] (v : ι → M) (w : ι → G) :
     LinearIndependent R (w • v) ↔ LinearIndependent R v := by
   refine ⟨fun h ↦ ?_, fun h ↦ h.group_smul w⟩
-  convert h.group_smul (fun i ↦ (w i)⁻¹)
+  convert! h.group_smul (fun i ↦ (w i)⁻¹)
   simp [funext_iff]
 
 -- This lemma cannot be proved with `LinearIndependent.group_smul` since the action of
@@ -202,7 +202,7 @@ theorem LinearIndependent.units_smul {v : ι → M} (hv : LinearIndependent R v)
 theorem LinearIndependent.units_smul_iff (v : ι → M) (w : ι → Rˣ) :
     LinearIndependent R (w • v) ↔ LinearIndependent R v := by
   refine ⟨fun h ↦ ?_, fun h ↦ h.units_smul w⟩
-  convert h.units_smul (fun i ↦ (w i)⁻¹)
+  convert! h.units_smul (fun i ↦ (w i)⁻¹)
   simp [funext_iff]
 
 theorem linearIndependent_span (hs : LinearIndependent R v) :
@@ -300,12 +300,12 @@ theorem eq_of_linearIndepOn_id_of_span_subtype [Nontrivial R] {s t : Set M}
     ⟨fun x => ⟨x.1, h x.2⟩, fun a b hab => Subtype.coe_injective (Subtype.mk.inj hab)⟩
   have h_surj : Surjective f := by
     apply surjective_of_linearIndependent_of_span hs f _
-    convert hst <;> simp [f, comp_def]
+    convert! hst <;> simp [f, comp_def]
   change s = t
   apply Subset.antisymm _ h
   intro x hx
   rcases h_surj ⟨x, hx⟩ with ⟨y, hy⟩
-  convert y.mem
+  convert! y.mem
   rw [← Subtype.mk.inj hy]
 
 theorem le_of_span_le_span [Nontrivial R] {s t u : Set M} (hl : LinearIndepOn R id u)
@@ -462,7 +462,7 @@ theorem LinearIndepOn.union {t : Set ι} (hs : LinearIndepOn R v s) (ht : Linear
   have hli := LinearIndependent.sum_type hs ht (by rwa [← image_eq_range, ← image_eq_range])
   have hdj := (hdj.of_span₀ hs.zero_notMem_image).of_image
   rw [LinearIndepOn]
-  convert (hli.comp _ (Equiv.Set.union hdj).injective) with ⟨x, hx | hx⟩
+  convert! (hli.comp _ (Equiv.Set.union hdj).injective) with ⟨x, hx | hx⟩
   · rw [comp_apply, Equiv.Set.union_apply_left _ hx, Sum.elim_inl]
   rw [comp_apply, Equiv.Set.union_apply_right _ hx, Sum.elim_inr]
 
@@ -475,7 +475,7 @@ theorem linearIndepOn_union_iff {t : Set ι} (hdj : Disjoint s t) :
     LinearIndepOn R v s ∧ LinearIndepOn R v t ∧ Disjoint (span R (v '' s)) (span R (v '' t)) := by
   refine ⟨fun h ↦ ⟨h.mono subset_union_left, h.mono subset_union_right, ?_⟩,
     fun h ↦ h.1.union h.2.1 h.2.2⟩
-  convert h.disjoint_span_image (s := (↑) ⁻¹' s) (t := (↑) ⁻¹' t) (hdj.preimage _) <;>
+  convert! h.disjoint_span_image (s := (↑) ⁻¹' s) (t := (↑) ⁻¹' t) (hdj.preimage _) <;>
   aesop
 
 theorem linearIndepOn_id_union_iff {s t : Set M} (hdj : Disjoint s t) :
diff --git a/Mathlib/LinearAlgebra/LinearIndependent/Defs.lean b/Mathlib/LinearAlgebra/LinearIndependent/Defs.lean
index e25725c53462ab..65b96f0f5c5b3a 100644
--- a/Mathlib/LinearAlgebra/LinearIndependent/Defs.lean
+++ b/Mathlib/LinearAlgebra/LinearIndependent/Defs.lean
@@ -148,7 +148,7 @@ theorem LinearIndepOn.injOn [Nontrivial R] (hv : LinearIndepOn R v s) : InjOn v
   injOn_iff_injective.2 <| LinearIndependent.injective hv
 
 theorem LinearIndependent.smul_left_injective (hv : LinearIndependent R v) (i : ι) :
-    Injective fun r : R ↦ r • v i := by convert hv.comp (Finsupp.single_injective i); simp
+    Injective fun r : R ↦ r • v i := by convert! hv.comp (Finsupp.single_injective i); simp
 
 theorem LinearIndependent.ne_zero [Nontrivial R] (i : ι) (hv : LinearIndependent R v) :
     v i ≠ 0 := by
@@ -251,7 +251,7 @@ theorem linearIndependent_iff''ₛ :
   exact linearIndependent_iff'ₛ.trans
     ⟨fun H s f g eq hv i ↦ if his : i ∈ s then H s f g hv i his else eq i his,
       fun H s f g eq i hi ↦ by
-      convert
+      convert!
         H s (fun j ↦ if j ∈ s then f j else 0) (fun j ↦ if j ∈ s then g j else 0)
           (fun j hj ↦ (if_neg hj).trans (if_neg hj).symm)
           (by simp_rw [ite_smul, zero_smul, Finset.sum_extend_by_zero, eq]) i <;>
@@ -611,7 +611,7 @@ theorem linearIndependent_iffₒₛ :
         (a := ∑ i ∈ s with g i ≤ f i, g i • v i + ∑ i ∈ s with f i < g i, f i • v i)]
       conv_lhs => rw [← add_assoc, ← Finset.sum_add_distrib]
       conv_rhs => rw [add_left_comm, ← Finset.sum_add_distrib]
-      convert heq
+      convert! heq
         <;> simp_rw [← Finset.sum_filter_add_sum_filter_not s (fun i => g i ≤ f i), not_le]
         <;> congr! 2 with i hi
         <;> simp only [Finset.mem_filter] at hi
@@ -648,7 +648,7 @@ nonrec theorem Fintype.linearIndependent_iffₒₛ [DecidableEq ι] [Fintype ι]
     · exact h.2 i (Finset.mem_compl.2 hi)
   · specialize h t₁ (fun i => if i ∈ t₁ ∨ i ∈ t₂ then f i else 0) ?_
     · rw [← Finset.sum_subset ht₁t₂.le_compl_left]
-      · convert heq using 2 with i hi i hi <;> simp [hi]
+      · convert! heq using 2 with i hi i hi <;> simp [hi]
       · intro i hi hi'
         simp [Finset.mem_compl.1 hi, hi']
     refine ⟨fun i hi => ?_, fun i hi => ?_⟩ <;> simpa [hi] using h i
@@ -732,9 +732,9 @@ theorem linearIndependent_iff' :
       ∀ s : Finset ι, ∀ g : ι → R, ∑ i ∈ s, g i • v i = 0 → ∀ i ∈ s, g i = 0 := by
   rw [linearIndependent_iff'ₛ]
   refine ⟨fun h s f ↦ ?_, fun h s f g ↦ ?_⟩
-  · convert h s f 0; simp_rw [Pi.zero_apply, zero_smul, Finset.sum_const_zero]
+  · convert! h s f 0; simp_rw [Pi.zero_apply, zero_smul, Finset.sum_const_zero]
   · rw [← sub_eq_zero, ← Finset.sum_sub_distrib]
-    convert h s (f - g) using 3; simp only [Pi.sub_apply, sub_smul, sub_eq_zero]
+    convert! h s (f - g) using 3; simp only [Pi.sub_apply, sub_smul, sub_eq_zero]
 
 /-- A version of `linearIndependent_iff` where the linear combination is a `Finset` sum
 of a function with support contained in the `Finset`. -/
@@ -744,7 +744,7 @@ theorem linearIndependent_iff'' :
   classical
   exact linearIndependent_iff'.trans
     ⟨fun H s g hg hv i => if his : i ∈ s then H s g hv i his else hg i his, fun H s g hg i hi => by
-      convert
+      convert!
         H s (fun j => if j ∈ s then g j else 0) (fun j hj => if_neg hj)
           (by simp_rw [ite_smul, zero_smul, Finset.sum_extend_by_zero, hg]) i
       exact (if_pos hi).symm⟩
diff --git a/Mathlib/LinearAlgebra/LinearIndependent/Lemmas.lean b/Mathlib/LinearAlgebra/LinearIndependent/Lemmas.lean
index 0f28bcfd0bfb91..53b78e43f53c4a 100644
--- a/Mathlib/LinearAlgebra/LinearIndependent/Lemmas.lean
+++ b/Mathlib/LinearAlgebra/LinearIndependent/Lemmas.lean
@@ -155,7 +155,7 @@ variable (hv : LinearIndependent R v)
 /-- See also `iSupIndep_iff_linearIndependent_of_ne_zero`. -/
 theorem LinearIndependent.iSupIndep_span_singleton (hv : LinearIndependent R v) :
     iSupIndep fun i => R ∙ v i := by
-  convert LinearMap.iSupIndep_map _ hv (iSupIndep_range_lsingle ι R R)
+  convert! LinearMap.iSupIndep_map _ hv (iSupIndep_range_lsingle ι R R)
   ext; simp [mem_span_singleton]
 
 end repr
@@ -346,7 +346,7 @@ private lemma LinearIndependent.pair_add_smul_add_smul_iff_aux (h : a * d ≠ b
   refine ⟨fun h' ↦ ⟨?_, h⟩, fun ⟨h₁, h₂⟩ ↦ pair_add_smul_add_smul_iff_aux _ _ _ _ h₂ h₁⟩
   suffices LinearIndependent R ![(a * d - b * c) • x, (a * d - b * c) • y] by
     rwa [pair_smul_iff (sub_ne_zero_of_ne h)] at this
-  convert pair_add_smul_add_smul_iff_aux d (-b) (-c) a (by simpa [mul_comm d a]) h' using 1
+  convert! pair_add_smul_add_smul_iff_aux d (-b) (-c) a (by simpa [mul_comm d a]) h' using 1
   ext i; fin_cases i <;> simp <;> module
 
 @[simp] lemma LinearIndependent.pair_add_smul_right_iff :
@@ -631,7 +631,7 @@ theorem linearIndepOn_id_pair {x y : V} (hx : x ≠ 0) (hy : ∀ a : K, a • x
 theorem linearIndepOn_pair_iff {i j : ι} (v : ι → V) (hij : i ≠ j) (hi : v i ≠ 0) :
     LinearIndepOn K v {i, j} ↔ ∀ (c : K), c • v i ≠ v j := by
   rw [pair_comm]
-  convert linearIndepOn_insert (s := {i}) (a := j) hij.symm
+  convert! linearIndepOn_insert (s := { i }) (a := j) hij.symm
   simp [hi, mem_span_singleton]
 
 /-- Also see `LinearIndependent.pair_iff` for the version over arbitrary rings. -/
@@ -749,7 +749,7 @@ theorem exists_linearIndepOn_extension {s t : Set ι} (hs : LinearIndepOn K v s)
 
 theorem exists_linearIndepOn_id_extension (hs : LinearIndepOn K id s) (hst : s ⊆ t) :
     ∃ b ⊆ t, s ⊆ b ∧ t ⊆ span K b ∧ LinearIndepOn K id b := by
-  convert exists_linearIndepOn_extension hs hst <;> simp
+  convert! exists_linearIndepOn_extension hs hst <;> simp
 
 variable (K t)
 
@@ -798,7 +798,7 @@ theorem LinearIndepOn.image_subset_span_image_extend (hs : LinearIndepOn K v s)
 
 theorem LinearIndepOn.subset_span_extend {s t : Set V} (hs : LinearIndepOn K id s) (hst : s ⊆ t) :
     t ⊆ span K (hs.extend hst) := by
-  convert hs.image_subset_span_image_extend hst <;> simp
+  convert! hs.image_subset_span_image_extend hst <;> simp
 
 theorem LinearIndepOn.span_image_extend_eq_span_image (hs : LinearIndepOn K v s) (hst : s ⊆ t) :
     span K (v '' hs.extend hst) = span K (v '' t) :=
diff --git a/Mathlib/LinearAlgebra/LinearPMap.lean b/Mathlib/LinearAlgebra/LinearPMap.lean
index 7e4edd421241f3..236586e4664d36 100644
--- a/Mathlib/LinearAlgebra/LinearPMap.lean
+++ b/Mathlib/LinearAlgebra/LinearPMap.lean
@@ -870,7 +870,7 @@ theorem le_graph_of_le {f g : E →ₗ.[R] F} (h : f ≤ g) : f.graph ≤ g.grap
   obtain ⟨y, hx⟩ := hx
   use ⟨y, h.1 y.2⟩
   simp only [hx, true_and]
-  convert hx.2 using 1
+  convert! hx.2 using 1
   refine (h.2 ?_).symm
   simp only [hx.1]
 
@@ -897,11 +897,11 @@ theorem existsUnique_from_graph {g : Submodule R (E × F)}
     (hg : ∀ {x : E × F} (_hx : x ∈ g) (_hx' : x.fst = 0), x.snd = 0) {a : E}
     (ha : a ∈ g.map (LinearMap.fst R E F)) : ∃! b : F, (a, b) ∈ g := by
   refine existsUnique_of_exists_of_unique ?_ ?_
-  · convert ha
+  · convert! ha
     simp
   intro y₁ y₂ hy₁ hy₂
   have hy : ((0 : E), y₁ - y₂) ∈ g := by
-    convert g.sub_mem hy₁ hy₂
+    convert! g.sub_mem hy₁ hy₂
     exact (sub_self _).symm
   exact sub_eq_zero.mp (hg hy (by simp))
 
@@ -973,7 +973,7 @@ theorem toLinearPMap_graph_eq (g : Submodule R (E × F))
   constructor <;> intro hx
   · rw [LinearPMap.mem_graph_iff] at hx
     rcases hx with ⟨y, hx1, hx2⟩
-    convert g.mem_graph_toLinearPMap hg y using 1
+    convert! g.mem_graph_toLinearPMap hg y using 1
     exact Prod.ext hx1.symm hx2.symm
   rw [LinearPMap.mem_graph_iff]
   have hx_fst : x_fst ∈ g.map (LinearMap.fst R E F) := by
diff --git a/Mathlib/LinearAlgebra/Matrix/Adjugate.lean b/Mathlib/LinearAlgebra/Matrix/Adjugate.lean
index 47e1149b0f264a..a0eef4c45f79cf 100644
--- a/Mathlib/LinearAlgebra/Matrix/Adjugate.lean
+++ b/Mathlib/LinearAlgebra/Matrix/Adjugate.lean
@@ -114,13 +114,13 @@ theorem cramer_transpose_row_self (i : n) : Aᵀ.cramer (A i) = Pi.single i A.de
 
 theorem cramer_row_self (i : n) (h : ∀ j, b j = A j i) : A.cramer b = Pi.single i A.det := by
   rw [← transpose_transpose A, det_transpose]
-  convert cramer_transpose_row_self Aᵀ i
+  convert! cramer_transpose_row_self Aᵀ i
   exact funext h
 
 @[simp]
 theorem cramer_one : cramer (1 : Matrix n n α) = 1 := by
   ext i j
-  convert congr_fun (cramer_row_self (1 : Matrix n n α) (Pi.single i 1) i _) j
+  convert! congr_fun (cramer_row_self (1 : Matrix n n α) (Pi.single i 1) i _) j
   · simp
   · intro j
     rw [Matrix.one_eq_pi_single, Pi.single_comm]
diff --git a/Mathlib/LinearAlgebra/Matrix/Block.lean b/Mathlib/LinearAlgebra/Matrix/Block.lean
index 8d6f1d7e092528..33723314f1fcab 100644
--- a/Mathlib/LinearAlgebra/Matrix/Block.lean
+++ b/Mathlib/LinearAlgebra/Matrix/Block.lean
@@ -68,9 +68,9 @@ protected theorem BlockTriangular.submatrix {f : n → m} (h : M.BlockTriangular
 theorem blockTriangular_reindex_iff {b : n → α} {e : m ≃ n} :
     (reindex e e M).BlockTriangular b ↔ M.BlockTriangular (b ∘ e) := by
   refine ⟨fun h => ?_, fun h => ?_⟩
-  · convert h.submatrix
+  · convert! h.submatrix
     simp only [reindex_apply, submatrix_submatrix, submatrix_id_id, Equiv.symm_comp_self]
-  · convert h.submatrix
+  · convert! h.submatrix
     simp only [comp_assoc b e e.symm, Equiv.self_comp_symm, comp_id]
 
 protected theorem BlockTriangular.transpose :
@@ -238,7 +238,12 @@ variable [CommRing R] [DecidableEq m] [Fintype m] [DecidableEq n] [Fintype n]
 
 theorem equiv_block_det (M : Matrix m m R) {p q : m → Prop} [DecidablePred p] [DecidablePred q]
     (e : ∀ x, q x ↔ p x) : (toSquareBlockProp M p).det = (toSquareBlockProp M q).det := by
-  convert Matrix.det_reindex_self (Equiv.subtypeEquivRight e) (toSquareBlockProp M q)
+  convert!
+    Matrix.det_reindex_self (Equiv.subtypeEquivRight e)
+      (toSquareBlockProp M q)
+        -- Removed `@[simp]` attribute,
+        -- as the LHS simplifies already to `M.toSquareBlock id i ⟨i, ⋯⟩ ⟨i, ⋯⟩`
+
 
 -- Removed `@[simp]` attribute,
 -- as the LHS simplifies already to `M.toSquareBlock id i ⟨i, ⋯⟩ ⟨i, ⋯⟩`
@@ -263,7 +268,8 @@ theorem twoBlockTriangular_det (M : Matrix m m R) (p : m → Prop) [DecidablePre
     (h : ∀ i, ¬p i → ∀ j, p j → M i j = 0) :
     M.det = (toSquareBlockProp M p).det * (toSquareBlockProp M fun i => ¬p i).det := by
   rw [det_toBlock M p]
-  convert det_fromBlocks_zero₂₁ (toBlock M p p) (toBlock M p fun j => ¬p j)
+  convert!
+    det_fromBlocks_zero₂₁ (toBlock M p p) (toBlock M p fun j => ¬p j)
       (toBlock M (fun j => ¬p j) fun j => ¬p j)
   ext i j
   exact h (↑i) i.2 (↑j) j.2
@@ -295,7 +301,7 @@ protected theorem BlockTriangular.det [DecidableEq α] [LinearOrder α] (hM : Bl
     let b' := fun i : { a // b a ≠ k } => b ↑i
     have h' : BlockTriangular (M.toSquareBlockProp fun i => b i ≠ k) b' := hM.submatrix
     have hb' : image b' univ = (image b univ).erase k := by
-      convert image_subtype_ne_univ_eq_image_erase k b
+      convert! image_subtype_ne_univ_eq_image_erase k b
     rw [ih _ (max'_mem _ _) h' hb']
     refine Finset.prod_congr rfl fun l hl => ?_
     let he : { a // b' a = l } ≃ { a // b a = l } :=
@@ -338,7 +344,7 @@ theorem det_matrixOfPolynomials {n : ℕ} (p : Fin n → R[X])
     (Matrix.of (fun (i j : Fin n) => (p j).coeff i)).det = 1 := by
   rw [Matrix.det_of_upperTriangular (Matrix.matrixOfPolynomials_blockTriangular p (fun i ↦
       Nat.le_of_eq (h_deg i)))]
-  convert prod_const_one with x _
+  convert! prod_const_one with x _
   rw [Matrix.of_apply, ← h_deg, coeff_natDegree, (h_monic x).leadingCoeff]
 
 /-! ### Invertible -/
@@ -415,8 +421,8 @@ theorem blockTriangular_inv_of_blockTriangular [LinearOrder α] [Invertible M]
   haveI : Invertible A := hM.invertibleToBlock _
   have hA : A.BlockTriangular b' := hM.submatrix
   have hb' : image b' univ ⊂ image b univ := by
-    convert image_subtype_univ_ssubset_image_univ k b _ (fun a => a < k) (lt_irrefl _)
-    convert max'_mem (α := α) _ _
+    convert! image_subtype_univ_ssubset_image_univ k b _ (fun a => a < k) (lt_irrefl _)
+    convert! max'_mem (α := α) _ _
   have hij' : b' ⟨j, hij.trans hi⟩ < b' ⟨i, hi⟩ := by simp_rw [b', hij]
   simp [A, hM.inv_toBlock k, (ih (image b' univ) hb' hA rfl hij').symm]
 
diff --git a/Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.lean b/Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.lean
index ed9025ce7ee7ef..7165bbd4490c99 100644
--- a/Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.lean
+++ b/Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.lean
@@ -180,7 +180,7 @@ lemma derivative_det_one_add_X_smul (M : Matrix n n R) :
     (derivative <| det (1 + (X : R[X]) • M.map C)).eval 0 = trace M := by
   let e := Matrix.reindexLinearEquiv R R (Fintype.equivFin n) (Fintype.equivFin n)
   rw [← Matrix.det_reindexLinearEquiv_self R[X] (Fintype.equivFin n)]
-  convert derivative_det_one_add_X_smul_aux (e M)
+  convert! derivative_det_one_add_X_smul_aux (e M)
   · ext; simp [map_add, e]
   · delta trace
     rw [← (Fintype.equivFin n).symm.sum_comp]
@@ -197,7 +197,7 @@ lemma det_one_add_X_smul (M : Matrix n n R) :
   rw [Algebra.smul_def (trace M), ← C_eq_algebraMap, pow_two, ← mul_assoc, add_assoc,
     ← add_mul, ← coeff_det_one_add_X_smul_one, ← coeff_divX, add_comm (C _), divX_mul_X_add,
     add_comm (1 : R[X]), ← C.map_one]
-  convert (divX_mul_X_add _).symm
+  convert! (divX_mul_X_add _).symm
   rw [coeff_zero_eq_eval_zero, eval_det_add_X_smul, det_one, eval_one]
 
 /-- The first two terms of the Taylor expansion of `det (1 + r • M)` at `r = 0`. -/
@@ -340,7 +340,7 @@ lemma isUnit_charpolyRev_of_isNilpotent (hM : IsNilpotent M) :
     IsUnit M.charpolyRev := by
   obtain ⟨k, hk⟩ := hM
   replace hk : 1 - (X : R[X]) • M.map C ∣ 1 := by
-    convert one_sub_dvd_one_sub_pow ((X : R[X]) • M.map C) k
+    convert! one_sub_dvd_one_sub_pow ((X : R[X]) • M.map C) k
     rw [← C.mapMatrix_apply, smul_pow, ← map_pow, hk, map_zero, smul_zero, sub_zero]
   apply isUnit_of_dvd_one
   rw [← det_one (R := R[X]) (n := n)]
diff --git a/Mathlib/LinearAlgebra/Matrix/Determinant/Basic.lean b/Mathlib/LinearAlgebra/Matrix/Determinant/Basic.lean
index 66b6beb66750b7..358af6787acc2c 100644
--- a/Mathlib/LinearAlgebra/Matrix/Determinant/Basic.lean
+++ b/Mathlib/LinearAlgebra/Matrix/Determinant/Basic.lean
@@ -78,7 +78,7 @@ theorem det_diagonal {d : n → R} : det (diagonal d) = ∏ i, d i := by
   refine (Finset.sum_eq_single 1 ?_ ?_).trans ?_
   · rintro σ - h2
     obtain ⟨x, h3⟩ := not_forall.1 (mt Equiv.ext h2)
-    convert mul_zero (ε σ)
+    convert! mul_zero (ε σ)
     apply Finset.prod_eq_zero (mem_univ x)
     exact if_neg h3
   · simp
@@ -111,7 +111,7 @@ theorem det_unique {n : Type*} [Unique n] [DecidableEq n] [Fintype n] (A : Matri
 theorem det_eq_elem_of_subsingleton [Subsingleton n] (A : Matrix n n R) (k : n) :
     det A = A k k := by
   have := uniqueOfSubsingleton k
-  convert det_unique A
+  convert! det_unique A
 
 theorem det_eq_elem_of_card_eq_one {A : Matrix n n R} (h : Fintype.card n = 1) (k : n) :
     det A = A k k :=
@@ -426,7 +426,7 @@ theorem det_updateRow_sum_aux (M : Matrix n n R) {j : n} (s : Finset n) (hj : j
 multiplied by the coefficient of that row. -/
 theorem det_updateRow_sum (A : Matrix n n R) (j : n) (c : n → R) :
     (A.updateRow j (∑ k, (c k) • A k)).det = (c j) • A.det := by
-  convert det_updateRow_sum_aux A (Finset.univ.erase j) (Finset.univ.notMem_erase j) c (c j)
+  convert! det_updateRow_sum_aux A (Finset.univ.erase j) (Finset.univ.notMem_erase j) c (c j)
   rw [← Finset.univ.add_sum_erase _ (Finset.mem_univ j)]
 
 /-- If we replace a column of a matrix by a linear combination of its columns, then the determinant
@@ -434,7 +434,7 @@ is multiplied by the coefficient of that column. -/
 theorem det_updateCol_sum (A : Matrix n n R) (j : n) (c : n → R) :
     (A.updateCol j (fun k ↦ ∑ i, (c i) • A k i)).det = (c j) • A.det := by
   rw [← det_transpose, ← updateRow_transpose, ← det_transpose A]
-  convert det_updateRow_sum A.transpose j c
+  convert! det_updateRow_sum A.transpose j c
   simp only [smul_eq_mul, Finset.sum_apply, Pi.smul_apply, transpose_apply]
 
 section DetEq
@@ -674,8 +674,9 @@ theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Mat
     (Matrix.fromBlocks A B 0 D).det = A.det * D.det := by
   classical
     simp_rw [det_apply']
-    convert Eq.symm <|
-      sum_subset (M := R) (subset_univ ((sumCongrHom m n).range : Set (Perm (m ⊕ n))).toFinset) ?_
+    convert!
+      Eq.symm <|
+        sum_subset (M := R) (subset_univ ((sumCongrHom m n).range : Set (Perm (m ⊕ n))).toFinset) ?_
     · simp_rw [sum_mul_sum, ← sum_product', univ_product_univ]
       refine sum_nbij (fun σ ↦ σ.fst.sumCongr σ.snd) ?_ ?_ ?_ ?_
       · intro σ₁₂ _
diff --git a/Mathlib/LinearAlgebra/Matrix/Hermitian.lean b/Mathlib/LinearAlgebra/Matrix/Hermitian.lean
index 65230e1edd6eb0..3721c87c14eb76 100644
--- a/Mathlib/LinearAlgebra/Matrix/Hermitian.lean
+++ b/Mathlib/LinearAlgebra/Matrix/Hermitian.lean
@@ -396,7 +396,7 @@ theorem fromBlocks₂₂ [Fintype n] [DecidableEq n] (A : Matrix m m α) (B : Ma
     (Matrix.fromBlocks A B Bᴴ D).IsHermitian ↔ (A - B * D⁻¹ * Bᴴ).IsHermitian := by
   rw [← isHermitian_submatrix_equiv (Equiv.sumComm n m), Equiv.sumComm_apply,
     fromBlocks_submatrix_sum_swap_sum_swap]
-  convert IsHermitian.fromBlocks₁₁ _ _ hD <;> simp
+  convert! IsHermitian.fromBlocks₁₁ _ _ hD <;> simp
 
 end IsHermitian
 
diff --git a/Mathlib/LinearAlgebra/Matrix/Ideal.lean b/Mathlib/LinearAlgebra/Matrix/Ideal.lean
index bc2193310aff7d..913dd83e452c2e 100644
--- a/Mathlib/LinearAlgebra/Matrix/Ideal.lean
+++ b/Mathlib/LinearAlgebra/Matrix/Ideal.lean
@@ -96,7 +96,7 @@ theorem single_mem_jacobson_matrix (I : Ideal R) :
   obtain rfl | qj := eq_or_ne q j
   · by_cases iq : i = q
     · simp [iq, N, zMx, single, mul_apply, sum_apply, ite_and, sub_mul]
-    · convert I.mul_mem_left (-M i p * x) zMx
+    · convert! I.mul_mem_left (-M i p * x) zMx
       simp [iq, N, single, mul_apply, sum_apply, ite_and, sub_mul]
       simp [sub_add, mul_add, mul_sub, mul_assoc]
   · simp [N, qj, sum_apply, mul_apply]
diff --git a/Mathlib/LinearAlgebra/Matrix/IsDiag.lean b/Mathlib/LinearAlgebra/Matrix/IsDiag.lean
index 30b3efdc4a4040..e06d2a106c838a 100644
--- a/Mathlib/LinearAlgebra/Matrix/IsDiag.lean
+++ b/Mathlib/LinearAlgebra/Matrix/IsDiag.lean
@@ -116,7 +116,7 @@ theorem IsDiag.conjTranspose [NonUnitalNonAssocSemiring α] [StarRing α] {A : M
 theorem isDiag_conjTranspose_iff [NonUnitalNonAssocSemiring α] [StarRing α] {A : Matrix n n α} :
     Aᴴ.IsDiag ↔ A.IsDiag :=
   ⟨fun ha => by
-    convert ha.conjTranspose
+    convert! ha.conjTranspose
     simp, IsDiag.conjTranspose⟩
 
 theorem IsDiag.submatrix [Zero α] {A : Matrix n n α} (ha : A.IsDiag) {f : m → n}
@@ -156,7 +156,7 @@ theorem isDiag_fromBlocks_iff [Zero α] {A : Matrix m m α} {B : Matrix m n α}
     · exact h Sum.inr_ne_inl
     · exact h (Sum.inr_injective.ne hij)
   · rintro ⟨ha, hb, hc, hd⟩
-    convert IsDiag.fromBlocks ha hd
+    convert! IsDiag.fromBlocks ha hd
 
 /-- A symmetric block matrix `A.fromBlocks B C D` is diagonal
 if `A` and `D` are diagonal and `B` is `0`. -/
diff --git a/Mathlib/LinearAlgebra/Matrix/Nondegenerate.lean b/Mathlib/LinearAlgebra/Matrix/Nondegenerate.lean
index b59f85df973763..b83592c1b37c2a 100644
--- a/Mathlib/LinearAlgebra/Matrix/Nondegenerate.lean
+++ b/Mathlib/LinearAlgebra/Matrix/Nondegenerate.lean
@@ -50,11 +50,11 @@ variable {m n R A : Type*} [CommRing R] [Fintype m] [Fintype n] [CommRing A] [Is
 
 lemma separatingRight_def : M.SeparatingRight ↔ (∀ w, (∀ v, v ⬝ᵥ M *ᵥ w = 0) → w = 0) := by
   refine forall_congr' fun w ↦ ⟨fun hM hw ↦ hM ?_, fun hM hw ↦ hM ?_⟩ <;>
-  convert hw
+  convert! hw
 
 lemma separatingLeft_def : M.SeparatingLeft ↔ (∀ v, (∀ w, v ⬝ᵥ M *ᵥ w = 0) → v = 0) := by
   refine forall_congr' fun v ↦ ⟨fun hM hv ↦ hM ?_, fun hM hv ↦ hM ?_⟩ <;>
-  convert hv
+  convert! hv
 
 lemma nondegenerate_def : M.Nondegenerate ↔
    (∀ v, (∀ w, v ⬝ᵥ M *ᵥ w = 0) → v = 0) ∧ (∀ w, (∀ v, v ⬝ᵥ M *ᵥ w = 0) → w = 0) := by
diff --git a/Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean b/Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean
index a8ac58e14b0fe7..a87d7dce5146b7 100644
--- a/Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean
+++ b/Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean
@@ -85,7 +85,7 @@ def invertibleOfDetInvertible [Invertible A.det] : Invertible A where
 
 theorem invOf_eq [Invertible A.det] [Invertible A] : ⅟A = ⅟A.det • A.adjugate := by
   letI := invertibleOfDetInvertible A
-  convert (rfl : ⅟A = _)
+  convert! (rfl : ⅟A = _)
 
 /-- `A.det` is invertible if `A` has a left inverse. -/
 @[implicit_reducible]
@@ -108,7 +108,7 @@ def detInvertibleOfInvertible [Invertible A] : Invertible A.det :=
 
 theorem det_invOf [Invertible A] [Invertible A.det] : (⅟A).det = ⅟A.det := by
   letI := detInvertibleOfInvertible A
-  convert (rfl : _ = ⅟A.det)
+  convert! (rfl : _ = ⅟A.det)
 
 /-- Together `Matrix.detInvertibleOfInvertible` and `Matrix.invertibleOfDetInvertible` form an
 equivalence, although both sides of the equiv are subsingleton anyway. -/
diff --git a/Mathlib/LinearAlgebra/Matrix/Permanent.lean b/Mathlib/LinearAlgebra/Matrix/Permanent.lean
index e4ab202d2fd799..f83a309ee18f62 100644
--- a/Mathlib/LinearAlgebra/Matrix/Permanent.lean
+++ b/Mathlib/LinearAlgebra/Matrix/Permanent.lean
@@ -61,7 +61,7 @@ theorem permanent_unique {n : Type*} [Unique n] [DecidableEq n] [Fintype n] (A :
 theorem permanent_eq_elem_of_subsingleton [Subsingleton n] (A : Matrix n n R) (k : n) :
     permanent A = A k k := by
   have := uniqueOfSubsingleton k
-  convert permanent_unique A
+  convert! permanent_unique A
 
 theorem permanent_eq_elem_of_card_eq_one {A : Matrix n n R} (h : card n = 1) (k : n) :
     permanent A = A k k :=
diff --git a/Mathlib/LinearAlgebra/Matrix/Polynomial.lean b/Mathlib/LinearAlgebra/Matrix/Polynomial.lean
index 31feb1f51db6cb..10d5c80ecfa7ae 100644
--- a/Mathlib/LinearAlgebra/Matrix/Polynomial.lean
+++ b/Mathlib/LinearAlgebra/Matrix/Polynomial.lean
@@ -64,7 +64,7 @@ theorem coeff_det_X_add_C_zero (A B : Matrix n n α) :
   rw [det_apply, finsetSum_coeff, det_apply]
   refine Finset.sum_congr rfl ?_
   rintro g -
-  convert coeff_smul (R := α) (sign g) _ 0
+  convert! coeff_smul (R := α) (sign g) _ 0
   rw [coeff_zero_prod]
   refine Finset.prod_congr rfl ?_
   simp
@@ -75,9 +75,9 @@ theorem coeff_det_X_add_C_card (A B : Matrix n n α) :
   refine Finset.sum_congr rfl ?_
   simp only [Finset.mem_univ, forall_true_left]
   intro g
-  convert coeff_smul (R := α) (sign g) _ _
+  convert! coeff_smul (R := α) (sign g) _ _
   rw [← mul_one (Fintype.card n)]
-  convert (coeff_prod_of_natDegree_le (R := α) _ _ _ _).symm
+  convert! (coeff_prod_of_natDegree_le (R := α) _ _ _ _).symm
   · simp [coeff_C]
   · rintro p -
     dsimp only [add_apply, smul_apply, map_apply, smul_eq_mul]
diff --git a/Mathlib/LinearAlgebra/Matrix/PosDef.lean b/Mathlib/LinearAlgebra/Matrix/PosDef.lean
index be0ab0acc9ca10..82b66009ab008c 100644
--- a/Mathlib/LinearAlgebra/Matrix/PosDef.lean
+++ b/Mathlib/LinearAlgebra/Matrix/PosDef.lean
@@ -568,7 +568,7 @@ theorem fromBlocks₂₂ [DecidableEq n] (A : Matrix m m R')
     (fromBlocks A B Bᴴ D).PosSemidef ↔ (A - B * D⁻¹ * Bᴴ).PosSemidef := by
   rw [← posSemidef_submatrix_equiv (Equiv.sumComm n m), Equiv.sumComm_apply,
     fromBlocks_submatrix_sum_swap_sum_swap]
-  convert fromBlocks₁₁ Bᴴ A hD <;> simp
+  convert! fromBlocks₁₁ Bᴴ A hD <;> simp
 
 end SchurComplement
 
diff --git a/Mathlib/LinearAlgebra/Matrix/Rank.lean b/Mathlib/LinearAlgebra/Matrix/Rank.lean
index 65cc0e496a4db4..5ea998e9342d3b 100644
--- a/Mathlib/LinearAlgebra/Matrix/Rank.lean
+++ b/Mathlib/LinearAlgebra/Matrix/Rank.lean
@@ -130,7 +130,7 @@ theorem rank_subsingleton [Subsingleton R] (A : Matrix m n R) : A.rank = 1 :=
 theorem cRank_one [Nontrivial R] [DecidableEq m] :
     (cRank (1 : Matrix m m R)) = lift.{uR} #m := by
   have h : LinearIndependent R (1 : Matrix m m R)ᵀ := by
-    convert Pi.linearIndependent_single_one m R
+    convert! Pi.linearIndependent_single_one m R
     simp [funext_iff, Matrix.one_eq_pi_single]
   rw [cRank, rank_span h, ← lift_umax, ← Cardinal.mk_range_eq_of_injective h.injective, lift_id']
 
@@ -218,7 +218,7 @@ lemma rank_mul_eq_right_of_isUnit_det [Fintype m] [DecidableEq m]
     (A * B).rank = B.rank := by
   let b : Basis m R (m → R) := Pi.basisFun R m
   replace hA : IsUnit (LinearMap.toMatrix b b A.mulVecLin).det := by
-    convert hA; rw [← LinearEquiv.eq_symm_apply]; rfl
+    convert! hA; rw [← LinearEquiv.eq_symm_apply]; rfl
   have hAB : mulVecLin (A * B) = (LinearEquiv.ofIsUnitDet hA).comp (mulVecLin B) := by ext; simp
   rw [rank, rank, hAB, LinearMap.range_comp, LinearEquiv.finrank_map_eq]
 
@@ -340,7 +340,7 @@ theorem cRank_diagonal [DecidableEq m] (w : m → R) :
   have h : LinearIndependent R w' := by
     have hli' := Pi.linearIndependent_single_of_ne_zero (R := R)
       (v := fun i : m ↦ if w i = 0 then (1 : R) else w i) (by simp [ite_eq_iff'])
-    convert hli'.comp Subtype.val Subtype.val_injective
+    convert! hli'.comp Subtype.val Subtype.val_injective
     ext ⟨j, hj⟩ k
     simp [w', diagonal, hj, Pi.single_apply, eq_comm]
   have hrw : insert 0 (range (diagonal w)ᵀ) = insert 0 (range w') := by
diff --git a/Mathlib/LinearAlgebra/Matrix/SchurComplement.lean b/Mathlib/LinearAlgebra/Matrix/SchurComplement.lean
index 8e12547a8067d1..6d108691f2d1be 100644
--- a/Mathlib/LinearAlgebra/Matrix/SchurComplement.lean
+++ b/Mathlib/LinearAlgebra/Matrix/SchurComplement.lean
@@ -97,13 +97,13 @@ theorem invOf_fromBlocks_zero₂₁_eq (A : Matrix m m α) (B : Matrix m n α) (
     [Invertible A] [Invertible D] [Invertible (fromBlocks A B 0 D)] :
     ⅟(fromBlocks A B 0 D) = fromBlocks (⅟A) (-(⅟A * B * ⅟D)) 0 (⅟D) := by
   letI := fromBlocksZero₂₁Invertible A B D
-  convert (rfl : ⅟(fromBlocks A B 0 D) = _)
+  convert! (rfl : ⅟(fromBlocks A B 0 D) = _)
 
 theorem invOf_fromBlocks_zero₁₂_eq (A : Matrix m m α) (C : Matrix n m α) (D : Matrix n n α)
     [Invertible A] [Invertible D] [Invertible (fromBlocks A 0 C D)] :
     ⅟(fromBlocks A 0 C D) = fromBlocks (⅟A) 0 (-(⅟D * C * ⅟A)) (⅟D) := by
   letI := fromBlocksZero₁₂Invertible A C D
-  convert (rfl : ⅟(fromBlocks A 0 C D) = _)
+  convert! (rfl : ⅟(fromBlocks A 0 C D) = _)
 
 /-- Both diagonal entries of an invertible upper-block-triangular matrix are invertible (by reading
 off the diagonal entries of the inverse). -/
@@ -234,8 +234,10 @@ def fromBlocks₂₂Invertible (A : Matrix m m α) (B : Matrix m n α) (C : Matr
     (D : Matrix n n α) [Invertible D] [Invertible (A - B * ⅟D * C)] :
     Invertible (fromBlocks A B C D) := by
   -- factor `fromBlocks` via `fromBlocks_eq_of_invertible₂₂`, and state the inverse we expect
-  convert Invertible.copy' _ _ (fromBlocks (⅟(A - B * ⅟D * C)) (-(⅟(A - B * ⅟D * C) * B * ⅟D))
-    (-(⅟D * C * ⅟(A - B * ⅟D * C))) (⅟D + ⅟D * C * ⅟(A - B * ⅟D * C) * B * ⅟D))
+  convert!
+    Invertible.copy' _ _
+      (fromBlocks (⅟(A - B * ⅟D * C)) (-(⅟(A - B * ⅟D * C) * B * ⅟D))
+        (-(⅟D * C * ⅟(A - B * ⅟D * C))) (⅟D + ⅟D * C * ⅟(A - B * ⅟D * C) * B * ⅟D))
       (fromBlocks_eq_of_invertible₂₂ _ _ _ _) _
   · -- the product is invertible because all the factors are
     letI : Invertible (1 : Matrix n n α) := invertibleOne
@@ -279,7 +281,7 @@ theorem invOf_fromBlocks₂₂_eq (A : Matrix m m α) (B : Matrix m n α) (C : M
       fromBlocks (⅟(A - B * ⅟D * C)) (-(⅟(A - B * ⅟D * C) * B * ⅟D))
         (-(⅟D * C * ⅟(A - B * ⅟D * C))) (⅟D + ⅟D * C * ⅟(A - B * ⅟D * C) * B * ⅟D) := by
   letI := fromBlocks₂₂Invertible A B C D
-  convert (rfl : ⅟(fromBlocks A B C D) = _)
+  convert! (rfl : ⅟(fromBlocks A B C D) = _)
 
 theorem invOf_fromBlocks₁₁_eq (A : Matrix m m α) (B : Matrix m n α) (C : Matrix n m α)
     (D : Matrix n n α) [Invertible A] [Invertible (D - C * ⅟A * B)]
@@ -288,7 +290,7 @@ theorem invOf_fromBlocks₁₁_eq (A : Matrix m m α) (B : Matrix m n α) (C : M
       fromBlocks (⅟A + ⅟A * B * ⅟(D - C * ⅟A * B) * C * ⅟A) (-(⅟A * B * ⅟(D - C * ⅟A * B)))
         (-(⅟(D - C * ⅟A * B) * C * ⅟A)) (⅟(D - C * ⅟A * B)) := by
   letI := fromBlocks₁₁Invertible A B C D
-  convert (rfl : ⅟(fromBlocks A B C D) = _)
+  convert! (rfl : ⅟(fromBlocks A B C D) = _)
 
 /-- If a block matrix is invertible and so is its bottom left element, then so is the corresponding
 Schur complement. -/
diff --git a/Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean b/Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean
index 9c348863e0b51e..6d74085bad5fd2 100644
--- a/Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean
+++ b/Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean
@@ -608,7 +608,7 @@ theorem Matrix.isAdjointPair_equiv (P : Matrix n n R) (h : IsUnit P) :
     dsimp only [Matrix.IsAdjointPair]
     simp only [Matrix.transpose_mul]
     simp only [← mul_assoc, P.transpose_nonsing_inv]
-    convert this using 2
+    convert! this using 2
     · rw [mul_assoc, mul_assoc, ← mul_assoc J]
       rfl
     · rw [mul_assoc, mul_assoc, ← mul_assoc _ _ J]
diff --git a/Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean b/Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean
index ea4c251f473285..4e3ba67f3014bf 100644
--- a/Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean
+++ b/Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean
@@ -386,7 +386,7 @@ theorem fin_two_induction (P : SL(2, R) → Prop)
     (h : ∀ (a b c d : R) (hdet : a * d - b * c = 1), P ⟨!![a, b; c, d], by rwa [det_fin_two_of]⟩)
     (g : SL(2, R)) : P g := by
   obtain ⟨m, hm⟩ := g
-  convert h (m 0 0) (m 0 1) (m 1 0) (m 1 1) (by rwa [det_fin_two] at hm)
+  convert! h (m 0 0) (m 0 1) (m 1 0) (m 1 1) (by rwa [det_fin_two] at hm)
   ext i j; fin_cases i <;> fin_cases j <;> rfl
 
 theorem fin_two_exists_eq_mk_of_apply_zero_one_eq_zero {R : Type*} [Field R] (g : SL(2, R))
diff --git a/Mathlib/LinearAlgebra/Matrix/ToLin.lean b/Mathlib/LinearAlgebra/Matrix/ToLin.lean
index da15e467ea8cd9..6d0658bc198844 100644
--- a/Mathlib/LinearAlgebra/Matrix/ToLin.lean
+++ b/Mathlib/LinearAlgebra/Matrix/ToLin.lean
@@ -882,7 +882,7 @@ theorem LinearMap.toMatrixAlgEquiv_mul (f g : M₁ →ₗ[R] M₁) :
 theorem Matrix.toLinAlgEquiv_mul (A B : Matrix n n R) :
     Matrix.toLinAlgEquiv v₁ (A * B) =
       (Matrix.toLinAlgEquiv v₁ A).comp (Matrix.toLinAlgEquiv v₁ B) := by
-  convert Matrix.toLin_mul v₁ v₁ v₁ A B
+  convert! Matrix.toLin_mul v₁ v₁ v₁ A B
 
 @[simp]
 theorem LinearMap.isUnit_toMatrix_iff {f : M₁ →ₗ[R] M₁} : IsUnit (f.toMatrix v₁ v₁) ↔ IsUnit f :=
diff --git a/Mathlib/LinearAlgebra/Matrix/Transvection.lean b/Mathlib/LinearAlgebra/Matrix/Transvection.lean
index 1f1dd3dc811b3f..0da7c4a92ddc50 100644
--- a/Mathlib/LinearAlgebra/Matrix/Transvection.lean
+++ b/Mathlib/LinearAlgebra/Matrix/Transvection.lean
@@ -230,7 +230,7 @@ theorem _root_.Matrix.mem_range_scalar_iff_commute_transvectionStruct {M : Matri
   refine ⟨fun h t => ?_, mem_range_scalar_of_commute_transvectionStruct⟩
   rw [mem_range_scalar_iff_commute_single] at h
   refine (Commute.one_left M).add_left ?_
-  convert (h _ _ t.hij).smul_left t.c using 1
+  convert! (h _ _ t.hij).smul_left t.c using 1
   rw [smul_single, smul_eq_mul, mul_one]
 
 end
diff --git a/Mathlib/LinearAlgebra/Matrix/ZPow.lean b/Mathlib/LinearAlgebra/Matrix/ZPow.lean
index 61805f4ef2bc90..14df76dae44d4f 100644
--- a/Mathlib/LinearAlgebra/Matrix/ZPow.lean
+++ b/Mathlib/LinearAlgebra/Matrix/ZPow.lean
@@ -97,7 +97,7 @@ theorem inv_zpow (A : M) : ∀ n : ℤ, A⁻¹ ^ n = (A ^ n)⁻¹
 
 @[simp]
 theorem zpow_neg_one (A : M) : A ^ (-1 : ℤ) = A⁻¹ := by
-  convert DivInvMonoid.zpow_neg' 0 A
+  convert! DivInvMonoid.zpow_neg' 0 A
   simp only [zpow_one, Int.ofNat_zero, Int.natCast_succ, zpow_eq_pow, zero_add]
 
 @[simp]
diff --git a/Mathlib/LinearAlgebra/Multilinear/Basic.lean b/Mathlib/LinearAlgebra/Multilinear/Basic.lean
index 866b95e89382c1..a5c8f4832b0fef 100644
--- a/Mathlib/LinearAlgebra/Multilinear/Basic.lean
+++ b/Mathlib/LinearAlgebra/Multilinear/Basic.lean
@@ -121,8 +121,8 @@ def mk' [DecidableEq ι] (f : (∀ i, M₁ i) → M₂)
       f (update m i (c • x)) = c • f (update m i x) := by aesop) :
     MultilinearMap R M₁ M₂ where
   toFun := f
-  map_update_add' m i x y := by convert h₁ m i x y
-  map_update_smul' m i c x := by convert h₂ m i c x
+  map_update_add' m i x y := by convert! h₁ m i x y
+  map_update_smul' m i c x := by convert! h₂ m i c x
 
 @[simp]
 theorem toFun_eq_coe : f.toFun = ⇑f :=
@@ -1108,7 +1108,7 @@ sending a multilinear map `g` to `g (f₁ ⬝ , ..., fₙ ⬝ )` is linear in `g
     change (g fun j ↦ update f i (f₁ + f₂) j <| x j) =
         (g fun j ↦ update f i f₁ j <| x j) + g fun j ↦ update f i f₂ j (x j)
     let c : Π (i : ι), (M₁ i →ₗ[R] M₁' i) → M₁' i := fun i f ↦ f (x i)
-    convert g.map_update_add (fun j ↦ f j (x j)) i (f₁ (x i)) (f₂ (x i)) with j j j
+    convert! g.map_update_add (fun j ↦ f j (x j)) i (f₁ (x i)) (f₂ (x i)) with j j j
     · exact Function.apply_update c f i (f₁ + f₂) j
     · exact Function.apply_update c f i f₁ j
     · exact Function.apply_update c f i f₂ j
@@ -1117,7 +1117,7 @@ sending a multilinear map `g` to `g (f₁ ⬝ , ..., fₙ ⬝ )` is linear in `g
     ext g x
     change (g fun j ↦ update f i (a • f₀) j <| x j) = a • g fun j ↦ update f i f₀ j (x j)
     let c : Π (i : ι), (M₁ i →ₗ[R] M₁' i) → M₁' i := fun i f ↦ f (x i)
-    convert g.map_update_smul (fun j ↦ f j (x j)) i a (f₀ (x i)) with j j j
+    convert! g.map_update_smul (fun j ↦ f j (x j)) i a (f₀ (x i)) with j j j
     · exact Function.apply_update c f i (a • f₀) j
     · exact Function.apply_update c f i f₀ j
 
diff --git a/Mathlib/LinearAlgebra/Multilinear/DirectSum.lean b/Mathlib/LinearAlgebra/Multilinear/DirectSum.lean
index 152d8a8ef0dc48..3215af10f7219b 100644
--- a/Mathlib/LinearAlgebra/Multilinear/DirectSum.lean
+++ b/Mathlib/LinearAlgebra/Multilinear/DirectSum.lean
@@ -59,7 +59,7 @@ theorem fromDirectSumEquiv_lof [Finite ι] [(i : ι) → DecidableEq (κ i)]
     fromDirectSumEquiv f (fun i => lof R _ _ _ (x i)) = f p x := by
   haveI : Fintype ι := Fintype.ofFinite ι
   rw [fromDirectSumEquiv, ← fromDFinsuppEquiv_single]
-  convert rfl
+  convert! rfl
 
 set_option backward.isDefEq.respectTransparency false in
 /-- Prefer using `fromDirectSumEquiv_lof` where possible. -/
@@ -70,7 +70,7 @@ theorem fromDirectSumEquiv_apply [Fintype ι] [(i : ι) → DecidableEq (κ i)]
     fromDirectSumEquiv f x =
       ∑ p ∈ Fintype.piFinset (fun i ↦ (x i).support), f p (fun i ↦ x i (p i)) := by
   rw [fromDirectSumEquiv, ← fromDFinsuppEquiv_apply]
-  convert rfl
+  convert! rfl
 
 set_option backward.isDefEq.respectTransparency false in
 @[simp]
@@ -80,6 +80,6 @@ theorem fromDirectSumEquiv_symm_apply [Finite ι] [(i : ι) → DecidableEq (κ
     fromDirectSumEquiv.symm f p = f.compLinearMap (fun i ↦ DirectSum.lof _ _ _ (p i)) := by
   haveI : Fintype ι := Fintype.ofFinite ι
   simp_rw [fromDirectSumEquiv, DirectSum.lof, ← fromDFinsuppEquiv_symm_apply]
-  convert rfl
+  convert! rfl
 
 end MultilinearMap
diff --git a/Mathlib/LinearAlgebra/Orientation.lean b/Mathlib/LinearAlgebra/Orientation.lean
index e4cad6ec900673..197742e8649f8b 100644
--- a/Mathlib/LinearAlgebra/Orientation.lean
+++ b/Mathlib/LinearAlgebra/Orientation.lean
@@ -213,7 +213,7 @@ theorem eq_or_eq_neg_of_isEmpty [IsEmpty ι] (o : Orientation R M ι) :
   intro h
   set f : (M [⋀^ι]→ₗ[R] R) ≃ₗ[R] R := AlternatingMap.constLinearEquivOfIsEmpty.symm
   have H : LinearIndependent R ![f x, 1] := by
-    convert h.map' f.toLinearMap f.ker
+    convert! h.map' f.toLinearMap f.ker
     ext i
     fin_cases i <;> simp [f]
   rw [linearIndependent_iff'] at H
diff --git a/Mathlib/LinearAlgebra/PerfectPairing/Basic.lean b/Mathlib/LinearAlgebra/PerfectPairing/Basic.lean
index baa0a277f9aa37..7ba478a8c4f8f8 100644
--- a/Mathlib/LinearAlgebra/PerfectPairing/Basic.lean
+++ b/Mathlib/LinearAlgebra/PerfectPairing/Basic.lean
@@ -71,7 +71,7 @@ noncomputable def toPerfPair : M ≃ₗ[R] Dual R N :=
 include p in
 lemma _root_.Module.IsReflexive.of_isPerfPair : IsReflexive R M where
   bijective_dual_eval' := by
-    convert (p.toPerfPair.trans p.flip.toPerfPair.dualMap.symm).bijective
+    convert! (p.toPerfPair.trans p.flip.toPerfPair.dualMap.symm).bijective
     ext x f
     simp
 
diff --git a/Mathlib/LinearAlgebra/Pi.lean b/Mathlib/LinearAlgebra/Pi.lean
index 71074f57f6e244..177c793ab94b68 100644
--- a/Mathlib/LinearAlgebra/Pi.lean
+++ b/Mathlib/LinearAlgebra/Pi.lean
@@ -216,7 +216,7 @@ theorem iSup_range_single_eq_iInf_ker_proj {I J : Set ι} (hd : Disjoint I J)
 
 theorem iSup_range_single [Finite ι] : ⨆ i, range (single R φ i) = ⊤ := by
   cases nonempty_fintype ι
-  convert top_unique (iInf_emptyset.ge.trans <| iInf_ker_proj_le_iSup_range_single R φ _)
+  convert! top_unique (iInf_emptyset.ge.trans <| iInf_ker_proj_le_iSup_range_single R φ _)
   · rename_i i
     exact ((@iSup_pos _ _ _ fun _ => range <| single R φ i) <| Finset.mem_univ i).symm
   · rw [Finset.coe_univ, Set.union_empty]
@@ -286,7 +286,7 @@ note [partially-applied ext lemmas]. -/
 @[ext]
 theorem pi_ext' (h : ∀ i, f.comp (single R φ i) = g.comp (single R φ i)) : f = g := by
   refine pi_ext fun i x => ?_
-  convert LinearMap.congr_fun (h i) x
+  convert! LinearMap.congr_fun (h i) x
 
 end Ext
 
@@ -341,7 +341,7 @@ variable (R φ)
 
 theorem single_eq_pi_diag (i : ι) : single R φ i = pi (diag i) := by
   ext x j
-  convert (update_apply 0 x i j _).symm
+  convert! (update_apply 0 x i j _).symm
   rfl
 
 theorem ker_single (i : ι) : ker (single R φ i) = ⊥ :=
diff --git a/Mathlib/LinearAlgebra/PiTensorProduct.lean b/Mathlib/LinearAlgebra/PiTensorProduct.lean
index b5f7840fcb52b0..01f6e08a3a1838 100644
--- a/Mathlib/LinearAlgebra/PiTensorProduct.lean
+++ b/Mathlib/LinearAlgebra/PiTensorProduct.lean
@@ -199,7 +199,7 @@ protected theorem induction_on' {motive : (⨂[R] i, s i) → Prop} (z : ⨂[R]
   refine AddCon.induction_on z fun x ↦ FreeAddMonoid.recOn x C0 ?_
   simp_rw [AddCon.coe_add]
   refine fun f y ih ↦ add _ _ ?_ ih
-  convert tprodCoeff f.1 f.2
+  convert! tprodCoeff f.1 f.2
 
 section DistribMulAction
 
diff --git a/Mathlib/LinearAlgebra/PiTensorProduct/DirectSum.lean b/Mathlib/LinearAlgebra/PiTensorProduct/DirectSum.lean
index 5144396ecb41c8..7741c57f651ac2 100644
--- a/Mathlib/LinearAlgebra/PiTensorProduct/DirectSum.lean
+++ b/Mathlib/LinearAlgebra/PiTensorProduct/DirectSum.lean
@@ -44,7 +44,7 @@ theorem ofDirectSumEquiv_tprod_lof [Fintype ι] [(i : ι) → DecidableEq (κ i)
       DirectSum.lof R _ _ p (⨂ₜ[R] i, x i) := by
   classical
   rw [ofDirectSumEquiv]
-  convert ofDFinsuppEquiv_tprod_single p x
+  convert! ofDFinsuppEquiv_tprod_single p x
 
 set_option backward.isDefEq.respectTransparency false in
 @[simp]
@@ -54,13 +54,13 @@ theorem ofDirectSumEquiv_symm_lof_tprod [Fintype ι] [(i : ι) → DecidableEq (
       (⨂ₜ[R] i, DirectSum.lof R _ _ (p i) (x i)) := by
   classical
   rw [ofDirectSumEquiv]
-  convert ofDFinsuppEquiv_symm_single_tprod p x
+  convert! ofDFinsuppEquiv_symm_single_tprod p x
 
 @[simp]
 theorem ofDirectSumEquiv_tprod_apply [Finite ι]
     (x : Π i, ⨁ j, M i j) (p : Π i, κ i) :
     ofDirectSumEquiv (tprod R x) p = ⨂ₜ[R] i, x i (p i) := by
   have : Fintype ι := Fintype.ofFinite ι
-  convert ofDFinsuppEquiv_tprod_apply _ _
+  convert! ofDFinsuppEquiv_tprod_apply _ _
 
 end PiTensorProduct
diff --git a/Mathlib/LinearAlgebra/PiTensorProduct/Dual.lean b/Mathlib/LinearAlgebra/PiTensorProduct/Dual.lean
index 29511070ae623a..817f50080c1b67 100644
--- a/Mathlib/LinearAlgebra/PiTensorProduct/Dual.lean
+++ b/Mathlib/LinearAlgebra/PiTensorProduct/Dual.lean
@@ -75,7 +75,7 @@ theorem dualDistribInvOfBasis_apply [Fintype ι] [∀ i, Fintype (κ i)] (b : Π
   simp only [dualDistribInvOfBasis, Basis.coe_dualBasis, ringLmapEquivSelf_symm_apply, coe_sum,
     coe_comp, coe_smulRight, End.one_apply, Finset.sum_apply, Function.comp_apply,
     applyₗ_apply_apply]
-  convert rfl
+  convert! rfl
 
 theorem dualDistrib_dualDistribInvOfBasis_left_inverse [Finite ι] [∀ i, Finite (κ i)]
     (b : Π i, Basis (κ i) R (M i)) :
diff --git a/Mathlib/LinearAlgebra/Projection.lean b/Mathlib/LinearAlgebra/Projection.lean
index d1ceefce5eb79a..0bde1432f96dad 100644
--- a/Mathlib/LinearAlgebra/Projection.lean
+++ b/Mathlib/LinearAlgebra/Projection.lean
@@ -645,7 +645,7 @@ open LinearMap in
 its range along its kernel. -/
 theorem IsIdempotentElem.eq_projection {T : E →ₗ[R] E} (hT : IsIdempotentElem T) :
     T = T.range.projection T.ker hT.isCompl := by
-  convert ofIsCompl_subtype_zero_eq hT.isCompl
+  convert! ofIsCompl_subtype_zero_eq hT.isCompl
   exact ofIsCompl_eq _ (by simp [hT.isProj_range.map_id]) (by simp) |>.symm
 
 open LinearMap in
diff --git a/Mathlib/LinearAlgebra/Projectivization/Independence.lean b/Mathlib/LinearAlgebra/Projectivization/Independence.lean
index 0515ae6526adf5..8e265ee8a07369 100644
--- a/Mathlib/LinearAlgebra/Projectivization/Independence.lean
+++ b/Mathlib/LinearAlgebra/Projectivization/Independence.lean
@@ -50,10 +50,10 @@ theorem independent_iff : Independent f ↔ LinearIndependent K (Projectivizatio
   refine ⟨?_, fun h => ?_⟩
   · rintro ⟨ff, hff, hh⟩
     choose a ha using fun i : ι => exists_smul_eq_mk_rep K (ff i) (hff i)
-    convert hh.units_smul a
+    convert! hh.units_smul a
     ext i
     exact (ha i).symm
-  · convert Independent.mk _ _ h
+  · convert! Independent.mk _ _ h
     · simp only [mk_rep, Function.comp_apply]
     · intro i
       apply rep_nonzero
@@ -83,10 +83,10 @@ theorem dependent_iff : Dependent f ↔ ¬LinearIndependent K (Projectivization.
   · rintro ⟨ff, hff, hh1⟩
     contrapose hh1
     choose a ha using fun i : ι => exists_smul_eq_mk_rep K (ff i) (hff i)
-    convert hh1.units_smul a⁻¹
+    convert! hh1.units_smul a⁻¹
     ext i
     simp only [← ha, inv_smul_smul, Pi.smul_apply', Pi.inv_apply, Function.comp_apply]
-  · convert Dependent.mk _ _ h
+  · convert! Dependent.mk _ _ h
     · simp only [mk_rep, Function.comp_apply]
     · exact fun i => rep_nonzero (f i)
 
diff --git a/Mathlib/LinearAlgebra/Projectivization/Subspace.lean b/Mathlib/LinearAlgebra/Projectivization/Subspace.lean
index b3e3267f65148b..54f457bc094798 100644
--- a/Mathlib/LinearAlgebra/Projectivization/Subspace.lean
+++ b/Mathlib/LinearAlgebra/Projectivization/Subspace.lean
@@ -222,7 +222,7 @@ def submodule : Projectivization.Subspace K V ≃o Submodule K V where
       exact s.mem_add _ _ hx₂ hy₂ hxy (hx₁ hx₂) (hy₁ hy₂)
     zero_mem' h := h.irrefl.elim
     smul_mem' c x h₁ h₂ := by
-      convert h₁ (right_ne_zero_of_smul h₂) using 1
+      convert! h₁ (right_ne_zero_of_smul h₂) using 1
       rw [Projectivization.mk_eq_mk_iff']
       exact ⟨c, rfl⟩ }
   invFun s :=
diff --git a/Mathlib/LinearAlgebra/QuadraticForm/IsometryEquiv.lean b/Mathlib/LinearAlgebra/QuadraticForm/IsometryEquiv.lean
index 0e1306c2675365..34157f8ca08d6e 100644
--- a/Mathlib/LinearAlgebra/QuadraticForm/IsometryEquiv.lean
+++ b/Mathlib/LinearAlgebra/QuadraticForm/IsometryEquiv.lean
@@ -154,7 +154,7 @@ noncomputable def isometryEquivWeightedSumSquares (Q : QuadraticForm K V)
     Q.IsometryEquiv (weightedSumSquares K fun i => Q (v i)) := by
   let iso := Q.isometryEquivBasisRepr v
   refine ⟨iso, fun m => ?_⟩
-  convert iso.map_app m
+  convert! iso.map_app m
   rw [basisRepr_eq_of_iIsOrtho _ _ hv₁]
 
 variable [FiniteDimensional K V]
diff --git a/Mathlib/LinearAlgebra/QuadraticForm/Prod.lean b/Mathlib/LinearAlgebra/QuadraticForm/Prod.lean
index 6367b68e3220c3..e257a5ded7dcb9 100644
--- a/Mathlib/LinearAlgebra/QuadraticForm/Prod.lean
+++ b/Mathlib/LinearAlgebra/QuadraticForm/Prod.lean
@@ -325,7 +325,7 @@ theorem nonneg_pi_iff {P} [Fintype ι] [AddCommMonoid P] [PartialOrder P] [IsOrd
   -- TODO: does this generalize to a useful lemma independent of `QuadraticMap`?
   · intro h i x
     classical
-    convert h (Pi.single i x) using 1
+    convert! h (Pi.single i x) using 1
     rw [Finset.sum_eq_single_of_mem i (Finset.mem_univ _) fun j _ hji => ?_, Pi.single_eq_same]
     rw [Pi.single_eq_of_ne hji, map_zero]
   · rintro h x
diff --git a/Mathlib/LinearAlgebra/QuadraticForm/Real.lean b/Mathlib/LinearAlgebra/QuadraticForm/Real.lean
index 9cc35276c8a4d7..1b211eea5ed143 100644
--- a/Mathlib/LinearAlgebra/QuadraticForm/Real.lean
+++ b/Mathlib/LinearAlgebra/QuadraticForm/Real.lean
@@ -42,8 +42,9 @@ noncomputable def isometryEquivSignWeightedSumSquares (w : ι → ℝ) :
     by_cases hi : w i = 0
     · simp [hi]
     · simp only [hi, ↓reduceDIte, Units.val_mk0, u]; field_simp; simp
-  convert QuadraticMap.isometryEquivBasisRepr (weightedSumSquares ℝ w)
-    ((Pi.basisFun ℝ ι).unitsSMul fun i => .mk0 _ (hu i))
+  convert!
+    QuadraticMap.isometryEquivBasisRepr (weightedSumSquares ℝ w)
+      ((Pi.basisFun ℝ ι).unitsSMul fun i => .mk0 _ (hu i))
   ext1 v
   classical
   suffices ∑ i, (w i / |(u i : ℝ)|) * v i ^ 2 = ∑ i, w i * (v i ^ 2 * |(u i : ℝ)|⁻¹) by
diff --git a/Mathlib/LinearAlgebra/QuadraticForm/Signature.lean b/Mathlib/LinearAlgebra/QuadraticForm/Signature.lean
index a853d78a5c77a3..9a26d36b877fdb 100644
--- a/Mathlib/LinearAlgebra/QuadraticForm/Signature.lean
+++ b/Mathlib/LinearAlgebra/QuadraticForm/Signature.lean
@@ -193,7 +193,7 @@ lemma sigPos_weightedSumSquares :
   let m : Set ι := {i | w i ≤ 0}
   convert_to sigPos _ = p.ncard
   have : p.ncard + m.ncard = Nat.card ι := by
-    convert Set.ncard_add_ncard_compl p
+    convert! Set.ncard_add_ncard_compl p
     ext
     grind
   have : p.ncard ≤ sigPos (weightedSumSquares 𝕜 w) :=
@@ -205,7 +205,7 @@ lemma sigPos_weightedSumSquares :
 lemma sigNeg_weightedSumSquares :
     sigNeg (weightedSumSquares 𝕜 w) = {i | w i < 0}.ncard := by
   simp only [sigNeg]
-  convert sigPos_weightedSumSquares (w := -w) using 2
+  convert! sigPos_weightedSumSquares (w := -w) using 2
   · ext; simp
   · simp
 
@@ -235,7 +235,7 @@ lemma sigPos_add_sigNeg_add_radical [FiniteDimensional 𝕜 M] :
   have : Invertible (2 : 𝕜) := invertibleOfNonzero (NeZero.ne _)
   obtain ⟨w, e⟩ := Q.equivalent_weightedSumSquares
   rw [e.sigPos_eq, e.sigNeg_eq, e.rank_radical_eq]
-  convert QuadraticForm.sigPos_add_sigNeg_add_radical₁ (w := w)
+  convert! QuadraticForm.sigPos_add_sigNeg_add_radical₁ (w := w)
   exact Eq.symm (Nat.card_fin (Module.finrank 𝕜 M))
 
 /-- Uniqueness part of **Sylvester's law of inertia** (positive part):
diff --git a/Mathlib/LinearAlgebra/QuadraticForm/TensorProduct.lean b/Mathlib/LinearAlgebra/QuadraticForm/TensorProduct.lean
index 0221d16b8f9460..e8a8255fb1cda8 100644
--- a/Mathlib/LinearAlgebra/QuadraticForm/TensorProduct.lean
+++ b/Mathlib/LinearAlgebra/QuadraticForm/TensorProduct.lean
@@ -75,8 +75,10 @@ theorem associated_tmul [Invertible (2 : A)]
   letI : Invertible (2 : A) := (Invertible.map (algebraMap R A) 2).copy 2 (map_ofNat _ _).symm
   rw [QuadraticMap.tmul, BilinMap.tmul]
   have : Subsingleton (Invertible (2 : A)) := inferInstance
-  convert associated_left_inverse A (LinearMap.BilinMap.tmul_isSymm
-    (QuadraticMap.associated_isSymm A Q₁) (QuadraticMap.associated_isSymm R Q₂))
+  convert!
+    associated_left_inverse A
+      (LinearMap.BilinMap.tmul_isSymm (QuadraticMap.associated_isSymm A Q₁)
+        (QuadraticMap.associated_isSymm R Q₂))
 
 end QuadraticMap
 
diff --git a/Mathlib/LinearAlgebra/Ray.lean b/Mathlib/LinearAlgebra/Ray.lean
index 49066eedb5baa7..bd982a4e4ff1ed 100644
--- a/Mathlib/LinearAlgebra/Ray.lean
+++ b/Mathlib/LinearAlgebra/Ray.lean
@@ -193,7 +193,7 @@ theorem add_left (hx : SameRay R x z) (hy : SameRay R y z) : SameRay R (x + y) z
   rcases hy.exists_pos hy₀ hz₀ with ⟨ry, rz₂, hry, hrz₂, Hy⟩
   refine Or.inr (Or.inr ⟨rx * ry, ry * rz₁ + rx * rz₂, mul_pos hrx hry, ?_, ?_⟩)
   · positivity
-  · convert congr(ry • $Hx + rx • $Hy) using 1 <;> module
+  · convert! congr(ry • $Hx + rx • $Hy) using 1 <;> module
 
 /-- If `y` and `z` are on the same ray as `x`, then so is `y + z`. -/
 theorem add_right (hy : SameRay R x y) (hz : SameRay R x z) : SameRay R x (y + z) :=
diff --git a/Mathlib/LinearAlgebra/RootSystem/Base.lean b/Mathlib/LinearAlgebra/RootSystem/Base.lean
index e3c8d35417f093..6d5f6cce995250 100644
--- a/Mathlib/LinearAlgebra/RootSystem/Base.lean
+++ b/Mathlib/LinearAlgebra/RootSystem/Base.lean
@@ -206,7 +206,7 @@ lemma pos_or_neg_of_sum_smul_root_mem (f : ι → ℤ)
     have hf' : f ≠ 0 := by rintro rfl; exact P.ne_zero k <| by simp [hk]
     rcases b.root_mem_or_neg_mem k with hk' | hk' <;> rw [hk] at hk'
     · left; exact this f hk' hf₀ hf'
-    · right; simpa using this (-f) (by convert hk'; simp) (by simpa only [support_neg]) (by simpa)
+    · right; simpa using this (-f) (by convert! hk'; simp) (by simpa only [support_neg]) (by simpa)
   intro f hf hf₀ hf'
   let f' : b.support → ℤ := fun i ↦ f i
   replace hf : ∑ j, f' j • P.root j ∈ AddSubmonoid.closure (P.root '' b.support) := by
diff --git a/Mathlib/LinearAlgebra/RootSystem/BaseExists.lean b/Mathlib/LinearAlgebra/RootSystem/BaseExists.lean
index 3c0810c9c02cd6..d367432da18e79 100644
--- a/Mathlib/LinearAlgebra/RootSystem/BaseExists.lean
+++ b/Mathlib/LinearAlgebra/RootSystem/BaseExists.lean
@@ -131,7 +131,7 @@ lemma linearIndepOn_root_baseOf (f : M →+ ℚ) (hf : ∀ i, f (P.root i) ≠ 0
     suffices (P.rootSpanMem ℚ i : M) ∈ span ℚ (P.root '' baseOf P.root f) by
       rw [← (injective_subtype (P.rootSpan ℚ)).mem_set_image, ← map_coe, SetLike.mem_coe, map_span,
         ← image_univ, ← image_comp]
-      convert this
+      convert! this
       aesop
     rw [← span_span_of_tower ℤ, ← Submodule.coe_toAddSubgroup, span_int_eq_addSubgroupClosure,
       AddSubgroup.closure_image_isAddIndecomposable_baseOf P.root (by simp) f (by simpa)]
diff --git a/Mathlib/LinearAlgebra/RootSystem/Defs.lean b/Mathlib/LinearAlgebra/RootSystem/Defs.lean
index e897ffc8ff4e15..504b4fa64c632c 100644
--- a/Mathlib/LinearAlgebra/RootSystem/Defs.lean
+++ b/Mathlib/LinearAlgebra/RootSystem/Defs.lean
@@ -459,7 +459,7 @@ lemma smul_coroot_eq_of_root_eq_smul [Finite ι] [IsAddTorsionFree N] (i j : ι)
   refine Module.eq_of_mapsTo_reflection_of_mem (f := P.root' i) (g := P.root' i)
     (finite_range P.coroot) (by simp [hij]) (by simp) (by simp [hij]) (by simp) ?_
     (P.mapsTo_coreflection_coroot i) (mem_range_self i)
-  convert P.mapsTo_coreflection_coroot j
+  convert! P.mapsTo_coreflection_coroot j
   ext x
   replace h : P.root' j = t • P.root' i := by ext; simp [h, root']
   simp [Module.preReflection_apply, coreflection_apply, h, smul_comm _ t, mul_smul]
diff --git a/Mathlib/LinearAlgebra/RootSystem/Finite/Nondegenerate.lean b/Mathlib/LinearAlgebra/RootSystem/Finite/Nondegenerate.lean
index 3c02df1e6cf6c2..3c70e81f32884e 100644
--- a/Mathlib/LinearAlgebra/RootSystem/Finite/Nondegenerate.lean
+++ b/Mathlib/LinearAlgebra/RootSystem/Finite/Nondegenerate.lean
@@ -124,13 +124,13 @@ lemma smul_coroot_eq_of_root_add_root_eq [P.IsAnisotropic] [IsDomain R] [IsTorsi
     rw [h₂, h₃] at h₁
     replace h₁ := congr_arg (fun n ↦ P.pairing j i • n) h₁
     simp only [add_smul, smul_add, ← mul_smul, smul_eq_mul] at h₁
-    convert h₁ using 1
+    convert! h₁ using 1
     · module
     · ring_nf
   simp only [h₄] at h₁
   apply smul_right_injective _ (r := lsq j) (RootPairing.IsAnisotropic.rootForm_root_ne_zero j)
   simp only
-  convert h₁ using 1
+  convert! h₁ using 1
   · module
   · module
 
@@ -281,7 +281,7 @@ lemma isCompl_rootSpan_ker_rootForm :
     rw [P.toPerfPair.finrank_eq, ← P.finrank_corootSpan_eq',
       Subspace.finrank_add_finrank_dualAnnihilator_eq (P.corootSpan R), Subspace.dual_finrank_eq]
   rw [aux, add_le_add_iff_left]
-  convert Submodule.finrank_mono P.corootSpan_dualAnnihilator_le_ker_rootForm
+  convert! Submodule.finrank_mono P.corootSpan_dualAnnihilator_le_ker_rootForm
   exact (LinearEquiv.finrank_map_eq _ _).symm
 
 lemma isCompl_corootSpan_ker_corootForm :
diff --git a/Mathlib/LinearAlgebra/RootSystem/GeckConstruction/Lemmas.lean b/Mathlib/LinearAlgebra/RootSystem/GeckConstruction/Lemmas.lean
index 78dcfd684d021f..5b6e32a7a88c6c 100644
--- a/Mathlib/LinearAlgebra/RootSystem/GeckConstruction/Lemmas.lean
+++ b/Mathlib/LinearAlgebra/RootSystem/GeckConstruction/Lemmas.lean
@@ -45,7 +45,7 @@ lemma root_sub_root_mem_of_mem_of_mem (hk : α k + α i - α j ∈ Φ)
     rw [add_comm, add_sub_assoc, left_eq_add, sub_eq_zero, P.root.injective.eq_iff] at hl
     exact hkj hl
   suffices 0 < P.pairingIn ℤ l i by
-    convert P.root_sub_root_mem_of_pairingIn_pos this hli using 1
+    convert! P.root_sub_root_mem_of_pairingIn_pos this hli using 1
     rw [hl]
     module
   have hkl : l ≠ k := by rintro rfl; exact hij <| by simpa [add_sub_assoc, sub_eq_zero] using hl
@@ -74,7 +74,7 @@ lemma root_sub_root_mem_of_mem_of_mem (hk : α k + α i - α j ∈ Φ)
   have : P.pairingIn ℤ l i = 1 - P.pairingIn ℤ j i := by
     apply algebraMap_injective ℤ R
     simp only [algebraMap_pairingIn, map_sub, map_one, algebraMap_pairingIn]
-    convert (P.coroot' i : M →ₗ[R] R).congr_arg hl using 1
+    convert! (P.coroot' i : M →ₗ[R] R).congr_arg hl using 1
     simp only [map_sub, map_add, LinearMap.flip_apply, root_coroot_eq_pairing, hki, pairing_same,
       sub_left_inj]
     ring
@@ -88,12 +88,13 @@ lemma root_add_root_mem_of_mem_of_mem (hk : α k + α i - α j ∈ Φ)
   let _i := P.indexNeg
   replace hk : α (-k) + α j - α i ∈ Φ := by
     rw [← neg_mem_range_root_iff]
-    convert hk using 1
+    convert! hk using 1
     simp only [indexNeg_neg, root_reflectionPerm, reflection_apply_self]
     module
   rw [← neg_mem_range_root_iff]
-  convert b.root_sub_root_mem_of_mem_of_mem j i (-k) hij.symm hj hi hk (by contrapose hkj; aesop)
-    (by convert P.neg_mem_range_root_iff.mpr hk' using 1; simp [neg_add_eq_sub]) using 1
+  convert!
+    b.root_sub_root_mem_of_mem_of_mem j i (-k) hij.symm hj hi hk (by contrapose hkj; aesop)
+      (by convert! P.neg_mem_range_root_iff.mpr hk' using 1; simp [neg_add_eq_sub]) using 1
   simp only [indexNeg_neg, root_reflectionPerm, reflection_apply_self]
   module
 
@@ -170,25 +171,25 @@ lemma chainBotCoeff_mul_chainTopCoeff.isNotG2 : P.IsNotG2 := by
         ← two_nsmul, h₂] at h₃
     exact P.nsmul_notMem_range_root ⟨_, h₃.symm⟩
   replace h₁ : 2 * (x + 1) + A * y ∈ s := by
-    convert IsG2.pairingIn_mem_zero_one_three P l i hli hli'
+    convert! IsG2.pairingIn_mem_zero_one_three P l i hli hli'
     replace h₁ : P.root l = (x + 1) • P.root i + y • P.root j := by rw [← h₁, ← h₀]; module
     rw [pairingIn_eq_add_of_root_eq_smul_add_smul (S := ℤ) (j := i) h₁, pairingIn_same,
       Int.zsmul_eq_mul, Int.zsmul_eq_mul]
     ring
   replace h₂ : 2 * x + A * (y - 1) ∈ s := by
-    convert IsG2.pairingIn_mem_zero_one_three P m i hmi hmi'
+    convert! IsG2.pairingIn_mem_zero_one_three P m i hmi hmi'
     replace h₂ : P.root m = x • P.root i + (y - 1) • P.root j := by rw [← h₂, ← h₀]; module
     rw [pairingIn_eq_add_of_root_eq_smul_add_smul (S := ℤ) (j := i) h₂, pairingIn_same,
       Int.zsmul_eq_mul, Int.zsmul_eq_mul]
     ring
   replace h₃ : 2 * (x + 1) + A * (y - 1) ∈ s := by
-    convert IsG2.pairingIn_mem_zero_one_three P n i hni hni'
+    convert! IsG2.pairingIn_mem_zero_one_three P n i hni hni'
     replace h₃ : P.root n = (x + 1) • P.root i + (y - 1) • P.root j := by rw [h₃, ← h₀]; module
     rw [pairingIn_eq_add_of_root_eq_smul_add_smul (S := ℤ) (j := i) h₃, pairingIn_same,
       Int.zsmul_eq_mul, Int.zsmul_eq_mul]
     ring
   replace h₀ : 2 * x + A * y ∈ s := by
-    convert IsG2.pairingIn_mem_zero_one_three P k i hki hki'
+    convert! IsG2.pairingIn_mem_zero_one_three P k i hki hki'
     rw [pairingIn_eq_add_of_root_eq_smul_add_smul (j := i) h₀.symm, pairingIn_same,
       Int.zsmul_eq_mul, Int.zsmul_eq_mul]
     ring
@@ -218,7 +219,7 @@ private lemma chainBotCoeff_mul_chainTopCoeff.aux_1
   have hkj_ne : k ≠ j ∧ P.root k ≠ -P.root j := (IsReduced.linearIndependent_iff _).mp <|
     P.linearIndependent_of_sub_mem_range_root <| h₂ ▸ mem_range_self m
   have hnk_notMem : P.root n - P.root k ∉ range P.root := by
-    convert b.sub_notMem_range_root hi hj using 2; rw [hn]; module
+    convert! b.sub_notMem_range_root hi hj using 2; rw [hn]; module
   /- Calculate some auxiliary relationships between root pairings. -/
   have aux₀ : P.pairingIn ℤ j i = - P.pairingIn ℤ m i := by
     suffices P.pairing j i = - P.pairing m i from
@@ -340,12 +341,12 @@ lemma chainBotCoeff_mul_chainTopCoeff :
   suffices (P.chainBotCoeff i m + 1) * (P.chainBotCoeff j (-k) + 1) =
       (P.chainBotCoeff j (-l) + 1) * (P.chainBotCoeff i k + 1) by simpa
   /- Establish basic relationships about roots and their sums / differences. -/
-  have him_mem : P.root i + P.root m ∈ range P.root := by rw [← h₂]; convert h₃ using 1; abel
+  have him_mem : P.root i + P.root m ∈ range P.root := by rw [← h₂]; convert! h₃ using 1; abel
   have hik_mem : P.root k + P.root i ∈ range P.root := h₁ ▸ mem_range_self l
   have hjk_mem : P.root j + P.root (-k) ∈ range P.root := by
-    convert mem_range_self (-m) using 1; simpa [sub_eq_add_neg] using congr(-$h₂)
+    convert! mem_range_self (-m) using 1; simpa [sub_eq_add_neg] using congr(-$h₂)
   have hjl_mem : P.root j + P.root (-l) ∈ range P.root := by
-    rw [h₁, ← neg_mem_range_root_iff] at h₃; convert h₃ using 1; simp [sub_eq_add_neg]
+    rw [h₁, ← neg_mem_range_root_iff] at h₃; convert! h₃ using 1; simp [sub_eq_add_neg]
   have h₁' : P.root (-k) - P.root i = P.root (-l) := by
     simp only [root_reflectionPerm, reflection_apply_self, indexNeg_neg]; rw [← h₁]; abel
   have h₂' : P.root (-k) + P.root j = P.root (-m) := by
diff --git a/Mathlib/LinearAlgebra/RootSystem/GeckConstruction/Semisimple.lean b/Mathlib/LinearAlgebra/RootSystem/GeckConstruction/Semisimple.lean
index e56ded4bca6605..0e63f34d9c13a4 100644
--- a/Mathlib/LinearAlgebra/RootSystem/GeckConstruction/Semisimple.lean
+++ b/Mathlib/LinearAlgebra/RootSystem/GeckConstruction/Semisimple.lean
@@ -129,7 +129,7 @@ lemma isNilpotent_e :
       apply IsReduced.linearIndependent P ?_ ?_
       · rintro rfl
         apply P.nsmul_notMem_range_root (n := P.chainTopCoeff i i + 2) (i := i)
-        convert hk₁ using 1
+        convert! hk₁ using 1
         module
       · contrapose hij
         rw [root_eq_neg_iff] at hij
diff --git a/Mathlib/LinearAlgebra/SesquilinearForm/Basic.lean b/Mathlib/LinearAlgebra/SesquilinearForm/Basic.lean
index acea5ae533874c..c69b973e4e8ff9 100644
--- a/Mathlib/LinearAlgebra/SesquilinearForm/Basic.lean
+++ b/Mathlib/LinearAlgebra/SesquilinearForm/Basic.lean
@@ -723,7 +723,7 @@ theorem Nondegenerate.congr (h : B.Nondegenerate) :
 theorem separatingLeft_congr_iff :
     (e₁.arrowCongr (e₂.arrowCongr (LinearEquiv.refl R M)) B).SeparatingLeft ↔ B.SeparatingLeft :=
   ⟨fun h ↦ by
-    convert h.congr e₁.symm e₂.symm
+    convert! h.congr e₁.symm e₂.symm
     ext x y
     simp,
    SeparatingLeft.congr e₁ e₂⟩
diff --git a/Mathlib/LinearAlgebra/Span/Basic.lean b/Mathlib/LinearAlgebra/Span/Basic.lean
index aaf8b9ca8ff941..8a8ce994c1f705 100644
--- a/Mathlib/LinearAlgebra/Span/Basic.lean
+++ b/Mathlib/LinearAlgebra/Span/Basic.lean
@@ -126,8 +126,9 @@ lemma linearMap_eq_iff_of_eq_span {V : Submodule R M} (f g : V →ₗ[R] N)
 lemma linearMap_eq_iff_of_span_eq_top (f g : M →ₗ[R] N)
     {S : Set M} (hM : span R S = ⊤) :
     f = g ↔ ∀ (s : S), f s = g s := by
-  convert linearMap_eq_iff_of_eq_span (f.comp (Submodule.subtype _))
-    (g.comp (Submodule.subtype _)) hM.symm
+  convert!
+    linearMap_eq_iff_of_eq_span (f.comp (Submodule.subtype _)) (g.comp (Submodule.subtype _))
+      hM.symm
   constructor
   · rintro rfl
     rfl
@@ -152,7 +153,7 @@ end
 theorem span_smul_eq_of_isUnit (s : Set M) (r : R) (hr : IsUnit r) : span R (r • s) = span R s := by
   apply le_antisymm
   · apply span_smul_le
-  · convert span_smul_le (r • s) ((hr.unit⁻¹ :) : R)
+  · convert! span_smul_le (r • s) ((hr.unit⁻¹ :) : R)
     simp [smul_smul]
 
 /-- We can regard `coe_iSup_of_chain` as the statement that `(↑) : (Submodule R M) → Set M` is
diff --git a/Mathlib/LinearAlgebra/Span/Defs.lean b/Mathlib/LinearAlgebra/Span/Defs.lean
index e23492dfda9cb5..294fcbbaa076c9 100644
--- a/Mathlib/LinearAlgebra/Span/Defs.lean
+++ b/Mathlib/LinearAlgebra/Span/Defs.lean
@@ -488,7 +488,7 @@ theorem span_singleton_smul_le {S} [SMul S R] [SMul S M] [IsScalarTower S R M]
 theorem span_singleton_group_smul_eq {G} [Group G] [SMul G R] [MulAction G M] [IsScalarTower G R M]
     (g : G) (x : M) : R ∙ g • x = R ∙ x := by
   refine le_antisymm (span_singleton_smul_le R g x) ?_
-  convert span_singleton_smul_le R g⁻¹ (g • x)
+  convert! span_singleton_smul_le R g⁻¹ (g • x)
   exact (inv_smul_smul g x).symm
 
 variable {R}
diff --git a/Mathlib/LinearAlgebra/SpecialLinearGroup.lean b/Mathlib/LinearAlgebra/SpecialLinearGroup.lean
index 21e37ff4747986..5c8c3afb9c550b 100644
--- a/Mathlib/LinearAlgebra/SpecialLinearGroup.lean
+++ b/Mathlib/LinearAlgebra/SpecialLinearGroup.lean
@@ -546,7 +546,7 @@ theorem centerCongr_toLin_equiv_trans_centerEquivRootsOfUnity_eq (g) :
       Matrix.SpecialLinearGroup.center_equiv_rootsOfUnity g := by
   nontriviality R
   by_cases hV : Subsingleton V
-  · convert Eq.refl (1 : Rˣ) <;>
+  · convert! Eq.refl (1 : Rˣ) <;>
     · apply rootsOfUnity.eq_one
       rw [← Module.finrank_eq_zero_iff_of_free (R := R)] at hV
       simp only [hV, sup_eq_right, zero_le_one, ← Module.finrank_eq_card_basis b]
diff --git a/Mathlib/LinearAlgebra/StdBasis.lean b/Mathlib/LinearAlgebra/StdBasis.lean
index 77cd82820b5c82..843555ee5da950 100644
--- a/Mathlib/LinearAlgebra/StdBasis.lean
+++ b/Mathlib/LinearAlgebra/StdBasis.lean
@@ -47,7 +47,7 @@ variable {η : Type*} {ιs : η → Type*} {Ms : η → Type*}
 theorem linearIndependent_single [Semiring R] [∀ i, AddCommMonoid (Ms i)] [∀ i, Module R (Ms i)]
     [DecidableEq η] (v : ∀ j, ιs j → Ms j) (hs : ∀ i, LinearIndependent R (v i)) :
     LinearIndependent R fun ji : Σ j, ιs j ↦ Pi.single ji.1 (v ji.1 ji.2) := by
-  convert (DFinsupp.linearIndependent_single _ hs).map_injOn _ DFinsupp.injective_pi_lapply.injOn
+  convert! (DFinsupp.linearIndependent_single _ hs).map_injOn _ DFinsupp.injective_pi_lapply.injOn
 
 theorem linearIndependent_single_one (ι R : Type*) [Semiring R] [DecidableEq ι] :
     LinearIndependent R (fun i : ι ↦ Pi.single i (1 : R)) := by
@@ -165,7 +165,7 @@ lemma AlgHom.eq_piEvalAlgHom {k G : Type*} [CommSemiring k] [NoZeroDivisors k] [
   have h2 : ∀ t ≠ s, φ (Pi.single t 1) = 0 := by
     refine fun _ _ ↦ (eq_zero_or_eq_zero_of_mul_eq_zero ?_).resolve_left hs
     rw [← map_mul]
-    convert map_zero φ
+    convert! map_zero φ
     ext u
     by_cases u = s <;> simp_all
   have h3 : φ (Pi.single s 1) = 1 := by
diff --git a/Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean b/Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean
index 26d2633edac6a8..a8e63217d9d82c 100644
--- a/Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean
+++ b/Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean
@@ -146,7 +146,7 @@ variable {R}
 @[simp]
 theorem ι_comp_lift {A : Type*} [Semiring A] [Algebra R A] (f : M →ₗ[R] A) :
     (lift R f).toLinearMap.comp (ι R) = f := by
-  convert (lift R).symm_apply_apply f
+  convert! (lift R).symm_apply_apply f
 
 @[simp]
 theorem lift_ι_apply {A : Type*} [Semiring A] [Algebra R A] (f : M →ₗ[R] A) (x) :
diff --git a/Mathlib/LinearAlgebra/TensorPower/Symmetric.lean b/Mathlib/LinearAlgebra/TensorPower/Symmetric.lean
index fd727321ca544b..3549e86257a213 100644
--- a/Mathlib/LinearAlgebra/TensorPower/Symmetric.lean
+++ b/Mathlib/LinearAlgebra/TensorPower/Symmetric.lean
@@ -72,11 +72,12 @@ lemma smul (r : R) (x y : ⨂[R] _, M) (h : addConGen (Rel R ι M) x y) :
   | of x y h => cases h with
     | perm e f =>
       apply isEmpty_or_nonempty ι |>.elim <;> intro h
-      · convert addConGen (Rel R ι M) |>.refl _
+      · convert! addConGen (Rel R ι M) |>.refl _
       · let i := Nonempty.some h
         classical
-        convert AddConGen.Rel.of _ _ <| SymmetricPower.Rel.perm (R := R) (ι := ι) e
-          <| Function.update f i (r • f i)
+        convert!
+          AddConGen.Rel.of _ _ <|
+            SymmetricPower.Rel.perm (R := R) (ι := ι) e <| Function.update f i (r • f i)
         · rw [MultilinearMap.map_update_smul, Function.update_eq_self]
         · simp_rw [Function.update_apply_equiv_apply, MultilinearMap.map_update_smul,
               ← Function.update_comp_equiv, Function.update_eq_self]; rfl
diff --git a/Mathlib/LinearAlgebra/TensorProduct/Basic.lean b/Mathlib/LinearAlgebra/TensorProduct/Basic.lean
index c9949b11f603e9..7c45ceb0d837f2 100644
--- a/Mathlib/LinearAlgebra/TensorProduct/Basic.lean
+++ b/Mathlib/LinearAlgebra/TensorProduct/Basic.lean
@@ -380,7 +380,7 @@ instance neg : Neg (M ⊗[R] N) where
 protected theorem neg_add_cancel (x : M ⊗[R] N) : -x + x = 0 :=
   x.induction_on
     (by rw [add_zero]; apply (Neg.aux R).map_zero)
-    (fun x y => by convert (add_tmul (R := R) (-x) x y).symm; rw [neg_add_cancel, zero_tmul])
+    (fun x y => by convert! (add_tmul (R := R) (-x) x y).symm; rw [neg_add_cancel, zero_tmul])
     fun x y hx hy => by
     suffices -x + x + (-y + y) = 0 by
       rw [← this]
diff --git a/Mathlib/LinearAlgebra/TensorProduct/DirectLimit.lean b/Mathlib/LinearAlgebra/TensorProduct/DirectLimit.lean
index fb860351f3ad63..5e43b9eb9e92b3 100644
--- a/Mathlib/LinearAlgebra/TensorProduct/DirectLimit.lean
+++ b/Mathlib/LinearAlgebra/TensorProduct/DirectLimit.lean
@@ -112,14 +112,14 @@ variable [DirectedSystem G (f · · ·)]
 
 instance : DirectedSystem (G · ⊗[R] M) (f ▷ M) where
   map_self i x := by
-    convert LinearMap.rTensor_id_apply M (G i) x; ext; apply DirectedSystem.map_self'
+    convert! LinearMap.rTensor_id_apply M (G i) x; ext; apply DirectedSystem.map_self'
   map_map _ _ _ _ _ x := by
-    convert ← (LinearMap.rTensor_comp_apply M _ _ x).symm; ext; apply DirectedSystem.map_map' f
+    convert! ← (LinearMap.rTensor_comp_apply M _ _ x).symm; ext; apply DirectedSystem.map_map' f
 
 instance : DirectedSystem (M ⊗[R] G ·) (M ◁ f) where
   map_self i x := by
-    convert LinearMap.lTensor_id_apply M _ x; ext; apply DirectedSystem.map_self'
+    convert! LinearMap.lTensor_id_apply M _ x; ext; apply DirectedSystem.map_self'
   map_map _ _ _ h₁ h₂ x := by
-    convert ← (LinearMap.lTensor_comp_apply M _ _ x).symm; ext; apply DirectedSystem.map_map' f
+    convert! ← (LinearMap.lTensor_comp_apply M _ _ x).symm; ext; apply DirectedSystem.map_map' f
 
 end TensorProduct
diff --git a/Mathlib/LinearAlgebra/TensorProduct/Graded/Internal.lean b/Mathlib/LinearAlgebra/TensorProduct/Graded/Internal.lean
index 72c3737ee2bc2d..4a8b903f686cc3 100644
--- a/Mathlib/LinearAlgebra/TensorProduct/Graded/Internal.lean
+++ b/Mathlib/LinearAlgebra/TensorProduct/Graded/Internal.lean
@@ -209,18 +209,19 @@ theorem tmul_coe_mul_zero_coe_tmul {j₁ : ι} (a₁ : A) (b₁ : ℬ j₁) (a
 
 theorem tmul_one_mul_coe_tmul {i₂ : ι} (a₁ : A) (a₂ : 𝒜 i₂) (b₂ : B) :
     (a₁ ᵍ⊗ₜ[R] (1 : B) * (a₂ : A) ᵍ⊗ₜ[R] b₂ : 𝒜 ᵍ⊗[R] ℬ) = (a₁ * a₂ : A) ᵍ⊗ₜ (b₂ : B) := by
-  convert tmul_zero_coe_mul_coe_tmul 𝒜 ℬ a₁ (@GradedMonoid.GOne.one _ (ℬ ·) _ _) a₂ b₂
+  convert! tmul_zero_coe_mul_coe_tmul 𝒜 ℬ a₁ (@GradedMonoid.GOne.one _ (ℬ ·) _ _) a₂ b₂
   rw [SetLike.coe_gOne, one_mul]
 
 theorem tmul_coe_mul_one_tmul {j₁ : ι} (a₁ : A) (b₁ : ℬ j₁) (b₂ : B) :
     (a₁ ᵍ⊗ₜ[R] (b₁ : B) * (1 : A) ᵍ⊗ₜ[R] b₂ : 𝒜 ᵍ⊗[R] ℬ) = (a₁ : A) ᵍ⊗ₜ (b₁ * b₂ : B) := by
-  convert tmul_coe_mul_zero_coe_tmul 𝒜 ℬ a₁ b₁ (@GradedMonoid.GOne.one _ (𝒜 ·) _ _) b₂
+  convert! tmul_coe_mul_zero_coe_tmul 𝒜 ℬ a₁ b₁ (@GradedMonoid.GOne.one _ (𝒜 ·) _ _) b₂
   rw [SetLike.coe_gOne, mul_one]
 
 theorem tmul_one_mul_one_tmul (a₁ : A) (b₂ : B) :
     (a₁ ᵍ⊗ₜ[R] (1 : B) * (1 : A) ᵍ⊗ₜ[R] b₂ : 𝒜 ᵍ⊗[R] ℬ) = (a₁ : A) ᵍ⊗ₜ (b₂ : B) := by
-  convert tmul_coe_mul_zero_coe_tmul 𝒜 ℬ
-    a₁ (GradedMonoid.GOne.one (A := (ℬ ·))) (GradedMonoid.GOne.one (A := (𝒜 ·))) b₂
+  convert!
+    tmul_coe_mul_zero_coe_tmul 𝒜 ℬ a₁ (GradedMonoid.GOne.one (A := (ℬ ·)))
+      (GradedMonoid.GOne.one (A := (𝒜 ·))) b₂
   · rw [SetLike.coe_gOne, mul_one]
   · rw [SetLike.coe_gOne, one_mul]
 
diff --git a/Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean b/Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
index 0b303cc6c32f63..53349052145c1f 100644
--- a/Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
+++ b/Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean
@@ -411,7 +411,7 @@ lemma LinearMap.ker_tensorProductMk {I : Ideal R} :
     ker (TensorProduct.mk R (R ⧸ I) Q 1) = I • ⊤ := by
   apply comap_injective_of_surjective (TensorProduct.lid R Q).surjective
   rw [← ker_comp]
-  convert rTensor_mkQ Q I
+  convert! rTensor_mkQ Q I
   · ext; simp
   rw [comap_equiv_eq_map_symm, map_symm_eq_iff, map_range_rTensor_subtype_lid]
 
diff --git a/Mathlib/LinearAlgebra/TensorProduct/Vanishing.lean b/Mathlib/LinearAlgebra/TensorProduct/Vanishing.lean
index 5d0421a6d01155..ebd9a892dc8712 100644
--- a/Mathlib/LinearAlgebra/TensorProduct/Vanishing.lean
+++ b/Mathlib/LinearAlgebra/TensorProduct/Vanishing.lean
@@ -164,7 +164,7 @@ theorem vanishesTrivially_of_sum_tmul_eq_zero (hm : Submodule.span R (Set.range
       Finset.sum_ite_eq', Finset.mem_univ, ↓reduceIte, rTensor_tmul, coe_subtype, Finsupp.sum_apply,
       Finsupp.sum_ite_eq', Finsupp.mem_support_iff, ne_eq, ite_not, en] at hkn
     simp only [Finset.univ_eq_attach, Finset.sum_attach ma (fun x ↦ (x.1 : ι →₀ R) i • x.2)]
-    convert hkn using 2 with x _
+    convert! hkn using 2 with x _
     split
     · next h'x => rw [h'x, zero_smul]
     · rfl
@@ -203,8 +203,8 @@ theorem vanishesTrivially_of_sum_tmul_eq_zero_of_rTensor_injective
     simp only [m'_eq, map_sum, rTensor_tmul, coe_subtype, Subtype.coind_coe, map_zero, hmn]
   have : VanishesTrivially R m' n := vanishesTrivially_of_sum_tmul_eq_zero R hm' hm'n
   unfold VanishesTrivially at this ⊢
-  convert this with κ _ a y j
-  convert (injective_iff_map_eq_zero' _).mp (injective_subtype (span R (Set.range m))) _
+  convert! this with κ _ a y j
+  convert! (injective_iff_map_eq_zero' _).mp (injective_subtype (span R (Set.range m))) _
   simp [m'_eq]
 
 /-- **Equational criterion for vanishing**
@@ -239,9 +239,9 @@ theorem rTensor_injective_of_forall_vanishesTrivially
   have := hMN hx
   rw [← e.vanishesTrivially_comp]
   unfold VanishesTrivially at this ⊢
-  convert this
+  convert! this
   symm
-  convert (injective_iff_map_eq_zero' _).mp (injective_subtype M') _
+  convert! (injective_iff_map_eq_zero' _).mp (injective_subtype M') _
   simp
 
 /-- Every expression $\sum_i m_i \otimes n_i$ which vanishes also vanishes trivially if and only if
diff --git a/Mathlib/LinearAlgebra/Transvection/Basic.lean b/Mathlib/LinearAlgebra/Transvection/Basic.lean
index add56dac91b8ed..02514b45847ed7 100644
--- a/Mathlib/LinearAlgebra/Transvection/Basic.lean
+++ b/Mathlib/LinearAlgebra/Transvection/Basic.lean
@@ -609,7 +609,7 @@ private theorem det_ofField [FiniteDimensional K V] (f : Dual K V) (v : V) :
     · simp [← hxy, hxi]
     · rw [Finsupp.single_eq_of_ne hxi]; simp [hxy]
     · rw [Finsupp.single_eq_of_ne hxy, zero_add, mul_assoc]
-      convert mul_zero _
+      convert! mul_zero _
       by_cases hxi : x = i
       · simp [← hxi, Finsupp.single_eq_of_ne hxy]
       · simp [Finsupp.single_eq_of_ne hxi]
diff --git a/Mathlib/LinearAlgebra/Vandermonde.lean b/Mathlib/LinearAlgebra/Vandermonde.lean
index 650931547fcca2..f206bd497007a8 100644
--- a/Mathlib/LinearAlgebra/Vandermonde.lean
+++ b/Mathlib/LinearAlgebra/Vandermonde.lean
@@ -211,7 +211,7 @@ theorem det_projVandermonde (v w : Fin n → R) : (projVandermonde v w).det =
   rw [projVandermonde_map, ← RingHom.map_det, IsFractionRing.coe_inj] at hdet
   apply_fun MvPolynomial.eval₂Hom (Int.castRingHom R) (fun x ↦ (if x.2 then v else w) x.1) at hdet
   rw [RingHom.map_det] at hdet
-  convert hdet <;>
+  convert! hdet <;>
   simp [← Matrix.ext_iff, projVandermonde_apply]
 
 /-- The formula for the determinant of a Vandermonde matrix. -/
@@ -300,7 +300,7 @@ private lemma of_eval_descPochhammer_eq_mul_of_choose {n : ℕ} (v : Fin n → 
     (of fun i j : Fin n => (descPochhammer ℤ j).eval (v i : ℤ)).det =
     (∏ i : Fin n, Nat.factorial i) *
       (of fun i j : Fin n => (Nat.choose (v i) j : ℤ)).det := by
-  convert det_mul_row (fun (i : Fin n) => ((Nat.factorial (i : ℕ)) : ℤ)) _
+  convert! det_mul_row (fun (i : Fin n) => ((Nat.factorial (i : ℕ)) : ℤ)) _
   · rw [of_apply, descPochhammer_eval_eq_descFactorial ℤ _ _]
     congr
     exact Nat.descFactorial_eq_factorial_mul_choose _ _
diff --git a/Mathlib/Logic/Encodable/Lattice.lean b/Mathlib/Logic/Encodable/Lattice.lean
index 5614535c2f0954..159951b6d7c8a0 100644
--- a/Mathlib/Logic/Encodable/Lattice.lean
+++ b/Mathlib/Logic/Encodable/Lattice.lean
@@ -45,7 +45,7 @@ theorem iUnion_decode₂_cases {f : β → Set α} {C : Set α → Prop} (H0 : C
     simp only [Option.mem_def, iUnion_of_empty, iUnion_empty, reduceCtorEq]
     apply H0
   | some b => by
-    convert H1 b
+    convert! H1 b
     simp
 
 open scoped Function in -- required for scoped `on` notation
diff --git a/Mathlib/Logic/Equiv/Fin/Basic.lean b/Mathlib/Logic/Equiv/Fin/Basic.lean
index bdd4576d780967..341c95b6f54503 100644
--- a/Mathlib/Logic/Equiv/Fin/Basic.lean
+++ b/Mathlib/Logic/Equiv/Fin/Basic.lean
@@ -316,12 +316,12 @@ theorem finAddFlip_apply_natAdd (k : Fin n) (m : ℕ) :
 theorem finAddFlip_apply_mk_left {k : ℕ} (h : k < m) (hk : k < m + n := Nat.lt_add_right n h)
     (hnk : n + k < n + m := Nat.add_lt_add_left h n) :
     finAddFlip (⟨k, hk⟩ : Fin (m + n)) = ⟨n + k, hnk⟩ := by
-  convert finAddFlip_apply_castAdd ⟨k, h⟩ n
+  convert! finAddFlip_apply_castAdd ⟨k, h⟩ n
 
 @[simp]
 theorem finAddFlip_apply_mk_right {k : ℕ} (h₁ : m ≤ k) (h₂ : k < m + n) :
     finAddFlip (⟨k, h₂⟩ : Fin (m + n)) = ⟨k - m, by lia⟩ := by
-  convert @finAddFlip_apply_natAdd n ⟨k - m, by lia⟩ m
+  convert! @finAddFlip_apply_natAdd n ⟨k - m, by lia⟩ m
   simp [Nat.add_sub_cancel' h₁]
 
 /-- Equivalence between `Fin m × Fin n` and `Fin (m * n)` -/
diff --git a/Mathlib/Logic/Equiv/Fintype.lean b/Mathlib/Logic/Equiv/Fintype.lean
index f1f25b68f0a7cf..6005758b19ffc1 100644
--- a/Mathlib/Logic/Equiv/Fintype.lean
+++ b/Mathlib/Logic/Equiv/Fintype.lean
@@ -73,7 +73,7 @@ def Equiv.Perm.viaFintypeEmbedding : Equiv.Perm β :=
 theorem Equiv.Perm.viaFintypeEmbedding_apply_image (a : α) :
     e.viaFintypeEmbedding f (f a) = f (e a) := by
   rw [Equiv.Perm.viaFintypeEmbedding]
-  convert Equiv.Perm.extendDomain_apply_image e (Function.Embedding.toEquivRange f) a
+  convert! Equiv.Perm.extendDomain_apply_image e (Function.Embedding.toEquivRange f) a
 
 theorem Equiv.Perm.viaFintypeEmbedding_apply_mem_range {b : β} (h : b ∈ Set.range f) :
     e.viaFintypeEmbedding f b = f (e (f.invOfMemRange ⟨b, h⟩)) := by
@@ -102,7 +102,7 @@ noncomputable def setDiffEquiv {s t : Set α} [Fintype s] [Fintype t]
   have hst (x : α) : x ∈ fs \ ft ↔ x ∈ s \ t := by simp [hs, ht]
   have hts (x : α) : x ∈ ft \ fs ↔ x ∈ t \ s := by simp [hs, ht]
   have hc : fs.card = ft.card := by
-    rw [← Fintype.subtype_card fs hs, ← Fintype.subtype_card ft ht]; convert h
+    rw [← Fintype.subtype_card fs hs, ← Fintype.subtype_card ft ht]; convert! h
   replace hc := Finset.card_sdiff_comm hc
   rw [← Fintype.subtype_card (fs \ ft) hst, ← Fintype.subtype_card (ft \ fs) hts] at hc
   exact ((Fintype.card_eq (_F := (_)) (_G := (_))).mp hc).some
diff --git a/Mathlib/Logic/Function/FiberPartition.lean b/Mathlib/Logic/Function/FiberPartition.lean
index e52d0455afe115..f85ea3cb6bcf99 100644
--- a/Mathlib/Logic/Function/FiberPartition.lean
+++ b/Mathlib/Logic/Function/FiberPartition.lean
@@ -49,7 +49,7 @@ def mkSelf (f : Y → Z) (y : Y) : (mk f y).val := ⟨y, rfl⟩
 lemma map_eq_image (f : Y → Z) (a : Fiber f) (x : a.1) : f x = a.image := by
   have := a.2.choose_spec
   rw [← Set.mem_singleton_iff, ← Set.mem_preimage]
-  convert x.prop
+  convert! x.prop
 
 lemma mk_image (f : Y → Z) (y : Y) : (Fiber.mk f y).image = f y :=
   (map_eq_image (x := mkSelf f y)).symm
diff --git a/Mathlib/Logic/Hydra.lean b/Mathlib/Logic/Hydra.lean
index 2245132e3e1a99..0990defc7d53f0 100644
--- a/Mathlib/Logic/Hydra.lean
+++ b/Mathlib/Logic/Hydra.lean
@@ -84,7 +84,7 @@ theorem cutExpand_add_left {t u} (s) : CutExpand r (s + t) (s + u) ↔ CutExpand
   exists₂_congr fun _ _ ↦ and_congr Iff.rfl <| by rw [add_assoc, add_assoc, add_left_cancel_iff]
 
 lemma cutExpand_add_right {s' s} (t) : CutExpand r (s' + t) (s + t) ↔ CutExpand r s' s := by
-  convert cutExpand_add_left t using 2 <;> apply add_comm
+  convert! cutExpand_add_left t using 2 <;> apply add_comm
 
 theorem cutExpand_add_single {a' a : α} (s : Multiset α) (h : r a' a) :
     CutExpand r (s + {a'}) (s + {a}) :=
diff --git a/Mathlib/Logic/Lemmas.lean b/Mathlib/Logic/Lemmas.lean
index df76040ca70913..0266bda809af21 100644
--- a/Mathlib/Logic/Lemmas.lean
+++ b/Mathlib/Logic/Lemmas.lean
@@ -66,5 +66,5 @@ lemma Prop.forall {f : Prop → Prop} : (∀ p, f p) ↔ f True ∧ f False :=
   ⟨fun h ↦ ⟨h _, h _⟩, by rintro ⟨h₁, h₀⟩ p; by_cases hp : p <;> simp only [hp] <;> assumption⟩
 
 lemma Prop.exists {f : Prop → Prop} : (∃ p, f p) ↔ f True ∨ f False :=
-  ⟨fun ⟨p, h⟩ ↦ by refine (em p).imp ?_ ?_ <;> intro H <;> convert h <;> simp [H],
+  ⟨fun ⟨p, h⟩ ↦ by refine (em p).imp ?_ ?_ <;> intro H <;> convert! h <;> simp [H],
     by rintro (h | h) <;> exact ⟨_, h⟩⟩
diff --git a/Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean b/Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean
index 928e78d8ca93b4..2a9879dab3d43c 100644
--- a/Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean
+++ b/Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean
@@ -141,7 +141,7 @@ theorem tendsto_measure_cthickening {μ : Measure α} {s : Set α}
     apply Tendsto.congr' _ tendsto_const_nhds
     filter_upwards [self_mem_nhdsWithin (α := ℝ)] with _ hr
     rw [cthickening_of_nonpos hr]
-  convert B.sup A
+  convert! B.sup A
   exact (nhdsLE_sup_nhdsGT 0).symm
 
 /-- If a closed set has a closed thickening with finite measure, then the measure of its closed
@@ -149,7 +149,7 @@ theorem tendsto_measure_cthickening {μ : Measure α} {s : Set α}
 theorem tendsto_measure_cthickening_of_isClosed {μ : Measure α} {s : Set α}
     (hs : ∃ R > 0, μ (cthickening R s) ≠ ∞) (h's : IsClosed s) :
     Tendsto (fun r => μ (cthickening r s)) (𝓝 0) (𝓝 (μ s)) := by
-  convert tendsto_measure_cthickening hs
+  convert! tendsto_measure_cthickening hs
   exact h's.closure_eq.symm
 
 /-- If a set has a thickening with finite measure, then the measures of its `r`-thickenings
@@ -166,7 +166,7 @@ theorem tendsto_measure_thickening {μ : Measure α} {s : Set α}
 theorem tendsto_measure_thickening_of_isClosed {μ : Measure α} {s : Set α}
     (hs : ∃ R > 0, μ (thickening R s) ≠ ∞) (h's : IsClosed s) :
     Tendsto (fun r => μ (thickening r s)) (𝓝[>] 0) (𝓝 (μ s)) := by
-  convert tendsto_measure_thickening hs
+  convert! tendsto_measure_thickening hs
   exact h's.closure_eq.symm
 
 variable [SecondCountableTopology α]
diff --git a/Mathlib/MeasureTheory/Constructions/BorelSpace/Order.lean b/Mathlib/MeasureTheory/Constructions/BorelSpace/Order.lean
index 73187d3cc152bd..1c5923dd759157 100644
--- a/Mathlib/MeasureTheory/Constructions/BorelSpace/Order.lean
+++ b/Mathlib/MeasureTheory/Constructions/BorelSpace/Order.lean
@@ -405,8 +405,8 @@ theorem Dense.borel_eq_generateFrom_Ioc_mem_aux {α : Type*} [TopologicalSpace 
     [OrderTopology α] [SecondCountableTopology α] {s : Set α} (hd : Dense s)
     (hbot : ∀ x, IsTop x → x ∈ s) (hIoo : ∀ x y : α, x < y → Ioo x y = ∅ → x ∈ s) :
     borel α = .generateFrom { S : Set α | ∃ l ∈ s, ∃ u ∈ s, l < u ∧ Ioc l u = S } := by
-  convert hd.orderDual.borel_eq_generateFrom_Ico_mem_aux hbot fun x y hlt he => hIoo y x hlt _
-    using 2
+  convert!
+    hd.orderDual.borel_eq_generateFrom_Ico_mem_aux hbot fun x y hlt he => hIoo y x hlt _ using 2
   · ext s
     constructor <;> rintro ⟨l, hl, u, hu, hlt, rfl⟩
     exacts [⟨u, hu, l, hl, hlt, Ico_toDual⟩, ⟨u, hu, l, hl, hlt, Ioc_toDual⟩]
@@ -642,7 +642,7 @@ section LinearOrder
 variable [LinearOrder α] [OrderTopology α] [SecondCountableTopology α]
 
 theorem measurable_of_Iio {f : δ → α} (hf : ∀ x, MeasurableSet (f ⁻¹' Iio x)) : Measurable f := by
-  convert measurable_generateFrom (α := δ) _
+  convert! measurable_generateFrom (α := δ) _
   · exact BorelSpace.measurable_eq.trans (borel_eq_generateFrom_Iio _)
   · rintro _ ⟨x, rfl⟩; exact hf x
 
@@ -651,7 +651,7 @@ theorem UpperSemicontinuous.measurable [TopologicalSpace δ] [OpensMeasurableSpa
   measurable_of_Iio fun y => (hf.isOpen_preimage y).measurableSet
 
 theorem measurable_of_Ioi {f : δ → α} (hf : ∀ x, MeasurableSet (f ⁻¹' Ioi x)) : Measurable f := by
-  convert measurable_generateFrom (α := δ) _
+  convert! measurable_generateFrom (α := δ) _
   · exact BorelSpace.measurable_eq.trans (borel_eq_generateFrom_Ioi _)
   · rintro _ ⟨x, rfl⟩; exact hf x
 
@@ -717,7 +717,7 @@ theorem Measurable.isLUB_of_mem {ι} [Countable ι] {f : ι → δ → α} {g g'
   classical
   rcases isEmpty_or_nonempty ι with hι | ⟨⟨i⟩⟩
   · rcases eq_empty_or_nonempty s with rfl | ⟨x, hx⟩
-    · convert g'_meas
+    · convert! g'_meas
       rwa [compl_empty, eqOn_univ] at hg'
     · have A : ∀ b ∈ s, IsBot (g b) := by simpa using hg
       have B : ∀ b ∈ s, g b = g x := by
diff --git a/Mathlib/MeasureTheory/Constructions/BorelSpace/Real.lean b/Mathlib/MeasureTheory/Constructions/BorelSpace/Real.lean
index 43f5a1ebb40c3d..a1acd8232edb4e 100644
--- a/Mathlib/MeasureTheory/Constructions/BorelSpace/Real.lean
+++ b/Mathlib/MeasureTheory/Constructions/BorelSpace/Real.lean
@@ -87,27 +87,27 @@ theorem borel_eq_generateFrom_Ici_rat : borel ℝ = .generateFrom (⋃ a : ℚ,
 
 theorem isPiSystem_Ioo_rat :
     IsPiSystem (⋃ (a : ℚ) (b : ℚ) (_ : a < b), {Ioo (a : ℝ) (b : ℝ)}) := by
-  convert isPiSystem_Ioo ((↑) : ℚ → ℝ) ((↑) : ℚ → ℝ)
+  convert! isPiSystem_Ioo ((↑) : ℚ → ℝ) ((↑) : ℚ → ℝ)
   ext x
   simp [eq_comm]
 
 theorem isPiSystem_Iio_rat : IsPiSystem (⋃ a : ℚ, {Iio (a : ℝ)}) := by
-  convert isPiSystem_image_Iio (((↑) : ℚ → ℝ) '' univ)
+  convert! isPiSystem_image_Iio (((↑) : ℚ → ℝ) '' univ)
   ext x
   simp only [iUnion_singleton_eq_range, mem_range, image_univ, mem_image, exists_exists_eq_and]
 
 theorem isPiSystem_Ioi_rat : IsPiSystem (⋃ a : ℚ, {Ioi (a : ℝ)}) := by
-  convert isPiSystem_image_Ioi (((↑) : ℚ → ℝ) '' univ)
+  convert! isPiSystem_image_Ioi (((↑) : ℚ → ℝ) '' univ)
   ext x
   simp only [iUnion_singleton_eq_range, mem_range, image_univ, mem_image, exists_exists_eq_and]
 
 theorem isPiSystem_Iic_rat : IsPiSystem (⋃ a : ℚ, {Iic (a : ℝ)}) := by
-  convert isPiSystem_image_Iic (((↑) : ℚ → ℝ) '' univ)
+  convert! isPiSystem_image_Iic (((↑) : ℚ → ℝ) '' univ)
   ext x
   simp only [iUnion_singleton_eq_range, mem_range, image_univ, mem_image, exists_exists_eq_and]
 
 theorem isPiSystem_Ici_rat : IsPiSystem (⋃ a : ℚ, {Ici (a : ℝ)}) := by
-  convert isPiSystem_image_Ici (((↑) : ℚ → ℝ) '' univ)
+  convert! isPiSystem_image_Ici (((↑) : ℚ → ℝ) '' univ)
   ext x
   simp only [iUnion_singleton_eq_range, mem_range, image_univ, mem_image, exists_exists_eq_and]
 
@@ -362,7 +362,7 @@ set_option linter.deprecated false in
   (since := "2026-04-30")]
 theorem Measurable.ennreal_tsum' {ι} [Countable ι] {f : ι → α → ℝ≥0∞} (h : ∀ i, Measurable (f i)) :
     Measurable (∑' i, f i) := by
-  convert Measurable.ennreal_tsum h with x
+  convert! Measurable.ennreal_tsum h with x
   exact tsum_apply (Pi.summable.2 fun _ => ENNReal.summable)
 
 set_option linter.deprecated false in
diff --git a/Mathlib/MeasureTheory/Constructions/Cylinders.lean b/Mathlib/MeasureTheory/Constructions/Cylinders.lean
index 694b449be7aca8..ab79a1f5f8f117 100644
--- a/Mathlib/MeasureTheory/Constructions/Cylinders.lean
+++ b/Mathlib/MeasureTheory/Constructions/Cylinders.lean
@@ -120,10 +120,10 @@ theorem comap_eval_le_generateFrom_squareCylinders_singleton
   simp only [mem_setOf_eq, mem_image, mem_univ_pi, forall_exists_index, and_imp]
   intro t ht h
   classical
-  refine ⟨fun j ↦ if hji : j = i then by convert t else univ, fun j ↦ ?_, ?_⟩
+  refine ⟨fun j ↦ if hji : j = i then by convert! t else univ, fun j ↦ ?_, ?_⟩
   · by_cases hji : j = i
     · simp only [hji, eq_mpr_eq_cast, dif_pos]
-      convert ht
+      convert! ht
       simp only [cast_heq]
     · simp only [hji, not_false_iff, dif_neg, MeasurableSet.univ]
   · #adaptation_note /-- Before https://github.com/leanprover/lean4/pull/13166
diff --git a/Mathlib/MeasureTheory/Constructions/Pi.lean b/Mathlib/MeasureTheory/Constructions/Pi.lean
index 232c8330843009..0b0f4c5a3436c7 100644
--- a/Mathlib/MeasureTheory/Constructions/Pi.lean
+++ b/Mathlib/MeasureTheory/Constructions/Pi.lean
@@ -928,8 +928,9 @@ theorem measurePreserving_arrowCongr' {α₁ β₁ α₂ β₂ : Type*} [Fintype
     MeasurePreserving (MeasurableEquiv.arrowCongr' eα eβ) (Measure.pi fun i ↦ μ i)
       (Measure.pi fun i ↦ ν i) := by
   classical
-  convert (measurePreserving_piCongrLeft (fun i : α₂ ↦ ν i) eα).comp
-    (measurePreserving_pi μ (fun i : α₁ ↦ ν (eα i)) hm)
+  convert!
+    (measurePreserving_piCongrLeft (fun i : α₂ ↦ ν i) eα).comp
+      (measurePreserving_pi μ (fun i : α₁ ↦ ν (eα i)) hm)
   simp only [MeasurableEquiv.arrowCongr', Equiv.arrowCongr', Equiv.arrowCongr, EquivLike.coe_coe,
     comp_def, MeasurableEquiv.coe_mk, Equiv.coe_fn_mk, MeasurableEquiv.piCongrLeft,
     Equiv.piCongrLeft, Equiv.symm_symm, Equiv.piCongrLeft', eq_rec_constant, Equiv.coe_fn_symm_mk]
diff --git a/Mathlib/MeasureTheory/Constructions/Polish/Basic.lean b/Mathlib/MeasureTheory/Constructions/Polish/Basic.lean
index 7eee18429465a9..58e8299525bb86 100644
--- a/Mathlib/MeasureTheory/Constructions/Polish/Basic.lean
+++ b/Mathlib/MeasureTheory/Constructions/Polish/Basic.lean
@@ -319,7 +319,7 @@ theorem _root_.MeasurableSet.analyticSet {α : Type*} [t : TopologicalSpace α]
       ∃ t' : TopologicalSpace α, t' ≤ t ∧ @PolishSpace α t' ∧ IsClosed[t'] s ∧ IsOpen[t'] s :=
     hs.isClopenable
   have A := @IsClosed.analyticSet α t' t'_polish s s_closed
-  convert @AnalyticSet.image_of_continuous α t' α t s A id (continuous_id_of_le t't)
+  convert! @AnalyticSet.image_of_continuous α t' α t s A id (continuous_id_of_le t't)
   simp only [id, image_id']
 
 /-- Given a Borel-measurable function from a Polish space to a second-countable space, there exists
@@ -364,7 +364,7 @@ protected lemma AnalyticSet.preimage {X Y : Type*} [TopologicalSpace X] [Topolog
     AnalyticSet (f ⁻¹' s) := by
   rcases analyticSet_iff_exists_polishSpace_range.1 hs with ⟨Z, _, _, g, hg, rfl⟩
   have : IsClosed {x : X × Z | f x.1 = g x.2} := isClosed_eq hf.fst' hg.snd'
-  convert this.analyticSet.image_of_continuous continuous_fst
+  convert! this.analyticSet.image_of_continuous continuous_fst
   ext x
   simp [eq_comm]
 
@@ -462,7 +462,7 @@ theorem measurablySeparable_range_of_disjoint [T2Space α] [MeasurableSpace α]
   -- by design, the cylinders around these points have images which are not Borel-separable.
   have M : ∀ n, ¬MeasurablySeparable (f '' cylinder x n) (g '' cylinder y n) := by
     intro n
-    convert (p n).2 using 3
+    convert! (p n).2 using 3
     · rw [pn_fst, ← mem_cylinder_iff_eq, mem_cylinder_iff]
       intro i hi
       rw [hx]
@@ -716,7 +716,7 @@ theorem MeasureTheory.measurableSet_range_of_continuous_injective {β : Type*} [
       exact ball_mem_nhds _ (half_pos (u_pos n))
     have diam_s : diam s ≤ u n := by
       apply (diam_mono hs isBounded_ball).trans
-      convert diam_ball (x := y) (half_pos (u_pos n)).le
+      convert! diam_ball (x := y) (half_pos (u_pos n)).le
       ring
     refine mem_iUnion.2 ⟨⟨s, sb⟩, ?_⟩
     refine mem_iUnion.2 ⟨⟨isBounded_ball.subset hs, diam_s⟩, ?_⟩
@@ -888,7 +888,7 @@ theorem MeasureTheory.borel_eq_borel_of_le {t t' : TopologicalSpace γ}
   have e := @Continuous.measurableEmbedding
     _ _ (@borel _ t') t' _ _ (@BorelSpace.mk _ _ (borel γ) rfl)
     t _ (@borel _ t) (@BorelSpace.mk _ t (@borel _ t) rfl) (continuous_id_of_le hle) injective_id
-  convert e.measurableSet_image.2 hs
+  convert! e.measurableSet_image.2 hs
   simp only [id_eq, image_id']
 
 /-- In a Polish space, a set is clopenable if and only if it is Borel-measurable. -/
diff --git a/Mathlib/MeasureTheory/Constructions/Polish/StronglyMeasurable.lean b/Mathlib/MeasureTheory/Constructions/Polish/StronglyMeasurable.lean
index cad138632b2913..1676161053d094 100644
--- a/Mathlib/MeasureTheory/Constructions/Polish/StronglyMeasurable.lean
+++ b/Mathlib/MeasureTheory/Constructions/Polish/StronglyMeasurable.lean
@@ -45,7 +45,7 @@ theorem measurableSet_exists_tendsto [IsCompletelyPseudoMetrizableSpace E]
   have : IsCompletelyPseudoMetrizableSpace s := isClosed_closure.isCompletelyPseudoMetrizableSpace
   let g i x : s := ⟨f i x, subset_closure <| mem_iUnion.2 ⟨i, ⟨x, rfl⟩⟩⟩
   have mg i : Measurable (g i) := (hf i).measurable.subtype_mk
-  convert MeasureTheory.measurableSet_exists_tendsto (l := l) mg with x
+  convert! MeasureTheory.measurableSet_exists_tendsto (l := l) mg with x
   refine ⟨fun ⟨c, hc⟩ ↦ ⟨⟨c, ?_⟩, tendsto_subtype_rng.2 hc⟩,
     fun ⟨c, hc⟩ ↦ ⟨c, tendsto_subtype_rng.1 hc⟩⟩
   exact mem_closure_of_tendsto hc (Eventually.of_forall fun i ↦ mem_iUnion.2 ⟨i, ⟨x, rfl⟩⟩)
diff --git a/Mathlib/MeasureTheory/Covering/Besicovitch.lean b/Mathlib/MeasureTheory/Covering/Besicovitch.lean
index 0752545b875445..3b7041eede15f7 100644
--- a/Mathlib/MeasureTheory/Covering/Besicovitch.lean
+++ b/Mathlib/MeasureTheory/Covering/Besicovitch.lean
@@ -441,7 +441,7 @@ theorem color_lt {i : Ordinal.{u}} (hi : i < p.lastStep) {N : ℕ}
         have I : (a : ℕ) < N := ha
         have J : G (Fin.last N) = i := by dsimp; simp only [G, if_true]
         have K : G a = g a := by simp [G, I.ne]
-        convert dist_le_add_of_nonempty_closedBall_inter_closedBall (hg _ I).2.1 }
+        convert! dist_le_add_of_nonempty_closedBall_inter_closedBall (hg _ I).2.1 }
   -- this is a contradiction
   exact hN.false sc
 
@@ -736,7 +736,7 @@ theorem exists_disjoint_closedBall_covering_ae_of_finiteMeasure_aux (μ : Measur
       · exact ht.2.2 p h'p
       · rcases Finset.mem_image.1 h'p with ⟨p', p'v, rfl⟩
         exact (hr p' (vs' p'v)).1.1
-    · convert hμv using 2
+    · convert! hμv using 2
       rw [Finset.set_biUnion_union, ← diff_diff, Finset.set_biUnion_finset_image]
   /- Define `F` associating to a finite good covering the above enlarged good covering, covering
     a proportion `1/(N+1)` of leftover points. Iterating `F`, one will get larger and larger good
diff --git a/Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean b/Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean
index 93ebccfc6e2d03..932bfe42ec0516 100644
--- a/Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean
+++ b/Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean
@@ -122,7 +122,7 @@ theorem card_le_of_separated (s : Finset E) (hs : ∀ c ∈ s, ‖c‖ ≤ 2)
     rintro c hc d hd hcd
     apply ball_disjoint_ball
     rw [dist_eq_norm]
-    convert h c hc d hd hcd
+    convert! h c hc d hd hcd
     norm_num
   have A_subset : A ⊆ ball (0 : E) ρ := by
     refine iUnion₂_subset fun x hx => ?_
@@ -410,7 +410,7 @@ theorem exists_normalized_aux3 {N : ℕ} {τ : ℝ} (a : SatelliteConfig E N τ)
       change i = last N at iN
       rw [iN, lastc, norm_zero] at hi
       exact lt_irrefl _ (zero_le_two.trans_lt hi)
-    convert (a.hlast i this).1 using 1
+    convert! (a.hlast i this).1 using 1
     rw [dist_eq_norm, lastc, sub_zero]
   have hj : 2 < ‖a.c j‖ := hi.trans_le hij
   set s := ‖a.c i‖
diff --git a/Mathlib/MeasureTheory/Covering/Differentiation.lean b/Mathlib/MeasureTheory/Covering/Differentiation.lean
index f0de450ec0453b..e90d23eca85b0d 100644
--- a/Mathlib/MeasureTheory/Covering/Differentiation.lean
+++ b/Mathlib/MeasureTheory/Covering/Differentiation.lean
@@ -696,7 +696,7 @@ theorem ae_tendsto_rnDeriv :
   have C : ∀ᵐ x ∂μ, Tendsto (fun a => t a / μ a) (v.filterAt x) (𝓝 (t.rnDeriv μ x)) :=
     v.ae_tendsto_rnDeriv_of_absolutelyContinuous (withDensity_absolutelyContinuous _ _)
   filter_upwards [A, B, C] with _ Ax Bx Cx
-  convert Ax.add Cx using 1
+  convert! Ax.add Cx using 1
   · ext1 a
     conv_lhs => rw [eq_add]
     simp only [Pi.add_apply, coe_add, ENNReal.add_div]
@@ -756,12 +756,12 @@ theorem ae_tendsto_lintegral_div' {f : α → ℝ≥0∞} (hf : Measurable f) (h
 theorem ae_tendsto_lintegral_div {f : α → ℝ≥0∞} (hf : AEMeasurable f μ) (h'f : (∫⁻ y, f y ∂μ) ≠ ∞) :
     ∀ᵐ x ∂μ, Tendsto (fun a => (∫⁻ y in a, f y ∂μ) / μ a) (v.filterAt x) (𝓝 (f x)) := by
   have A : (∫⁻ y, hf.mk f y ∂μ) ≠ ∞ := by
-    convert h'f using 1
+    convert! h'f using 1
     apply lintegral_congr_ae
     exact hf.ae_eq_mk.symm
   filter_upwards [v.ae_tendsto_lintegral_div' hf.measurable_mk A, hf.ae_eq_mk] with x hx h'x
   rw [h'x]
-  convert hx using 1
+  convert! hx using 1
   ext1 a
   congr 1
   apply lintegral_congr_ae
diff --git a/Mathlib/MeasureTheory/Covering/LiminfLimsup.lean b/Mathlib/MeasureTheory/Covering/LiminfLimsup.lean
index e36abca910d255..a645729572b49b 100644
--- a/Mathlib/MeasureTheory/Covering/LiminfLimsup.lean
+++ b/Mathlib/MeasureTheory/Covering/LiminfLimsup.lean
@@ -198,7 +198,7 @@ theorem blimsup_cthickening_mul_ae_eq (p : ℕ → Prop) (s : ℕ → Set α) {M
         (blimsup (fun i => cthickening (r i) (s i)) atTop p : Set α) := by
     clear p hr r; intro p r hr
     have hr' : Tendsto (fun i => M * r i) atTop (𝓝[>] 0) := by
-      convert TendstoNhdsWithinIoi.const_mul hM hr <;> simp only [mul_zero]
+      convert! TendstoNhdsWithinIoi.const_mul hM hr <;> simp only [mul_zero]
     refine eventuallyLE_antisymm_iff.mpr ⟨?_, ?_⟩
     · exact blimsup_cthickening_ae_le_of_eventually_mul_le μ p (inv_pos.mpr hM) hr'
         (Eventually.of_forall fun i => by rw [inv_mul_cancel_left₀ hM.ne' (r i)])
@@ -247,7 +247,7 @@ theorem blimsup_thickening_mul_ae_eq_aux (p : ℕ → Prop) (s : ℕ → Set α)
       (blimsup (fun i => thickening (r i) (s i)) atTop p : Set α) := by
   have h₁ := blimsup_cthickening_ae_eq_blimsup_thickening (s := s) μ hr hr'
   have h₂ := blimsup_cthickening_mul_ae_eq μ p s hM r hr
-  replace hr : Tendsto (fun i => M * r i) atTop (𝓝 0) := by convert hr.const_mul M; simp
+  replace hr : Tendsto (fun i => M * r i) atTop (𝓝 0) := by convert! hr.const_mul M; simp
   replace hr' : ∀ᶠ i in atTop, p i → 0 < M * r i := hr'.mono fun i hi hip ↦ mul_pos hM (hi hip)
   have h₃ := blimsup_cthickening_ae_eq_blimsup_thickening (s := s) μ hr hr'
   exact h₃.symm.trans (h₂.trans h₁)
diff --git a/Mathlib/MeasureTheory/Covering/Vitali.lean b/Mathlib/MeasureTheory/Covering/Vitali.lean
index 1231404865d3c7..771a3e685df3c6 100644
--- a/Mathlib/MeasureTheory/Covering/Vitali.lean
+++ b/Mathlib/MeasureTheory/Covering/Vitali.lean
@@ -457,7 +457,7 @@ protected def vitaliFamily [PseudoMetricSpace α] [MeasurableSpace α] [OpensMea
       exact t'_disj hq hq' (ne_of_apply_ne _ hqq')
     · rintro - ⟨q, hq, rfl⟩
       exact (t't hq).2.2.2.2.1
-    · convert μt' using 3
+    · convert! μt' using 3
       rw [biUnion_image]
 
 end Vitali
diff --git a/Mathlib/MeasureTheory/Function/AEMeasurableOrder.lean b/Mathlib/MeasureTheory/Function/AEMeasurableOrder.lean
index 3cdb2645007327..6162320fd09227 100644
--- a/Mathlib/MeasureTheory/Function/AEMeasurableOrder.lean
+++ b/Mathlib/MeasureTheory/Function/AEMeasurableOrder.lean
@@ -75,7 +75,7 @@ theorem MeasureTheory.aemeasurable_of_exist_almost_disjoint_supersets {α : Type
     have : ∀ᵐ x ∂μ, x ∉ t := by
       have : μ t = 0 := le_antisymm μt bot_le
       change μ _ = 0
-      convert this
+      convert! this
       ext y
       simp only [mem_setOf_eq, mem_compl_iff, not_notMem]
     filter_upwards [this] with x hx
diff --git a/Mathlib/MeasureTheory/Function/AbsolutelyContinuous.lean b/Mathlib/MeasureTheory/Function/AbsolutelyContinuous.lean
index df91f7a9ea0f7e..4c5921c67f0353 100644
--- a/Mathlib/MeasureTheory/Function/AbsolutelyContinuous.lean
+++ b/Mathlib/MeasureTheory/Function/AbsolutelyContinuous.lean
@@ -81,7 +81,7 @@ def totalLengthFilter : Filter (ℕ × (ℕ → X × X)) := Filter.comap
 lemma hasBasis_totalLengthFilter : totalLengthFilter.HasBasis (fun (ε : ℝ) => 0 < ε)
     (fun (ε : ℝ) =>
       {E : ℕ × (ℕ → X × X) | ∑ i ∈ Finset.range E.1, dist (E.2 i).1 (E.2 i).2 < ε}) := by
-  convert Filter.HasBasis.comap (α := ℝ) _ (nhds_basis_Ioo_pos _) using 1
+  convert! Filter.HasBasis.comap (α := ℝ) _ (nhds_basis_Ioo_pos _) using 1
   ext ε E
   simp only [mem_setOf_eq, zero_sub, zero_add, mem_preimage, mem_Ioo, iff_and_self]
   suffices 0 ≤ ∑ i ∈ Finset.range E.1, dist (E.2 i).1 (E.2 i).2 by grind
@@ -119,7 +119,7 @@ lemma tendsto_volume_totalLengthFilter_nhds_zero :
     totalLengthFilter (𝓝 0) := by
   apply tendsto_of_tendsto_of_tendsto_of_le_of_le tendsto_const_nhds
     (h := fun E ↦ ENNReal.ofReal (∑ i ∈ Finset.range E.1, (dist (E.2 i).1 (E.2 i).2)))
-  · convert ENNReal.tendsto_ofReal (Filter.tendsto_comap)
+  · convert! ENNReal.tendsto_ofReal (Filter.tendsto_comap)
     simp
   · intro; simp
   · intro E
@@ -220,7 +220,7 @@ theorem const_mul {f : ℝ → ℝ} (α : ℝ) (hf : AbsolutelyContinuousOnInter
 lemma uniformity_eq_comap_totalLengthFilter :
     uniformity X = comap (fun x ↦ (1, fun _ ↦ x)) totalLengthFilter := by
   refine Filter.HasBasis.eq_of_same_basis Metric.uniformity_basis_dist ?_
-  convert hasBasis_totalLengthFilter.comap _
+  convert! hasBasis_totalLengthFilter.comap _
   simp
 
 /-- If `f` is absolutely continuous on `uIcc a b`, then `f` is uniformly continuous on `uIcc a b`.
@@ -229,7 +229,7 @@ theorem uniformContinuousOn (hf : AbsolutelyContinuousOnInterval f a b) :
     UniformContinuousOn f (uIcc a b) := by
   simp only [UniformContinuousOn, Filter.tendsto_iff_comap, uniformity_eq_comap_totalLengthFilter]
   simp only [AbsolutelyContinuousOnInterval, Filter.tendsto_iff_comap] at hf
-  convert Filter.comap_mono hf
+  convert! Filter.comap_mono hf
   · simp only [comap_inf, comap_principal]
     congr
     ext p
@@ -339,7 +339,7 @@ theorem boundedVariationOn (hf : AbsolutelyContinuousOnInterval f a b) :
   set δ' := (b - a) / (n + 1)
   have hδ₃ : δ' < δ := by
     dsimp only [δ']
-    convert mul_lt_mul_of_pos_right hn hab₁ using 1 <;> field
+    convert! mul_lt_mul_of_pos_right hn hab₁ using 1 <;> field
   have h_mono : Monotone fun (i : ℕ) ↦ a + ↑i * δ' := by
     apply Monotone.const_add
     apply Monotone.mul_const Nat.mono_cast
@@ -348,7 +348,7 @@ theorem boundedVariationOn (hf : AbsolutelyContinuousOnInterval f a b) :
   -- The variation of `f` on `[a, b]` is the sum of the variations on these subintervals.
   have v_sum : eVariationOn f (Icc a b) =
       ∑ i ∈ Finset.range (n + 1), eVariationOn f (Icc (a + i * δ') (a + (i + 1) * δ')) := by
-    convert eVariationOn.sum' f (I := fun i ↦ a + i * δ') h_mono |>.symm
+    convert! eVariationOn.sum' f (I := fun i ↦ a + i * δ') h_mono |>.symm
     · simp
     · simp only [Nat.cast_add, Nat.cast_one, δ']; field
     · norm_cast
@@ -366,10 +366,10 @@ theorem boundedVariationOn (hf : AbsolutelyContinuousOnInterval f a b) :
           intro i hi
           constructor <;> exact this (hp₂ _)
         · rw [PairwiseDisjoint]
-          convert hp₁.pairwise_disjoint_on_Ioc_succ.set_pairwise (Finset.range p.1) using 3
+          convert! hp₁.pairwise_disjoint_on_Ioc_succ.set_pairwise (Finset.range p.1) using 3
           rw [uIoc_of_le (hp₁ (by lia)), Nat.succ_eq_succ]
       · suffices p.2.val p.1 - p.2.val 0 < δ by
-          convert this
+          convert! this
           rw [← Finset.sum_range_sub]
           congr; ext i
           rw [dist_comm, Real.dist_eq, abs_eq_self.mpr]
@@ -383,7 +383,7 @@ theorem boundedVariationOn (hf : AbsolutelyContinuousOnInterval f a b) :
     have not_top : ∑ i ∈ Finset.range p.1, edist (f (p.2.val (i + 1))) (f (p.2.val i)) ≠ ⊤ := by
       simp [edist_ne_top]
     rw [← ENNReal.ofReal_toReal not_top]
-    convert ENNReal.ofReal_le_ofReal (veq.symm ▸ vf.le)
+    convert! ENNReal.ofReal_le_ofReal (veq.symm ▸ vf.le)
     simp
   -- Reduce to goal that the variation of `f` on each of these subintervals is finite.
   simp only [BoundedVariationOn, v_sum, ne_eq, ENNReal.sum_eq_top, Finset.mem_range, not_exists,
@@ -394,10 +394,10 @@ theorem boundedVariationOn (hf : AbsolutelyContinuousOnInterval f a b) :
     fun hC ↦ by simp [hC] at this
   -- Verify that `[a + i * δ', a + (i + 1) * δ']` is indeed a subinterval of `[a, b]`
   apply v_each
-  · convert h_mono (show 0 ≤ i by lia); simp
-  · convert h_mono (show i ≤ i + 1 by lia); norm_cast
+  · convert! h_mono (show 0 ≤ i by lia); simp
+  · convert! h_mono (show i ≤ i + 1 by lia); norm_cast
   · rw [add_mul, ← add_assoc]; simpa
-  · convert h_mono (show i + 1 ≤ n + 1 by lia)
+  · convert! h_mono (show i + 1 ≤ n + 1 by lia)
     · norm_cast
     · simp only [Nat.cast_add, Nat.cast_one, δ']; field
 
diff --git a/Mathlib/MeasureTheory/Function/ConditionalExpectation/RadonNikodym.lean b/Mathlib/MeasureTheory/Function/ConditionalExpectation/RadonNikodym.lean
index e526d90c26324f..14f9101d8a0118 100644
--- a/Mathlib/MeasureTheory/Function/ConditionalExpectation/RadonNikodym.lean
+++ b/Mathlib/MeasureTheory/Function/ConditionalExpectation/RadonNikodym.lean
@@ -139,7 +139,7 @@ lemma toReal_rnDeriv_trim (hm : m ≤ m𝓧) [IsFiniteMeasure μ] [hsf : SigmaFi
   have : SigmaFinite (@Measure.map _ _ m𝓧 m id ν) := by rwa [← trim_eq_map hm]
   have h := toReal_rnDeriv_map_ae_eq_trim hμν (measurable_id'' hm)
   simp_rw [MeasurableSpace.comap_id, id_def, trim_eq_map] at h
-  convert h <;> rw [MeasurableSpace.comap_id]
+  convert! h <;> rw [MeasurableSpace.comap_id]
 
 /-- The Radon-Nikodym derivative `∂(μ.trim hm)/∂(ν.trim hm)` of the trimmed measures
 (for `hm : m ≤ m0` stating that `m` is a sub-sigma-algebra of `m0`) is a.e.-equal to the
diff --git a/Mathlib/MeasureTheory/Function/ConditionalExpectation/Real.lean b/Mathlib/MeasureTheory/Function/ConditionalExpectation/Real.lean
index 3940c8db23ca6b..1d1f0188296f34 100644
--- a/Mathlib/MeasureTheory/Function/ConditionalExpectation/Real.lean
+++ b/Mathlib/MeasureTheory/Function/ConditionalExpectation/Real.lean
@@ -195,8 +195,9 @@ theorem Integrable.uniformIntegrable_condExp {ι : Type*} [IsFiniteMeasure μ] {
     have : C ^ ENNReal.toReal 1 * μ {x | ENNReal.ofNNReal C ≤ ‖μ[g|ℱ n] x‖₊} ≤
         eLpNorm μ[g | ℱ n] 1 μ ^ ENNReal.toReal 1 := by
       rw [ENNReal.toReal_one, ENNReal.rpow_one]
-      convert mul_meas_ge_le_pow_eLpNorm μ one_ne_zero ENNReal.one_ne_top
-        (stronglyMeasurable_condExp.mono (hℱ n)).aestronglyMeasurable C
+      convert!
+        mul_meas_ge_le_pow_eLpNorm μ one_ne_zero ENNReal.one_ne_top
+          (stronglyMeasurable_condExp.mono (hℱ n)).aestronglyMeasurable C
       · rw [ENNReal.toReal_one, ENNReal.rpow_one, enorm_eq_nnnorm]
     rw [ENNReal.toReal_one, ENNReal.rpow_one, mul_comm, ←
       ENNReal.le_div_iff_mul_le (Or.inl (ENNReal.coe_ne_zero.2 hCpos.ne'))
diff --git a/Mathlib/MeasureTheory/Function/ConditionalLExpectation.lean b/Mathlib/MeasureTheory/Function/ConditionalLExpectation.lean
index 22d78436867250..d2ffb8746fd924 100644
--- a/Mathlib/MeasureTheory/Function/ConditionalLExpectation.lean
+++ b/Mathlib/MeasureTheory/Function/ConditionalLExpectation.lean
@@ -336,7 +336,7 @@ theorem condLExp_tsum [Countable ι] {X : ι → Ω → ℝ≥0∞}
 theorem condLExp_finsetSum (s : Finset ι) {X : ι → Ω → ℝ≥0∞}
     (hX : ∀ i, AEMeasurable[mΩ₀] (X i) P) :
     P⁻[∑ i ∈ s, X i|mΩ] =ᵐ[P] ∑ i ∈ s, P⁻[X i|mΩ] := by
-  convert condLExp_tsum mΩ (fun i : s ↦ hX i)
+  convert! condLExp_tsum mΩ (fun i : s ↦ hX i)
   · simp [Finset.sum_attach]
   · simp [Finset.sum_attach _ (f := (P⁻[X ·|mΩ]))]
 
diff --git a/Mathlib/MeasureTheory/Function/ContinuousMapDense.lean b/Mathlib/MeasureTheory/Function/ContinuousMapDense.lean
index 3995e5cbafa6f1..f6d6346dc46161 100644
--- a/Mathlib/MeasureTheory/Function/ContinuousMapDense.lean
+++ b/Mathlib/MeasureTheory/Function/ContinuousMapDense.lean
@@ -173,7 +173,7 @@ theorem MemLp.exists_hasCompactSupport_eLpNorm_sub_le
   rcases exists_continuous_eLpNorm_sub_le_of_closed hp s_closed isOpen_interior sk hsμ.ne c δpos.ne'
     with ⟨f, f_cont, I2, _f_bound, f_support, f_mem⟩
   have I3 : eLpNorm (f - t.indicator fun _y => c) p μ ≤ ε := by
-    convert
+    convert!
       (hδ _ _
           (f_mem.aestronglyMeasurable.sub
             (aestronglyMeasurable_const.indicator s_closed.measurableSet))
@@ -270,7 +270,7 @@ theorem MemLp.exists_boundedContinuous_eLpNorm_sub_le [μ.WeaklyRegular] (hp : p
       δpos.ne' with
     ⟨f, f_cont, I2, f_bound, -, f_mem⟩
   have I3 : eLpNorm (f - t.indicator fun _y => c) p μ ≤ ε := by
-    convert
+    convert!
       (hδ _ _
           (f_mem.aestronglyMeasurable.sub
             (aestronglyMeasurable_const.indicator s_closed.measurableSet))
diff --git a/Mathlib/MeasureTheory/Function/ConvergenceInDistribution.lean b/Mathlib/MeasureTheory/Function/ConvergenceInDistribution.lean
index 28b2401cbfa22e..687d86922ab32e 100644
--- a/Mathlib/MeasureTheory/Function/ConvergenceInDistribution.lean
+++ b/Mathlib/MeasureTheory/Function/ConvergenceInDistribution.lean
@@ -81,7 +81,7 @@ lemma tendstoInDistribution_of_identDistrib [OpensMeasurableSpace E] (i : ι)
   forall_aemeasurable j := (hX j).aemeasurable_snd
   aemeasurable_limit := hZ.aemeasurable_snd
   tendsto := by
-    convert tendsto_const_nhds with j
+    convert! tendsto_const_nhds with j
     exact (hX j).map_eq.symm.trans hZ.map_eq
 
 protected lemma TendstoInDistribution.congr [OpensMeasurableSpace E] {T : Ω' → E}
@@ -90,7 +90,7 @@ protected lemma TendstoInDistribution.congr [OpensMeasurableSpace E] {T : Ω' 
   forall_aemeasurable i := (h.forall_aemeasurable i).congr (hXY i)
   aemeasurable_limit := h.aemeasurable_limit.congr hZT
   tendsto := by
-    convert h.tendsto using 2 with n
+    convert! h.tendsto using 2 with n
     · simpa using Measure.map_congr (hXY n).symm
     · rw! [Measure.map_congr hZT]
       rfl
@@ -122,7 +122,7 @@ theorem TendstoInDistribution.continuous_comp {F : Type*} [OpensMeasurableSpace
   forall_aemeasurable := fun n ↦ hg.measurable.comp_aemeasurable (h.forall_aemeasurable n)
   aemeasurable_limit := hg.measurable.comp_aemeasurable h.aemeasurable_limit
   tendsto := by
-    convert ProbabilityMeasure.tendsto_map_of_tendsto_of_continuous _ _ h.tendsto hg
+    convert! ProbabilityMeasure.tendsto_map_of_tendsto_of_continuous _ _ h.tendsto hg
     · simp only [ProbabilityMeasure.map, ProbabilityMeasure.coe_mk, Subtype.mk.injEq]
       rw [AEMeasurable.map_map_of_aemeasurable hg.aemeasurable (h.forall_aemeasurable _)]
     · simp only [ProbabilityMeasure.map, ProbabilityMeasure.coe_mk]
@@ -167,7 +167,7 @@ lemma tendstoInDistribution_of_tendstoInMeasure_sub {X : ι → Ω'' → E}
   simp_rw [Metric.tendsto_nhds, Real.dist_eq]
   suffices ∀ ε > 0, ∀ᶠ n in l, |∫ ω, F ω ∂(μ''.map (Y n)) - ∫ ω, F ω ∂(μ'.map Z)| < L * ε by
     intro ε hε
-    convert this (ε / L) (by positivity)
+    convert! this (ε / L) (by positivity)
     field_simp
   intro ε hε
   -- We cut the difference into three pieces, two of which are small by the convergence assumptions
@@ -215,7 +215,11 @@ lemma tendstoInDistribution_of_tendstoInMeasure_sub {X : ι → Ω'' → E}
         · exact fun x hx ↦ hF_lip.norm_sub_le_of_le hx.le
       · refine setIntegral_mono h_int_sub.integrableOn integrableOn_const fun a ↦ ?_
         rw [← dist_eq_norm]
-        convert hF_bounded _ _
+        convert!
+          hF_bounded _
+            _
+              -- The goal is now a simple computation
+
     -- The goal is now a simple computation
     _ = L * (ε / 2) * μ''.real {x | ‖Y n x - X n x‖ < ε / 2}
         + M * μ''.real {ω | ε / 2 ≤ ‖Y n ω - X n ω‖} := by
@@ -275,7 +279,7 @@ theorem TendstoInDistribution.prodMk_of_tendstoInMeasure_const
     (fun n ω ↦ (X n ω, Y n ω)) (fun ω ↦ (Z ω, c)) ?_ ?_ (fun i ↦ (hX i).prodMk (hY_meas i))
   · exact hXZ.continuous_comp (g := fun x ↦ (x, c)) (by fun_prop)
   · suffices TendstoInMeasure μ'' (fun n ω ↦ ((0 : E), Y n ω - c)) l 0 by
-      convert this with n ω
+      convert! this with n ω
       simp
     simpa [tendstoInMeasure_iff_norm] using hY
 
diff --git a/Mathlib/MeasureTheory/Function/ConvergenceInMeasure.lean b/Mathlib/MeasureTheory/Function/ConvergenceInMeasure.lean
index 3c3374ac5983aa..f148a1ad721cb9 100644
--- a/Mathlib/MeasureTheory/Function/ConvergenceInMeasure.lean
+++ b/Mathlib/MeasureTheory/Function/ConvergenceInMeasure.lean
@@ -97,10 +97,10 @@ lemma tendstoInMeasure_iff_dist [PseudoMetricSpace E] {f : ι → α → E} {l :
     TendstoInMeasure μ f l g
       ↔ ∀ ε, 0 < ε → Tendsto (fun i => μ { x | ε ≤ dist (f i x) (g x) }) l (𝓝 0) := by
   refine ⟨fun h ε hε ↦ ?_, fun h ↦ ?_⟩
-  · convert h (ENNReal.ofReal ε) (ENNReal.ofReal_pos.mpr hε) with i a
+  · convert! h (ENNReal.ofReal ε) (ENNReal.ofReal_pos.mpr hε) with i a
     rw [edist_dist, ENNReal.ofReal_le_ofReal_iff (by positivity)]
   · refine tendstoInMeasure_of_ne_top fun ε hε hε_top ↦ ?_
-    convert h ε.toReal (ENNReal.toReal_pos hε.ne' hε_top) with i a
+    convert! h ε.toReal (ENNReal.toReal_pos hε.ne' hε_top) with i a
     rw [edist_dist, ENNReal.le_ofReal_iff_toReal_le hε_top (by positivity)]
 
 /-- `TendstoInMeasure` expressed with the real-valued measure of a set defined with a distance.
@@ -421,8 +421,9 @@ theorem tendstoInMeasure_of_tendsto_eLpNorm_of_stronglyMeasurable [SeminormedAdd
   refine (hfg δ hδ).mono fun n hn => ?_
   refine le_trans ?_ hn
   rw [one_div, ← ENNReal.inv_mul_le_iff, inv_inv]
-  · convert mul_meas_ge_le_pow_eLpNorm' μ hp_ne_zero hp_ne_top
-      ((hf n).sub hg).aestronglyMeasurable ε using 6
+  · convert!
+      mul_meas_ge_le_pow_eLpNorm' μ hp_ne_zero hp_ne_top ((hf n).sub hg).aestronglyMeasurable ε
+      using 6
     simp [edist_eq_enorm_sub]
   · simp [hε_top]
   · simp [hε.ne']
diff --git a/Mathlib/MeasureTheory/Function/Holder.lean b/Mathlib/MeasureTheory/Function/Holder.lean
index ccb7fbb4daa228..28a09ce608dfff 100644
--- a/Mathlib/MeasureTheory/Function/Holder.lean
+++ b/Mathlib/MeasureTheory/Function/Holder.lean
@@ -216,7 +216,7 @@ variable (E q) in
 @[simp]
 protected lemma smul_zero (f : Lp 𝕜 p μ) :
     f • (0 : Lp E q μ) = (0 : Lp E r μ) := by
-  convert MemLp.zero (ε := E) |>.toLp_zero
+  convert! MemLp.zero (ε := E) |>.toLp_zero
   apply MemLp.toLp_congr _ _ ?_
   filter_upwards [Lp.coeFn_zero E q μ] with x hx
   rw [Pi.smul_apply', hx]
@@ -226,7 +226,7 @@ variable (𝕜 p) in
 @[simp]
 protected lemma zero_smul (f : Lp E q μ) :
     (0 : Lp 𝕜 p μ) • f = (0 : Lp E r μ) := by
-  convert MemLp.zero (ε := E) |>.toLp_zero
+  convert! MemLp.zero (ε := E) |>.toLp_zero
   apply MemLp.toLp_congr _ _ ?_
   filter_upwards [Lp.coeFn_zero 𝕜 p μ] with x hx
   rw [Pi.smul_apply', hx]
diff --git a/Mathlib/MeasureTheory/Function/Jacobian.lean b/Mathlib/MeasureTheory/Function/Jacobian.lean
index 8e63936b49ceb7..ff39870cbab334 100644
--- a/Mathlib/MeasureTheory/Function/Jacobian.lean
+++ b/Mathlib/MeasureTheory/Function/Jacobian.lean
@@ -312,7 +312,7 @@ theorem addHaar_image_le_mul_of_det_lt (A : E →L[ℝ] E) {m : ℝ≥0}
     have L2 :
       Tendsto (fun ε => μ (closedBall 0 ε + A '' closedBall 0 1)) (𝓝[>] 0)
         (𝓝 (d * μ (closedBall 0 1))) := by
-      convert L1
+      convert! L1
       exact (addHaar_image_continuousLinearMap _ _ _).symm
     have I : d * μ (closedBall 0 1) < m * μ (closedBall 0 1) := by
       gcongr; exacts [(measure_closedBall_pos μ _ zero_lt_one).ne', measure_closedBall_lt_top.ne]
@@ -447,7 +447,7 @@ theorem mul_le_addHaar_image_of_lt_det (A : E →L[ℝ] E) {m : ℝ≥0}
   -- let `δ` be small enough, and `f` approximated by `B` up to `δ`.
   filter_upwards [L1, L2]
   intro δ h1δ h2δ s f hf
-  have hf' : ApproximatesLinearOn f (B : E →L[ℝ] E) s δ := by convert hf
+  have hf' : ApproximatesLinearOn f (B : E →L[ℝ] E) s δ := by convert! hf
   let F := hf'.toPartialEquiv h1δ
   -- the condition to be checked can be reformulated in terms of the inverse maps
   suffices H : μ (F.symm '' F.target) ≤ (m⁻¹ : ℝ≥0) * μ F.target by
diff --git a/Mathlib/MeasureTheory/Function/JacobianOneDim.lean b/Mathlib/MeasureTheory/Function/JacobianOneDim.lean
index f5b5d41c319392..5264d529c5154c 100644
--- a/Mathlib/MeasureTheory/Function/JacobianOneDim.lean
+++ b/Mathlib/MeasureTheory/Function/JacobianOneDim.lean
@@ -371,7 +371,7 @@ theorem lintegral_image_eq_lintegral_deriv_mul_of_antitoneOn (hs : MeasurableSet
       (fun x hx ↦ hasDerivWithinAt_neg _ _) neg_injective.injOn _
   simp only [abs_neg, abs_one, ENNReal.ofReal_one, one_mul] at B
   rw [A, ← image_comp] at B
-  convert B using 4 with x hx x <;> simp [n, e]
+  convert! B using 4 with x hx x <;> simp [n, e]
 
 /-- Change of variable formula for differentiable functions, set version: if a real function `f` is
 antitone and differentiable on a measurable set `s`, then the measure of `f '' s` is given by the
@@ -399,7 +399,7 @@ theorem integrableOn_image_iff_integrableOn_deriv_smul_of_antitoneOn (hs : Measu
       (fun x hx ↦ hasDerivWithinAt_neg _ _) neg_injective.injOn _
   simp only [abs_neg, abs_one, one_smul] at B
   rw [A, ← image_comp] at B
-  convert B using 3 with x hx x <;> simp [n, e]
+  convert! B using 3 with x hx x <;> simp [n, e]
 
 /-- Change of variable formula for differentiable functions: if a real function `f` is
 antitone and differentiable on a measurable set `s`, then the Bochner integral of a function
@@ -417,7 +417,7 @@ theorem integral_image_eq_integral_deriv_smul_of_antitoneOn (hs : MeasurableSet
       (fun x hx ↦ hasDerivWithinAt_neg _ _) neg_injective.injOn _
   simp only [abs_neg, abs_one, one_smul] at B
   rw [A, ← image_comp] at B
-  convert B using 3 with x hx x <;> simp [n, e]
+  convert! B using 3 with x hx x <;> simp [n, e]
 
 @[deprecated (since := "2026-03-19")] alias integral_image_eq_integral_deriv_smul_of_antitone :=
   integral_image_eq_integral_deriv_smul_of_antitoneOn
diff --git a/Mathlib/MeasureTheory/Function/L1Space/HasFiniteIntegral.lean b/Mathlib/MeasureTheory/Function/L1Space/HasFiniteIntegral.lean
index ec8059a833779b..703320228a8ae9 100644
--- a/Mathlib/MeasureTheory/Function/L1Space/HasFiniteIntegral.lean
+++ b/Mathlib/MeasureTheory/Function/L1Space/HasFiniteIntegral.lean
@@ -329,7 +329,7 @@ theorem ae_tendsto_enorm (h : ∀ᵐ a ∂μ, Tendsto (fun n ↦ F' n a) atTop <
 
 theorem ae_tendsto_ofReal_norm (h : ∀ᵐ a ∂μ, Tendsto (fun n => F n a) atTop <| 𝓝 <| f a) :
     ∀ᵐ a ∂μ, Tendsto (fun n => ENNReal.ofReal ‖F n a‖) atTop <| 𝓝 <| ENNReal.ofReal ‖f a‖ := by
-  convert ae_tendsto_enorm h <;> simp
+  convert! ae_tendsto_enorm h <;> simp
 
 @[deprecated (since := "2026-01-26")] alias all_ae_tendsto_ofReal_norm := ae_tendsto_ofReal_norm
 
diff --git a/Mathlib/MeasureTheory/Function/L1Space/Integrable.lean b/Mathlib/MeasureTheory/Function/L1Space/Integrable.lean
index 3dc82d61b0eb64..8c740a971237b9 100644
--- a/Mathlib/MeasureTheory/Function/L1Space/Integrable.lean
+++ b/Mathlib/MeasureTheory/Function/L1Space/Integrable.lean
@@ -676,7 +676,7 @@ theorem Integrable.measure_enorm_ge_lt_top {E : Type*} [TopologicalSpace E] [Con
 where `‖f x‖ ≥ ε` is finite for all positive `ε`. -/
 theorem Integrable.measure_norm_ge_lt_top {f : α → β} (hf : Integrable f μ) {ε : ℝ} (hε : 0 < ε) :
     μ { x | ε ≤ ‖f x‖ } < ∞ := by
-  convert Integrable.measure_enorm_ge_lt_top hf (ofReal_pos.mpr hε) ofReal_ne_top with x
+  convert! Integrable.measure_enorm_ge_lt_top hf (ofReal_pos.mpr hε) ofReal_ne_top with x
   rw [← Real.enorm_of_nonneg hε.le, enorm_le_iff_norm_le, Real.norm_of_nonneg hε.le]
 
 /-- A non-quantitative version of Markov inequality for integrable functions: the measure of points
diff --git a/Mathlib/MeasureTheory/Function/L2Space.lean b/Mathlib/MeasureTheory/Function/L2Space.lean
index b50619bda4e7a9..7cd7e845df0c0f 100644
--- a/Mathlib/MeasureTheory/Function/L2Space.lean
+++ b/Mathlib/MeasureTheory/Function/L2Space.lean
@@ -46,13 +46,13 @@ theorem MemLp.integrable_sq {f : α → ℝ} (h : MemLp f 2 μ) : Integrable (fu
 theorem memLp_two_iff_integrable_sq_norm {f : α → F} (hf : AEStronglyMeasurable f μ) :
     MemLp f 2 μ ↔ Integrable (fun x => ‖f x‖ ^ 2) μ := by
   rw [← memLp_one_iff_integrable]
-  convert (memLp_norm_rpow_iff hf two_ne_zero ENNReal.ofNat_ne_top).symm
+  convert! (memLp_norm_rpow_iff hf two_ne_zero ENNReal.ofNat_ne_top).symm
   · simp
   · rw [div_eq_mul_inv, ENNReal.mul_inv_cancel two_ne_zero ENNReal.ofNat_ne_top]
 
 theorem memLp_two_iff_integrable_sq {f : α → ℝ} (hf : AEStronglyMeasurable f μ) :
     MemLp f 2 μ ↔ Integrable (fun x => f x ^ 2) μ := by
-  convert memLp_two_iff_integrable_sq_norm hf using 3
+  convert! memLp_two_iff_integrable_sq_norm hf using 3
   simp
 
 end
diff --git a/Mathlib/MeasureTheory/Function/LocallyIntegrable.lean b/Mathlib/MeasureTheory/Function/LocallyIntegrable.lean
index 820f1f744a5fb7..14d1260b68cf3c 100644
--- a/Mathlib/MeasureTheory/Function/LocallyIntegrable.lean
+++ b/Mathlib/MeasureTheory/Function/LocallyIntegrable.lean
@@ -395,7 +395,7 @@ theorem locallyIntegrable_map_homeomorph [BorelSpace X] [BorelSpace Y] (e : X 
     refine ⟨e.symm ⁻¹' U, e.symm.continuous.continuousAt.preimage_mem_nhds hU, ?_⟩
     apply (integrableOn_map_equiv e.toMeasurableEquiv).2
     simp only [Homeomorph.toMeasurableEquiv_coe]
-    convert h'U
+    convert! h'U
     ext x
     simp only [mem_preimage, Homeomorph.symm_apply_apply]
 
diff --git a/Mathlib/MeasureTheory/Function/LpSeminorm/Basic.lean b/Mathlib/MeasureTheory/Function/LpSeminorm/Basic.lean
index 264378743af347..c97a714f7b9a26 100644
--- a/Mathlib/MeasureTheory/Function/LpSeminorm/Basic.lean
+++ b/Mathlib/MeasureTheory/Function/LpSeminorm/Basic.lean
@@ -479,7 +479,7 @@ theorem eLpNorm_norm_rpow (f : α → F) (hq_pos : 0 < q) :
     eLpNorm (fun x => ‖f x‖ ^ q) p μ = eLpNorm f (p * ENNReal.ofReal q) μ ^ q := by
   rw [← eLpNorm_enorm_rpow f hq_pos]
   symm
-  convert eLpNorm_ofReal (fun x ↦ ‖f x‖ ^ q) (by filter_upwards with x using by positivity)
+  convert! eLpNorm_ofReal (fun x ↦ ‖f x‖ ^ q) (by filter_upwards with x using by positivity)
   rw [Function.comp_apply, ← ofReal_norm_eq_enorm]
   exact ENNReal.ofReal_rpow_of_nonneg (by positivity) (by positivity)
 
diff --git a/Mathlib/MeasureTheory/Function/LpSeminorm/ChebyshevMarkov.lean b/Mathlib/MeasureTheory/Function/LpSeminorm/ChebyshevMarkov.lean
index 68a48e35d97618..47f427129e434b 100644
--- a/Mathlib/MeasureTheory/Function/LpSeminorm/ChebyshevMarkov.lean
+++ b/Mathlib/MeasureTheory/Function/LpSeminorm/ChebyshevMarkov.lean
@@ -45,7 +45,7 @@ theorem mul_meas_ge_le_pow_eLpNorm (hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞
 theorem mul_meas_ge_le_pow_eLpNorm' (hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
     {f : α → ε'} (hf : AEStronglyMeasurable f μ) (ε : ℝ≥0∞) :
     ε ^ p.toReal * μ { x | ε ≤ ‖f x‖ₑ } ≤ eLpNorm f p μ ^ p.toReal := by
-  convert mul_meas_ge_le_pow_eLpNorm μ hp_ne_zero hp_ne_top hf (ε ^ p.toReal) using 4
+  convert! mul_meas_ge_le_pow_eLpNorm μ hp_ne_zero hp_ne_top hf (ε ^ p.toReal) using 4
   ext x
   rw [ENNReal.rpow_le_rpow_iff (ENNReal.toReal_pos hp_ne_zero hp_ne_top)]
 
diff --git a/Mathlib/MeasureTheory/Function/LpSeminorm/CompareExp.lean b/Mathlib/MeasureTheory/Function/LpSeminorm/CompareExp.lean
index 5ec76f65f1599f..5b7f2cad5a9a59 100644
--- a/Mathlib/MeasureTheory/Function/LpSeminorm/CompareExp.lean
+++ b/Mathlib/MeasureTheory/Function/LpSeminorm/CompareExp.lean
@@ -198,7 +198,7 @@ theorem eLpNorm_le_eLpNorm_mul_eLpNorm_top (p : ℝ≥0∞) {f : α → E} (hf :
   calc
     eLpNorm (fun x ↦ b (f x) (g x)) p μ ≤ c * eLpNorm g ∞ μ * eLpNorm f p μ :=
       eLpNorm_le_eLpNorm_top_mul_eLpNorm p g hf (flip b) c <| by
-        convert h using 3 with x
+        convert! h using 3 with x
         simp only [mul_assoc, mul_comm ‖f x‖₊]
     _ = c * eLpNorm f p μ * eLpNorm g ∞ μ := by
       simp only [mul_assoc]; rw [mul_comm (eLpNorm _ _ _)]
diff --git a/Mathlib/MeasureTheory/Function/LpSeminorm/TriangleInequality.lean b/Mathlib/MeasureTheory/Function/LpSeminorm/TriangleInequality.lean
index 719fd51155c75f..563f5f2398056d 100644
--- a/Mathlib/MeasureTheory/Function/LpSeminorm/TriangleInequality.lean
+++ b/Mathlib/MeasureTheory/Function/LpSeminorm/TriangleInequality.lean
@@ -67,7 +67,7 @@ theorem eLpNorm_add_le' (hf : AEStronglyMeasurable f μ) (hg : AEStronglyMeasura
   · simp
   rcases lt_or_ge p 1 with (h'p | h'p)
   · simp only [eLpNorm_eq_eLpNorm' hp (h'p.trans ENNReal.one_lt_top).ne]
-    convert eLpNorm'_add_le_of_le_one hf ENNReal.toReal_nonneg _
+    convert! eLpNorm'_add_le_of_le_one hf ENNReal.toReal_nonneg _
     · have : p ∈ Set.Ioo (0 : ℝ≥0∞) 1 := ⟨hp.bot_lt, h'p⟩
       simp only [LpAddConst, if_pos this]
     · simpa using ENNReal.toReal_mono ENNReal.one_ne_top h'p.le
@@ -157,7 +157,7 @@ theorem memLp_finsetSum [ContinuousAdd ε']
 theorem memLp_finsetSum' [ContinuousAdd ε']
     {ι} (s : Finset ι) {f : ι → α → ε'} (hf : ∀ i ∈ s, MemLp (f i) p μ) :
     MemLp (∑ i ∈ s, f i) p μ := by
-  convert memLp_finsetSum s hf using 1
+  convert! memLp_finsetSum s hf using 1
   ext x
   simp
 
diff --git a/Mathlib/MeasureTheory/Function/LpSpace/Basic.lean b/Mathlib/MeasureTheory/Function/LpSpace/Basic.lean
index 147002bccaf105..f63f2d81c39617 100644
--- a/Mathlib/MeasureTheory/Function/LpSpace/Basic.lean
+++ b/Mathlib/MeasureTheory/Function/LpSpace/Basic.lean
@@ -499,7 +499,7 @@ theorem memLp_enorm_rpow_iff {q : ℝ≥0∞} {f : α → ε} (hf : AEStronglyMe
     (q_top : q ≠ ∞) : MemLp (‖f ·‖ₑ ^ q.toReal) (p / q) μ ↔ MemLp f p μ := by
   refine ⟨fun h => ?_, fun h => h.enorm_rpow_div q⟩
   apply (memLp_enorm_iff hf).1
-  convert h.enorm_rpow_div q⁻¹ using 1
+  convert! h.enorm_rpow_div q⁻¹ using 1
   · ext x
     have : q.toReal * q.toReal⁻¹ = 1 :=
       CommGroupWithZero.mul_inv_cancel q.toReal <| ENNReal.toReal_ne_zero.mpr ⟨q_zero, q_top⟩
@@ -511,7 +511,7 @@ theorem memLp_norm_rpow_iff {q : ℝ≥0∞} {f : α → E} (hf : AEStronglyMeas
     (q_top : q ≠ ∞) : MemLp (fun x : α => ‖f x‖ ^ q.toReal) (p / q) μ ↔ MemLp f p μ := by
   refine ⟨fun h => ?_, fun h => h.norm_rpow_div q⟩
   apply (memLp_norm_iff hf).1
-  convert h.norm_rpow_div q⁻¹ using 1
+  convert! h.norm_rpow_div q⁻¹ using 1
   · ext x
     rw [Real.norm_eq_abs, Real.abs_rpow_of_nonneg (norm_nonneg _), ← Real.rpow_mul (abs_nonneg _),
       ENNReal.toReal_inv, mul_inv_cancel₀, abs_of_nonneg (norm_nonneg _), Real.rpow_one]
@@ -521,12 +521,12 @@ theorem memLp_norm_rpow_iff {q : ℝ≥0∞} {f : α → E} (hf : AEStronglyMeas
 
 theorem MemLp.enorm_rpow {f : α → ε} (hf : MemLp f p μ) (hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞) :
     MemLp (fun x : α => ‖f x‖ₑ ^ p.toReal) 1 μ := by
-  convert hf.enorm_rpow_div p
+  convert! hf.enorm_rpow_div p
   rw [div_eq_mul_inv, ENNReal.mul_inv_cancel hp_ne_zero hp_ne_top]
 
 theorem MemLp.norm_rpow {f : α → E} (hf : MemLp f p μ) (hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞) :
     MemLp (fun x : α => ‖f x‖ ^ p.toReal) 1 μ := by
-  convert hf.norm_rpow_div p
+  convert! hf.norm_rpow_div p
   rw [div_eq_mul_inv, ENNReal.mul_inv_cancel hp_ne_zero hp_ne_top]
 
 theorem AEEqFun.compMeasurePreserving_mem_Lp {β : Type*} [MeasurableSpace β]
@@ -749,7 +749,7 @@ theorem _root_.MeasureTheory.memLp_re_im_iff {f : α → K} :
       MemLp f p μ := by
   refine ⟨?_, fun hf => ⟨hf.re, hf.im⟩⟩
   rintro ⟨hre, him⟩
-  convert MeasureTheory.MemLp.add (ε := K) hre.ofReal (him.ofReal.const_mul RCLike.I)
+  convert! MeasureTheory.MemLp.add (ε := K) hre.ofReal (him.ofReal.const_mul RCLike.I)
   ext1 x
   rw [Pi.add_apply, mul_comm, RCLike.re_add_im]
 
diff --git a/Mathlib/MeasureTheory/Function/LpSpace/ContinuousCompMeasurePreserving.lean b/Mathlib/MeasureTheory/Function/LpSpace/ContinuousCompMeasurePreserving.lean
index a7b7ce02d11820..1e39d75dd2318e 100644
--- a/Mathlib/MeasureTheory/Function/LpSpace/ContinuousCompMeasurePreserving.lean
+++ b/Mathlib/MeasureTheory/Function/LpSpace/ContinuousCompMeasurePreserving.lean
@@ -80,7 +80,7 @@ theorem Filter.Tendsto.compMeasurePreservingLp {α : Type*} {l : Filter α}
   replace hg : Tendsto (fun a ↦ ⟨g a, hgm a⟩ : α → {g : C(X, Y) // MeasurePreserving g μ ν})
       l (𝓝 ⟨g₀, hgm₀⟩) :=
     tendsto_subtype_rng.2 hg
-  convert this.comp (hf.prodMk_nhds hg)
+  convert! this.comp (hf.prodMk_nhds hg)
 
 variable {Z : Type*} [TopologicalSpace Z] {f : Z → Lp E p ν} {g : Z → C(X, Y)} {s : Set Z} {z : Z}
 
diff --git a/Mathlib/MeasureTheory/Function/LpSpace/ContinuousFunctions.lean b/Mathlib/MeasureTheory/Function/LpSpace/ContinuousFunctions.lean
index 90abd693575fbb..908bb9a40641d8 100644
--- a/Mathlib/MeasureTheory/Function/LpSpace/ContinuousFunctions.lean
+++ b/Mathlib/MeasureTheory/Function/LpSpace/ContinuousFunctions.lean
@@ -53,7 +53,7 @@ variable [IsFiniteMeasure μ]
 theorem mem_Lp (f : α →ᵇ E) : f.toContinuousMap.toAEEqFun μ ∈ Lp E p μ := by
   refine Lp.mem_Lp_of_ae_bound ‖f‖ ?_
   filter_upwards [f.toContinuousMap.coeFn_toAEEqFun μ] with x _
-  convert f.norm_coe_le_norm x using 2
+  convert! f.norm_coe_le_norm x using 2
 
 /-- The `Lp`-norm of a bounded continuous function is at most a constant (depending on the measure
 of the whole space) times its sup-norm. -/
@@ -64,7 +64,7 @@ theorem Lp_nnnorm_le (f : α →ᵇ E) :
   refine (f.toContinuousMap.coeFn_toAEEqFun μ).mono ?_
   intro x hx
   rw [← NNReal.coe_le_coe, coe_nnnorm, coe_nnnorm]
-  convert f.norm_coe_le_norm x using 2
+  convert! f.norm_coe_le_norm x using 2
 
 /-- The `Lp`-norm of a bounded continuous function is at most a constant (depending on the measure
 of the whole space) times its sup-norm. -/
@@ -151,7 +151,7 @@ theorem range_toLp :
       MeasureTheory.Lp.boundedContinuousFunction E p μ := by
   refine SetLike.ext' ?_
   have := (linearIsometryBoundedOfCompact α E 𝕜).surjective
-  convert Function.Surjective.range_comp this (BoundedContinuousFunction.toLp (E := E) p μ 𝕜)
+  convert! Function.Surjective.range_comp this (BoundedContinuousFunction.toLp (E := E) p μ 𝕜)
   rw [← BoundedContinuousFunction.range_toLp p μ (𝕜 := 𝕜), Submodule.coe_toAddSubgroup,
     LinearMap.coe_range, ContinuousLinearMap.coe_coe]
 
@@ -191,7 +191,7 @@ then in fact `g n` converges uniformly to `h`. -/
 theorem hasSum_of_hasSum_Lp {β : Type*} [μ.IsOpenPosMeasure]
     {g : β → C(α, E)} {f : C(α, E)} (hg : Summable g)
     (hg2 : HasSum (toLp (E := E) p μ 𝕜 ∘ g) (toLp (E := E) p μ 𝕜 f)) : HasSum g f := by
-  convert Summable.hasSum hg
+  convert! Summable.hasSum hg
   exact toLp_injective μ (hg2.unique ((toLp p μ 𝕜).hasSum <| Summable.hasSum hg))
 
 variable (μ) {𝕜 : Type*} [NontriviallyNormedField 𝕜] [NormedSpace 𝕜 E]
diff --git a/Mathlib/MeasureTheory/Function/LpSpace/Indicator.lean b/Mathlib/MeasureTheory/Function/LpSpace/Indicator.lean
index d1cfeb32149697..a3afde2ca260c0 100644
--- a/Mathlib/MeasureTheory/Function/LpSpace/Indicator.lean
+++ b/Mathlib/MeasureTheory/Function/LpSpace/Indicator.lean
@@ -48,7 +48,7 @@ theorem exists_eLpNorm_indicator_le (hp : p ≠ ∞) (c : E) {ε : ℝ≥0∞} (
       Filter.Tendsto (fun x : ℝ≥0 => ((‖c‖₊ * x ^ (1 / p.toReal) : ℝ≥0) : ℝ≥0∞)) (𝓝 0)
         (𝓝 (0 : ℝ≥0)) := by
       rw [ENNReal.tendsto_coe]
-      convert (NNReal.continuousAt_rpow_const (Or.inr hp₀')).tendsto.const_mul _
+      convert! (NNReal.continuousAt_rpow_const (Or.inr hp₀')).tendsto.const_mul _
       simp [hp₀''.ne']
     have hε' : 0 < ε := hε.bot_lt
     obtain ⟨δ, hδ, hδε'⟩ := NNReal.nhds_zero_basis.eventually_iff.mp (this.eventually_le_const hε')
@@ -180,8 +180,8 @@ theorem tendsto_indicatorConstLp_set [hp₁ : Fact (1 ≤ p)] {β : Type*} {l :
   rw [tendsto_iff_dist_tendsto_zero]
   have hp₀ : p ≠ 0 := (one_pos.trans_le hp₁.out).ne'
   simp only [dist_indicatorConstLp_eq_norm, norm_indicatorConstLp hp₀ hp]
-  convert tendsto_const_nhds.mul
-    (((ENNReal.tendsto_toReal ENNReal.zero_ne_top).comp h).rpow_const _)
+  convert!
+    tendsto_const_nhds.mul (((ENNReal.tendsto_toReal ENNReal.zero_ne_top).comp h).rpow_const _)
   · simp [ENNReal.toReal_eq_zero_iff, hp, hp₀]
   · simp
 
diff --git a/Mathlib/MeasureTheory/Function/SimpleFunc.lean b/Mathlib/MeasureTheory/Function/SimpleFunc.lean
index e7461fef837241..b77aae45ac6ad5 100644
--- a/Mathlib/MeasureTheory/Function/SimpleFunc.lean
+++ b/Mathlib/MeasureTheory/Function/SimpleFunc.lean
@@ -1259,7 +1259,7 @@ protected theorem induction {α γ} [MeasurableSpace α] [AddZeroClass γ]
   induction s using Finset.induction generalizing f with
   | empty =>
     rw [Finset.coe_empty, diff_eq_empty, range_subset_singleton] at h
-    convert const 0 MeasurableSet.univ
+    convert! const 0 MeasurableSet.univ
     ext x
     simp [h]
   | insert x s hxs ih =>
@@ -1271,10 +1271,10 @@ protected theorem induction {α γ} [MeasurableSpace α] [AddZeroClass γ]
       rw [image_compl_preimage, union_diff_distrib, diff_diff_comm, h, Finset.coe_insert,
         insert_diff_self_of_notMem, diff_eq_empty.mpr, Set.empty_union]
       · rw [Set.image_subset_iff]
-        convert Set.subset_univ _
+        convert! Set.subset_univ _
         exact preimage_const_of_mem (mem_singleton _)
       · rwa [Finset.mem_coe]
-    convert add _ Pg (const x mx)
+    convert! add _ Pg (const x mx)
     · ext1 y
       by_cases hy : y ∈ f ⁻¹' {x}
       · simpa [g, hy]
@@ -1301,7 +1301,7 @@ protected theorem induction' {α γ} [MeasurableSpace α] [Nonempty γ] {P : Sim
   induction s using Finset.induction generalizing f with
   | empty =>
     rw [Finset.coe_empty, diff_eq_empty, range_subset_singleton] at h
-    convert const c
+    convert! const c
     ext x
     simp [h]
   | insert x s hxs ih =>
@@ -1313,10 +1313,10 @@ protected theorem induction' {α γ} [MeasurableSpace α] [Nonempty γ] {P : Sim
       rw [image_compl_preimage, union_diff_distrib, diff_diff_comm, h, Finset.coe_insert,
         insert_diff_self_of_notMem, diff_eq_empty.mpr, Set.empty_union]
       · rw [Set.image_subset_iff]
-        convert Set.subset_univ _
+        convert! Set.subset_univ _
         exact preimage_const_of_mem (mem_singleton _)
       · rwa [Finset.mem_coe]
-    convert pcw mx.compl Pg (const x)
+    convert! pcw mx.compl Pg (const x)
     · ext1 y
       by_cases hy : y ∈ f ⁻¹' {x}
       · simpa [g, hy]
@@ -1360,7 +1360,7 @@ theorem Measurable.ennreal_induction {motive : (α → ℝ≥0∞) → Prop}
     (iSup : ∀ ⦃f : ℕ → α → ℝ≥0∞⦄, (∀ n, Measurable (f n)) → Monotone f →
       (∀ n, motive (f n)) → motive fun x => ⨆ n, f n x)
     ⦃f : α → ℝ≥0∞⦄ (hf : Measurable f) : motive f := by
-  convert iSup (fun n => (eapprox f n).measurable) (monotone_eapprox f) _ using 2
+  convert! iSup (fun n => (eapprox f n).measurable) (monotone_eapprox f) _ using 2
   · rw [iSup_eapprox_apply hf]
   · exact fun n =>
       SimpleFunc.induction (fun c s hs => indicator c hs)
@@ -1384,9 +1384,12 @@ lemma Measurable.ennreal_sigmaFinite_induction [SigmaFinite μ] {motive : (α 
       (∀ n, motive (f n)) → motive fun x => ⨆ n, f n x)
     ⦃f : α → ℝ≥0∞⦄ (hf : Measurable f) : motive f := by
   refine Measurable.ennreal_induction (fun c s hs ↦ ?_) add iSup hf
-  convert iSup (f := fun n ↦ (s ∩ spanningSets μ n).indicator fun _ ↦ c)
-    (fun n ↦ measurable_const.indicator (hs.inter (measurableSet_spanningSets ..)))
-    (fun m n hmn a ↦ by dsimp; grw [hmn])
-    (fun n ↦ indicator _ (hs.inter (measurableSet_spanningSets ..))
-      (measure_inter_lt_top_of_right_ne_top (measure_spanningSets_lt_top ..).ne)) with a
+  convert!
+    iSup (f := fun n ↦ (s ∩ spanningSets μ n).indicator fun _ ↦ c)
+      (fun n ↦ measurable_const.indicator (hs.inter (measurableSet_spanningSets ..)))
+      (fun m n hmn a ↦ by dsimp; grw [hmn])
+      (fun n ↦
+        indicator _ (hs.inter (measurableSet_spanningSets ..))
+          (measure_inter_lt_top_of_right_ne_top (measure_spanningSets_lt_top ..).ne)) with
+    a
   simp [← Set.indicator_iUnion_apply (M := ℝ≥0∞) rfl, ← Set.inter_iUnion]
diff --git a/Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean b/Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean
index 3ac718ef4842d6..4c7c2cefcbf398 100644
--- a/Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean
+++ b/Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean
@@ -96,7 +96,7 @@ theorem tendsto_approxOn_Lp_eLpNorm [OpensMeasurableSpace E] {f : β → E} (hf
   have hp : 0 < p.toReal := toReal_pos hp_zero hp_ne_top
   suffices Tendsto (fun n => ∫⁻ x, ‖approxOn f hf s y₀ h₀ n x - f x‖ₑ ^ p.toReal ∂μ) atTop (𝓝 0) by
     simp only [eLpNorm_eq_lintegral_rpow_enorm_toReal hp_zero hp_ne_top]
-    convert continuous_rpow_const.continuousAt.tendsto.comp this
+    convert! continuous_rpow_const.continuousAt.tendsto.comp this
     simp [zero_rpow_of_pos (_root_.inv_pos.mpr hp)]
   -- We simply check the conditions of the Dominated Convergence Theorem:
   -- (1) The function "`p`-th power of distance between `f` and the approximation" is measurable
@@ -119,7 +119,7 @@ theorem tendsto_approxOn_Lp_eLpNorm [OpensMeasurableSpace E] {f : β → E} (hf
     filter_upwards [hμ] with a ha
     have : Tendsto (fun n => (approxOn f hf s y₀ h₀ n) a - f a) atTop (𝓝 (f a - f a)) :=
       (tendsto_approxOn hf h₀ ha).sub tendsto_const_nhds
-    convert continuous_rpow_const.continuousAt.tendsto.comp (tendsto_coe.mpr this.nnnorm)
+    convert! continuous_rpow_const.continuousAt.tendsto.comp (tendsto_coe.mpr this.nnnorm)
     simp [zero_rpow_of_pos hp]
   -- Then we apply the Dominated Convergence Theorem
   simpa using tendsto_lintegral_of_dominated_convergence _ hF_meas h_bound h_fin h_lim
@@ -131,7 +131,7 @@ theorem memLp_approxOn [BorelSpace E] {f : β → E} {μ : Measure β} (fmeas :
   suffices eLpNorm (fun x => approxOn f fmeas s y₀ h₀ n x - y₀) p μ < ⊤ by
     have : MemLp (fun x => approxOn f fmeas s y₀ h₀ n x - y₀) p μ :=
       ⟨(approxOn f fmeas s y₀ h₀ n - const β y₀).aestronglyMeasurable, this⟩
-    convert eLpNorm_add_lt_top this hi₀
+    convert! eLpNorm_add_lt_top this hi₀
     ext x
     simp
   have hf' : MemLp (fun x => ‖f x - y₀‖) p μ := by
@@ -140,11 +140,11 @@ theorem memLp_approxOn [BorelSpace E] {f : β → E} {μ : Measure β} (fmeas :
       fun_prop
     refine ⟨h_meas.aemeasurable.aestronglyMeasurable, ?_⟩
     rw [eLpNorm_norm]
-    convert eLpNorm_add_lt_top hf hi₀.neg with x
+    convert! eLpNorm_add_lt_top hf hi₀.neg with x
     simp [sub_eq_add_neg]
   have : ∀ᵐ x ∂μ, ‖approxOn f fmeas s y₀ h₀ n x - y₀‖ ≤ ‖‖f x - y₀‖ + ‖f x - y₀‖‖ := by
     filter_upwards with x
-    convert norm_approxOn_y₀_le fmeas h₀ x n using 1
+    convert! norm_approxOn_y₀_le fmeas h₀ x n using 1
     rw [Real.norm_eq_abs, abs_of_nonneg]
     positivity
   calc
@@ -531,8 +531,7 @@ protected theorem aestronglyMeasurable (f : Lp.simpleFunc E p μ) :
 
 theorem toSimpleFunc_eq_toFun (f : Lp.simpleFunc E p μ) : toSimpleFunc f =ᵐ[μ] f :=
   show ⇑(toSimpleFunc f) =ᵐ[μ] ⇑(f : α →ₘ[μ] E) by
-    convert (AEEqFun.coeFn_mk (toSimpleFunc f)
-          (toSimpleFunc f).aestronglyMeasurable).symm using 2
+    convert! (AEEqFun.coeFn_mk (toSimpleFunc f) (toSimpleFunc f).aestronglyMeasurable).symm using 2
     exact (Classical.choose_spec f.2).symm
 
 /-- `toSimpleFunc f` satisfies the predicate `MemLp`. -/
@@ -633,7 +632,7 @@ protected theorem induction (hp_pos : p ≠ 0) (hp_ne_top : p ≠ ∞) {P : Lp.s
   apply SimpleFunc.induction
   · intro c s hs hf
     by_cases hc : c = 0
-    · convert indicatorConst 0 MeasurableSet.empty (by simp) using 1
+    · convert! indicatorConst 0 MeasurableSet.empty (by simp) using 1
       ext1
       simp [hc]
     exact indicatorConst c hs
@@ -673,7 +672,7 @@ lemma isDenseEmbedding (hp_ne_top : p ≠ ∞) :
         (SimpleFunc.approxOn f (Lp.stronglyMeasurable f).measurable (range f ∪ {0}) 0 _ n)
         (SimpleFunc.memLp_approxOn_range (Lp.stronglyMeasurable f).measurable hfi' n),
       fun n => mem_range_self _, ?_⟩
-  convert SimpleFunc.tendsto_approxOn_range_Lp hp_ne_top (Lp.stronglyMeasurable f).measurable hfi'
+  convert! SimpleFunc.tendsto_approxOn_range_Lp hp_ne_top (Lp.stronglyMeasurable f).measurable hfi'
   rw [toLp_coeFn f (Lp.memLp f)]
 
 protected theorem isDenseInducing (hp_ne_top : p ≠ ∞) :
@@ -838,7 +837,7 @@ theorem MemLp.induction [_i : Fact (1 ≤ p)] (hp_ne_top : p ≠ ∞) (motive :
     apply SimpleFunc.induction
     · intro c s hs h
       by_cases hc : c = 0
-      · subst hc; convert indicator 0 MeasurableSet.empty (by simp) using 1; ext; simp
+      · subst hc; convert! indicator 0 MeasurableSet.empty (by simp) using 1; ext; simp
       have hp_pos : p ≠ 0 := (lt_of_lt_of_le zero_lt_one _i.elim).ne'
       exact indicator c hs (SimpleFunc.measure_lt_top_of_memLp_indicator hp_pos hp_ne_top hc hs h)
     · intro f g hfg hf hg int_fg
@@ -874,7 +873,8 @@ theorem MemLp.induction_dense (hp_ne_top : p ≠ ∞) (P : (α → E) → Prop)
     rcases hf.exists_simpleFunc_eLpNorm_sub_lt hp_ne_top ηpos.ne' with ⟨f', hf', f'_mem⟩
     rcases H f' η ηpos.ne' f'_mem with ⟨g, hg, Pg⟩
     refine ⟨g, ?_, Pg⟩
-    convert (hη _ _ (hf.aestronglyMeasurable.sub f'.aestronglyMeasurable)
+    convert!
+      (hη _ _ (hf.aestronglyMeasurable.sub f'.aestronglyMeasurable)
           (f'.aestronglyMeasurable.sub (h2P g Pg)) hf'.le hg).le using 2
     simp only [sub_add_sub_cancel]
   apply SimpleFunc.induction
@@ -884,7 +884,7 @@ theorem MemLp.induction_dense (hp_ne_top : p ≠ ∞) (P : (α → E) → Prop)
           εpos with ⟨g, hg, Pg⟩
       rw [← eLpNorm_neg, neg_sub] at hg
       refine ⟨g, ?_, Pg⟩
-      convert hg
+      convert! hg
       ext x
       simp
     · have : μ s < ∞ := SimpleFunc.measure_lt_top_of_memLp_indicator hp_pos hp_ne_top hc hs Hs
@@ -898,8 +898,9 @@ theorem MemLp.induction_dense (hp_ne_top : p ≠ ∞) (P : (α → E) → Prop)
     rcases hf η ηpos.ne' int_ff'.1 with ⟨g, hg, Pg⟩
     rcases hf' η ηpos.ne' int_ff'.2 with ⟨g', hg', Pg'⟩
     refine ⟨g + g', ?_, h1P g g' Pg Pg'⟩
-    convert (hη _ _ (f.aestronglyMeasurable.sub (h2P g Pg))
-          (f'.aestronglyMeasurable.sub (h2P g' Pg')) hg hg').le using 2
+    convert!
+      (hη _ _ (f.aestronglyMeasurable.sub (h2P g Pg)) (f'.aestronglyMeasurable.sub (h2P g' Pg')) hg
+          hg').le using 2
     rw [SimpleFunc.coe_add]
     abel
 
diff --git a/Mathlib/MeasureTheory/Function/SpecialFunctions/RCLike.lean b/Mathlib/MeasureTheory/Function/SpecialFunctions/RCLike.lean
index b7d4dfea404dc2..c22984209c3549 100644
--- a/Mathlib/MeasureTheory/Function/SpecialFunctions/RCLike.lean
+++ b/Mathlib/MeasureTheory/Function/SpecialFunctions/RCLike.lean
@@ -65,13 +65,15 @@ theorem RCLike.measurable_ofReal : Measurable ((↑) : ℝ → 𝕜) :=
 
 theorem measurable_of_re_im (hre : Measurable fun x => RCLike.re (f x))
     (him : Measurable fun x => RCLike.im (f x)) : Measurable f := by
-  convert Measurable.add (M := 𝕜) (RCLike.measurable_ofReal.comp hre)
+  convert!
+    Measurable.add (M := 𝕜) (RCLike.measurable_ofReal.comp hre)
       ((RCLike.measurable_ofReal.comp him).mul_const RCLike.I)
   exact (RCLike.re_add_im _).symm
 
 theorem aemeasurable_of_re_im (hre : AEMeasurable (fun x => RCLike.re (f x)) μ)
     (him : AEMeasurable (fun x => RCLike.im (f x)) μ) : AEMeasurable f μ := by
-  convert AEMeasurable.add (M := 𝕜) (RCLike.measurable_ofReal.comp_aemeasurable hre)
+  convert!
+    AEMeasurable.add (M := 𝕜) (RCLike.measurable_ofReal.comp_aemeasurable hre)
       ((RCLike.measurable_ofReal.comp_aemeasurable him).mul_const RCLike.I)
   exact (RCLike.re_add_im _).symm
 
diff --git a/Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean b/Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean
index d0eb5710e8fbe5..027f07c90e84bf 100644
--- a/Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean
+++ b/Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean
@@ -115,7 +115,7 @@ This version works for functions between empty types. -/
 theorem stronglyMeasurable_const' (hf : ∀ x y, f x = f y) : StronglyMeasurable f := by
   nontriviality α
   inhabit α
-  convert stronglyMeasurable_const (β := β) using 1
+  convert! stronglyMeasurable_const (β := β) using 1
   exact funext fun x => hf x default
 
 variable [MeasurableSingletonClass α]
@@ -183,7 +183,7 @@ theorem tendsto_approxBounded_of_norm_le {β} {f : α → β} [NormedAddCommGrou
   · rw [norm_eq_zero] at hfx0
     rw [hfx0] at h_tendsto ⊢
     have h_tendsto_norm : Tendsto (fun n => ‖hf.approx n x‖) atTop (𝓝 0) := by
-      convert h_tendsto.norm
+      convert! h_tendsto.norm
       rw [norm_zero]
     refine squeeze_zero_norm (fun n => ?_) h_tendsto_norm
     calc
@@ -1139,7 +1139,7 @@ protected theorem add [AddZeroClass β] [ContinuousAdd β] (hf : FinStronglyMeas
 protected theorem neg [SubtractionMonoid β] [ContinuousNeg β] (hf : FinStronglyMeasurable f μ) :
     FinStronglyMeasurable (-f) μ := by
   refine ⟨fun n ↦ -hf.approx n, fun n ↦ ?_, fun x ↦ (hf.tendsto_approx x).neg⟩
-  suffices μ (Function.support fun x ↦ -(hf.approx n) x) < ∞ by convert this
+  suffices μ (Function.support fun x ↦ -(hf.approx n) x) < ∞ by convert! this
   rw [Function.support_fun_neg (hf.approx n)]
   exact hf.fin_support_approx n
 
diff --git a/Mathlib/MeasureTheory/Function/UnifTight.lean b/Mathlib/MeasureTheory/Function/UnifTight.lean
index 8f7f929b4aa6dc..da99d5069c6ba9 100644
--- a/Mathlib/MeasureTheory/Function/UnifTight.lean
+++ b/Mathlib/MeasureTheory/Function/UnifTight.lean
@@ -160,7 +160,7 @@ theorem unifTight_of_subsingleton [Subsingleton ι] (hp_top : p ≠ ∞)
   obtain ⟨i⟩ := hι
   obtain ⟨s, _, hμs, hfε⟩ := (hf i).exists_eLpNorm_indicator_compl_lt hp_top (coe_ne_zero.2 hε.ne')
   refine ⟨s, ne_of_lt hμs, fun j => ?_⟩
-  convert hfε.le
+  convert! hfε.le
 
 /-- This lemma is less general than `MeasureTheory.unifTight_finite` which applies to
 all sequences indexed by a finite type. -/
diff --git a/Mathlib/MeasureTheory/Function/UniformIntegrable.lean b/Mathlib/MeasureTheory/Function/UniformIntegrable.lean
index a53c3a3b783dea..dcab66cc8c31de 100644
--- a/Mathlib/MeasureTheory/Function/UniformIntegrable.lean
+++ b/Mathlib/MeasureTheory/Function/UniformIntegrable.lean
@@ -220,7 +220,7 @@ theorem MemLp.integral_indicator_norm_ge_le (hf : MemLp f 1 μ) (hmeas : Strongl
   obtain ⟨M, hM⟩ := this (ENNReal.ofReal ε) (ENNReal.ofReal_pos.2 hε)
   simp only [sub_zero] at hM
   refine ⟨M, ?_⟩
-  convert hM M le_rfl
+  convert! hM M le_rfl
   simp only [coe_nnnorm, ENNReal.ofReal_eq_coe_nnreal (norm_nonneg _)]
   rfl
 
@@ -286,7 +286,7 @@ theorem MemLp.eLpNorm_indicator_norm_ge_le (hf : MemLp f p μ) (hmeas : Strongly
   rw [ENNReal.rpow_mul]
   gcongr
   rw [ENNReal.ofReal_rpow_of_pos hε]
-  convert hM using 3 with x
+  convert! hM using 3 with x
   rw [enorm_indicator_eq_indicator_enorm, enorm_indicator_eq_indicator_enorm]
   have hiff : M ^ (1 / p.toReal) ≤ ‖f x‖₊ ↔ M ≤ ‖‖f x‖ ^ p.toReal‖₊ := by
     rw [coe_nnnorm, coe_nnnorm, Real.norm_rpow_of_nonneg (norm_nonneg _), norm_norm,
@@ -397,7 +397,7 @@ theorem MemLp.eLpNorm_indicator_le (hp_one : 1 ≤ p) (hp_top : p ≠ ∞) (hf :
   obtain ⟨⟨f', hf', heq⟩, _⟩ := hf
   obtain ⟨δ, hδpos, hδ⟩ := (hℒp.ae_eq heq).eLpNorm_indicator_le_of_meas hp_one hp_top hf' hε
   refine ⟨δ, hδpos, fun s hs hμs => ?_⟩
-  convert hδ s hs hμs using 1
+  convert! hδ s hs hμs using 1
   rw [eLpNorm_indicator_eq_eLpNorm_restrict hs, eLpNorm_indicator_eq_eLpNorm_restrict hs]
   exact eLpNorm_congr_ae heq.restrict
 
@@ -416,7 +416,7 @@ theorem unifIntegrable_subsingleton [Subsingleton ι] (hp_one : 1 ≤ p) (hp_top
   · obtain ⟨i⟩ := hι
     obtain ⟨δ, hδpos, hδ⟩ := (hf i).eLpNorm_indicator_le hp_one hp_top hε
     refine ⟨δ, hδpos, fun j s hs hμs => ?_⟩
-    convert hδ s hs hμs
+    convert! hδ s hs hμs
   · exact ⟨1, zero_lt_one, fun i => False.elim <| hι <| Nonempty.intro i⟩
 
 /-- This lemma is less general than `MeasureTheory.unifIntegrable_finite` which applies to
@@ -530,7 +530,7 @@ theorem tendsto_Lp_finite_of_tendsto_ae [IsFiniteMeasure μ] (hp : 1 ≤ p) (hp'
     exact fun n => (hf n).ae_eq_mk
   filter_upwards [hfg, h_ae_forall_eq, hg.1.ae_eq_mk] with x hx_tendsto hxf_eq hxg_eq
   rw [← hxg_eq]
-  convert hx_tendsto using 1
+  convert! hx_tendsto using 1
   ext1 n
   exact (hxf_eq n).symm
 
@@ -917,7 +917,7 @@ theorem uniformIntegrable_average
 /-- The averaging of a uniformly integrable real-valued sequence is also uniformly integrable. -/
 theorem uniformIntegrable_average_real (hp : 1 ≤ p) {f : ℕ → α → ℝ} (hf : UniformIntegrable f p μ) :
     UniformIntegrable (fun n => (∑ i ∈ Finset.range n, f i) / (n : α → ℝ)) p μ := by
-  convert uniformIntegrable_average hp hf using 2 with n
+  convert! uniformIntegrable_average hp hf using 2 with n
   ext x
   simp [div_eq_inv_mul]
 
diff --git a/Mathlib/MeasureTheory/Group/Arithmetic.lean b/Mathlib/MeasureTheory/Group/Arithmetic.lean
index d478081cf97664..d0e38d0e2b78e3 100644
--- a/Mathlib/MeasureTheory/Group/Arithmetic.lean
+++ b/Mathlib/MeasureTheory/Group/Arithmetic.lean
@@ -336,11 +336,11 @@ export MeasurableNeg (measurable_neg)
 instance (priority := 100) measurableDiv_of_mul_inv (G : Type*) [MeasurableSpace G]
     [DivInvMonoid G] [MeasurableMul G] [MeasurableInv G] : MeasurableDiv G where
   measurable_const_div c := by
-    convert measurable_inv.const_mul c using 1
+    convert! measurable_inv.const_mul c using 1
     ext1
     apply div_eq_mul_inv
   measurable_div_const c := by
-    convert measurable_id.mul_const c⁻¹ using 1
+    convert! measurable_id.mul_const c⁻¹ using 1
     ext1
     apply div_eq_mul_inv
 
diff --git a/Mathlib/MeasureTheory/Group/FundamentalDomain.lean b/Mathlib/MeasureTheory/Group/FundamentalDomain.lean
index 5858e90e8e10b6..dbdaa3f8f8bcc1 100644
--- a/Mathlib/MeasureTheory/Group/FundamentalDomain.lean
+++ b/Mathlib/MeasureTheory/Group/FundamentalDomain.lean
@@ -311,7 +311,7 @@ theorem measure_set_eq (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDoma
     (hA₀ : MeasurableSet A) (hA : ∀ g : G, (fun x => g • x) ⁻¹' A = A) : μ (A ∩ s) = μ (A ∩ t) := by
   have : ∫⁻ x in s, A.indicator 1 x ∂μ = ∫⁻ x in t, A.indicator 1 x ∂μ := by
     refine hs.setLIntegral_eq ht (Set.indicator A fun _ => 1) fun g x ↦ ?_
-    convert (Set.indicator_comp_right (g • · : α → α) (g := fun _ ↦ (1 : ℝ≥0∞))).symm
+    convert! (Set.indicator_comp_right (g • · : α → α) (g := fun _ ↦ (1 : ℝ≥0∞))).symm
     rw [hA g]
   simpa [Measure.restrict_apply hA₀, lintegral_indicator hA₀] using this
 
@@ -818,7 +818,7 @@ theorem IsFundamentalDomain.quotientMeasureEqMeasurePreimage_of_zero
   apply fund_dom_s.quotientMeasureEqMeasurePreimage
   ext U meas_U
   simp only [Measure.coe_zero, Pi.zero_apply]
-  convert (measure_inter_null_of_null_right (h := vol_s) (Quotient.mk α_mod_G ⁻¹' U)).symm
+  convert! (measure_inter_null_of_null_right (h := vol_s) (Quotient.mk α_mod_G ⁻¹' U)).symm
   rw [measure_map_restrict_apply (meas_U := meas_U)]
 
 /-- If a measure `μ` on a quotient satisfies `QuotientMeasureEqMeasurePreimage` with respect to a
@@ -844,7 +844,7 @@ lemma QuotientMeasureEqMeasurePreimage.sigmaFiniteQuotient
     rw [fund_dom_s.measure_eq_tsum (A n)]
     exact measure_iUnion_le _
   · rw [← image_iUnion, hA']
-    refine image_univ_of_surjective (by convert Quotient.mk'_surjective)
+    refine image_univ_of_surjective (by convert! Quotient.mk'_surjective)
 
 /-- A measure `μ` on `α ⧸ G` satisfying `QuotientMeasureEqMeasurePreimage` and having finite
 covolume is a finite measure. -/
@@ -857,7 +857,7 @@ theorem QuotientMeasureEqMeasurePreimage.isFiniteMeasure_quotient
   rw [h𝓕.projection_respects_measure (μ := μ)]
   have : Fact (ν 𝓕 < ∞) := by
     apply Fact.mk
-    convert Ne.lt_top h
+    convert! Ne.lt_top h
     exact (h𝓕.covolume_eq_volume ν).symm
   infer_instance
 
diff --git a/Mathlib/MeasureTheory/Group/Integral.lean b/Mathlib/MeasureTheory/Group/Integral.lean
index 4355cfc14dadae..e1a4f711b47a4d 100644
--- a/Mathlib/MeasureTheory/Group/Integral.lean
+++ b/Mathlib/MeasureTheory/Group/Integral.lean
@@ -156,7 +156,7 @@ theorem Integrable.comp_div_left {f : G → F} [IsInvInvariant μ] [IsMulLeftInv
 theorem integrable_comp_div_left (f : G → F) [IsInvInvariant μ] [IsMulLeftInvariant μ] (g : G) :
     Integrable (fun t => f (g / t)) μ ↔ Integrable f μ := by
   refine ⟨fun h => ?_, fun h => h.comp_div_left g⟩
-  convert h.comp_inv.comp_mul_left g⁻¹
+  convert! h.comp_inv.comp_mul_left g⁻¹
   simp_rw [div_inv_eq_mul, mul_inv_cancel_left]
 
 @[to_additive]
diff --git a/Mathlib/MeasureTheory/Group/LIntegral.lean b/Mathlib/MeasureTheory/Group/LIntegral.lean
index 2ec2a9425c6c62..76f023b666b4fe 100644
--- a/Mathlib/MeasureTheory/Group/LIntegral.lean
+++ b/Mathlib/MeasureTheory/Group/LIntegral.lean
@@ -52,7 +52,7 @@ with respect to a left-invariant measure. -/
       respect to a left-invariant measure. -/]
 theorem lintegral_mul_left_eq_self [IsMulLeftInvariant μ] (f : G → ℝ≥0∞) (g : G) :
     (∫⁻ x, f (g * x) ∂μ) = ∫⁻ x, f x ∂μ := by
-  convert (lintegral_map_equiv f <| MeasurableEquiv.mulLeft g).symm
+  convert! (lintegral_map_equiv f <| MeasurableEquiv.mulLeft g).symm
   simp [map_mul_left_eq_self μ g]
 
 /-- Translating a function by right-multiplication does not change its Lebesgue integral
@@ -62,7 +62,7 @@ with respect to a right-invariant measure. -/
       respect to a right-invariant measure. -/]
 theorem lintegral_mul_right_eq_self [IsMulRightInvariant μ] (f : G → ℝ≥0∞) (g : G) :
     (∫⁻ x, f (x * g) ∂μ) = ∫⁻ x, f x ∂μ := by
-  convert (lintegral_map_equiv f <| MeasurableEquiv.mulRight g).symm using 1
+  convert! (lintegral_map_equiv f <| MeasurableEquiv.mulRight g).symm using 1
   simp [map_mul_right_eq_self μ g]
 
 @[to_additive]
diff --git a/Mathlib/MeasureTheory/Group/Measure.lean b/Mathlib/MeasureTheory/Group/Measure.lean
index 4003e5696d3968..af02ac7c38eb0b 100644
--- a/Mathlib/MeasureTheory/Group/Measure.lean
+++ b/Mathlib/MeasureTheory/Group/Measure.lean
@@ -102,7 +102,7 @@ theorem MeasurePreserving.mul_right (μ : Measure G) [IsMulRightInvariant μ] (g
 @[to_additive]
 instance Subgroup.smulInvariantMeasure {G α : Type*} [Group G] [MulAction G α] [MeasurableSpace α]
     {μ : Measure α} [SMulInvariantMeasure G α μ] (H : Subgroup G) : SMulInvariantMeasure H α μ :=
-  ⟨fun y s hs => by convert SMulInvariantMeasure.measure_preimage_smul (μ := μ) (y : G) hs⟩
+  ⟨fun y s hs => by convert! SMulInvariantMeasure.measure_preimage_smul (μ := μ) (y : G) hs⟩
 
 /-- An alternative way to prove that `μ` is left invariant under multiplication. -/
 @[to_additive /-- An alternative way to prove that `μ` is left invariant under addition. -/]
@@ -775,7 +775,7 @@ variable [Group G] [TopologicalSpace G] (μ : Measure G) [IsHaarMeasure μ]
 
 @[to_additive (attr := simp)]
 theorem haar_singleton [ContinuousMul G] [BorelSpace G] (g : G) : μ {g} = μ {(1 : G)} := by
-  convert measure_preimage_mul μ g⁻¹ _
+  convert! measure_preimage_mul μ g⁻¹ _
   simp only [mul_one, preimage_mul_left_singleton, inv_inv]
 
 @[to_additive IsAddHaarMeasure.smul]
diff --git a/Mathlib/MeasureTheory/Group/Prod.lean b/Mathlib/MeasureTheory/Group/Prod.lean
index e023d84c5d03ab..beebced4fd664b 100644
--- a/Mathlib/MeasureTheory/Group/Prod.lean
+++ b/Mathlib/MeasureTheory/Group/Prod.lean
@@ -100,7 +100,7 @@ theorem measurable_measure_mul_right (hs : MeasurableSet s) :
   suffices
     Measurable fun y =>
       μ ((fun x => (x, y)) ⁻¹' ((fun z : G × G => ((1 : G), z.1 * z.2)) ⁻¹' univ ×ˢ s))
-    by convert this using 1; ext1 x; congr 1 with y : 1; simp
+    by convert! this using 1; ext1 x; congr 1 with y : 1; simp
   apply measurable_measure_prodMk_right
   apply measurable_const.prodMk measurable_mul (MeasurableSet.univ.prod hs)
   infer_instance
@@ -134,8 +134,8 @@ where `S` is the map `(x, y) ↦ (x, xy)` and `R` is `Prod.swap`. -/
 /-- The map `(x, y) ↦ (y + x, - x)` is measure-preserving. -/]
 theorem measurePreserving_mul_prod_inv [IsMulLeftInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.2 * z.1, z.1⁻¹)) (μ.prod ν) (μ.prod ν) := by
-  convert (measurePreserving_prod_inv_mul_swap ν μ).comp (measurePreserving_prod_mul_swap μ ν)
-    using 1
+  convert!
+    (measurePreserving_prod_inv_mul_swap ν μ).comp (measurePreserving_prod_mul_swap μ ν) using 1
   ext1 ⟨x, y⟩
   simp_rw [Function.comp_apply, mul_inv_rev, inv_mul_cancel_right]
 
@@ -234,7 +234,7 @@ theorem measure_mul_lintegral_eq [IsMulLeftInvariant ν] (sm : MeasurableSet s)
     fun x => measurable_const.indicator (measurable_mul_const _ sm)
   have : ∀ x y, s.indicator (fun _ : G => (1 : ℝ≥0∞)) (y * x) =
       ((fun z => z * x) ⁻¹' s).indicator (fun b : G => 1) y := by
-    intro x y; symm; convert indicator_comp_right (M := ℝ≥0∞) fun y => y * x using 2; ext1; rfl
+    intro x y; symm; convert! indicator_comp_right (M := ℝ≥0∞) fun y => y * x using 2; ext1; rfl
   simp_rw [this, lintegral_mul_const _ (ms _), lintegral_indicator (measurable_mul_const _ sm),
     setLIntegral_one]
 
@@ -388,8 +388,8 @@ theorem measurePreserving_div_prod [IsMulRightInvariant μ] :
 /-- The map `(x, y) ↦ (x + y, - x)` is measure-preserving. -/]
 theorem measurePreserving_mul_prod_inv_right [IsMulRightInvariant μ] [IsMulRightInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1 * z.2, z.1⁻¹)) (μ.prod ν) (μ.prod ν) := by
-  convert (measurePreserving_prod_div_swap ν μ).comp (measurePreserving_prod_mul_swap_right μ ν)
-    using 1
+  convert!
+    (measurePreserving_prod_div_swap ν μ).comp (measurePreserving_prod_mul_swap_right μ ν) using 1
   ext1 ⟨x, y⟩
   simp_rw [Function.comp_apply, div_mul_eq_div_div_swap, div_self', one_div]
 
diff --git a/Mathlib/MeasureTheory/Integral/Average.lean b/Mathlib/MeasureTheory/Integral/Average.lean
index 9b00b672cd1b28..ca8f317c0a3bf5 100644
--- a/Mathlib/MeasureTheory/Integral/Average.lean
+++ b/Mathlib/MeasureTheory/Integral/Average.lean
@@ -446,7 +446,7 @@ theorem integral_sub_average (μ : Measure α) [IsFiniteMeasure μ] (f : α →
   by_cases hf : Integrable f μ
   · rw [integral_sub hf (integrable_const _), integral_average, sub_self]
   refine integral_undef fun h => hf ?_
-  convert h.add (integrable_const (⨍ a, f a ∂μ))
+  convert! h.add (integrable_const (⨍ a, f a ∂μ))
   exact (sub_add_cancel _ _).symm
 
 theorem setAverage_sub_setAverage (hs : μ s ≠ ∞) (f : α → E) :
diff --git a/Mathlib/MeasureTheory/Integral/Bochner/Basic.lean b/Mathlib/MeasureTheory/Integral/Bochner/Basic.lean
index f7d635f4f3f771..d88526387b4e6d 100644
--- a/Mathlib/MeasureTheory/Integral/Bochner/Basic.lean
+++ b/Mathlib/MeasureTheory/Integral/Bochner/Basic.lean
@@ -580,7 +580,7 @@ theorem tendsto_integral_norm_approxOn_sub
     (fmeas : Measurable f) (hf : Integrable f μ) [SeparableSpace (range f ∪ {0} : Set E)] :
     Tendsto (fun n ↦ ∫ x, ‖SimpleFunc.approxOn f fmeas (range f ∪ {0}) 0 (by simp) n x - f x‖ ∂μ)
       atTop (𝓝 0) := by
-  convert (tendsto_toReal zero_ne_top).comp (tendsto_approxOn_range_L1_enorm fmeas hf) with n
+  convert! (tendsto_toReal zero_ne_top).comp (tendsto_approxOn_range_L1_enorm fmeas hf) with n
   rw [integral_norm_eq_lintegral_enorm]
   · simp
   · apply (SimpleFunc.aestronglyMeasurable _).sub
@@ -828,7 +828,7 @@ lemma integral_tendsto_of_tendsto_of_antitone {μ : Measure α} {f : ℕ → α
   suffices Tendsto (fun n ↦ ∫ x, -f n x ∂μ) atTop (𝓝 (∫ x, -F x ∂μ)) by
     suffices Tendsto (fun n ↦ ∫ x, - -f n x ∂μ) atTop (𝓝 (∫ x, - -F x ∂μ)) by
       simpa [neg_neg] using this
-    convert this.neg <;> rw [integral_neg]
+    convert! this.neg <;> rw [integral_neg]
   refine integral_tendsto_of_tendsto_of_monotone (fun n ↦ (hf n).neg) hF.neg ?_ ?_
   · filter_upwards [h_mono] with x hx n m hnm using neg_le_neg_iff.mpr <| hx hnm
   · filter_upwards [h_tendsto] with x hx using hx.neg
@@ -904,11 +904,11 @@ lemma tendsto_of_integral_tendsto_of_antitone {μ : Measure α} {f : ℕ → α
   let F' : α → ℝ := fun a ↦ - F a
   suffices ∀ᵐ a ∂μ, Tendsto (fun i ↦ f' i a) atTop (𝓝 (F' a)) by
     filter_upwards [this] with a ha_tendsto
-    convert ha_tendsto.neg
+    convert! ha_tendsto.neg
     · simp [f']
     · simp [F']
   refine tendsto_of_integral_tendsto_of_monotone (fun n ↦ (hf_int n).neg) hF_int.neg ?_ ?_ ?_
-  · convert hf_tendsto.neg
+  · convert! hf_tendsto.neg
     · rw [integral_neg]
     · rw [integral_neg]
   · filter_upwards [hf_mono] with a ha i j hij
@@ -1076,9 +1076,10 @@ theorem integral_map_of_stronglyMeasurable {β} [MeasurableSpace β] {φ : α 
   have : SeparableSpace (range f ∪ {0} : Set G) := hfm.separableSpace_range_union_singleton
   refine tendsto_nhds_unique
     (tendsto_integral_approxOn_of_measurable_of_range_subset hfm.measurable hfi _ Subset.rfl) ?_
-  convert tendsto_integral_approxOn_of_measurable_of_range_subset (hfm.measurable.comp hφ)
-    ((integrable_map_measure hfm.aestronglyMeasurable hφ.aemeasurable).1 hfi) (range f ∪ {0})
-    (union_subset_union_left {0} (range_comp_subset_range φ f)) using 1
+  convert!
+    tendsto_integral_approxOn_of_measurable_of_range_subset (hfm.measurable.comp hφ)
+      ((integrable_map_measure hfm.aestronglyMeasurable hφ.aemeasurable).1 hfi) (range f ∪ {0})
+      (union_subset_union_left {0} (range_comp_subset_range φ f)) using 1
   ext1 i
   simp only [SimpleFunc.integral_eq, hφ, SimpleFunc.measurableSet_preimage, map_measureReal_apply,
     ← preimage_comp]
@@ -1217,13 +1218,13 @@ theorem integral_mul_norm_le_Lp_mul_Lq {E} [NormedAddCommGroup E] {f g : α →
   -- we can now apply `ENNReal.lintegral_mul_le_Lp_mul_Lq` (up to the `toReal` application)
   refine ENNReal.toReal_mono ?_ ?_
   · refine ENNReal.mul_ne_top ?_ ?_
-    · convert hf.eLpNorm_ne_top
+    · convert! hf.eLpNorm_ne_top
       rw [eLpNorm_eq_lintegral_rpow_enorm_toReal]
       · rw [ENNReal.toReal_ofReal hpq.nonneg]
       · rw [Ne, ENNReal.ofReal_eq_zero, not_le]
         exact hpq.pos
       · finiteness
-    · convert hg.eLpNorm_ne_top
+    · convert! hg.eLpNorm_ne_top
       rw [eLpNorm_eq_lintegral_rpow_enorm_toReal]
       · rw [ENNReal.toReal_ofReal hpq.symm.nonneg]
       · rw [Ne, ENNReal.ofReal_eq_zero, not_le]
diff --git a/Mathlib/MeasureTheory/Integral/Bochner/ContinuousLinearMap.lean b/Mathlib/MeasureTheory/Integral/Bochner/ContinuousLinearMap.lean
index 7db4535b5b5386..222cd4649f08e9 100644
--- a/Mathlib/MeasureTheory/Integral/Bochner/ContinuousLinearMap.lean
+++ b/Mathlib/MeasureTheory/Integral/Bochner/ContinuousLinearMap.lean
@@ -62,7 +62,7 @@ theorem integral_comp_commSL [CompleteSpace E] (hσ : ∀ (r : ℝ) (x : 𝕜),
       integral_add (μ := μ) (L.integrable_comp f_int) (L.integrable_comp g_int), hf, hg]
   · exact isClosed_eq L.continuous_integral_comp_L1 (L.continuous.comp continuous_integral)
   · intro f g hfg _ hf
-    convert hf using 1 <;> clear hf
+    convert! hf using 1 <;> clear hf
     · exact integral_congr_ae (hfg.fun_comp L).symm
     · rw [integral_congr_ae hfg.symm]
 
@@ -279,7 +279,7 @@ theorem integral_withDensity_eq_integral_smul {f : X → ℝ≥0} (f_meas : Meas
     have C2 : Continuous fun u : Lp E 1 (μ.withDensity fun x => f x) => ∫ x, f x • u x ∂μ := by
       have : Continuous ((fun u : Lp E 1 μ => ∫ x, u x ∂μ) ∘ withDensitySMulLI (E := E) μ f_meas) :=
         continuous_integral.comp (withDensitySMulLI (E := E) μ f_meas).continuous
-      convert this with u
+      convert! this with u
       simp only [Function.comp_apply, withDensitySMulLI_apply]
       exact integral_congr_ae (memL1_smul_of_L1_withDensity f_meas u).coeFn_toLp.symm
     exact isClosed_eq C1 C2
diff --git a/Mathlib/MeasureTheory/Integral/Bochner/L1.lean b/Mathlib/MeasureTheory/Integral/Bochner/L1.lean
index 090ff83c850f09..007107e5c9cab4 100644
--- a/Mathlib/MeasureTheory/Integral/Bochner/L1.lean
+++ b/Mathlib/MeasureTheory/Integral/Bochner/L1.lean
@@ -468,7 +468,7 @@ theorem posPart_toSimpleFunc (f : α →₁ₛ[μ] ℝ) :
   have ae_eq : ∀ᵐ a ∂μ, toSimpleFunc (posPart f) a = max ((toSimpleFunc f) a) 0 := by
     filter_upwards [toSimpleFunc_eq_toFun (posPart f), Lp.coeFn_posPart (f : α →₁[μ] ℝ),
       toSimpleFunc_eq_toFun f] with _ _ h₂ h₃
-    convert h₂ using 1
+    convert! h₂ using 1
     rw [h₃]
   refine ae_eq.mono fun a h => ?_
   rw [h, eq]
diff --git a/Mathlib/MeasureTheory/Integral/Bochner/Set.lean b/Mathlib/MeasureTheory/Integral/Bochner/Set.lean
index 6b999846d27886..eb2412a769ea7c 100644
--- a/Mathlib/MeasureTheory/Integral/Bochner/Set.lean
+++ b/Mathlib/MeasureTheory/Integral/Bochner/Set.lean
@@ -128,7 +128,7 @@ theorem integral_biUnion_finset {ι : Type*} (t : Finset ι) {s : ι → Set X}
 theorem integral_iUnion_fintype {ι : Type*} [Fintype ι] {s : ι → Set X}
     (hs : ∀ i, MeasurableSet (s i)) (h's : Pairwise (Disjoint on s))
     (hf : ∀ i, IntegrableOn f (s i) μ) : ∫ x in ⋃ i, s i, f x ∂μ = ∑ i, ∫ x in s i, f x ∂μ := by
-  convert integral_biUnion_finset Finset.univ (fun i _ => hs i) _ fun i _ => hf i
+  convert! integral_biUnion_finset Finset.univ (fun i _ => hs i) _ fun i _ => hf i
   · simp
   · simp [pairwise_univ, h's]
 
@@ -214,7 +214,7 @@ theorem integral_biUnion_eq_sum_powerset {ι : Type*} {t : Finset ι} {s : ι 
     rcases hu.2 with ⟨i, hi⟩
     exact (hf i (hu.1 hi)).mono (biInter_subset_of_mem hi) le_rfl
   congr with x
-  convert Finset.indicator_biUnion_eq_sum_powerset t s f x with u hu
+  convert! Finset.indicator_biUnion_eq_sum_powerset t s f x with u hu
   rw [indicator_smul_apply]
   norm_cast
 
@@ -298,7 +298,7 @@ theorem tendsto_setIntegral_of_antitone
   rcases hfi with ⟨i₀, hi₀⟩
   suffices Tendsto (∫ x in s i₀, f x ∂μ - ∫ x in s i₀ \ s ·, f x ∂μ) atTop
       (𝓝 (∫ x in s i₀, f x ∂μ - ∫ x in ⋃ i, s i₀ \ s i, f x ∂μ)) by
-    convert this.congr' <| (eventually_ge_atTop i₀).mono fun i hi ↦ ?_
+    convert! this.congr' <| (eventually_ge_atTop i₀).mono fun i hi ↦ ?_
     · rw [← diff_iInter, setIntegral_diff _ hi₀ (iInter_subset _ _), sub_sub_cancel]
       exact .iInter_of_antitone h_anti hsm
     · rw [setIntegral_diff (hsm i) hi₀ (h_anti hi), sub_sub_cancel]
@@ -885,7 +885,7 @@ theorem integrableOn_iUnion_of_summable_integral_norm {f : X → E} {s : ι →
     rw [← NNReal.summable_coe]; exact h
   have S'' := ENNReal.tsum_coe_eq S'.hasSum
   simp_rw [ENNReal.coe_nnreal_eq, NNReal.coe_mk, coe_nnnorm] at S''
-  convert ENNReal.ofReal_lt_top
+  convert! ENNReal.ofReal_lt_top
 
 variable [TopologicalSpace X] [BorelSpace X] [T2Space X] [IsLocallyFiniteMeasure μ]
 
@@ -1037,7 +1037,7 @@ theorem measure_le_lintegral_thickenedIndicatorAux (μ : Measure X) {E : Set X}
 theorem measure_le_lintegral_thickenedIndicator (μ : Measure X) {E : Set X}
     (E_mble : MeasurableSet E) {δ : ℝ} (δ_pos : 0 < δ) :
     μ E ≤ ∫⁻ x, (thickenedIndicator δ_pos E x : ℝ≥0∞) ∂μ := by
-  convert measure_le_lintegral_thickenedIndicatorAux μ E_mble δ
+  convert! measure_le_lintegral_thickenedIndicatorAux μ E_mble δ
   dsimp
   simp only [thickenedIndicatorAux_lt_top.ne, ENNReal.coe_toNNReal, Ne, not_false_iff]
 
diff --git a/Mathlib/MeasureTheory/Integral/Bochner/SumMeasure.lean b/Mathlib/MeasureTheory/Integral/Bochner/SumMeasure.lean
index bdd361605c7e20..a7884a48fe0db4 100644
--- a/Mathlib/MeasureTheory/Integral/Bochner/SumMeasure.lean
+++ b/Mathlib/MeasureTheory/Integral/Bochner/SumMeasure.lean
@@ -57,7 +57,7 @@ lemma integrable_sum_measure
     Integrable f (Measure.sum μ) := by
   refine ⟨aestronglyMeasurable_sum_measure_iff.mpr fun i ↦ (hf i).aestronglyMeasurable, ?_⟩
   · rw [HasFiniteIntegral, lintegral_sum_measure]
-    convert h.tsum_ofReal_lt_top with i
+    convert! h.tsum_ofReal_lt_top with i
     rw [ofReal_integral_eq_lintegral_ofReal (hf i).norm]
     · simp_rw [ofReal_norm_eq_enorm]
     · exact ae_of_all _ fun _ ↦ by positivity
@@ -65,7 +65,7 @@ lemma integrable_sum_measure
 omit [Countable ι] in
 lemma Integrable.summable_integral (hf : Integrable f (Measure.sum μ)) :
     Summable (fun i ↦ ∫ x, ‖f x‖ ∂μ i) := by
-  convert ENNReal.summable_toReal (f := fun i ↦ ∫⁻ x, ‖f x‖ₑ ∂μ i) ?_ with i
+  convert! ENNReal.summable_toReal (f := fun i ↦ ∫⁻ x, ‖f x‖ₑ ∂μ i) ?_ with i
   · rw [← integral_toReal ?_ (by simp)]
     · simp
     · exact (hf.aestronglyMeasurable.mono_measure (Measure.le_sum _ i)).enorm
@@ -153,7 +153,7 @@ lemma integral_sum_dirac [FiniteDimensional ℝ E] (hc : ∀ i, c i ≠ ∞) :
     rw [integral_smul_measure, integral_dirac]
   · rw [integral_undef hf, tsum_eq_zero_of_not_summable]
     apply mt Summable.norm
-    convert mt (integrable_sum_dirac hc) hf
+    convert! mt (integrable_sum_dirac hc) hf
     simp [norm_smul]
 
 lemma hasSum_integral_sum_dirac [CompleteSpace E] (hc : ∀ i, c i ≠ ∞)
diff --git a/Mathlib/MeasureTheory/Integral/Bochner/VitaliCaratheodory.lean b/Mathlib/MeasureTheory/Integral/Bochner/VitaliCaratheodory.lean
index 3b0ff2458cebd0..135a554ad5a100 100644
--- a/Mathlib/MeasureTheory/Integral/Bochner/VitaliCaratheodory.lean
+++ b/Mathlib/MeasureTheory/Integral/Bochner/VitaliCaratheodory.lean
@@ -150,7 +150,7 @@ theorem SimpleFunc.exists_le_lowerSemicontinuous_lintegral_ge (f : α →ₛ ℝ
     simp only [SimpleFunc.coe_add, ENNReal.coe_add, Pi.add_apply]
     rw [lintegral_add_left f₁.measurable.coe_nnreal_ennreal,
       lintegral_add_left g₁cont.measurable.coe_nnreal_ennreal]
-    convert add_le_add g₁int g₂int using 1
+    convert! add_le_add g₁int g₂int using 1
     conv_lhs => rw [← ENNReal.add_halves ε]
     abel
 
@@ -246,9 +246,9 @@ theorem exists_lt_lowerSemicontinuous_lintegral_ge_of_aemeasurable [SigmaFinite
         lintegral_add_left g0_cont.measurable _
       _ ≤ (∫⁻ x, f x ∂μ) + ε / 2 + (0 + ε / 2) := by
         refine add_le_add ?_ ?_
-        · convert g0_int using 2
+        · convert! g0_int using 2
           exact lintegral_congr_ae (fmeas.ae_eq_mk.fun_comp _)
-        · convert g1_int
+        · convert! g1_int
           simp only [smeas, μs, lintegral_const, Set.univ_inter, MeasurableSet.univ,
             lintegral_indicator, mul_zero, restrict_apply]
       _ = (∫⁻ x, f x ∂μ) + ε := by simp only [add_assoc, ENNReal.add_halves, zero_add]
@@ -267,7 +267,7 @@ theorem exists_lt_lowerSemicontinuous_integral_gt_nnreal [SigmaFinite μ] (f : 
       (∀ᵐ x ∂μ, g x < ⊤) ∧
       Integrable (fun x => (g x).toReal) μ ∧ (∫ x, (g x).toReal ∂μ) < (∫ x, ↑(f x) ∂μ) + ε := by
   have fmeas : AEMeasurable f μ := by
-    convert fint.aestronglyMeasurable.real_toNNReal.aemeasurable
+    convert! fint.aestronglyMeasurable.real_toNNReal.aemeasurable
     simp only [Real.toNNReal_coe]
   lift ε to ℝ≥0 using εpos.le
   obtain ⟨δ, δpos, hδε⟩ : ∃ δ : ℝ≥0, 0 < δ ∧ δ < ε := exists_between εpos
@@ -285,7 +285,7 @@ theorem exists_lt_lowerSemicontinuous_integral_gt_nnreal [SigmaFinite μ] (f : 
   refine ⟨g, f_lt_g, gcont, g_lt_top, ?_, ?_⟩
   · refine ⟨gcont.measurable.ennreal_toReal.aemeasurable.aestronglyMeasurable, ?_⟩
     simp only [hasFiniteIntegral_iff_norm, Real.norm_eq_abs, abs_of_nonneg ENNReal.toReal_nonneg]
-    convert gint_ne.lt_top using 1
+    convert! gint_ne.lt_top using 1
   · rw [integral_eq_lintegral_of_nonneg_ae, integral_eq_lintegral_of_nonneg_ae]
     · calc
         ENNReal.toReal (∫⁻ a : α, ENNReal.ofReal (g a).toReal ∂μ) =
@@ -351,7 +351,7 @@ theorem SimpleFunc.exists_upperSemicontinuous_le_lintegral_le (f : α →ₛ ℝ
     simp only [SimpleFunc.coe_add, ENNReal.coe_add, Pi.add_apply]
     rw [lintegral_add_left f₁.measurable.coe_nnreal_ennreal,
       lintegral_add_left g₁cont.measurable.coe_nnreal_ennreal]
-    convert add_le_add g₁int g₂int using 1
+    convert! add_le_add g₁int g₂int using 1
     conv_lhs => rw [← ENNReal.add_halves ε]
     abel
 
@@ -371,7 +371,7 @@ theorem exists_upperSemicontinuous_le_lintegral_le (f : α → ℝ≥0) (int_f :
     simp only [lt_iSup_iff] at this
     rcases this with ⟨fs, fs_le_f, int_fs⟩
     refine ⟨fs, fun x => by simpa only [ENNReal.coe_le_coe] using fs_le_f x, ?_⟩
-    convert int_fs.le
+    convert! int_fs.le
     rw [← SimpleFunc.lintegral_eq_lintegral]
     simp only [SimpleFunc.coe_map, Function.comp_apply]
   have int_fs_lt_top : (∫⁻ x, fs x ∂μ) ≠ ∞ := by
@@ -410,7 +410,7 @@ theorem exists_upperSemicontinuous_le_integral_le (f : α → ℝ≥0)
     exact Filter.Eventually.of_forall fun x => by simp [gf x]
   · rw [integral_eq_lintegral_of_nonneg_ae, integral_eq_lintegral_of_nonneg_ae]
     · rw [sub_le_iff_le_add]
-      convert ENNReal.toReal_mono _ gint
+      convert! ENNReal.toReal_mono _ gint
       · simp
       · rw [ENNReal.toReal_add Ig.ne ENNReal.coe_ne_top]; simp
       · simpa using Ig.ne
@@ -450,7 +450,7 @@ theorem exists_lt_lowerSemicontinuous_integral_lt [SigmaFinite μ] (f : α → 
   case int =>
     show Integrable (fun x => EReal.toReal (g x)) μ
     rw [integrable_congr ae_g]
-    convert gp_integrable.sub gm_integrable
+    convert! gp_integrable.sub gm_integrable
     simp
   case intlt =>
     show (∫ x : α, (g x).toReal ∂μ) < (∫ x : α, f x ∂μ) + ε
@@ -463,7 +463,7 @@ theorem exists_lt_lowerSemicontinuous_integral_lt [SigmaFinite μ] (f : α → 
           exact integral_sub gp_integrable gm_integrable
         _ < (∫ x : α, ↑(fp x) ∂μ) + ↑δ - ∫ x : α, ↑(gm x) ∂μ := by
           apply sub_lt_sub_right
-          convert gpint
+          convert! gpint
           simp only [EReal.toReal_coe_ennreal]
         _ ≤ (∫ x : α, ↑(fp x) ∂μ) + ↑δ - ((∫ x : α, ↑(fm x) ∂μ) - δ) := sub_le_sub_left gmint _
         _ = (∫ x : α, f x ∂μ) + 2 * δ := by
@@ -517,7 +517,7 @@ theorem exists_upperSemicontinuous_lt_integral_gt [SigmaFinite μ] (f : α → 
   · exact
       continuous_neg.comp_lowerSemicontinuous_antitone gcont fun x y hxy =>
         EReal.neg_le_neg_iff.2 hxy
-  · convert g_integrable.neg
+  · convert! g_integrable.neg
     simp
   · simpa [bot_lt_iff_ne_bot, lt_top_iff_ne_top] using g_lt_top
   · simp_rw [integral_neg, lt_neg_add_iff_add_lt] at gint
diff --git a/Mathlib/MeasureTheory/Integral/BoundedContinuousFunction.lean b/Mathlib/MeasureTheory/Integral/BoundedContinuousFunction.lean
index 64ea8fb026eedc..93eea6cfffa9d6 100644
--- a/Mathlib/MeasureTheory/Integral/BoundedContinuousFunction.lean
+++ b/Mathlib/MeasureTheory/Integral/BoundedContinuousFunction.lean
@@ -29,7 +29,7 @@ section NNRealValued
 
 lemma apply_le_nndist_zero {X : Type*} [TopologicalSpace X] (f : X →ᵇ ℝ≥0) (x : X) :
     f x ≤ nndist 0 f := by
-  convert nndist_coe_le_nndist x
+  convert! nndist_coe_le_nndist x
   simp only [coe_zero, Pi.zero_apply, NNReal.nndist_zero_eq_val]
 
 variable {X : Type*} [MeasurableSpace X] [TopologicalSpace X]
@@ -111,7 +111,7 @@ lemma norm_integral_le_mul_norm [IsFiniteMeasure μ] (f : X →ᵇ E) :
 
 lemma norm_integral_le_norm [IsProbabilityMeasure μ] (f : X →ᵇ E) :
     ‖∫ x, f x ∂μ‖ ≤ ‖f‖ := by
-  convert f.norm_integral_le_mul_norm μ
+  convert! f.norm_integral_le_mul_norm μ
   simp
 
 lemma isBounded_range_integral
diff --git a/Mathlib/MeasureTheory/Integral/CircleAverage.lean b/Mathlib/MeasureTheory/Integral/CircleAverage.lean
index e9b95d5b59e2ee..73b84211699661 100644
--- a/Mathlib/MeasureTheory/Integral/CircleAverage.lean
+++ b/Mathlib/MeasureTheory/Integral/CircleAverage.lean
@@ -364,7 +364,7 @@ theorem circleAverage_sum {ι : Type*} {s : Finset ι} {f : ι → ℂ → E}
 theorem circleAverage_fun_sum {ι : Type*} {s : Finset ι} {f : ι → ℂ → E}
     (h : ∀ i ∈ s, CircleIntegrable (f i) c R) :
     circleAverage (fun z ↦ ∑ i ∈ s, f i z) c R = ∑ i ∈ s, circleAverage (f i) c R := by
-  convert circleAverage_sum h
+  convert! circleAverage_sum h
   simp
 
 /-- Circle averages commute with subtraction. -/
diff --git a/Mathlib/MeasureTheory/Integral/CircleIntegral.lean b/Mathlib/MeasureTheory/Integral/CircleIntegral.lean
index 4fbb583658c89e..31aacc8c725e1c 100644
--- a/Mathlib/MeasureTheory/Integral/CircleIntegral.lean
+++ b/Mathlib/MeasureTheory/Integral/CircleIntegral.lean
@@ -214,7 +214,7 @@ protected theorem sum {ι : Type*} (s : Finset ι) {f : ι → ℂ → E}
 theorem fun_sum {c : ℂ} {R : ℝ} {ι : Type*} (s : Finset ι) {f : ι → ℂ → E}
     (h : ∀ i ∈ s, CircleIntegrable (f i) c R) :
     CircleIntegrable (fun z ↦ ∑ i ∈ s, f i z) c R := by
-  convert CircleIntegrable.sum s h
+  convert! CircleIntegrable.sum s h
   simp
 
 /-- `finsum`s of circle integrable functions are circle integrable. -/
@@ -571,8 +571,9 @@ theorem integral_sub_zpow_of_ne {n : ℤ} (hn : n ≠ -1) (c w : ℂ) (R : ℝ)
   have hd : ∀ z, z ≠ w ∨ -1 ≤ n →
       HasDerivAt (fun z => (z - w) ^ (n + 1) / (n + 1)) ((z - w) ^ n) z := by
     intro z hne
-    convert ((hasDerivAt_zpow (n + 1) _ (hne.imp _ _)).comp z
-      ((hasDerivAt_id z).sub_const w)).div_const _ using 1
+    convert!
+      ((hasDerivAt_zpow (n + 1) _ (hne.imp _ _)).comp z ((hasDerivAt_id z).sub_const w)).div_const
+        _ using 1
     · have hn' : (n + 1 : ℂ) ≠ 0 := by
         rwa [Ne, ← eq_neg_iff_add_eq_zero, ← Int.cast_one, ← Int.cast_neg, Int.cast_inj]
       simp [mul_div_cancel_left₀ _ hn']
@@ -660,7 +661,7 @@ theorem hasSum_two_pi_I_cauchyPowerSeries_integral {f : ℂ → E} {c : ℂ} {R
     simp only [smul_smul]
     refine HasSum.smul_const ?_ _
     have : ‖w / (circleMap c R θ - c)‖ < 1 := by simpa [abs_of_pos hR] using hwR.2
-    convert (hasSum_geometric_of_norm_lt_one this).mul_right _ using 1
+    convert! (hasSum_geometric_of_norm_lt_one this).mul_right _ using 1
     simp [← sub_sub, ← mul_inv, sub_mul, div_mul_cancel₀ _ (circleMap_ne_center hR.ne')]
 
 /-- For any circle integrable function `f`, the power series `cauchyPowerSeries f c R`, `R > 0`,
diff --git a/Mathlib/MeasureTheory/Integral/CurveIntegral/Poincare.lean b/Mathlib/MeasureTheory/Integral/CurveIntegral/Poincare.lean
index 405444b82178c8..62f2fc4d343778 100644
--- a/Mathlib/MeasureTheory/Integral/CurveIntegral/Poincare.lean
+++ b/Mathlib/MeasureTheory/Integral/CurveIntegral/Poincare.lean
@@ -309,7 +309,7 @@ theorem curveIntegral_segment_add_eq_of_hasFDerivWithinAt_symmetric (hs : Convex
     simp [φ, ha, hb, hc, hs.lineMap_mem]
   have := φ.curveIntegral_add_curveIntegral_eq_of_hasFDerivWithinAt (t := range φ) (ω := ω)
     (dω := dω) ?_ ?_ ?_ ?_ ?_
-  · convert this using 2
+  · convert! this using 2
     · dsimp [φ]
       rw [← Path.cast_segment (lineMap_apply_one a b) (lineMap_apply_one a c), curveIntegral_cast]
     · dsimp [φ]
diff --git a/Mathlib/MeasureTheory/Integral/DivergenceTheorem.lean b/Mathlib/MeasureTheory/Integral/DivergenceTheorem.lean
index 89d8197593ca08..6ed8ecd44c52e5 100644
--- a/Mathlib/MeasureTheory/Integral/DivergenceTheorem.lean
+++ b/Mathlib/MeasureTheory/Integral/DivergenceTheorem.lean
@@ -455,8 +455,9 @@ theorem integral_divergence_prod_Icc_of_hasFDerivAt_off_countable_of_le (f g : 
           ((∫ x in Icc a.1 b.1, g (x, b.2)) - ∫ x in Icc a.1 b.1, g (x, a.2)) := by
       have : ∀ (a b : ℝ¹) (f : ℝ¹ → E),
           ∫ x in Icc a b, f x = ∫ x in Icc (a 0) (b 0), f fun _ => x := fun a b f ↦ by
-        convert (((volume_preserving_funUnique (Fin 1) ℝ).symm _).setIntegral_preimage_emb
-          (MeasurableEquiv.measurableEmbedding _) f _).symm
+        convert!
+          (((volume_preserving_funUnique (Fin 1) ℝ).symm _).setIntegral_preimage_emb
+              (MeasurableEquiv.measurableEmbedding _) f _).symm
         exact ((OrderIso.funUnique (Fin 1) ℝ).symm.preimage_Icc a b).symm
       simp only [Fin.sum_univ_two, this]
       rfl
diff --git a/Mathlib/MeasureTheory/Integral/DominatedConvergence.lean b/Mathlib/MeasureTheory/Integral/DominatedConvergence.lean
index 2515789dde32af..cedc1691703db0 100644
--- a/Mathlib/MeasureTheory/Integral/DominatedConvergence.lean
+++ b/Mathlib/MeasureTheory/Integral/DominatedConvergence.lean
@@ -118,15 +118,16 @@ theorem integral_tsum {ι} [Countable ι] {f : ι → α → G} (hf : ∀ i, AES
     intro x hx
     rw [← ENNReal.tsum_coe_ne_top_iff_summable_coe]
     exact hx.ne
-  convert (MeasureTheory.hasSum_integral_of_dominated_convergence (fun i a => ‖f i a‖₊) hf _ hhh
-          ⟨_, _⟩ _).tsum_eq.symm
+  convert!
+    (MeasureTheory.hasSum_integral_of_dominated_convergence (fun i a => ‖f i a‖₊) hf _ hhh ⟨_, _⟩
+        _).tsum_eq.symm
   · intro n
     filter_upwards with x
     rfl
   · fun_prop
   · dsimp [HasFiniteIntegral]
     have : ∫⁻ a, ∑' n, ‖f n a‖ₑ ∂μ < ⊤ := by rwa [lintegral_tsum hf'', lt_top_iff_ne_top]
-    convert this using 1
+    convert! this using 1
     apply lintegral_congr_ae
     simp_rw [← coe_nnnorm, ← NNReal.coe_tsum, enorm_eq_nnnorm, NNReal.nnnorm_eq]
     filter_upwards [hhh] with a ha
diff --git a/Mathlib/MeasureTheory/Integral/FinMeasAdditive.lean b/Mathlib/MeasureTheory/Integral/FinMeasAdditive.lean
index e492295f3a9e7f..538cd8f0eefad9 100644
--- a/Mathlib/MeasureTheory/Integral/FinMeasAdditive.lean
+++ b/Mathlib/MeasureTheory/Integral/FinMeasAdditive.lean
@@ -121,7 +121,7 @@ theorem map_iUnion_fin_meas_set_eq_sum (T : Set α → β) (T_empty : T ∅ = 0)
   rw [←
     h_add (S a) (⋃ i ∈ s, S i) (hS_meas a) (measurableSet_biUnion _ fun i _ => hS_meas i)
       (hps a (Finset.mem_insert_self a s))]
-  · congr; convert Finset.iSup_insert a s S
+  · congr; convert! Finset.iSup_insert a s S
   · exact (measure_biUnion_lt_top s.finite_toSet fun i hi ↦
       (hps i <| Finset.mem_insert_of_mem hi).lt_top).ne
   · simp_rw [Set.disjoint_iUnion_right]
@@ -462,7 +462,7 @@ theorem setToSimpleFunc_nonneg' (T : Set α → G' →L[ℝ] G'')
   rw [mem_range] at hi
   obtain ⟨y, hy⟩ := Set.mem_range.mp hi
   rw [← hy]
-  convert hf y
+  convert! hf y
 
 theorem setToSimpleFunc_mono [IsOrderedAddMonoid G']
     {T : Set α → G' →L[ℝ] G''} (h_add : FinMeasAdditive μ T)
diff --git a/Mathlib/MeasureTheory/Integral/Gamma.lean b/Mathlib/MeasureTheory/Integral/Gamma.lean
index 811127816954fa..4126186d275ec7 100644
--- a/Mathlib/MeasureTheory/Integral/Gamma.lean
+++ b/Mathlib/MeasureTheory/Integral/Gamma.lean
@@ -62,13 +62,13 @@ theorem integral_rpow_mul_exp_neg_mul_rpow {p q b : ℝ} (hp : 0 < p) (hq : -1 <
 
 theorem integral_exp_neg_rpow {p : ℝ} (hp : 0 < p) :
     ∫ x in Ioi (0 : ℝ), exp (-x ^ p) = Gamma (1 / p + 1) := by
-  convert (integral_rpow_mul_exp_neg_rpow hp neg_one_lt_zero) using 1
+  convert! (integral_rpow_mul_exp_neg_rpow hp neg_one_lt_zero) using 1
   · simp_rw [rpow_zero, one_mul]
   · rw [zero_add, Gamma_add_one (one_div_ne_zero (ne_of_gt hp))]
 
 theorem integral_exp_neg_mul_rpow {p b : ℝ} (hp : 0 < p) (hb : 0 < b) :
     ∫ x in Ioi (0 : ℝ), exp (-b * x ^ p) = b ^ (-1 / p) * Gamma (1 / p + 1) := by
-  convert (integral_rpow_mul_exp_neg_mul_rpow hp neg_one_lt_zero hb) using 1
+  convert! (integral_rpow_mul_exp_neg_mul_rpow hp neg_one_lt_zero hb) using 1
   · simp_rw [rpow_zero, one_mul]
   · rw [zero_add, Gamma_add_one (one_div_ne_zero (ne_of_gt hp)), mul_assoc]
 
@@ -130,14 +130,14 @@ theorem Complex.integral_rpow_mul_exp_neg_mul_rpow {p q b : ℝ} (hp : 1 ≤ p)
 
 theorem Complex.integral_exp_neg_rpow {p : ℝ} (hp : 1 ≤ p) :
     ∫ x : ℂ, rexp (-‖x‖ ^ p) = π * Real.Gamma (2 / p + 1) := by
-  convert (integral_rpow_mul_exp_neg_rpow hp (by linarith : (-2 : ℝ) < 0)) using 1
+  convert! (integral_rpow_mul_exp_neg_rpow hp (by linarith : (-2 : ℝ) < 0)) using 1
   · simp_rw [rpow_zero, one_mul]
   · rw [zero_add, Real.Gamma_add_one (div_ne_zero two_ne_zero (by linarith))]
     ring
 
 theorem Complex.integral_exp_neg_mul_rpow {p b : ℝ} (hp : 1 ≤ p) (hb : 0 < b) :
     ∫ x : ℂ, rexp (-b * ‖x‖ ^ p) = π * b ^ (-2 / p) * Real.Gamma (2 / p + 1) := by
-  convert (integral_rpow_mul_exp_neg_mul_rpow hp (by linarith : (-2 : ℝ) < 0)) hb using 1
+  convert! (integral_rpow_mul_exp_neg_mul_rpow hp (by linarith : (-2 : ℝ) < 0)) hb using 1
   · simp_rw [rpow_zero, one_mul]
   · rw [zero_add, Real.Gamma_add_one (div_ne_zero two_ne_zero (by linarith))]
     ring
diff --git a/Mathlib/MeasureTheory/Integral/IntegrableOn.lean b/Mathlib/MeasureTheory/Integral/IntegrableOn.lean
index 65f7220c975804..36d51fedf392d0 100644
--- a/Mathlib/MeasureTheory/Integral/IntegrableOn.lean
+++ b/Mathlib/MeasureTheory/Integral/IntegrableOn.lean
@@ -560,7 +560,7 @@ protected theorem IntegrableAtFilter.neg {f : α → E} (hf : IntegrableAtFilter
 protected theorem integrableAtFilter_neg_iff {f : α → E} :
     IntegrableAtFilter (-f) l μ ↔ IntegrableAtFilter f l μ := by
   refine ⟨fun h ↦ ?_, fun h ↦ h.neg⟩
-  convert h.neg; simp
+  convert! h.neg; simp
 
 protected theorem IntegrableAtFilter.sub {f g : α → E}
     (hf : IntegrableAtFilter f l μ) (hg : IntegrableAtFilter g l μ) :
@@ -579,7 +579,7 @@ private theorem integrableAtFilter_smul_iff' {𝕜 : Type*} [NormedField 𝕜] [
     {f : α → E} {c : 𝕜} (hc : c ≠ 0) :
     IntegrableAtFilter (c • f) l μ ↔ IntegrableAtFilter f l μ := by
   refine ⟨fun hf ↦ ?_, fun h ↦ h.smul c⟩
-  convert hf.smul c⁻¹
+  convert! hf.smul c⁻¹
   simp [← smul_assoc, inv_mul_cancel₀ hc]
 
 theorem integrableAtFilter_smul_iff {𝕜 : Type*} [NormedField 𝕜] [NormedSpace 𝕜 E]
diff --git a/Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean b/Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean
index 1077560b9d9c1a..b62c43f212d74d 100644
--- a/Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean
+++ b/Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean
@@ -484,7 +484,7 @@ theorem AECover.integral_tendsto_of_countably_generated [l.IsCountablyGenerated]
     (hφ : AECover μ l φ) {f : α → E} (hfi : Integrable f μ) :
     Tendsto (fun i => ∫ x in φ i, f x ∂μ) l (𝓝 <| ∫ x, f x ∂μ) :=
   suffices h : Tendsto (fun i => ∫ x : α, (φ i).indicator f x ∂μ) l (𝓝 (∫ x : α, f x ∂μ)) from by
-    convert h using 2; rw [integral_indicator (hφ.measurableSet _)]
+    convert! h using 2; rw [integral_indicator (hφ.measurableSet _)]
   tendsto_integral_filter_of_dominated_convergence (fun x => ‖f x‖)
     (Eventually.of_forall fun i => hfi.aestronglyMeasurable.indicator <| hφ.measurableSet i)
     (Eventually.of_forall fun _ => ae_of_all _ fun _ => norm_indicator_le_norm_self _ _) hfi.norm
@@ -1036,7 +1036,7 @@ lemma _root_.HasCompactSupport.enorm_le_lintegral_Ici_deriv
   have : ‖f' x‖ₑ ≤ ∫⁻ y in Iic x, ‖deriv f' y‖ₑ := by
     rw [← HasCompactSupport.integral_Iic_deriv_eq hf' h'f' x]
     exact enorm_integral_le_lintegral_enorm _
-  convert this with y
+  convert! this with y
   · simp [f', I, Completion.enorm_coe]
   · rw [fderiv_comp_deriv _ I.differentiableAt (hf.differentiable one_ne_zero _)]
     simp only [ContinuousLinearMap.fderiv]
@@ -1156,7 +1156,7 @@ theorem integral_comp_rpow_Ioi (g : ℝ → E) {p : ℝ} (hp : p ≠ 0) :
 
 theorem integral_comp_rpow_Ioi_of_pos {g : ℝ → E} {p : ℝ} (hp : 0 < p) :
     (∫ x in Ioi 0, (p * x ^ (p - 1)) • g (x ^ p)) = ∫ y in Ioi 0, g y := by
-  convert integral_comp_rpow_Ioi g hp.ne'
+  convert! integral_comp_rpow_Ioi g hp.ne'
   rw [abs_of_nonneg hp.le]
 
 theorem integral_comp_mul_left_Ioi (g : ℝ → E) (a : ℝ) {b : ℝ} (hb : 0 < b) :
@@ -1219,7 +1219,7 @@ theorem integrableOn_Ioi_comp_mul_left_iff (f : ℝ → E) (c : ℝ) {a : ℝ} (
     IntegrableOn (fun x => f (a * x)) (Ioi c) ↔ IntegrableOn f (Ioi <| a * c) := by
   rw [← integrable_indicator_iff (measurableSet_Ioi : MeasurableSet <| Ioi c)]
   rw [← integrable_indicator_iff (measurableSet_Ioi : MeasurableSet <| Ioi <| a * c)]
-  convert integrable_comp_mul_left_iff ((Ioi (a * c)).indicator f) ha.ne' using 2
+  convert! integrable_comp_mul_left_iff ((Ioi (a * c)).indicator f) ha.ne' using 2
   ext1 x
   rw [← indicator_comp_right, preimage_const_mul_Ioi₀ _ ha, mul_comm a c,
     mul_div_cancel_right₀ _ ha.ne', Function.comp_def]
diff --git a/Mathlib/MeasureTheory/Integral/IntervalIntegral/AbsolutelyContinuousFun.lean b/Mathlib/MeasureTheory/Integral/IntervalIntegral/AbsolutelyContinuousFun.lean
index b07e47e869a726..c3ba8e3b8bd16a 100644
--- a/Mathlib/MeasureTheory/Integral/IntervalIntegral/AbsolutelyContinuousFun.lean
+++ b/Mathlib/MeasureTheory/Integral/IntervalIntegral/AbsolutelyContinuousFun.lean
@@ -87,9 +87,9 @@ lemma exists_dist_slope_lt_pairwiseDisjoint_hasSum {f f' : ℝ → F} {d b η :
     filter_upwards [hf, hu₄] with x hx₁ hx₂
     grind
   have vol_sum : volume (⋃ z : u, Icc z.val.1 z.val.2) = ENNReal.ofReal (b - d) := by
-    convert Real.volume_Ioo ▸
-      measure_eq_measure_of_null_diff (by simp only [iUnion_subset_iff]; grind) hu₄
-      using 2
+    convert!
+      Real.volume_Ioo ▸
+        measure_eq_measure_of_null_diff (by simp only [iUnion_subset_iff]; grind) hu₄ using 2
     simp
   rw [measure_iUnion this (by simp)] at vol_sum
   simp_rw [Real.volume_Icc] at vol_sum
@@ -142,11 +142,11 @@ lemma AbsolutelyContinuousOnInterval.dist_le_of_pairwiseDisjoint_hasSum {f : ℝ
   replace hu₃ : Tendsto T atTop (totalLengthFilter ⊓ 𝓟 (disjWithin d b)) := by
     refine tendsto_inf.mpr ⟨?_, hT.tendsto.mono_left (by simp)⟩
     simp only [totalLengthFilter, tendsto_comap_iff]
-    convert hu₃.const_sub (b - d) with s
+    convert! hu₃.const_sub (b - d) with s
     · simp only [comp_apply]
       rw [Finset.sum_congr rfl (g := fun i ↦ ((T s).2 i).2 - ((T s).2 i).1)
             (fun i hi ↦ by rw [dist_comm, Real.dist_eq, abs_of_nonneg (by grind)])]
-      convert (u_coe s).sum_intervalGapsWithin_eq_sub_sub_sum rfl id
+      convert! (u_coe s).sum_intervalGapsWithin_eq_sub_sub_sum rfl id
       exact u_coe_sum s fun x y ↦ y - x
     · abel
   rw [HasSum] at hu₄
@@ -234,7 +234,7 @@ theorem AbsolutelyContinuousOnInterval.integral_deriv_eq_sub {f : ℝ → ℝ} {
   have g_ae_deriv_zero : ∀ᵐ x, x ∈ uIcc a b → HasDerivAt g 0 x := by
     filter_upwards [hf.ae_differentiableAt, hf.intervalIntegrable_deriv.ae_hasDerivAt_integral]
       with x hx₁ hx₂ hx₃
-    convert (hx₁ hx₃).hasDerivAt.sub (hx₂ hx₃ a (by simp))
+    convert! (hx₁ hx₃).hasDerivAt.sub (hx₂ hx₃ a (by simp))
     abel
   obtain ⟨C, hC⟩ := g_ac.const_of_ae_hasDerivAt_zero g_ae_deriv_zero
   have : f a = g a := by simp [g]
diff --git a/Mathlib/MeasureTheory/Integral/IntervalIntegral/Basic.lean b/Mathlib/MeasureTheory/Integral/IntervalIntegral/Basic.lean
index 0ad3a9f100f3c7..389f6c57e35e44 100644
--- a/Mathlib/MeasureTheory/Integral/IntervalIntegral/Basic.lean
+++ b/Mathlib/MeasureTheory/Integral/IntervalIntegral/Basic.lean
@@ -395,7 +395,7 @@ theorem comp_mul_left (hf : IntervalIntegrable f volume a b) {c : ℝ}
   rw [← Real.smul_map_volume_mul_right (inv_ne_zero hc), IntegrableOn, Measure.restrict_smul,
     integrable_smul_measure (by simpa : ENNReal.ofReal |c⁻¹| ≠ 0) ENNReal.ofReal_ne_top,
     ← IntegrableOn, MeasurableEmbedding.integrableOn_map_iff A]
-  convert hf using 1
+  convert! hf using 1
   · ext; simp only [comp_apply]; congr 1; field
   · rw [preimage_mul_const_uIcc (inv_ne_zero hc)]; field_simp
 
@@ -429,7 +429,7 @@ theorem comp_add_right (hf : IntervalIntegrable f volume a b) (c : ℝ)
   have A : MeasurableEmbedding fun x => x + c :=
     (Homeomorph.addRight c).isClosedEmbedding.measurableEmbedding
   rw [← map_add_right_eq_self volume c] at hf
-  convert (MeasurableEmbedding.integrableOn_map_iff A).mp hf using 1
+  convert! (MeasurableEmbedding.integrableOn_map_iff A).mp hf using 1
   rw [preimage_add_const_uIcc]
 
 theorem comp_add_right_iff {c : ℝ} (h : ‖f (min a b + c)‖ₑ ≠ ⊤ := by finiteness) :
@@ -752,7 +752,7 @@ theorem norm_integral_le_of_norm_le {g : ℝ → ℝ} (hab : a ≤ b)
 theorem norm_integral_le_of_norm_le_const_ae {a b C : ℝ} {f : ℝ → E}
     (h : ∀ᵐ x, x ∈ Ι a b → ‖f x‖ ≤ C) : ‖∫ x in a..b, f x‖ ≤ C * |b - a| := by
   rw [norm_integral_eq_norm_integral_uIoc]
-  convert norm_setIntegral_le_of_norm_le_const_ae' _ h using 1
+  convert! norm_setIntegral_le_of_norm_le_const_ae' _ h using 1
   · rw [uIoc, Real.volume_real_Ioc_of_le inf_le_sup, max_sub_min_eq_abs]
   · simp [uIoc, Real.volume_Ioc]
 
@@ -1185,13 +1185,13 @@ theorem integral_Ici_sub_Ici' [NoAtoms μ] (hf : IntegrableOn f (Ici a) μ)
 theorem integral_Iic_add_Ioi (h_left : IntegrableOn f (Iic b) μ)
     (h_right : IntegrableOn f (Ioi b) μ) :
     (∫ x in Iic b, f x ∂μ) + (∫ x in Ioi b, f x ∂μ) = ∫ (x : ℝ), f x ∂μ := by
-  convert (setIntegral_union (Iic_disjoint_Ioi <| Eq.le rfl) measurableSet_Ioi h_left h_right).symm
+  convert! (setIntegral_union (Iic_disjoint_Ioi <| Eq.le rfl) measurableSet_Ioi h_left h_right).symm
   rw [Iic_union_Ioi, Measure.restrict_univ]
 
 theorem integral_Iio_add_Ici (h_left : IntegrableOn f (Iio b) μ)
     (h_right : IntegrableOn f (Ici b) μ) :
     (∫ x in Iio b, f x ∂μ) + (∫ x in Ici b, f x ∂μ) = ∫ (x : ℝ), f x ∂μ := by
-  convert (setIntegral_union (Iio_disjoint_Ici <| Eq.le rfl) measurableSet_Ici h_left h_right).symm
+  convert! (setIntegral_union (Iio_disjoint_Ici <| Eq.le rfl) measurableSet_Ici h_left h_right).symm
   rw [Iio_union_Ici, Measure.restrict_univ]
 
 /-- If `μ` is a finite measure then `∫ x in a..b, c ∂μ = (μ (Iic b) - μ (Iic a)) • c`. -/
diff --git a/Mathlib/MeasureTheory/Integral/IntervalIntegral/DerivIntegrable.lean b/Mathlib/MeasureTheory/Integral/IntervalIntegral/DerivIntegrable.lean
index feec94bf533f67..cece367a6eb62f 100644
--- a/Mathlib/MeasureTheory/Integral/IntervalIntegral/DerivIntegrable.lean
+++ b/Mathlib/MeasureTheory/Integral/IntervalIntegral/DerivIntegrable.lean
@@ -65,7 +65,7 @@ lemma MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_le
     rw [hfg (by grind [Icc_diff_both])]
     exact hx₁.hasDerivAt.tendsto_slope.comp <|
       tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within _
-      (by convert tendsto_const_nhds.add (tendsto_inv_atTop_nhds_zero_nat (𝕜 := ℝ)); simp)
+      (by convert! tendsto_const_nhds.add (tendsto_inv_atTop_nhds_zero_nat (𝕜 := ℝ)); simp)
       (by simp [eventually_ne_atTop 0])
   · calc
       _ = liminf (fun (n : ℕ) ↦ ENNReal.ofReal (∫ (x : ℝ) in Icc a b, (G (n : ℝ)⁻¹) x)) atTop := by
@@ -78,8 +78,8 @@ lemma MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_le
         refine Filter.liminf_le_of_frequently_le'
           (Filter.Frequently.of_forall fun n ↦ ENNReal.ofReal_le_ofReal ?_)
         rw [integral_Icc_eq_integral_Ioc, ← intervalIntegral.integral_of_le hab]
-        convert hg.monotoneOn (Icc a (b + (n : ℝ)⁻¹)) |>.intervalIntegral_slope_le hab (by simp)
-          using 2
+        convert!
+          hg.monotoneOn (Icc a (b + (n : ℝ)⁻¹)) |>.intervalIntegral_slope_le hab (by simp) using 2
         simp [g]
       _ = ENNReal.ofReal (f b - f a) := by grind
 
@@ -136,7 +136,7 @@ theorem MonotoneOn.intervalIntegral_deriv_mem_uIcc {f : ℝ → ℝ} {a b : ℝ}
         ENNReal.ofReal_le_ofReal_iff (by linarith),
         integral_Icc_eq_integral_Ioc,
         ← intervalIntegral.integral_of_le hab] at ebound
-    convert ebound using 1
+    convert! ebound using 1
     refine intervalIntegral.integral_congr_ae ?_
     rw [uIoc_of_le hab]
     filter_upwards [h₂] with x _ _
diff --git a/Mathlib/MeasureTheory/Integral/IntervalIntegral/DistLEIntegral.lean b/Mathlib/MeasureTheory/Integral/IntervalIntegral/DistLEIntegral.lean
index 69c3d8daa36936..734ba83cf45c3e 100644
--- a/Mathlib/MeasureTheory/Integral/IntervalIntegral/DistLEIntegral.lean
+++ b/Mathlib/MeasureTheory/Integral/IntervalIntegral/DistLEIntegral.lean
@@ -136,7 +136,7 @@ lemma norm_sub_le_mul_volume_of_norm_lineDeriv_le
     have := (hfd t ht).hasLineDerivAt.scomp_of_eq (𝕜 := ℝ) t ((hasDerivAt_id t).sub_const t)
     simpa [g, lineMap_apply_module', Function.comp_def, sub_smul, add_comm _ a] using this
   suffices ‖g 1 - g 0‖ ≤ C * volume.real {t ∈ Ioo 0 1 | deriv g t ≠ 0} by
-    convert this using 1
+    convert! this using 1
     · simp [g]
     · congr 2 with t
       simp +contextual [(hdg _ _).deriv]
diff --git a/Mathlib/MeasureTheory/Integral/IntervalIntegral/FundThmCalculus.lean b/Mathlib/MeasureTheory/Integral/IntervalIntegral/FundThmCalculus.lean
index 8ff8a8dff342d0..66de604c14ee97 100644
--- a/Mathlib/MeasureTheory/Integral/IntervalIntegral/FundThmCalculus.lean
+++ b/Mathlib/MeasureTheory/Integral/IntervalIntegral/FundThmCalculus.lean
@@ -1057,7 +1057,7 @@ theorem sub_le_integral_of_hasDeriv_right_of_le_Ico (hab : a ≤ b)
   calc
     g b - g a ≤ ∫ y in a..b, (G' y).toReal := main (right_mem_Icc.2 hab)
     _ ≤ (∫ y in a..b, φ y) + ε := by
-      convert hG'.le <;>
+      convert! hG'.le <;>
         · rw [intervalIntegral.integral_of_le hab]
           simp only [integral_Icc_eq_integral_Ioc', Real.volume_singleton]
 
@@ -1097,8 +1097,9 @@ theorem integral_le_sub_of_hasDeriv_right_of_le (hab : a ≤ b) (hcont : Continu
     (hderiv : ∀ x ∈ Ioo a b, HasDerivWithinAt g (g' x) (Ioi x) x) (φint : IntegrableOn φ (Icc a b))
     (hφg : ∀ x ∈ Ioo a b, φ x ≤ g' x) : (∫ y in a..b, φ y) ≤ g b - g a := by
   rw [← neg_le_neg_iff]
-  convert sub_le_integral_of_hasDeriv_right_of_le hab hcont.neg (fun x hx => (hderiv x hx).neg)
-    φint.neg fun x hx => neg_le_neg (hφg x hx) using 1
+  convert!
+    sub_le_integral_of_hasDeriv_right_of_le hab hcont.neg (fun x hx => (hderiv x hx).neg) φint.neg
+      fun x hx => neg_le_neg (hφg x hx) using 1
   · abel
   · simp only [← integral_neg]; rfl
 
@@ -1210,7 +1211,7 @@ lemma integral_unitInterval_deriv_eq_sub [RCLike 𝕜] [NormedSpace 𝕜 E] [IsS
   have hderiv' (t) (ht : t ∈ Set.uIcc (0 : ℝ) 1) : HasDerivAt (f ∘ γ) (z₁ • (f' ∘ γ) t) t := by
     refine (hderiv t <| (Set.uIcc_of_le (α := ℝ) zero_le_one).symm ▸ ht).scomp t <| .const_add _ ?_
     simp [hasDerivAt_iff_isLittleO, sub_smul]
-  convert (integral_eq_sub_of_hasDerivAt hderiv' hint) using 1
+  convert! (integral_eq_sub_of_hasDerivAt hderiv' hint) using 1
   · simp_rw [← integral_smul, Function.comp_apply, γ]
   · simp only [γ, Function.comp_apply, one_smul, zero_smul, add_zero]
 
@@ -1248,7 +1249,7 @@ theorem integrableOn_deriv_right_of_nonneg (hcont : ContinuousOn g (Icc a b))
     rw [← integral_Ioc_eq_integral_Ioo, ← intervalIntegral.integral_of_le hab.le]
     refine integral_le_sub_of_hasDeriv_right_of_le hab.le hcont hderiv ?_ fun x hx => ?_
     · rwa [integrableOn_Icc_iff_integrableOn_Ioo]
-    · convert NNReal.coe_le_coe.2 (fle x)
+    · convert! NNReal.coe_le_coe.2 (fle x)
       simp only [Real.norm_of_nonneg (g'pos x hx), coe_nnnorm]
   exact lt_irrefl _ (hf.trans_le (ENNReal.ofReal_le_ofReal B))
 
diff --git a/Mathlib/MeasureTheory/Integral/IntervalIntegral/Periodic.lean b/Mathlib/MeasureTheory/Integral/IntervalIntegral/Periodic.lean
index 31a388bca768f7..0d1bfe992dd6fa 100644
--- a/Mathlib/MeasureTheory/Integral/IntervalIntegral/Periodic.lean
+++ b/Mathlib/MeasureTheory/Integral/IntervalIntegral/Periodic.lean
@@ -172,7 +172,7 @@ protected theorem lintegral_preimage (t : ℝ) (f : AddCircle T → ℝ≥0∞)
   simp only [measurableEquivIoc, equivIoc, QuotientAddGroup.equivIocMod, MeasurableEquiv.symm_mk,
     MeasurableEquiv.coe_mk, Equiv.coe_fn_symm_mk] at this
   rw [← (AddCircle.measurePreserving_mk T t).map_eq]
-  convert this.symm using 1
+  convert! this.symm using 1
   · rw [← map_comap_subtype_coe m _]
     exact MeasurableEmbedding.lintegral_map (MeasurableEmbedding.subtype_coe m) _
   · congr 1
@@ -307,7 +307,7 @@ theorem intervalIntegrable {t : ℝ} (h₁f : Function.Periodic f T)
   apply IntervalIntegrable.trans_iterate
   -- Show integrability over a shifted period
   intro k hk
-  convert (IntervalIntegrable.comp_sub_right h₂f ((k - n₁) * T) (by aesop)) using 1
+  convert! (IntervalIntegrable.comp_sub_right h₂f ((k - n₁) * T) (by aesop)) using 1
   · funext x
     simpa using (h₁f.sub_int_mul_eq (k - n₁)).symm
   · simp [a, Nat.cast_add]
diff --git a/Mathlib/MeasureTheory/Integral/IntervalIntegral/TrapezoidalRule.lean b/Mathlib/MeasureTheory/Integral/IntervalIntegral/TrapezoidalRule.lean
index 7b9f1657ed9c6c..243d55e8c4436f 100644
--- a/Mathlib/MeasureTheory/Integral/IntervalIntegral/TrapezoidalRule.lean
+++ b/Mathlib/MeasureTheory/Integral/IntervalIntegral/TrapezoidalRule.lean
@@ -158,8 +158,9 @@ private lemma trapezoidal_error_le_of_lt' {f : ℝ → ℝ} {ζ : ℝ} {a b : 
       ∀ t ∈ Icc a b, |φ t| ≤ c / (n + 1) * (t - a) ^ (n + 1) := by
     intro t ht
     have hB (x) : HasDerivAt (fun y ↦ c / (n + 1) * (y - a) ^ (n + 1)) (c * (x - a) ^ n) x := by
-      convert (hasDerivAt_const x (c / (n + 1))).mul
-        (((hasDerivAt_id x).sub (hasDerivAt_const x a)).pow (n + 1)) using 1
+      convert!
+        (hasDerivAt_const x (c / (n + 1))).mul
+          (((hasDerivAt_id x).sub (hasDerivAt_const x a)).pow (n + 1)) using 1
       simp [sub_eq_add_neg, field]
     simpa [Real.norm_eq_abs, h0] using image_norm_le_of_norm_deriv_right_le_deriv_boundary
       (fun x hx ↦ (h x hx).continuousWithinAt)
diff --git a/Mathlib/MeasureTheory/Integral/Layercake.lean b/Mathlib/MeasureTheory/Integral/Layercake.lean
index ba4b7c4ec100fb..1de6ce83f26a5c 100644
--- a/Mathlib/MeasureTheory/Integral/Layercake.lean
+++ b/Mathlib/MeasureTheory/Integral/Layercake.lean
@@ -310,7 +310,7 @@ theorem lintegral_comp_eq_lintegral_meas_le_mul_of_measurable (μ : Measure α)
         intro n
         have I : ν {a | f a ≤ M} = 0 := by
           rw [Measure.restrict_apply (measurableSet_le f_mble measurable_const)]
-          convert measure_empty (μ := μ)
+          convert! measure_empty (μ := μ)
           rw [← disjoint_iff_inter_eq_empty]
           exact disjoint_left.mpr (fun a ha ↦ by simpa using ha)
         have J : μ {a | u n < f a} < ∞ := by
@@ -523,7 +523,7 @@ theorem Integrable.integral_eq_integral_meas_lt
   have rhs_finite : ∫⁻ (t : ℝ) in Set.Ioi 0, μ {a | t < f a} < ∞ := by simp only [← key, lhs_finite]
   have rhs_integrand_finite : ∀ (t : ℝ), t > 0 → μ {a | t < f a} < ∞ :=
     fun t ht ↦ measure_gt_lt_top f_intble ht
-  convert (ENNReal.toReal_eq_toReal_iff' lhs_finite.ne rhs_finite.ne).mpr key
+  convert! (ENNReal.toReal_eq_toReal_iff' lhs_finite.ne rhs_finite.ne).mpr key
   · exact integral_eq_lintegral_of_nonneg_ae f_nn f_intble.aestronglyMeasurable
   · have aux := @integral_eq_lintegral_of_nonneg_ae _ _ ((volume : Measure ℝ).restrict (Set.Ioi 0))
       (fun t ↦ μ.real {a : α | t < f a}) ?_ ?_
diff --git a/Mathlib/MeasureTheory/Integral/Lebesgue/Add.lean b/Mathlib/MeasureTheory/Integral/Lebesgue/Add.lean
index e59a967062f5d4..743d2be2664ca1 100644
--- a/Mathlib/MeasureTheory/Integral/Lebesgue/Add.lean
+++ b/Mathlib/MeasureTheory/Integral/Lebesgue/Add.lean
@@ -189,7 +189,7 @@ theorem lintegral_iSup_directed [Countable β] {f : β → α → ℝ≥0∞} (h
           apply_rules [hz₁, hz₂]
         · simp only [aeSeq, hx, if_false]
           exact le_rfl
-  convert lintegral_iSup_directed_of_measurable (aeSeq.measurable hf p) h_ae_seq_directed using 1
+  convert! lintegral_iSup_directed_of_measurable (aeSeq.measurable hf p) h_ae_seq_directed using 1
   · simp_rw [← iSup_apply]
     rw [lintegral_congr_ae (aeSeq.iSup hf hp).symm]
   · congr 1
diff --git a/Mathlib/MeasureTheory/Integral/Lebesgue/Basic.lean b/Mathlib/MeasureTheory/Integral/Lebesgue/Basic.lean
index 2174ec185b4d0c..d7c476b5600c03 100644
--- a/Mathlib/MeasureTheory/Integral/Lebesgue/Basic.lean
+++ b/Mathlib/MeasureTheory/Integral/Lebesgue/Basic.lean
@@ -201,7 +201,7 @@ theorem iSup_lintegral_le {ι : Sort*} (f : ι → α → ℝ≥0∞) :
 
 theorem iSup₂_lintegral_le {ι : Sort*} {ι' : ι → Sort*} (f : ∀ i, ι' i → α → ℝ≥0∞) :
     ⨆ (i) (j), ∫⁻ a, f i j a ∂μ ≤ ∫⁻ a, ⨆ (i) (j), f i j a ∂μ := by
-  convert (monotone_lintegral μ).le_map_iSup₂ f with a
+  convert! (monotone_lintegral μ).le_map_iSup₂ f with a
   simp only [iSup_apply]
 
 theorem le_iInf_lintegral {ι : Sort*} (f : ι → α → ℝ≥0∞) :
@@ -211,7 +211,7 @@ theorem le_iInf_lintegral {ι : Sort*} (f : ι → α → ℝ≥0∞) :
 
 theorem le_iInf₂_lintegral {ι : Sort*} {ι' : ι → Sort*} (f : ∀ i, ι' i → α → ℝ≥0∞) :
     ∫⁻ a, ⨅ (i) (h : ι' i), f i h a ∂μ ≤ ⨅ (i) (h : ι' i), ∫⁻ a, f i h a ∂μ := by
-  convert (monotone_lintegral μ).map_iInf₂_le f with a
+  convert! (monotone_lintegral μ).map_iInf₂_le f with a
   simp only [iInf_apply]
 
 theorem lintegral_mono_ae {f g : α → ℝ≥0∞} (h : ∀ᵐ a ∂μ, f a ≤ g a) :
@@ -453,7 +453,7 @@ theorem hasSum_lintegral_measure {ι} {_ : MeasurableSpace α} (f : α → ℝ
 theorem lintegral_of_isEmpty {α} [MeasurableSpace α] [IsEmpty α] (μ : Measure α) (f : α → ℝ≥0∞) :
     ∫⁻ x, f x ∂μ = 0 := by
   have : Subsingleton (Measure α) := inferInstance
-  convert lintegral_zero_measure f
+  convert! lintegral_zero_measure f
 
 theorem setLIntegral_empty (f : α → ℝ≥0∞) : ∫⁻ x in ∅, f x ∂μ = 0 := by
   rw [Measure.restrict_empty, lintegral_zero_measure]
@@ -463,7 +463,7 @@ theorem setLIntegral_univ (f : α → ℝ≥0∞) : ∫⁻ x in univ, f x ∂μ
 
 theorem setLIntegral_measure_zero (s : Set α) (f : α → ℝ≥0∞) (hs' : μ s = 0) :
     ∫⁻ x in s, f x ∂μ = 0 := by
-  convert lintegral_zero_measure _
+  convert! lintegral_zero_measure _
   exact Measure.restrict_eq_zero.2 hs'
 
 -- TODO: Need a better way of rewriting inside of an integral
diff --git a/Mathlib/MeasureTheory/Integral/Lebesgue/Countable.lean b/Mathlib/MeasureTheory/Integral/Lebesgue/Countable.lean
index 5a8927334b5a16..c2f2922c833a09 100644
--- a/Mathlib/MeasureTheory/Integral/Lebesgue/Countable.lean
+++ b/Mathlib/MeasureTheory/Integral/Lebesgue/Countable.lean
@@ -110,7 +110,7 @@ theorem _root_.NNReal.count_const_le_le_of_tsum_le [MeasurableSingletonClass α]
   apply
     ENNReal.count_const_le_le_of_tsum_le (measurable_coe_nnreal_ennreal.comp a_mble) _
       (mod_cast ε_ne_zero) (@ENNReal.coe_ne_top ε)
-  convert ENNReal.coe_le_coe.mpr tsum_le_c
+  convert! ENNReal.coe_le_coe.mpr tsum_le_c
   simp_rw [Function.comp_apply]
   rw [ENNReal.tsum_coe_eq a_summable.hasSum]
 
@@ -344,7 +344,7 @@ theorem exists_lt_lintegral_simpleFunc_of_lt_lintegral {m : MeasurableSpace α}
   simp_rw [lintegral_eq_nnreal, lt_iSup_iff] at hL
   rcases hL with ⟨g₀, hg₀, g₀L⟩
   have h'L : L < ∫⁻ x, g₀ x ∂μ := by
-    convert g₀L
+    convert! g₀L
     rw [← SimpleFunc.lintegral_eq_lintegral, SimpleFunc.coe_map]
     simp only [Function.comp_apply]
   rcases SimpleFunc.exists_lt_lintegral_simpleFunc_of_lt_lintegral h'L with ⟨g, hg, gL, gtop⟩
diff --git a/Mathlib/MeasureTheory/Integral/Lebesgue/Map.lean b/Mathlib/MeasureTheory/Integral/Lebesgue/Map.lean
index 71390c0290ab17..251ec24fe6e155 100644
--- a/Mathlib/MeasureTheory/Integral/Lebesgue/Map.lean
+++ b/Mathlib/MeasureTheory/Integral/Lebesgue/Map.lean
@@ -30,7 +30,7 @@ theorem lintegral_map {f : β → ℝ≥0∞} {g : α → β} (hf : Measurable f
   simp only [← Function.comp_apply (f := f) (g := g)]
   rw [lintegral_eq_iSup_eapprox_lintegral (hf.comp hg)]
   congr with n : 1
-  convert SimpleFunc.lintegral_map _ hg
+  convert! SimpleFunc.lintegral_map _ hg
   ext1 x; simp only [eapprox_comp hf hg, coe_comp]
 
 theorem lintegral_map' {f : β → ℝ≥0∞} {g : α → β}
diff --git a/Mathlib/MeasureTheory/Integral/PeakFunction.lean b/Mathlib/MeasureTheory/Integral/PeakFunction.lean
index 304af2d3216ccf..8a0dd8259cb67d 100644
--- a/Mathlib/MeasureTheory/Integral/PeakFunction.lean
+++ b/Mathlib/MeasureTheory/Integral/PeakFunction.lean
@@ -84,7 +84,7 @@ theorem integrableOn_peak_smul_of_integrableOn_of_tendsto
       filter_upwards [self_mem_ae_restrict (hs.inter u_open.measurableSet)] with x hx
       rw [inter_comm] at hx
       exact (norm_lt_of_mem_ball (hu x hx)).le
-  convert A.union B
+  convert! A.union B
   simp only [diff_union_inter]
 
 /-- If a sequence of peak functions `φᵢ` converges uniformly to zero away from a point `x₀` and its
@@ -335,7 +335,7 @@ theorem tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_measure_n
     exact tendsto_setIntegral_peak_smul_of_integrableOn_of_tendsto hs.measurableSet
       hs.measurableSet (Subset.rfl) (self_mem_nhdsWithin)
       hs.measure_lt_top.ne (Eventually.of_forall hnφ) A B C hmg hcg
-  convert this
+  convert! this
   simp_rw [φ, ← smul_smul, integral_smul]
 
 /-- If a continuous function `c` realizes its maximum at a unique point `x₀` in a compact set `s`,
@@ -463,7 +463,7 @@ theorem tendsto_integral_comp_smul_smul_of_integrable'
     have A : ContinuousAt g (x₀ - 0) := by simpa using h'g
     exact A.comp <| by fun_prop
   simp only [f, sub_zero] at this
-  convert this using 2 with c
+  convert! this using 2 with c
   conv_rhs => rw [← integral_add_left_eq_self x₀ (μ := μ)
     (f := fun x ↦ (c ^ finrank ℝ F * φ (c • x)) • g (x₀ - x)), ← integral_neg_eq_self]
   simp [sub_eq_add_neg]
diff --git a/Mathlib/MeasureTheory/Integral/Prod.lean b/Mathlib/MeasureTheory/Integral/Prod.lean
index d30a559f11e351..cacb8dbefad4f7 100644
--- a/Mathlib/MeasureTheory/Integral/Prod.lean
+++ b/Mathlib/MeasureTheory/Integral/Prod.lean
@@ -153,7 +153,7 @@ theorem integrable_measure_prodMk_left {s : Set (α × β)} (hs : MeasurableSet
     (h2s : (μ.prod ν) s ≠ ∞) : Integrable (fun x => ν.real (Prod.mk x ⁻¹' s)) μ := by
   refine ⟨(measurable_measure_prodMk_left hs).ennreal_toReal.aemeasurable.aestronglyMeasurable, ?_⟩
   simp_rw [hasFiniteIntegral_iff_enorm, measureReal_def, enorm_eq_ofReal toReal_nonneg]
-  convert h2s.lt_top using 1
+  convert! h2s.lt_top using 1
   rw [prod_apply hs]
   apply lintegral_congr_ae
   filter_upwards [ae_measure_lt_top hs h2s] with x hx
@@ -287,7 +287,7 @@ theorem integrable_prod_iff' [SFinite μ] ⦃f : α × β → E⦄
     (h1f : AEStronglyMeasurable f (μ.prod ν)) :
     Integrable f (μ.prod ν) ↔
       (∀ᵐ y ∂ν, Integrable (fun x => f (x, y)) μ) ∧ Integrable (fun y => ∫ x, ‖f (x, y)‖ ∂μ) ν := by
-  convert integrable_prod_iff h1f.prod_swap using 1
+  convert! integrable_prod_iff h1f.prod_swap using 1
   rw [funext fun _ => Function.comp_apply.symm, integrable_swap_iff]
 
 theorem Integrable.prod_left_ae [SFinite μ] ⦃f : α × β → E⦄ (hf : Integrable f (μ.prod ν)) :
@@ -508,7 +508,7 @@ theorem integral_prod (f : α × β → E) (hf : Integrable f (μ.prod ν)) :
   · rintro f g - i_f i_g hf hg
     simp_rw [integral_add' i_f i_g, integral_integral_add' i_f i_g, hf, hg]
   · exact isClosed_eq continuous_integral continuous_integral_integral
-  · rintro f g hfg - hf; convert hf using 1
+  · rintro f g hfg - hf; convert! hf using 1
     · exact integral_congr_ae hfg.symm
     · apply integral_congr_ae
       filter_upwards [ae_ae_of_ae_prod hfg] with x hfgx using integral_congr_ae (ae_eq_symm hfgx)
diff --git a/Mathlib/MeasureTheory/Integral/RieszMarkovKakutani/Real.lean b/Mathlib/MeasureTheory/Integral/RieszMarkovKakutani/Real.lean
index 58018d923fbe92..f7835beb238390 100644
--- a/Mathlib/MeasureTheory/Integral/RieszMarkovKakutani/Real.lean
+++ b/Mathlib/MeasureTheory/Integral/RieszMarkovKakutani/Real.lean
@@ -481,7 +481,7 @@ lemma _root_.MeasureTheory.Measure.exists_innerRegular_eq_of_isCompact
     by infer_instance, ?_, fun g ↦ ?_⟩
   · rw [Measure.map_apply (by fun_prop) hK.measurableSet.compl]
     simp
-  convert hν' (g.compContinuous ⟨Subtype.val, by fun_prop⟩)
+  convert! hν' (g.compContinuous ⟨Subtype.val, by fun_prop⟩)
   · simp only [BoundedContinuousFunction.compContinuous_apply, ContinuousMap.coe_mk]
     rw [← integral_map (φ := Subtype.val) (by fun_prop) (by fun_prop)]
     simp only [map_comap_subtype_coe hK.measurableSet, μ', Measure.restrict_eq_self_of_ae_mem h]
diff --git a/Mathlib/MeasureTheory/Integral/SetToL1.lean b/Mathlib/MeasureTheory/Integral/SetToL1.lean
index ef5286cfbd74a0..d76247acbc2e38 100644
--- a/Mathlib/MeasureTheory/Integral/SetToL1.lean
+++ b/Mathlib/MeasureTheory/Integral/SetToL1.lean
@@ -754,7 +754,7 @@ theorem setToFun_finsetSum' (hT : DominatedFinMeasAdditive μ T C) {ι} (s : Fin
     simp only [his, Finset.sum_insert, not_false_iff]
     rw [setToFun_add hT (hf i (Finset.mem_insert_self i s)) _]
     · rw [ih fun i hi => hf i (Finset.mem_insert_of_mem hi)]
-    · convert integrable_finsetSum s fun i hi => hf i (Finset.mem_insert_of_mem hi) with x
+    · convert! integrable_finsetSum s fun i hi => hf i (Finset.mem_insert_of_mem hi) with x
       simp
 
 @[deprecated (since := "2026-04-08")] alias setToFun_finset_sum' := setToFun_finsetSum'
@@ -762,7 +762,7 @@ theorem setToFun_finsetSum' (hT : DominatedFinMeasAdditive μ T C) {ι} (s : Fin
 theorem setToFun_finsetSum (hT : DominatedFinMeasAdditive μ T C) {ι} (s : Finset ι) {f : ι → α → E}
     (hf : ∀ i ∈ s, Integrable (f i) μ) :
     (setToFun μ T hT fun a => ∑ i ∈ s, f i a) = ∑ i ∈ s, setToFun μ T hT (f i) := by
-  convert setToFun_finsetSum' hT s hf with a; simp
+  convert! setToFun_finsetSum' hT s hf with a; simp
 
 @[deprecated (since := "2026-04-08")] alias setToFun_finset_sum := setToFun_finsetSum
 
@@ -1225,7 +1225,7 @@ theorem tendsto_setToFun_of_dominated_convergence (hT : DominatedFinMeasAdditive
   suffices
     Tendsto (fun n => L1.setToL1 hT ((fs_int n).toL1 (fs n))) atTop
       (𝓝 (L1.setToL1 hT (f_int.toL1 f))) by
-    convert this with n
+    convert! this with n
     · exact setToFun_eq hT (fs_int n)
     · exact setToFun_eq hT f_int
   -- the convergence of setToL1 follows from the convergence of the L1 functions
@@ -1237,7 +1237,7 @@ theorem tendsto_setToFun_of_dominated_convergence (hT : DominatedFinMeasAdditive
     (tendsto_toReal zero_ne_top).comp
       (tendsto_lintegral_norm_of_dominated_convergence fs_measurable
         bound_integrable.hasFiniteIntegral h_bound h_lim)
-  convert lintegral_norm_tendsto_zero with n
+  convert! lintegral_norm_tendsto_zero with n
   rw [L1.norm_def]
   congr 1
   refine lintegral_congr_ae ?_
diff --git a/Mathlib/MeasureTheory/MeasurableSpace/Basic.lean b/Mathlib/MeasureTheory/MeasurableSpace/Basic.lean
index 3314bd93f84f19..fe1d878ffac013 100644
--- a/Mathlib/MeasureTheory/MeasurableSpace/Basic.lean
+++ b/Mathlib/MeasureTheory/MeasurableSpace/Basic.lean
@@ -254,7 +254,7 @@ for functions between empty types. -/
 theorem measurable_const' {f : β → α} (hf : ∀ x y, f x = f y) : Measurable f := by
   nontriviality β
   inhabit β
-  convert @measurable_const α β _ _ (f default) using 2
+  convert! @measurable_const α β _ _ (f default) using 2
   apply hf
 
 @[fun_prop]
@@ -315,7 +315,7 @@ which takes a constant value `b ≠ 0` on a set `A` and `0` elsewhere. -/
 lemma measurable_indicator_const_iff [Zero β] [MeasurableSingletonClass β] (b : β) [NeZero b] :
     Measurable (s.indicator (fun (_ : α) ↦ b)) ↔ MeasurableSet s := by
   constructor <;> intro h
-  · convert h (MeasurableSet.singleton (0 : β)).compl
+  · convert! h (MeasurableSet.singleton (0 : β)).compl
     ext a
     simp [NeZero.ne b]
   · exact measurable_const.indicator h
diff --git a/Mathlib/MeasureTheory/MeasurableSpace/Card.lean b/Mathlib/MeasureTheory/MeasurableSpace/Card.lean
index a9717ac2de143d..4b72b2e6a457fb 100644
--- a/Mathlib/MeasureTheory/MeasurableSpace/Card.lean
+++ b/Mathlib/MeasureTheory/MeasurableSpace/Card.lean
@@ -77,7 +77,7 @@ theorem generateMeasurableRec_mono (s : Set (Set α)) : Monotone (generateMeasur
   intro i j h x hx
   rcases h.eq_or_lt with (rfl | h)
   · exact hx
-  · convert iUnion_mem_generateMeasurableRec fun _ => ⟨i, h, hx⟩
+  · convert! iUnion_mem_generateMeasurableRec fun _ => ⟨i, h, hx⟩
     exact (iUnion_const x).symm
 
 /-- An inductive principle for the elements of `generateMeasurableRec`. -/
diff --git a/Mathlib/MeasureTheory/MeasurableSpace/Constructions.lean b/Mathlib/MeasureTheory/MeasurableSpace/Constructions.lean
index 99dceda0cffb8e..dc0b5f1b5f7f16 100644
--- a/Mathlib/MeasureTheory/MeasurableSpace/Constructions.lean
+++ b/Mathlib/MeasureTheory/MeasurableSpace/Constructions.lean
@@ -86,7 +86,7 @@ theorem measurable_to_nat {f : α → ℕ} : (∀ y, MeasurableSet (f ⁻¹' {f
 theorem measurable_to_bool {f : α → Bool} (h : MeasurableSet (f ⁻¹' {true})) : Measurable f := by
   apply measurable_to_countable'
   rintro (- | -)
-  · convert h.compl
+  · convert! h.compl
     rw [← preimage_compl, Bool.compl_singleton, Bool.not_true]
   exact h
 
@@ -245,7 +245,7 @@ theorem MeasurableSet.image_inclusion' {s t : Set α} (h : s ⊆ t) {u : Set s}
     (hs : MeasurableSet (Subtype.val ⁻¹' s : Set t)) (hu : MeasurableSet u) :
     MeasurableSet (inclusion h '' u) := by
   rcases hu with ⟨u, hu, rfl⟩
-  convert (measurable_subtype_coe hu).inter hs
+  convert! (measurable_subtype_coe hu).inter hs
   ext ⟨x, hx⟩
   simpa [@and_comm _ (_ = x)] using and_comm
 
@@ -257,7 +257,7 @@ theorem MeasurableSet.image_inclusion {s t : Set α} (h : s ⊆ t) {u : Set s}
 theorem MeasurableSet.of_union_cover {s t u : Set α} (hs : MeasurableSet s) (ht : MeasurableSet t)
     (h : univ ⊆ s ∪ t) (hsu : MeasurableSet (((↑) : s → α) ⁻¹' u))
     (htu : MeasurableSet (((↑) : t → α) ⁻¹' u)) : MeasurableSet u := by
-  convert (hs.subtype_image hsu).union (ht.subtype_image htu)
+  convert! (hs.subtype_image hsu).union (ht.subtype_image htu)
   simp [image_preimage_eq_inter_range, ← inter_union_distrib_left, univ_subset_iff.1 h]
 
 theorem measurable_of_measurable_union_cover {f : α → β} (s t : Set α) (hs : MeasurableSet s)
@@ -707,7 +707,7 @@ theorem measurableSet_pi_of_nonempty {s : Set δ} {t : ∀ i, Set (X i)} (hs : s
   classical
     rcases h with ⟨f, hf⟩
     refine ⟨fun hst i hi => ?_, MeasurableSet.pi hs⟩
-    convert measurable_update f (a := i) hst
+    convert! measurable_update f (a := i) hst
     rw [update_preimage_pi hi]
     exact fun j hj _ => hf j hj
 
diff --git a/Mathlib/MeasureTheory/MeasurableSpace/CountablyGenerated.lean b/Mathlib/MeasureTheory/MeasurableSpace/CountablyGenerated.lean
index 0961470694952c..fa2ca1b8c85896 100644
--- a/Mathlib/MeasureTheory/MeasurableSpace/CountablyGenerated.lean
+++ b/Mathlib/MeasureTheory/MeasurableSpace/CountablyGenerated.lean
@@ -231,7 +231,7 @@ instance (priority := 50) MeasurableSingletonClass.of_separatesPoints [Measurabl
     [Countable α] [SeparatesPoints α] : MeasurableSingletonClass α where
   measurableSet_singleton x := by
     choose s hsm hxs hys using fun y (h : x ≠ y) ↦ exists_measurableSet_of_ne h
-    convert MeasurableSet.iInter fun y ↦ .iInter fun h ↦ hsm y h
+    convert! MeasurableSet.iInter fun y ↦ .iInter fun h ↦ hsm y h
     ext y
     rcases eq_or_ne x y with rfl | h
     · simpa
@@ -251,7 +251,7 @@ instance countablySeparated_of_separatesPoints [MeasurableSpace α]
   rcases h with ⟨b, hbc, hb⟩
   refine ⟨⟨b, hbc, fun t ht ↦ hb.symm ▸ .basic t ht, ?_⟩⟩
   rw [hb] at ‹SeparatesPoints _›
-  convert separating_of_generateFrom b
+  convert! separating_of_generateFrom b
   simp
 
 variable (α)
diff --git a/Mathlib/MeasureTheory/MeasurableSpace/Embedding.lean b/Mathlib/MeasureTheory/MeasurableSpace/Embedding.lean
index b3ee9530748549..d2ea336fb442ce 100644
--- a/Mathlib/MeasureTheory/MeasurableSpace/Embedding.lean
+++ b/Mathlib/MeasureTheory/MeasurableSpace/Embedding.lean
@@ -142,15 +142,16 @@ variable {α₁ α₂ α₃ : Type*} {mα : MeasurableSpace α} {mβ : Measurabl
 lemma MeasurableSet.of_union_range_cover (hi₁ : MeasurableEmbedding i₁)
     (hi₂ : MeasurableEmbedding i₂) (h : univ ⊆ range i₁ ∪ range i₂)
     (hs₁ : MeasurableSet (i₁ ⁻¹' s)) (hs₂ : MeasurableSet (i₂ ⁻¹' s)) : MeasurableSet s := by
-  convert (hi₁.measurableSet_image' hs₁).union (hi₂.measurableSet_image' hs₂)
+  convert! (hi₁.measurableSet_image' hs₁).union (hi₂.measurableSet_image' hs₂)
   simp [image_preimage_eq_range_inter, ← union_inter_distrib_right, univ_subset_iff.1 h]
 
 lemma MeasurableSet.of_union₃_range_cover (hi₁ : MeasurableEmbedding i₁)
     (hi₂ : MeasurableEmbedding i₂) (hi₃ : MeasurableEmbedding i₃)
     (h : univ ⊆ range i₁ ∪ range i₂ ∪ range i₃) (hs₁ : MeasurableSet (i₁ ⁻¹' s))
     (hs₂ : MeasurableSet (i₂ ⁻¹' s)) (hs₃ : MeasurableSet (i₃ ⁻¹' s)) : MeasurableSet s := by
-  convert (hi₁.measurableSet_image' hs₁).union (hi₂.measurableSet_image' hs₂) |>.union
-    (hi₃.measurableSet_image' hs₃)
+  convert!
+    (hi₁.measurableSet_image' hs₁).union (hi₂.measurableSet_image' hs₂) |>.union
+      (hi₃.measurableSet_image' hs₃)
   simp [image_preimage_eq_range_inter, ← union_inter_distrib_right, univ_subset_iff.1 h]
 
 lemma Measurable.of_union_range_cover (hi₁ : MeasurableEmbedding i₁)
diff --git a/Mathlib/MeasureTheory/MeasurableSpace/Instances.lean b/Mathlib/MeasureTheory/MeasurableSpace/Instances.lean
index 2d7013c9d3ec07..6c939e5717ea98 100644
--- a/Mathlib/MeasureTheory/MeasurableSpace/Instances.lean
+++ b/Mathlib/MeasureTheory/MeasurableSpace/Instances.lean
@@ -50,7 +50,7 @@ instance IterateMulAct.instDiscreteMeasurableSpace {α : Type*} {f : α → α}
 instance (priority := 100) Subsingleton.measurableSingletonClass
     {α} [MeasurableSpace α] [Subsingleton α] : MeasurableSingletonClass α := by
   refine ⟨fun i => ?_⟩
-  convert MeasurableSet.univ
+  convert! MeasurableSet.univ
   simp [Set.eq_univ_iff_forall, eq_iff_true_of_subsingleton]
 
 instance Bool.instMeasurableSingletonClass : MeasurableSingletonClass Bool := ⟨fun _ => trivial⟩
diff --git a/Mathlib/MeasureTheory/MeasurableSpace/Prod.lean b/Mathlib/MeasureTheory/MeasurableSpace/Prod.lean
index d007a5cd20a036..d12c7b09873ddd 100644
--- a/Mathlib/MeasureTheory/MeasurableSpace/Prod.lean
+++ b/Mathlib/MeasureTheory/MeasurableSpace/Prod.lean
@@ -110,7 +110,7 @@ lemma MeasurableEmbedding.prodMk_left {β γ : Type*} [MeasurableSingletonClass
   measurable := Measurable.prodMk measurable_const hf.measurable
   measurableSet_image' := by
     intro s hs
-    convert (MeasurableSet.singleton x).prod (hf.measurableSet_image.mpr hs)
+    convert! (MeasurableSet.singleton x).prod (hf.measurableSet_image.mpr hs)
     ext x
     simp [Prod.ext_iff, eq_comm, ← exists_and_left, and_left_comm]
 
diff --git a/Mathlib/MeasureTheory/Measure/AEMeasurable.lean b/Mathlib/MeasureTheory/Measure/AEMeasurable.lean
index c1246409e14512..3905185f5bf840 100644
--- a/Mathlib/MeasureTheory/Measure/AEMeasurable.lean
+++ b/Mathlib/MeasureTheory/Measure/AEMeasurable.lean
@@ -347,7 +347,7 @@ lemma aemeasurable_indicator_const_iff {s} [MeasurableSingletonClass β] (b : β
     AEMeasurable (s.indicator (fun _ ↦ b)) μ ↔ NullMeasurableSet s μ := by
   classical
   constructor <;> intro h
-  · convert h.nullMeasurable (MeasurableSet.singleton (0 : β)).compl
+  · convert! h.nullMeasurable (MeasurableSet.singleton (0 : β)).compl
     rw [indicator_const_preimage_eq_union s {0}ᶜ b]
     simp [NeZero.ne b]
   · exact (aemeasurable_indicator_iff₀ h).mpr aemeasurable_const
@@ -404,7 +404,7 @@ lemma MeasureTheory.NullMeasurable.aemeasurable {f : α → β}
   · rw [restrict_piecewise_compl, restrict_eq]
     refine measurable_generateFrom fun s hs ↦ .of_subtype_image ?_
     rw [preimage_comp, Subtype.image_preimage_coe]
-    convert (hTm s hs).diff hvm using 1
+    convert! (hTm s hs).diff hvm using 1
     rw [inter_comm]
     refine Set.ext fun x ↦ and_congr_left fun hxv ↦ ⟨fun hx ↦ ?_, fun hx ↦ hTf s hs hx⟩
     exact by_contra fun hx' ↦ hxv <| mem_biUnion hs ⟨hUf s hs hx, hx'⟩
diff --git a/Mathlib/MeasureTheory/Measure/AddContent.lean b/Mathlib/MeasureTheory/Measure/AddContent.lean
index 8e9deafbdd1e8a..be96ec8bd423ce 100644
--- a/Mathlib/MeasureTheory/Measure/AddContent.lean
+++ b/Mathlib/MeasureTheory/Measure/AddContent.lean
@@ -121,7 +121,7 @@ lemma addContent_biUnion {ι : Type*} {a : Finset ι} {f : ι → Set α} (hf :
 lemma addContent_iUnion {ι : Type*} [Fintype ι] {f : ι → Set α} (hf : ∀ i, f i ∈ C)
     (h_dis : Pairwise (Disjoint on f)) (h_mem : ⋃ i, f i ∈ C) :
     m (⋃ i, f i) = ∑ i, m (f i) := by
-  convert addContent_biUnion (a := Finset.univ) (f := f) (m := m) ?_ ?_ ?_ using 1
+  convert! addContent_biUnion (a := Finset.univ) (f := f) (m := m) ?_ ?_ ?_ using 1
   · simp
   · simpa
   · simpa [Set.PairwiseDisjoint, Set.pairwise_univ] using h_dis
@@ -130,7 +130,7 @@ lemma addContent_iUnion {ι : Type*} [Fintype ι] {f : ι → Set α} (hf : ∀
 lemma addContent_union' (hs : s ∈ C) (ht : t ∈ C) (hst : s ∪ t ∈ C) (h_dis : Disjoint s t) :
     m (s ∪ t) = m s + m t := by
   have A : s ∪ t = ⋃ i, ![s, t] i := by ext; simp
-  convert addContent_iUnion (f := ![s, t]) (m := m) (fun i ↦ ?_) (fun i j hij ↦ ?_) ?_ using 2
+  convert! addContent_iUnion (f := ![s, t]) (m := m) (fun i ↦ ?_) (fun i j hij ↦ ?_) ?_ using 2
   · simp [Fin.univ_castSuccEmb, add_comm]
   · fin_cases i <;> simpa
   · #adaptation_note /-- Before https://github.com/leanprover/lean4/pull/13166
@@ -257,7 +257,7 @@ private lemma AddContent.supClosureFun_apply_of_mem (hC : IsSetSemiring C)
         have := hI hs
         rwa [hC.mem_supClosure_iff] at this
       refine ⟨P.parts, PC, P.disjoint, ?_⟩
-      convert P.sup_parts.symm
+      convert! P.sup_parts.symm
       simp [sUnion_eq_biUnion]
     choose! J hJC hJdisj hJs using A
     have H {a i} (hi : i ∈ I) (ha : a ∈ J i) : a ⊆ i := by
diff --git a/Mathlib/MeasureTheory/Measure/CharacteristicFunction/TaylorExpansion.lean b/Mathlib/MeasureTheory/Measure/CharacteristicFunction/TaylorExpansion.lean
index 01eca816954e13..bfb217a1a6f464 100644
--- a/Mathlib/MeasureTheory/Measure/CharacteristicFunction/TaylorExpansion.lean
+++ b/Mathlib/MeasureTheory/Measure/CharacteristicFunction/TaylorExpansion.lean
@@ -128,7 +128,7 @@ lemma taylorWithinEval_charFun_two_zero (hX : AEMeasurable X P)
     taylorWithinEval (charFun (P.map X)) 2 univ 0 t =
       1 + (P[X] : ℝ) * t * I - (P[X ^ 2] : ℝ) * t ^ 2 / 2 := by
   have : IsProbabilityMeasure (P.map X) := Measure.isProbabilityMeasure_map hX
-  convert taylorWithinEval_charFun_zero hint t with x
+  convert! taylorWithinEval_charFun_zero hint t with x
   simp only [Pi.pow_apply, Nat.reduceAdd, Finset.sum_range_succ, Finset.range_one,
     Finset.sum_singleton, Nat.factorial_zero, Nat.cast_one, inv_one, pow_zero, mul_one,
     integral_const, probReal_univ, smul_eq_mul, ofReal_one, Nat.factorial_one, pow_one, one_mul,
@@ -151,7 +151,7 @@ lemma taylorWithinEval_charFun_two_zero' (hX : AEMeasurable X P)
 lemma taylor_charFun_two (hX : AEMeasurable X P) (h0 : P[X] = 0) (h1 : P[X ^ 2] = 1) :
     (fun t ↦ charFun (P.map X) t - (1 - t ^ 2 / 2)) =o[𝓝 0] fun t ↦ t ^ 2 := by
   simp_rw [← taylorWithinEval_charFun_two_zero' (by fun_prop) h0 h1]
-  convert taylor_isLittleO_univ ?_
+  convert! taylor_isLittleO_univ ?_
   · simp
   refine contDiff_charFun <|
     (memLp_two_iff_integrable_sq (by fun_prop)).2 (.of_integral_ne_zero ?_)
diff --git a/Mathlib/MeasureTheory/Measure/Content.lean b/Mathlib/MeasureTheory/Measure/Content.lean
index 153a127c993edc..f542176289b271 100644
--- a/Mathlib/MeasureTheory/Measure/Content.lean
+++ b/Mathlib/MeasureTheory/Measure/Content.lean
@@ -173,7 +173,7 @@ theorem innerContent_iSup_nat [R1Space G] (U : ℕ → Opens G) :
   rcases K.isCompact.finite_compact_cover t (SetLike.coe ∘ U) (fun i _ => (U i).isOpen) ht with
     ⟨K', h1K', h2K', h3K'⟩
   let L : ℕ → Compacts G := fun n => ⟨K' n, h1K' n⟩
-  convert le_trans (h3 t L) _
+  convert! le_trans (h3 t L) _
   · ext1
     rw [Compacts.coe_finset_sup, Finset.sup_eq_iSup]
     exact h3K'
@@ -204,7 +204,7 @@ theorem is_mul_left_invariant_innerContent [Group G] [SeparatelyContinuousMul G]
     (h : ∀ (g : G) {K : Compacts G}, μ (K.map _ <| continuous_const_mul g) = μ K) (g : G)
     (U : Opens G) :
     μ.innerContent (Opens.comap (Homeomorph.mulLeft g) U) = μ.innerContent U := by
-  convert μ.innerContent_comap (Homeomorph.mulLeft g) (fun K => h g) U
+  convert! μ.innerContent_comap (Homeomorph.mulLeft g) (fun K => h g) U
 
 @[to_additive]
 theorem innerContent_pos_of_is_mul_left_invariant [Group G] [IsTopologicalGroup G]
@@ -276,7 +276,7 @@ theorem outerMeasure_preimage (f : G ≃ₜ G) (h : ∀ ⦃K : Compacts G⦄, μ
   refine inducedOuterMeasure_preimage _ μ.innerContent_iUnion_nat μ.innerContent_mono _
     (fun _ => f.isOpen_preimage) ?_
   intro s hs
-  convert μ.innerContent_comap f h ⟨s, hs⟩
+  convert! μ.innerContent_comap f h ⟨s, hs⟩
 
 theorem outerMeasure_lt_top_of_isCompact [WeaklyLocallyCompactSpace G]
     {K : Set G} (hK : IsCompact K) :
@@ -292,7 +292,7 @@ theorem outerMeasure_lt_top_of_isCompact [WeaklyLocallyCompactSpace G]
 theorem is_mul_left_invariant_outerMeasure [Group G] [SeparatelyContinuousMul G]
     (h : ∀ (g : G) {K : Compacts G}, μ (K.map _ <| continuous_const_mul g) = μ K) (g : G)
     (A : Set G) : μ.outerMeasure ((g * ·) ⁻¹' A) = μ.outerMeasure A := by
-  convert μ.outerMeasure_preimage (Homeomorph.mulLeft g) (fun K => h g) A
+  convert! μ.outerMeasure_preimage (Homeomorph.mulLeft g) (fun K => h g) A
 
 theorem outerMeasure_caratheodory (A : Set G) :
     MeasurableSet[μ.outerMeasure.caratheodory] A ↔
@@ -306,7 +306,7 @@ theorem outerMeasure_caratheodory (A : Set G) :
 theorem outerMeasure_pos_of_is_mul_left_invariant [Group G] [IsTopologicalGroup G]
     (h3 : ∀ (g : G) {K : Compacts G}, μ (K.map _ <| continuous_const_mul g) = μ K) (K : Compacts G)
     (hK : μ K ≠ 0) {U : Set G} (h1U : IsOpen U) (h2U : U.Nonempty) : 0 < μ.outerMeasure U := by
-  convert μ.innerContent_pos_of_is_mul_left_invariant h3 K hK ⟨U, h1U⟩ h2U
+  convert! μ.innerContent_pos_of_is_mul_left_invariant h3 K hK ⟨U, h1U⟩ h2U
   exact μ.outerMeasure_opens ⟨U, h1U⟩
 
 variable [S : MeasurableSpace G] [BorelSpace G]
diff --git a/Mathlib/MeasureTheory/Measure/Decomposition/IntegralRNDeriv.lean b/Mathlib/MeasureTheory/Measure/Decomposition/IntegralRNDeriv.lean
index 840aa43436c9ae..1a0daa3c7fba7e 100644
--- a/Mathlib/MeasureTheory/Measure/Decomposition/IntegralRNDeriv.lean
+++ b/Mathlib/MeasureTheory/Measure/Decomposition/IntegralRNDeriv.lean
@@ -109,7 +109,7 @@ lemma mul_le_integral_rnDeriv_of_ac [IsFiniteMeasure μ] [IsFiniteMeasure ν]
     filter_upwards [h_rnDeriv_eq] with x hx
     rw [hx]
   rw [h_eq, mul_comm, ← div_le_iff₀, div_eq_inv_mul, inv_inv] at h
-  · convert h
+  · convert! h
     · simp only [div_eq_inv_mul, Measure.smul_apply, smul_eq_mul, ENNReal.toReal_mul,
       ENNReal.toReal_inv, μ', measureReal_def]
   · simp [ENNReal.toReal_pos_iff, hν, measureReal_def]
diff --git a/Mathlib/MeasureTheory/Measure/Decomposition/Lebesgue.lean b/Mathlib/MeasureTheory/Measure/Decomposition/Lebesgue.lean
index c837b44cfe44ff..aeb22b3bca062a 100644
--- a/Mathlib/MeasureTheory/Measure/Decomposition/Lebesgue.lean
+++ b/Mathlib/MeasureTheory/Measure/Decomposition/Lebesgue.lean
@@ -456,7 +456,7 @@ theorem singularPart_smul_right (μ ν : Measure α) (r : ℝ≥0) (hr : r ≠ 0
         smul_absolutelyContinuous
     · rw [ENNReal.smul_def r, withDensity_smul_measure, ← withDensity_smul]
       swap; · exact (measurable_rnDeriv _ _).const_smul _
-      convert haveLebesgueDecomposition_add μ ν
+      convert! haveLebesgueDecomposition_add μ ν
       ext x
       simp only [Pi.smul_apply]
       rw [← ENNReal.smul_def, smul_inv_smul₀ hr]
@@ -812,7 +812,7 @@ theorem iSup_mem_measurableLE (f : ℕ → α → ℝ≥0∞) (hf : ∀ n, f n 
 
 theorem iSup_mem_measurableLE' (f : ℕ → α → ℝ≥0∞) (hf : ∀ n, f n ∈ measurableLE μ ν) (n : ℕ) :
     (⨆ (k) (_ : k ≤ n), f k) ∈ measurableLE μ ν := by
-  convert iSup_mem_measurableLE f hf n
+  convert! iSup_mem_measurableLE f hf n
   simp
 
 section SuprLemmas
@@ -863,19 +863,19 @@ theorem haveLebesgueDecomposition_of_finiteMeasure [IsFiniteMeasure μ] [IsFinit
           fun n ↦ ?_
         · rw [← hf₂ n]
           apply lintegral_mono
-          convert iSup_le_le f n n le_rfl
+          convert! iSup_le_le f n n le_rfl
           simp only [iSup_apply]
         · exact le_sSup ⟨⨆ (k : ℕ) (_ : k ≤ n), f k, iSup_mem_measurableLE' _ hf₁ _, rfl⟩
       · intro n
         refine Measurable.aemeasurable ?_
-        convert (iSup_mem_measurableLE _ hf₁ n).1
+        convert! (iSup_mem_measurableLE _ hf₁ n).1
         simp
       · refine Filter.Eventually.of_forall fun a ↦ ?_
         simp [iSup_monotone' f _]
       · refine Filter.Eventually.of_forall fun a ↦ ?_
         simp [tendsto_atTop_iSup (iSup_monotone' f a)]
     have hξm : Measurable ξ := by
-      convert Measurable.iSup fun n ↦ (iSup_mem_measurableLE _ hf₁ n).1
+      convert! Measurable.iSup fun n ↦ (iSup_mem_measurableLE _ hf₁ n).1
       simp [hξ]
     -- we see that `ξ` has the largest integral among all functions in `measurableLE`
     have hξle A (hA : MeasurableSet A) : ∫⁻ a in A, ξ a ∂ν ≤ μ A := by
diff --git a/Mathlib/MeasureTheory/Measure/Dirac.lean b/Mathlib/MeasureTheory/Measure/Dirac.lean
index cb243e9b08f88c..bf1e8ebe5f210a 100644
--- a/Mathlib/MeasureTheory/Measure/Dirac.lean
+++ b/Mathlib/MeasureTheory/Measure/Dirac.lean
@@ -161,9 +161,9 @@ lemma exists_sum_smul_dirac [Countable α] (μ : Measure α) :
     · simp only [Pi.one_apply, mul_one]
       congr 1
       refine (measurableAtom_eq_of_mem ?_).symm
-      convert h_points_mem _
+      convert! h_points_mem _
       simp
-    · convert h_points_mem _
+    · convert! h_points_mem _
       simp
   · simp only [ne_eq, mul_eq_zero, indicator_apply_eq_zero, Pi.one_apply, one_ne_zero, imp_false,
       Subtype.forall, Set.mem_range, Subtype.exists, Subtype.mk.injEq, forall_exists_index]
@@ -177,7 +177,7 @@ lemma exists_sum_smul_dirac [Countable α] (μ : Measure α) :
       simp only at h_points_mem
       rw [← hz, ← hsy]
       refine measurableAtom_eq_of_mem ?_
-      convert h_points_mem
+      convert! h_points_mem
     rw [← h2, h1]
 
 /-- Given that `α` is a countable, measurable space with all singleton sets measurable,
@@ -365,7 +365,7 @@ lemma ae_mem_finset_iff : (∀ᵐ a ∂μ, a ∈ s) ↔ μ = ∑ a ∈ s, μ {a}
 lemma ae_eq_or_eq_iff_eq_dirac_add_dirac (ha : a₁ ≠ a₂) :
     (∀ᵐ a ∂μ, a = a₁ ∨ a = a₂) ↔ μ = μ {a₁} • .dirac a₁ + μ {a₂} • .dirac a₂ := by
   -- FIXME: Why does `simpa using ...` not work?
-  convert ae_mem_finset_iff (s := .cons a₁ {a₂} <| by simpa) <;> simp
+  convert! ae_mem_finset_iff (s := .cons a₁ { a₂ } <| by simpa) <;> simp
 
 lemma ae_mem_finset_iff_map_eq_sum_dirac {μ : Measure β} (hf : AEMeasurable f μ) :
     (∀ᵐ b ∂μ, f b ∈ s) ↔ μ.map f = ∑ a ∈ s, μ (f ⁻¹' {a}) • .dirac a := by
@@ -377,6 +377,6 @@ lemma ae_eq_or_eq_iff_map_eq_dirac_add_dirac {μ : Measure β} (hf : AEMeasurabl
     (∀ᵐ b ∂μ, f b = a₁ ∨ f b = a₂) ↔
       μ.map f = μ (f ⁻¹' {a₁}) • .dirac a₁ + μ (f ⁻¹' {a₂}) • .dirac a₂ := by
   -- FIXME: Why does `simpa using ...` not work?
-  convert ae_mem_finset_iff_map_eq_sum_dirac (s := .cons a₁ {a₂} <| by simpa) hf <;> simp
+  convert! ae_mem_finset_iff_map_eq_sum_dirac (s := .cons a₁ { a₂ } <| by simpa) hf <;> simp
 
 end MeasureTheory.Measure
diff --git a/Mathlib/MeasureTheory/Measure/DiracProba.lean b/Mathlib/MeasureTheory/Measure/DiracProba.lean
index 34922400c30591..a2189b3c2f9972 100644
--- a/Mathlib/MeasureTheory/Measure/DiracProba.lean
+++ b/Mathlib/MeasureTheory/Measure/DiracProba.lean
@@ -150,7 +150,7 @@ lemma tendsto_diracProbaEquivSymm_iff_tendsto [T0Space X] [CompletelyRegularSpac
   rw [← (diracProbaEquiv (X := X)).symm_comp_self, ← tendsto_map'_iff] at key
   simp only [tendsto_map'_iff, map_map, Equiv.self_comp_symm, map_id] at key
   simp only [← key, diracProba_comp_diracProbaEquiv_symm_eq_val]
-  convert tendsto_subtype_rng.symm
+  convert! tendsto_subtype_rng.symm
   exact apply_rangeSplitting (fun x ↦ diracProba x) μ
 
 /-- In a T0 topological space, `diracProbaEquiv` is continuous. -/
diff --git a/Mathlib/MeasureTheory/Measure/Doubling.lean b/Mathlib/MeasureTheory/Measure/Doubling.lean
index 06ca589f864dad..bf9d8c7e21a59c 100644
--- a/Mathlib/MeasureTheory/Measure/Doubling.lean
+++ b/Mathlib/MeasureTheory/Measure/Doubling.lean
@@ -123,7 +123,7 @@ theorem eventually_measure_le_scaling_constant_mul (K : ℝ) :
 theorem eventually_measure_le_scaling_constant_mul' (K : ℝ) (hK : 0 < K) :
     ∀ᶠ r in 𝓝[>] 0, ∀ x,
       μ (closedBall x r) ≤ scalingConstantOf μ K⁻¹ * μ (closedBall x (K * r)) := by
-  convert eventually_nhdsGT_zero_mul_left hK (eventually_measure_le_scaling_constant_mul μ K⁻¹)
+  convert! eventually_nhdsGT_zero_mul_left hK (eventually_measure_le_scaling_constant_mul μ K⁻¹)
   simp [inv_mul_cancel_left₀ hK.ne']
 
 /-- A scale below which the doubling measure `μ` satisfies good rescaling properties when one
diff --git a/Mathlib/MeasureTheory/Measure/EverywherePos.lean b/Mathlib/MeasureTheory/Measure/EverywherePos.lean
index 4b4b2a71a0b422..b98ed1f0691845 100644
--- a/Mathlib/MeasureTheory/Measure/EverywherePos.lean
+++ b/Mathlib/MeasureTheory/Measure/EverywherePos.lean
@@ -295,7 +295,7 @@ theorem innerRegularWRT_preimage_one_hasCompactSupport_measure_ne_top_of_group :
       exists_continuous_one_zero_of_isCompact_of_isGδ L_comp L_Gδ isClosed_empty
         (disjoint_empty L)
     exact ⟨f, f_cont, f_comp, Lf⟩
-  · convert hr using 1
+  · convert! hr using 1
     apply measure_congr
     exact everywherePosSubset_ae_eq_of_measure_ne_top K_closed.measurableSet
       K_comp.measure_lt_top.ne
diff --git a/Mathlib/MeasureTheory/Measure/FiniteMeasure.lean b/Mathlib/MeasureTheory/Measure/FiniteMeasure.lean
index de2ae8045dd2a6..d754a8f67e6cdb 100644
--- a/Mathlib/MeasureTheory/Measure/FiniteMeasure.lean
+++ b/Mathlib/MeasureTheory/Measure/FiniteMeasure.lean
@@ -565,7 +565,7 @@ theorem tendsto_zero_of_tendsto_zero_mass {γ : Type*} {F : Filter γ} {μs : γ
     (mass_lim : Tendsto (fun i ↦ (μs i).mass) F (𝓝 0)) : Tendsto μs F (𝓝 0) := by
   rw [tendsto_iff_forall_testAgainstNN_tendsto]
   intro f
-  convert tendsto_zero_testAgainstNN_of_tendsto_zero_mass mass_lim f
+  convert! tendsto_zero_testAgainstNN_of_tendsto_zero_mass mass_lim f
   rw [zero_testAgainstNN_apply]
 
 /-- A characterization of weak convergence in terms of integrals of bounded continuous
@@ -775,7 +775,7 @@ instance : ContinuousAdd (FiniteMeasure Ω) := by
       (𝓝 (∫⁻ x, g x ∂p.2)) := by
     rw [nhds_prod_eq]
     exact (tendsto_iff_forall_lintegral_tendsto.1 tendsto_id g).comp tendsto_snd
-  convert A.add B with q <;> simp
+  convert! A.add B with q <;> simp
 
 instance : ContinuousSMul ℝ≥0 (FiniteMeasure Ω) := by
   refine ⟨continuous_iff_continuousAt.2 (fun p ↦ ?_)⟩
@@ -787,7 +787,7 @@ instance : ContinuousSMul ℝ≥0 (FiniteMeasure Ω) := by
       (𝓝 (∫ x, g x ∂p.2)) := by
     rw [nhds_prod_eq]
     exact (tendsto_iff_forall_integral_tendsto.1 tendsto_id g).comp tendsto_snd
-  convert A.smul B with q <;> simp
+  convert! A.smul B with q <;> simp
 
 variable {X : Type*} [TopologicalSpace X] {μs : X → FiniteMeasure Ω}
 
@@ -960,7 +960,7 @@ lemma tendsto_map_of_tendsto_of_continuous {ι : Type*} {L : Filter ι}
     Tendsto (fun i ↦ (νs i).map f) L (𝓝 (ν.map f)) := by
   rw [FiniteMeasure.tendsto_iff_forall_lintegral_tendsto] at lim ⊢
   intro g
-  convert lim (g.compContinuous ⟨f, f_cont⟩) <;>
+  convert! lim (g.compContinuous ⟨f, f_cont⟩) <;>
   · simp only [map, compContinuous_apply, ContinuousMap.coe_mk]
     refine lintegral_map ?_ f_cont.measurable
     exact (ENNReal.continuous_coe.comp g.continuous).measurable
diff --git a/Mathlib/MeasureTheory/Measure/Haar/Basic.lean b/Mathlib/MeasureTheory/Measure/Haar/Basic.lean
index 00cfba26cd54c9..51ac4de88e7806 100644
--- a/Mathlib/MeasureTheory/Measure/Haar/Basic.lean
+++ b/Mathlib/MeasureTheory/Measure/Haar/Basic.lean
@@ -180,7 +180,7 @@ theorem index_pos (K : PositiveCompacts G) {V : Set G} (hV : (interior V).Nonemp
   · rintro ⟨t, h1t, h2t⟩; rw [Finset.card_eq_zero] at h2t; subst h2t
     obtain ⟨g, hg⟩ := K.interior_nonempty
     change g ∈ (∅ : Set G)
-    convert h1t (interior_subset hg); symm
+    convert! h1t (interior_subset hg); symm
     simp only [Finset.notMem_empty, iUnion_of_empty, iUnion_empty]
   · exact index_defined K.isCompact hV
 
@@ -252,7 +252,7 @@ theorem mul_left_index_le {K : Set G} (hK : IsCompact K) {V : Set G} (hV : (inte
 theorem is_left_invariant_index {K : Set G} (hK : IsCompact K) (g : G) {V : Set G}
     (hV : (interior V).Nonempty) : index ((fun h => g * h) '' K) V = index K V := by
   refine le_antisymm (mul_left_index_le hK hV g) ?_
-  convert mul_left_index_le (hK.image <| continuous_const_mul g) hV g⁻¹
+  convert! mul_left_index_le (hK.image <| continuous_const_mul g) hV g⁻¹
   rw [image_image]
   simp
 
diff --git a/Mathlib/MeasureTheory/Measure/Haar/InnerProductSpace.lean b/Mathlib/MeasureTheory/Measure/Haar/InnerProductSpace.lean
index e3d00126766a35..ded8c0bfb1516a 100644
--- a/Mathlib/MeasureTheory/Measure/Haar/InnerProductSpace.lean
+++ b/Mathlib/MeasureTheory/Measure/Haar/InnerProductSpace.lean
@@ -103,7 +103,7 @@ noncomputable def OrthonormalBasis.measurableEquiv (b : OrthonormalBasis ι ℝ
 /-- The measurable equivalence defined by an orthonormal basis is volume preserving. -/
 theorem OrthonormalBasis.measurePreserving_measurableEquiv (b : OrthonormalBasis ι ℝ F) :
     MeasurePreserving b.measurableEquiv volume volume := by
-  convert (b.measurableEquiv.symm.measurable.measurePreserving _).symm
+  convert! (b.measurableEquiv.symm.measurable.measurePreserving _).symm
   rw [← (EuclideanSpace.basisFun ι ℝ).addHaar_eq_volume]
   erw [MeasurableEquiv.coe_toEquiv_symm, Basis.map_addHaar _ b.repr.symm.toContinuousLinearEquiv]
   exact b.addHaar_eq_volume.symm
@@ -124,7 +124,7 @@ variable [Fintype ι]
 theorem EuclideanSpace.volume_preserving_symm_measurableEquiv_toLp :
     MeasurePreserving (MeasurableEquiv.toLp 2 (ι → ℝ)).symm := by
   suffices volume = map (MeasurableEquiv.toLp 2 (ι → ℝ)) volume by
-    convert ((MeasurableEquiv.toLp 2 (ι → ℝ)).measurable.measurePreserving _).symm
+    convert! ((MeasurableEquiv.toLp 2 (ι → ℝ)).measurable.measurePreserving _).symm
   rw [← addHaarMeasure_eq_volume_pi, ← Basis.parallelepiped_basisFun, ← Basis.addHaar_def,
     MeasurableEquiv.coe_toLp, ← PiLp.coe_symm_continuousLinearEquiv 2 ℝ, Basis.map_addHaar]
   exact (EuclideanSpace.basisFun _ _).addHaar_eq_volume.symm
@@ -189,7 +189,7 @@ private noncomputable def volumePreservingSymmMeasurableEquivToLpProdAux :
 theorem WithLp.volume_preserving_symm_measurableEquiv_toLp_prod :
     MeasurePreserving (MeasurableEquiv.toLp 2 (U × V)).symm := by
   suffices MeasurePreserving (volumePreservingSymmMeasurableEquivToLpProdAux U V) by
-    convert this
+    convert! this
     ext uv
     <;> simp [volumePreservingSymmMeasurableEquivToLpProdAux, MeasurableEquiv.coe_sumPiEquivProdPi,
       LinearEquiv.prodCongr_symm, MeasurableEquiv.prodCongr]
@@ -224,7 +224,7 @@ theorem MeasureTheory.volume_eq_of_finrank_eq_one (h : Module.finrank ℝ E = 1)
     let f : ℝ ≃ₗᵢ[ℝ] E := (LinearIsometryEquiv.toSpanUnitSingleton (‖v‖⁻¹ • v)
       (by simp [norm_smul, hv])).trans (LinearIsometryEquiv.ofTop E _ hv')
     rw [map_map (by fun_prop) (by fun_prop)]
-    convert f.measurePreserving.map_eq.symm
+    convert! f.measurePreserving.map_eq.symm
     ext x
     simp [f, mul_comm, smul_smul]
   _ = ‖v‖ₑ • (volume : Measure ℝ).map (· • v) := by
diff --git a/Mathlib/MeasureTheory/Measure/Haar/NormedSpace.lean b/Mathlib/MeasureTheory/Measure/Haar/NormedSpace.lean
index 164f7466ddbba5..c954fefea00122 100644
--- a/Mathlib/MeasureTheory/Measure/Haar/NormedSpace.lean
+++ b/Mathlib/MeasureTheory/Measure/Haar/NormedSpace.lean
@@ -178,7 +178,7 @@ theorem integrable_comp_smul_iff {E : Type*} [NormedAddCommGroup E] [NormedSpace
   suffices
     ∀ {g : E → F} (_ : Integrable g μ) {S : ℝ} (_ : S ≠ 0), Integrable (fun x => g (S • x)) μ by
     refine ⟨fun hf => ?_, fun hf => this hf hR⟩
-    convert this hf (inv_ne_zero hR)
+    convert! this hf (inv_ne_zero hR)
     rw [← mul_smul, mul_inv_cancel₀ hR, one_smul]
   -- now prove
   intro g hg S hS
diff --git a/Mathlib/MeasureTheory/Measure/Haar/OfBasis.lean b/Mathlib/MeasureTheory/Measure/Haar/OfBasis.lean
index 9913bc5efcf083..7d99663857af69 100644
--- a/Mathlib/MeasureTheory/Measure/Haar/OfBasis.lean
+++ b/Mathlib/MeasureTheory/Measure/Haar/OfBasis.lean
@@ -99,7 +99,7 @@ theorem parallelepiped_orthonormalBasis_one_dim (b : OrthonormalBasis ι ℝ ℝ
     apply Fintype.equivFinOfCardEq
     simp only [← finrank_eq_card_basis b.toBasis, finrank_self]
   have B : parallelepiped (b.reindex e) = parallelepiped b := by
-    convert parallelepiped_comp_equiv b e.symm
+    convert! parallelepiped_comp_equiv b e.symm
     ext i
     simp only [OrthonormalBasis.coe_reindex]
   rw [← B]
@@ -191,7 +191,7 @@ def parallelepiped (b : Basis ι ℝ E) : PositiveCompacts E where
   interior_nonempty' := by
     suffices H : Set.Nonempty (interior (b.equivFunL.symm.toHomeomorph '' Icc 0 1)) by
       dsimp only [_root_.parallelepiped]
-      convert H
+      convert! H
       exact (b.equivFun_symm_apply _).symm
     have A : Set.Nonempty (interior (Icc (0 : ι → ℝ) 1)) := by
       rw [← pi_univ_Icc, interior_pi_set (@finite_univ ι _)]
diff --git a/Mathlib/MeasureTheory/Measure/Haar/Quotient.lean b/Mathlib/MeasureTheory/Measure/Haar/Quotient.lean
index 32894df84231ee..3d3fd8c253abcf 100644
--- a/Mathlib/MeasureTheory/Measure/Haar/Quotient.lean
+++ b/Mathlib/MeasureTheory/Measure/Haar/Quotient.lean
@@ -133,7 +133,7 @@ lemma MeasureTheory.QuotientMeasureEqMeasurePreimage.mulInvariantMeasure_quotien
   map_mul_left_eq_self x := by
     ext A hA
     obtain ⟨x₁, h⟩ := @Quotient.exists_rep _ (QuotientGroup.leftRel Γ) x
-    convert measure_preimage_smul μ x₁ A using 1
+    convert! measure_preimage_smul μ x₁ A using 1
     · rw [← h, Measure.map_apply (measurable_const_mul _) hA]
       simp [← MulAction.Quotient.coe_smul_out, ← Quotient.mk''_eq_mk]
     exact smulInvariantMeasure_quotient ν
@@ -175,7 +175,7 @@ theorem MeasureTheory.Measure.IsMulLeftInvariant.quotientMeasureEqMeasurePreimag
   symm
   suffices (μ' V / ν (QuotientGroup.mk ⁻¹' V ∩ s)) = 1 by rw [this, one_smul]
   rw [Measure.map_apply meas_π meas_V, Measure.restrict_apply]
-  · convert ENNReal.div_self ..
+  · convert! ENNReal.div_self ..
     · exact trans hV.symm neZeroV
     · exact trans hV.symm neTopV
   exact measurableSet_quotient.mp meas_V
@@ -192,7 +192,7 @@ theorem MeasureTheory.leftInvariantIsQuotientMeasureEqMeasurePreimage [IsFiniteM
   have finiteCovol : μ univ < ⊤ := measure_lt_top μ univ
   rw [fund_dom_s.covolume_eq_volume] at h
   by_cases meas_s_ne_zero : ν s = 0
-  · convert fund_dom_s.quotientMeasureEqMeasurePreimage_of_zero meas_s_ne_zero
+  · convert! fund_dom_s.quotientMeasureEqMeasurePreimage_of_zero meas_s_ne_zero
     rw [← @measure_univ_eq_zero, ← h, meas_s_ne_zero]
   apply IsMulLeftInvariant.quotientMeasureEqMeasurePreimage_of_set (fund_dom_s := fund_dom_s)
     (meas_V := MeasurableSet.univ)
@@ -201,7 +201,7 @@ theorem MeasureTheory.leftInvariantIsQuotientMeasureEqMeasurePreimage [IsFiniteM
   · rw [← h]
     simp
   · rw [← h]
-    convert finiteCovol.ne
+    convert! finiteCovol.ne
 
 end mulInvariantMeasure
 
@@ -364,7 +364,7 @@ lemma _root_.MeasureTheory.IsFundamentalDomain.absolutelyContinuous_map
     ext g
     rw [Set.mem_smul_set_iff_inv_smul_mem, mem_preimage, mem_preimage]
     congr! 1
-    convert QuotientGroup.mk_mul_of_mem g (γ⁻¹).2 using 1
+    convert! QuotientGroup.mk_mul_of_mem g (γ⁻¹).2 using 1
   exact MeasurableSet.preimage s_meas meas_π
 
 attribute [-instance] Quotient.instMeasurableSpace
diff --git a/Mathlib/MeasureTheory/Measure/Haar/Unique.lean b/Mathlib/MeasureTheory/Measure/Haar/Unique.lean
index 10afcab099b9c8..133510ba04c807 100644
--- a/Mathlib/MeasureTheory/Measure/Haar/Unique.lean
+++ b/Mathlib/MeasureTheory/Measure/Haar/Unique.lean
@@ -505,7 +505,7 @@ lemma measure_preimage_isMulLeftInvariant_eq_smul_of_hasCompactSupport
       have T := tendsto_pi_nhds.1 (thickenedIndicator_tendsto_indicator_closure
         (fun n ↦ (u_mem n).1) u_lim ({1} : Set ℝ)) (f x)
       simp only [thickenedIndicator_apply, closure_singleton] at T
-      convert NNReal.tendsto_coe.2 T
+      convert! NNReal.tendsto_coe.2 T
       simp
   have M n : ∫ (x : G), v n (f x) ∂μ' = ∫ (x : G), v n (f x) ∂(haarScalarFactor μ' μ • μ) := by
     apply integral_isMulLeftInvariant_eq_smul_of_hasCompactSupport μ' μ (vf_cont n)
@@ -556,7 +556,7 @@ lemma smul_measure_isMulInvariant_le_of_isCompact_closure [LocallyCompactSpace G
   obtain ⟨-, hf, ⟨f, f_cont, f_comp, rfl⟩, νf⟩ :
       ∃ K ⊆ s, (∃ f, Continuous f ∧ HasCompactSupport f ∧ K = f ⁻¹' {1}) ∧ r < ν K :=
     innerRegularWRT_preimage_one_hasCompactSupport_measure_ne_top_of_group ⟨hs, this⟩ r
-      (by convert hr)
+      (by convert! hr)
   calc
   r < ν (f ⁻¹' {1}) := νf
   _ = μ' (f ⁻¹' {1}) :=
diff --git a/Mathlib/MeasureTheory/Measure/HasOuterApproxClosed.lean b/Mathlib/MeasureTheory/Measure/HasOuterApproxClosed.lean
index b65527be4250b1..0f8e45df09884c 100644
--- a/Mathlib/MeasureTheory/Measure/HasOuterApproxClosed.lean
+++ b/Mathlib/MeasureTheory/Measure/HasOuterApproxClosed.lean
@@ -81,7 +81,7 @@ theorem measure_of_cont_bdd_of_tendsto_filter_indicator {ι : Type*} {L : Filter
     (fs_bdd : ∀ᶠ i in L, ∀ᵐ ω : Ω ∂μ, fs i ω ≤ c)
     (fs_lim : ∀ᵐ ω ∂μ, Tendsto (fun i ↦ fs i ω) L (𝓝 (indicator E (fun _ ↦ (1 : ℝ≥0)) ω))) :
     Tendsto (fun n ↦ lintegral μ fun ω ↦ fs n ω) L (𝓝 (μ E)) := by
-  convert tendsto_lintegral_nn_filter_of_le_const μ fs_bdd fs_lim
+  convert! tendsto_lintegral_nn_filter_of_le_const μ fs_bdd fs_lim
   have aux : ∀ ω, indicator E (fun _ ↦ (1 : ℝ≥0∞)) ω = ↑(indicator E (fun _ ↦ (1 : ℝ≥0)) ω) :=
     fun ω ↦ by simp only [ENNReal.coe_indicator, ENNReal.coe_one]
   simp_rw [← aux, lintegral_indicator E_mble]
diff --git a/Mathlib/MeasureTheory/Measure/HasOuterApproxClosedProd.lean b/Mathlib/MeasureTheory/Measure/HasOuterApproxClosedProd.lean
index 18e0aca5126b8e..cd69af236c79ac 100644
--- a/Mathlib/MeasureTheory/Measure/HasOuterApproxClosedProd.lean
+++ b/Mathlib/MeasureTheory/Measure/HasOuterApproxClosedProd.lean
@@ -81,7 +81,7 @@ lemma ext_of_lintegral_prod_mul_prod_boundedContinuousFunction
       ∫⁻ p, (∏ i, f i (p.1 i)) * ∏ j, g j (p.2 j) ∂μ =
       ∫⁻ p, (∏ i, f i (p.1 i)) * ∏ j, g j (p.2 j) ∂ν) :
     μ = ν := by
-  have hμν : μ univ = ν univ := by convert h 1 1 <;> simp
+  have hμν : μ univ = ν univ := by convert! h 1 1 <;> simp
   have : IsFiniteMeasure ν := ⟨by simp [← hμν]⟩
   let π : Set (Set ((Π i, X i) × (Π j, Y j))) :=
     Set.image2 (fun s t ↦ s ×ˢ t) (Set.univ.pi '' (Set.univ.pi fun _ ↦ {s | IsClosed s}))
@@ -150,7 +150,7 @@ lemma ext_of_lintegral_prod_mul_prod_boundedContinuousFunction
     · simp
     · exact fun j _ ↦ HasOuterApproxClosed.apprSeq_apply_le_one (ht j) _ _
     · exact fun i _ ↦ HasOuterApproxClosed.apprSeq_apply_le_one (hs i) _ _
-  convert tendsto_nhds_unique h1 h2 <;>
+  convert! tendsto_nhds_unique h1 h2 <;>
     simp [(MeasurableSet.univ_pi (fun i ↦ (hs i).measurableSet)).prod
       (.univ_pi (fun j ↦ (ht j).measurableSet))]
 
@@ -180,13 +180,15 @@ lemma ext_of_integral_prod_mul_prod_boundedContinuousFunction
     simp_rw [this]
     exact h (fun i ↦ ⟨⟨fun x ↦ (f i x), by fun_prop⟩, (f i).map_bounded'⟩)
       (fun j ↦ ⟨⟨fun y ↦ (g j y), by fun_prop⟩, (g j).map_bounded'⟩)
-  · convert (lintegral_lt_top_of_nnreal μ
-      ((∏ i, (f i).compContinuous ⟨Function.eval i ∘ Prod.fst, by fun_prop⟩) *
-      (∏ j, (g j).compContinuous ⟨Function.eval j ∘ Prod.snd, by fun_prop⟩))).ne
+  · convert!
+    (lintegral_lt_top_of_nnreal μ
+        ((∏ i, (f i).compContinuous ⟨Function.eval i ∘ Prod.fst, by fun_prop⟩) *
+          (∏ j, (g j).compContinuous ⟨Function.eval j ∘ Prod.snd, by fun_prop⟩))).ne
     simp
-  · convert (lintegral_lt_top_of_nnreal ν
-      ((∏ i, (f i).compContinuous ⟨Function.eval i ∘ Prod.fst, by fun_prop⟩) *
-      (∏ j, (g j).compContinuous ⟨Function.eval j ∘ Prod.snd, by fun_prop⟩))).ne
+  · convert!
+    (lintegral_lt_top_of_nnreal ν
+        ((∏ i, (f i).compContinuous ⟨Function.eval i ∘ Prod.fst, by fun_prop⟩) *
+          (∏ j, (g j).compContinuous ⟨Function.eval j ∘ Prod.snd, by fun_prop⟩))).ne
     simp
 
 /-- The product of two finite measures `μ` and `ν` is the only finite measure `ξ` such that
@@ -282,8 +284,9 @@ lemma ext_of_integral_prod_mul_prod_boundedContinuousFunction'
     μ = ν := by
   have := Fintype.ofFinite ι; have := Fintype.ofFinite κ
   refine ext_of_integral_prod_mul_prod_boundedContinuousFunction fun f g ↦ ?_
-  convert h (∏ i, (f i).compContinuous ⟨Function.eval i, by fun_prop⟩)
-    (∏ j, (g j).compContinuous ⟨Function.eval j, by fun_prop⟩) <;> simp
+  convert!
+    h (∏ i, (f i).compContinuous ⟨Function.eval i, by fun_prop⟩)
+      (∏ j, (g j).compContinuous ⟨Function.eval j, by fun_prop⟩) <;> simp
 
 lemma eq_prod_of_integral_prod_mul_prod_boundedContinuousFunction' {μ : Measure (Π i, X i)}
     {ν : Measure (Π j, Y j)} {ξ : Measure ((Π i, X i) × (Π j, Y j))}
@@ -300,7 +303,7 @@ lemma ext_of_integral_prod_mul_boundedContinuousFunction' {μ ν : Measure ((Π
     μ = ν := by
   have := Fintype.ofFinite ι
   refine ext_of_integral_prod_mul_boundedContinuousFunction fun f g ↦ ?_
-  convert h (∏ i, (f i).compContinuous ⟨Function.eval i, by fun_prop⟩) g <;> simp
+  convert! h (∏ i, (f i).compContinuous ⟨Function.eval i, by fun_prop⟩) g <;> simp
 
 lemma eq_prod_of_integral_prod_mul_boundedContinuousFunction' {μ : Measure (Π i, X i)}
     {ν : Measure T} {ξ : Measure ((Π i, X i) × T)}
@@ -316,7 +319,7 @@ lemma ext_of_integral_mul_prod_boundedContinuousFunction' {μ ν : Measure (Z ×
     μ = ν := by
   have := Fintype.ofFinite κ
   refine ext_of_integral_mul_prod_boundedContinuousFunction fun f g ↦ ?_
-  convert h f (∏ j, (g j).compContinuous ⟨Function.eval j, by fun_prop⟩) <;> simp
+  convert! h f (∏ j, (g j).compContinuous ⟨Function.eval j, by fun_prop⟩) <;> simp
 
 lemma eq_prod_of_integral_mul_prod_boundedContinuousFunction' {μ : Measure Z}
     {ν : Measure (Π j, Y j)} {ξ : Measure (Z × (Π j, Y j))}
diff --git a/Mathlib/MeasureTheory/Measure/Hausdorff.lean b/Mathlib/MeasureTheory/Measure/Hausdorff.lean
index a11ef8c5fd104f..68c834bf0221d7 100644
--- a/Mathlib/MeasureTheory/Measure/Hausdorff.lean
+++ b/Mathlib/MeasureTheory/Measure/Hausdorff.lean
@@ -347,7 +347,7 @@ theorem mkMetric_top : (mkMetric (fun _ => ∞ : ℝ≥0∞ → ℝ≥0∞) : Ou
 `mkMetric m₁ hm₁ ≤ mkMetric m₂ hm₂`. -/
 theorem mkMetric_mono {m₁ m₂ : ℝ≥0∞ → ℝ≥0∞} (hle : m₁ ≤ᶠ[𝓝[≥] 0] m₂) :
     (mkMetric m₁ : OuterMeasure X) ≤ mkMetric m₂ := by
-  convert @mkMetric_mono_smul X _ _ m₂ _ ENNReal.one_ne_top one_ne_zero _ <;> simp [*]
+  convert! @mkMetric_mono_smul X _ _ m₂ _ ENNReal.one_ne_top one_ne_zero _ <;> simp [*]
 
 theorem isometry_comap_mkMetric (m : ℝ≥0∞ → ℝ≥0∞) {f : X → Y} (hf : Isometry f)
     (H : Monotone m ∨ Surjective f) : comap f (mkMetric m) = mkMetric m := by
@@ -459,7 +459,7 @@ theorem mkMetric_top : (mkMetric (fun _ => ∞ : ℝ≥0∞ → ℝ≥0∞) : Me
 `mkMetric m₁ hm₁ ≤ mkMetric m₂ hm₂`. -/
 theorem mkMetric_mono {m₁ m₂ : ℝ≥0∞ → ℝ≥0∞} (hle : m₁ ≤ᶠ[𝓝[≥] 0] m₂) :
     (mkMetric m₁ : Measure X) ≤ mkMetric m₂ := by
-  convert @mkMetric_mono_smul X _ _ _ _ m₂ _ ENNReal.one_ne_top one_ne_zero _ <;> simp [*]
+  convert! @mkMetric_mono_smul X _ _ _ _ m₂ _ ENNReal.one_ne_top one_ne_zero _ <;> simp [*]
 
 /-- A formula for `MeasureTheory.Measure.mkMetric`. -/
 theorem mkMetric_apply (m : ℝ≥0∞ → ℝ≥0∞) (s : Set X) :
@@ -624,7 +624,7 @@ theorem hausdorffMeasure_zero_singleton (x : X) : μH[0] ({x} : Set X) = 1 := by
         ⨅ (t : ℕ → Set X) (_ : {x} ⊆ ⋃ n, t n) (_ : ∀ n, ediam (t n) ≤ 1),
           ∑' n, ⨆ _ : (t n).Nonempty, ediam (t n) ^ (0 : ℝ) by
       apply le_trans this _
-      convert le_iSup₂ (α := ℝ≥0∞) (1 : ℝ≥0∞) zero_lt_one
+      convert! le_iSup₂ (α := ℝ≥0∞) (1 : ℝ≥0∞) zero_lt_one
       rfl
     simp only [ENNReal.rpow_zero, le_iInf_iff]
     intro t hst _
diff --git a/Mathlib/MeasureTheory/Measure/IntegralCharFun.lean b/Mathlib/MeasureTheory/Measure/IntegralCharFun.lean
index 0054b5b030e455..3bd1c948d35cb9 100644
--- a/Mathlib/MeasureTheory/Measure/IntegralCharFun.lean
+++ b/Mathlib/MeasureTheory/Measure/IntegralCharFun.lean
@@ -153,7 +153,7 @@ lemma measureReal_abs_dual_gt_le_integral_charFunDual {E : Type*} [NormedAddComm
     {μ : Measure E} [IsProbabilityMeasure μ] (L : StrongDual ℝ E) {r : ℝ} (hr : 0 < r) :
     μ.real {x | r < |L x|} ≤ 2⁻¹ * r * ‖∫ t in -2 * r⁻¹..2 * r⁻¹, 1 - charFunDual μ (t • L)‖ := by
   have : IsProbabilityMeasure (μ.map L) := Measure.isProbabilityMeasure_map (by fun_prop)
-  convert measureReal_abs_gt_le_integral_charFun (μ := μ.map L) hr with x
+  convert! measureReal_abs_gt_le_integral_charFun (μ := μ.map L) hr with x
   · rw [map_measureReal_apply (by fun_prop)]
     · simp
     · exact MeasurableSet.preimage measurableSet_Ioi (by fun_prop)
@@ -167,7 +167,7 @@ lemma measureReal_abs_inner_gt_le_integral_charFun {E : Type*} [SeminormedAddCom
     μ.real {x | r < |⟪a, x⟫|} ≤ 2⁻¹ * r * ‖∫ t in -2 * r⁻¹..2 * r⁻¹, 1 - charFun μ (t • a)‖ := by
   have : IsProbabilityMeasure (μ.map (fun x ↦ ⟪a, x⟫)) :=
     Measure.isProbabilityMeasure_map (by fun_prop)
-  convert measureReal_abs_gt_le_integral_charFun (μ := μ.map (fun x ↦ ⟪a, x⟫)) hr with x
+  convert! measureReal_abs_gt_le_integral_charFun (μ := μ.map (fun x ↦ ⟪a, x⟫)) hr with x
   · rw [map_measureReal_apply (by fun_prop)]
     · simp
     · exact MeasurableSet.preimage measurableSet_Ioi (by fun_prop)
diff --git a/Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean b/Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean
index eb313f7840861e..2dc9ea038c1f84 100644
--- a/Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean
+++ b/Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean
@@ -547,7 +547,7 @@ theorem volume_regionBetween_eq_lintegral [SFinite μ] (hf : AEMeasurable f (μ.
         (EventuallyEq.rfl.comp₂ _ <| quasiMeasurePreserving_fst.ae_eq_comp hg.ae_eq_mk)
   rw [lintegral_congr_ae h₁, ←
     volume_regionBetween_eq_lintegral' hf.measurable_mk hg.measurable_mk hs]
-  convert h₂ using 1
+  convert! h₂ using 1
   · rw [Measure.restrict_prod_eq_prod_univ]
     exact (Measure.restrict_eq_self _ (regionBetween_subset f g s)).symm
   · rw [Measure.restrict_prod_eq_prod_univ]
diff --git a/Mathlib/MeasureTheory/Measure/Lebesgue/Complex.lean b/Mathlib/MeasureTheory/Measure/Lebesgue/Complex.lean
index d1b0929c2746cd..318dd706e70c28 100644
--- a/Mathlib/MeasureTheory/Measure/Lebesgue/Complex.lean
+++ b/Mathlib/MeasureTheory/Measure/Lebesgue/Complex.lean
@@ -51,7 +51,7 @@ theorem measurableEquivRealProd_symm_apply (p : ℝ × ℝ) :
     measurableEquivRealProd.symm p = { re := p.1, im := p.2 } := rfl
 
 theorem volume_preserving_equiv_pi : MeasurePreserving measurableEquivPi := by
-  convert (measurableEquivPi.symm.measurable.measurePreserving volume).symm
+  convert! (measurableEquivPi.symm.measurable.measurePreserving volume).symm
   rw [← addHaarMeasure_eq_volume_pi, ← Basis.parallelepiped_basisFun, ← Basis.addHaar,
     measurableEquivPi, Homeomorph.toMeasurableEquiv_symm_coe,
     ContinuousLinearEquiv.coe_symm_toHomeomorph, Basis.map_addHaar, eq_comm]
diff --git a/Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean b/Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean
index 5f07bfb9acf284..e15b507c8f573c 100644
--- a/Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean
+++ b/Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean
@@ -78,7 +78,7 @@ theorem parallelepiped_basisFun (ι : Type*) [Fintype ι] :
     (Pi.basisFun ℝ ι).parallelepiped = TopologicalSpace.PositiveCompacts.piIcc01 ι :=
   SetLike.coe_injective <| by
     refine Eq.trans ?_ ((uIcc_of_le ?_).trans (Set.pi_univ_Icc _ _).symm)
-    · classical convert parallelepiped_single (ι := ι) 1
+    · classical convert! parallelepiped_single (ι := ι) 1
     · exact zero_le_one
 
 /-- A parallelepiped can be expressed on the standard basis. -/
@@ -114,12 +114,12 @@ open Measure TopologicalSpace.PositiveCompacts Module
 
 /-- The Haar measure equals the Lebesgue measure on `ℝ`. -/
 theorem addHaarMeasure_eq_volume : addHaarMeasure Icc01 = volume := by
-  convert (addHaarMeasure_unique volume Icc01).symm; simp [Icc01]
+  convert! (addHaarMeasure_unique volume Icc01).symm; simp [Icc01]
 
 /-- The Haar measure equals the Lebesgue measure on `ℝ^ι`. -/
 theorem addHaarMeasure_eq_volume_pi (ι : Type*) [Fintype ι] :
     addHaarMeasure (piIcc01 ι) = volume := by
-  convert (addHaarMeasure_unique volume (piIcc01 ι)).symm
+  convert! (addHaarMeasure_unique volume (piIcc01 ι)).symm
   simp only [piIcc01, volume_pi_pi fun _ => Icc (0 : ℝ) 1, PositiveCompacts.coe_mk,
     Compacts.coe_mk, Finset.prod_const_one, ENNReal.ofReal_one, Real.volume_Icc, one_smul, sub_zero]
 
@@ -189,12 +189,12 @@ theorem addHaar_submodule {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]
     SetLike.mem_coe]
   intro y hym hyn
   have A : (c ^ n - c ^ m) • x ∈ s := by
-    convert s.sub_mem hym hyn using 1
+    convert! s.sub_mem hym hyn using 1
     simp only [sub_smul, neg_sub_neg, add_sub_add_right_eq_sub]
   have H : c ^ n - c ^ m ≠ 0 := by
     simpa only [sub_eq_zero, Ne] using (pow_right_strictAnti₀ cpos cone).injective.ne hmn.symm
   have : x ∈ s := by
-    convert s.smul_mem (c ^ n - c ^ m)⁻¹ A
+    convert! s.smul_mem (c ^ n - c ^ m)⁻¹ A
     rw [smul_smul, inv_mul_cancel₀ H, one_smul]
   exact hx this
 
@@ -284,7 +284,7 @@ equal to `μ s` times the absolute value of the inverse of the determinant of `f
 theorem addHaar_preimage_linearEquiv (f : E ≃ₗ[ℝ] E) (s : Set E) :
     μ (f ⁻¹' s) = ENNReal.ofReal |LinearMap.det (f.symm : E →ₗ[ℝ] E)| * μ s := by
   have A : LinearMap.det (f : E →ₗ[ℝ] E) ≠ 0 := (LinearEquiv.isUnit_det' f).ne_zero
-  convert addHaar_preimage_linearMap μ A s
+  convert! addHaar_preimage_linearMap μ A s
   simp only [LinearEquiv.det_coe_symm]
 
 /-- The preimage of a set `s` under a continuous linear equiv `f` has measure
@@ -783,8 +783,9 @@ theorem tendsto_addHaar_inter_smul_one_of_density_one_aux (s : Set E) (hs : Meas
     apply B.congr' _
     filter_upwards [self_mem_nhdsWithin]
     rintro r (rpos : 0 < r)
-    convert I (closedBall x r) sᶜ (measure_closedBall_pos μ _ rpos).ne'
-      measure_closedBall_lt_top.ne hs.compl
+    convert!
+      I (closedBall x r) sᶜ (measure_closedBall_pos μ _ rpos).ne' measure_closedBall_lt_top.ne
+        hs.compl
     rw [compl_compl]
   have L' : Tendsto (fun r : ℝ => μ (sᶜ ∩ ({x} + r • t)) / μ ({x} + r • t)) (𝓝[>] 0) (𝓝 0) :=
     tendsto_addHaar_inter_smul_zero_of_density_zero μ sᶜ x L t ht h''t
diff --git a/Mathlib/MeasureTheory/Measure/Lebesgue/VolumeOfBalls.lean b/Mathlib/MeasureTheory/Measure/Lebesgue/VolumeOfBalls.lean
index 09c30c53a7e780..81fef1f10b6d72 100644
--- a/Mathlib/MeasureTheory/Measure/Lebesgue/VolumeOfBalls.lean
+++ b/Mathlib/MeasureTheory/Measure/Lebesgue/VolumeOfBalls.lean
@@ -94,7 +94,7 @@ theorem MeasureTheory.measure_lt_one_eq_integral_div_gamma {p : ℝ} (hp : 0 < p
   -- The measure `ν` is the measure on `F` defined by `μ`
   -- Since we have two different topologies, it is necessary to specify the topology of E
   let ν : Measure F := @Measure.map E F mE _ φ μ
-  convert (measure_unitBall_eq_integral_div_gamma ν hp) using 1
+  convert! (measure_unitBall_eq_integral_div_gamma ν hp) using 1
   · rw [@Measure.map_apply E F mE _ μ φ _ _ measurableSet_ball]
     · congr!
       simp_rw [Metric.ball, dist_zero_right]
@@ -127,7 +127,7 @@ theorem MeasureTheory.measure_le_eq_lt [Nontrivial E] (r : ℝ) :
   -- The measure `ν` is the measure on `F` defined by `μ`
   -- Since we have two different topologies, it is necessary to specify the topology of E
   let ν : Measure F := @Measure.map E F mE _ φ μ
-  convert addHaar_closedBall_eq_addHaar_ball ν 0 r using 1
+  convert! addHaar_closedBall_eq_addHaar_ball ν 0 r using 1
   · rw [@Measure.map_apply E F mE _ μ φ _ _ measurableSet_closedBall]
     · congr!
       simp_rw [Metric.closedBall, dist_zero_right]
@@ -171,9 +171,10 @@ theorem MeasureTheory.volume_sum_rpow_lt_one (hp : 1 ≤ p) :
   simp_rw [← toLp_neg, ← toLp_add, ← toLp_smul, eq_norm,
     norm_eq_abs] at eq_zero nm_zero nm_neg nm_add nm_smul
   -- We use `measure_lt_one_eq_integral_div_gamma` with `g` equals to the norm `L_p`
-  convert (measure_lt_one_eq_integral_div_gamma (volume : Measure (ι → ℝ))
-    (g := fun x => (∑ i, |x i| ^ p) ^ (1 / p)) nm_zero nm_neg nm_add (eq_zero _).mp
-    (fun r x => nm_smul r x) (by linarith : 0 < p)) using 4
+  convert!
+    (measure_lt_one_eq_integral_div_gamma (volume : Measure (ι → ℝ)) (g := fun x =>
+      (∑ i, |x i| ^ p) ^ (1 / p)) nm_zero nm_neg nm_add (eq_zero _).mp (fun r x => nm_smul r x)
+      (by linarith : 0 < p)) using 4
   · rw [rpow_lt_one_iff' _ (one_div_pos.mpr h₁)]
     exact Finset.sum_nonneg' (fun _ => rpow_nonneg (abs_nonneg _) _)
   · simp_rw [← rpow_mul (h₂ _), div_mul_cancel₀ _ (ne_of_gt h₁), Real.rpow_one,
@@ -194,7 +195,7 @@ theorem MeasureTheory.volume_sum_rpow_lt [Nonempty ι] {p : ℝ} (hp : 1 ≤ p)
       exact not_le.mpr (lt_of_lt_of_le (Set.mem_setOf.mp hx) hr) (h₂ x)
     rw [this, measure_empty, ← zero_eq_ofReal.mpr hr, zero_pow Fin.pos'.ne', zero_mul]
   · rw [← volume_sum_rpow_lt_one _ hp, ← ofReal_pow (le_of_lt hr), ← finrank_pi ℝ]
-    convert addHaar_smul_of_nonneg volume (le_of_lt hr) {x : ι → ℝ | ∑ i, |x i| ^ p < 1} using 2
+    convert! addHaar_smul_of_nonneg volume (le_of_lt hr) {x : ι → ℝ | ∑ i, |x i| ^ p < 1} using 2
     simp_rw [← Set.preimage_smul_inv₀ (ne_of_gt hr), Set.preimage_setOf_eq, Pi.smul_apply,
       smul_eq_mul, abs_mul, mul_rpow (abs_nonneg _) (abs_nonneg _), abs_inv,
       inv_rpow (abs_nonneg _), ← Finset.mul_sum, abs_eq_self.mpr (le_of_lt hr),
@@ -244,9 +245,10 @@ theorem Complex.volume_sum_rpow_lt_one {p : ℝ} (hp : 1 ≤ p) :
     norm_smul_le (β := PiLp (.ofReal p) (fun _ : ι => ℂ)) r (toLp (.ofReal p) x)
   simp_rw [← toLp_neg, ← toLp_add, ← toLp_smul, eq_norm] at eq_zero nm_zero nm_neg nm_add nm_smul
   -- We use `measure_lt_one_eq_integral_div_gamma` with `g` equals to the norm `L_p`
-  convert measure_lt_one_eq_integral_div_gamma (volume : Measure (ι → ℂ))
-    (g := fun x => (∑ i, ‖x i‖ ^ p) ^ (1 / p)) nm_zero nm_neg nm_add (eq_zero _).mp
-    (fun r x => nm_smul r x) (by linarith : 0 < p) using 4
+  convert!
+    measure_lt_one_eq_integral_div_gamma (volume : Measure (ι → ℂ)) (g := fun x =>
+      (∑ i, ‖x i‖ ^ p) ^ (1 / p)) nm_zero nm_neg nm_add (eq_zero _).mp (fun r x => nm_smul r x)
+      (by linarith : 0 < p) using 4
   · rw [rpow_lt_one_iff' _ (one_div_pos.mpr h₁)]
     exact Finset.sum_nonneg' (fun _ => rpow_nonneg (norm_nonneg _) _)
   · simp_rw [← rpow_mul (h₂ _), div_mul_cancel₀ _ (ne_of_gt h₁), Real.rpow_one,
@@ -268,7 +270,7 @@ theorem Complex.volume_sum_rpow_lt [Nonempty ι] {p : ℝ} (hp : 1 ≤ p) (r : 
       exact not_le.mpr (lt_of_lt_of_le (Set.mem_setOf.mp hx) hr) (h₂ x)
     rw [this, measure_empty, ← zero_eq_ofReal.mpr hr, zero_pow Fin.pos'.ne', zero_mul]
   · rw [← Complex.volume_sum_rpow_lt_one _ hp, ← ENNReal.ofReal_pow (le_of_lt hr)]
-    convert addHaar_smul_of_nonneg volume (le_of_lt hr) {x : ι → ℂ |  ∑ i, ‖x i‖ ^ p < 1} using 2
+    convert! addHaar_smul_of_nonneg volume (le_of_lt hr) {x : ι → ℂ | ∑ i, ‖x i‖ ^ p < 1} using 2
     · simp_rw [← Set.preimage_smul_inv₀ (ne_of_gt hr), Set.preimage_setOf_eq, Pi.smul_apply,
         norm_smul, mul_rpow (norm_nonneg _) (norm_nonneg _), Real.norm_eq_abs, abs_inv, inv_rpow
         (abs_nonneg _), ← Finset.mul_sum, abs_eq_self.mpr (le_of_lt hr), inv_mul_lt_iff₀
@@ -318,7 +320,7 @@ theorem volume_ball (x : EuclideanSpace ℝ ι) (r : ℝ) :
     rw [← (PiLp.volume_preserving_toLp ι).measure_preimage
       measurableSet_ball.nullMeasurableSet]
     simp only [Set.preimage, ball_zero_eq _ zero_le_one, one_pow, Set.mem_setOf_eq]
-    convert volume_sum_rpow_lt_one ι one_le_two using 4
+    convert! volume_sum_rpow_lt_one ι one_le_two using 4
     · simp [sq_abs]
     · rw [Gamma_add_one (by simp), Gamma_one_half_eq, ← mul_assoc, mul_div_cancel₀ _
         two_ne_zero, one_mul]
@@ -350,7 +352,7 @@ theorem volume_ball (x : E) (r : ℝ) :
   have : Nonempty (Fin (finrank ℝ E)) := Fin.pos_iff_nonempty.mp finrank_pos
   have := EuclideanSpace.volume_ball (Fin (finrank ℝ E)) ((stdOrthonormalBasis ℝ E).repr x) r
   simp_rw [Fintype.card_fin] at this
-  convert this
+  convert! this
   simp only [LinearIsometryEquiv.preimage_ball, LinearIsometryEquiv.symm_symm]
 
 theorem volume_closedBall (x : E) (r : ℝ) :
diff --git a/Mathlib/MeasureTheory/Measure/LevyConvergence.lean b/Mathlib/MeasureTheory/Measure/LevyConvergence.lean
index 1abf40924cdce2..9d6a3d1213e098 100644
--- a/Mathlib/MeasureTheory/Measure/LevyConvergence.lean
+++ b/Mathlib/MeasureTheory/Measure/LevyConvergence.lean
@@ -165,7 +165,7 @@ lemma ProbabilityMeasure.tendsto_of_tight_of_separatesPoints (𝕜 : Type*) [RCL
     isCompact_closure_of_isTightMeasureSet (by simpa using h_tight)
   obtain ⟨μ', -, hμ' : Tendsto _ _ _⟩ := h_compact.ultrafilter_le_nhds (U.map μ)
     (.trans (by simp) (monotone_principal subset_closure))
-  suffices (μ' : Measure E) = μ₀ by convert hμ'; ext; rw [this]
+  suffices (μ' : Measure E) = μ₀ by convert! hμ'; ext; rw [this]
   refine ext_of_forall_mem_subalgebra_integral_eq_of_pseudoEMetric_complete_countable hA
     fun g hg ↦ tendsto_nhds_unique ?_ ((hμ g hg).comp hU)
   rw [ProbabilityMeasure.tendsto_iff_forall_integral_rclike_tendsto 𝕜] at hμ'
diff --git a/Mathlib/MeasureTheory/Measure/LevyProkhorovMetric.lean b/Mathlib/MeasureTheory/Measure/LevyProkhorovMetric.lean
index a00d9467c09c39..89b493ffe35e45 100644
--- a/Mathlib/MeasureTheory/Measure/LevyProkhorovMetric.lean
+++ b/Mathlib/MeasureTheory/Measure/LevyProkhorovMetric.lean
@@ -180,7 +180,7 @@ lemma levyProkhorovDist_triangle [OpensMeasurableSpace Ω] (μ ν κ : Measure 
     levyProkhorovDist μ κ ≤ levyProkhorovDist μ ν + levyProkhorovDist ν κ := by
   have dμν_finite := (levyProkhorovEDist_lt_top μ ν).ne
   have dνκ_finite := (levyProkhorovEDist_lt_top ν κ).ne
-  convert ENNReal.toReal_mono ?_ <| levyProkhorovEDist_triangle μ ν κ
+  convert! ENNReal.toReal_mono ?_ <| levyProkhorovEDist_triangle μ ν κ
   · simp only [levyProkhorovDist, ENNReal.toReal_add dμν_finite dνκ_finite]
   · exact ENNReal.add_ne_top.mpr ⟨dμν_finite, dνκ_finite⟩
 
@@ -250,7 +250,7 @@ lemma levyProkhorovDist_le_of_forall_le
     refine (ofReal_lt_ofReal_iff ?_).mp ?_
     · exact ENNReal.toReal_pos ε_gt.bot_lt.ne' ε_lt_top.ne
     · simpa [ofReal_toReal_eq_iff.mpr ε_lt_top.ne] using ε_gt
-  convert h ε.toReal B ε_gt' B_mble
+  convert! h ε.toReal B ε_gt' B_mble
   exact (ENNReal.ofReal_toReal ε_lt_top.ne).symm
 
 /-! ### Equipping measures with the Lévy-Prokhorov metric -/
@@ -389,8 +389,10 @@ lemma BoundedContinuousFunction.integral_le_of_levyProkhorovEDist_lt (μ ν : Me
               ≤ (fun (t : ℝ) ↦ ν.real (thickening ε {a | t ≤ f a}) + ε) := by
     intro t
     simp only [measureReal_def]
-    convert ENNReal.toReal_mono ?_ <| left_measure_le_of_levyProkhorovEDist_lt hμν
-      (B := {a | t ≤ f a}) (f.continuous.measurable measurableSet_Ici)
+    convert!
+      ENNReal.toReal_mono ?_ <|
+        left_measure_le_of_levyProkhorovEDist_lt hμν (B := {a | t ≤ f a})
+          (f.continuous.measurable measurableSet_Ici)
     · rw [ENNReal.toReal_add (measure_ne_top ν _) ofReal_ne_top, ENNReal.toReal_ofReal ε_pos.le]
     · exact ENNReal.add_ne_top.mpr ⟨measure_ne_top ν _, ofReal_ne_top⟩
   have intble₁ : IntegrableOn (fun t ↦ μ.real {a | t ≤ f a}) (Ioc 0 ‖f‖) := by
@@ -528,7 +530,7 @@ lemma ProbabilityMeasure.toMeasure_add_pos_gt_mem_nhds (P : ProbabilityMeasure 
   filter_upwards [gt_mem_sets_of_limsInf_gt (α := ℝ≥0∞) isBounded_ge_of_bot
       (show P.toMeasure G - ε < limsInf ((𝓝 P).map (fun Q ↦ Q.toMeasure G)) from aux)] with Q hQ
   simp only [preimage_setOf_eq, mem_setOf_eq] at hQ
-  convert ENNReal.add_lt_add_right ε_top hQ
+  convert! ENNReal.add_lt_add_right ε_top hQ
   exact (tsub_add_cancel_of_le easy).symm
 
 variable [SeparableSpace Ω]
@@ -555,10 +557,10 @@ lemma SeparableSpace.exists_measurable_partition_diam_le {ε : ℝ} (ε_pos : 0
   · exact fun n ↦ Bornology.IsBounded.subset isBounded_ball <| disjointed_subset Bs n
   · intro n
     apply (diam_mono (disjointed_subset Bs n) isBounded_ball).trans
-    convert diam_ball half_ε_pos.le
+    convert! diam_ball half_ε_pos.le
     ring
   · have aux : ⋃ n, Bs n = univ := by
-      convert DenseRange.iUnion_uniformity_ball xs_dense <| Metric.dist_mem_uniformity half_ε_pos
+      convert! DenseRange.iUnion_uniformity_ball xs_dense <| Metric.dist_mem_uniformity half_ε_pos
       exact (ball_eq_ball' _ _).symm
     simpa only [← aux] using iUnion_disjointed
   · exact disjoint_disjointed Bs
diff --git a/Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean b/Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean
index be40a58cb107f2..615cf047d4df96 100644
--- a/Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean
+++ b/Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean
@@ -224,7 +224,7 @@ theorem exists_measurable_superset_iff_measure_eq_zero :
 
 theorem measure_biUnion_lt_top {s : Set β} {f : β → Set α} (hs : s.Finite)
     (hfin : ∀ i ∈ s, μ (f i) < ∞) : μ (⋃ i ∈ s, f i) < ∞ := by
-  convert (measure_biUnion_finset_le (μ := μ) hs.toFinset f).trans_lt _ using 3
+  convert! (measure_biUnion_finset_le (μ := μ) hs.toFinset f).trans_lt _ using 3
   · ext
     rw [Finite.mem_toFinset]
   · simpa only [ENNReal.sum_lt_top, Finite.mem_toFinset]
diff --git a/Mathlib/MeasureTheory/Measure/MutuallySingular.lean b/Mathlib/MeasureTheory/Measure/MutuallySingular.lean
index 6674a829ce78d8..302749961949c7 100644
--- a/Mathlib/MeasureTheory/Measure/MutuallySingular.lean
+++ b/Mathlib/MeasureTheory/Measure/MutuallySingular.lean
@@ -203,8 +203,8 @@ lemma exists_null_set_measure_lt_of_disjoint (h : Disjoint μ ν) {ε : ℝ≥0}
 
 lemma mutuallySingular_of_disjoint (h : Disjoint μ ν) : μ ⟂ₘ ν := by
   have h' (n : ℕ) : ∃ s, μ s = 0 ∧ ν sᶜ ≤ (1 / 2) ^ n := by
-    convert exists_null_set_measure_lt_of_disjoint h (ε := (1 / 2) ^ (n + 1))
-      <| pow_pos (by simp) (n + 1)
+    convert!
+      exists_null_set_measure_lt_of_disjoint h (ε := (1 / 2) ^ (n + 1)) <| pow_pos (by simp) (n + 1)
     conv =>
       -- this tweak is needed due to the known issue of `norm_cast` with numeric fractions
       enter [1, 1]
diff --git a/Mathlib/MeasureTheory/Measure/Portmanteau.lean b/Mathlib/MeasureTheory/Measure/Portmanteau.lean
index 1aef701d6a14a0..d080e0073cee30 100644
--- a/Mathlib/MeasureTheory/Measure/Portmanteau.lean
+++ b/Mathlib/MeasureTheory/Measure/Portmanteau.lean
@@ -517,7 +517,7 @@ lemma integral_le_liminf_integral_of_forall_isOpen_measure_le_liminf_measure
                   f.continuous f_nn h_opens
   rw [@integral_eq_lintegral_of_nonneg_ae Ω _ μ f (Eventually.of_forall f_nn)
         f.continuous.measurable.aestronglyMeasurable]
-  convert ENNReal.toReal_mono ?_ same
+  convert! ENNReal.toReal_mono ?_ same
   · simp only [fun i ↦ @integral_eq_lintegral_of_nonneg_ae Ω _ (μs i) f (Eventually.of_forall f_nn)
                         f.continuous.measurable.aestronglyMeasurable]
     let g := BoundedContinuousFunction.comp _ Real.lipschitzWith_toNNReal f
@@ -534,7 +534,7 @@ lemma integral_le_liminf_integral_of_forall_isOpen_measure_le_liminf_measure
     · intro x hx
       obtain ⟨i, hi⟩ := hx.exists
       apply le_trans hi
-      convert obs i with x
+      convert! obs i with x
       have aux := ENNReal.ofReal_eq_coe_nnreal (f_nn x)
       simp only [ContinuousMap.toFun_eq_coe, BoundedContinuousFunction.coe_toContinuousMap] at aux
       rw [aux]
@@ -567,7 +567,7 @@ theorem tendsto_of_forall_isOpen_le_liminf_nat {μ : ProbabilityMeasure Ω}
     · exact ⟨0, by simp⟩
   have obs := ENNReal.coe_mono h_opens
   simp only [ProbabilityMeasure.ennreal_coeFn_eq_coeFn_toMeasure, aux] at obs
-  convert obs
+  convert! obs
   simp only [Function.comp_apply, ProbabilityMeasure.ennreal_coeFn_eq_coeFn_toMeasure]
 
 /-- One implication of the portmanteau theorem: if for all open sets `G` we have the liminf
@@ -628,7 +628,7 @@ lemma tendsto_of_forall_isClosed_limsup_le_nat {μs : ℕ → ProbabilityMeasure
       ⟨1, by simp⟩ ⟨0, by simp⟩
   have obs := ENNReal.coe_mono h
   simp only [ProbabilityMeasure.ennreal_coeFn_eq_coeFn_toMeasure, aux] at obs
-  convert obs
+  convert! obs
   simp
 
 /-- One implication of the portmanteau theorem: if for all closed sets `F` we have the limsup
@@ -790,7 +790,7 @@ lemma ProbabilityMeasure.exists_lt_measure_biUnion_of_isOpen
   rw [← G_eq] at this
   rcases ((tendsto_order.1 this).1 r hr).exists with ⟨n, hn⟩
   refine ⟨(Finset.range (n + 1)).image f, by grind, ?_, ?_⟩
-  · convert hn
+  · convert! hn
     simp [accumulate_def]
   · simpa [G_eq] using fun i _ ↦ subset_iUnion f i
 
diff --git a/Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean b/Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean
index a3db8bac502b3f..89b72124f705da 100644
--- a/Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean
+++ b/Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean
@@ -642,7 +642,7 @@ lemma tendsto_map_of_tendsto_of_continuous {ι : Type*} {L : Filter ι}
       (𝓝 (ν.map f_cont.measurable.aemeasurable)) := by
   rw [ProbabilityMeasure.tendsto_iff_forall_lintegral_tendsto] at lim ⊢
   intro g
-  convert lim (g.compContinuous ⟨f, f_cont⟩) <;>
+  convert! lim (g.compContinuous ⟨f, f_cont⟩) <;>
   · simp only [map, compContinuous_apply, ContinuousMap.coe_mk]
     refine lintegral_map ?_ f_cont.measurable
     exact (ENNReal.continuous_coe.comp g.continuous).measurable
diff --git a/Mathlib/MeasureTheory/Measure/Prod.lean b/Mathlib/MeasureTheory/Measure/Prod.lean
index e14709c68ecd9c..e9f92b71955eb6 100644
--- a/Mathlib/MeasureTheory/Measure/Prod.lean
+++ b/Mathlib/MeasureTheory/Measure/Prod.lean
@@ -907,7 +907,8 @@ theorem prod_of_left {α β γ} [MeasurableSpace α] [MeasurableSpace β] [Measu
     (h2f : ∀ᵐ y ∂ν, QuasiMeasurePreserving (fun x => f (x, y)) μ τ) :
     QuasiMeasurePreserving f (μ.prod ν) τ := by
   rw [← prod_swap]
-  convert (QuasiMeasurePreserving.prod_of_right (hf.comp measurable_swap) h2f).comp
+  convert!
+    (QuasiMeasurePreserving.prod_of_right (hf.comp measurable_swap) h2f).comp
       ((measurable_swap.measurePreserving (ν.prod μ)).symm
           MeasurableEquiv.prodComm).quasiMeasurePreserving
 
@@ -1038,7 +1039,7 @@ theorem setLIntegral_prod_symm [SFinite μ] {s : Set α} {t : Set β} (f : α ×
     setLIntegral_prod]
   · rfl
   · refine AEMeasurable.comp_measurable ?_ measurable_swap
-    convert hf
+    convert! hf
     rw [← Measure.prod_restrict, Measure.prod_swap, Measure.prod_restrict]
 
 /-- The reversed version of **Tonelli's Theorem**. In this version `f` is in curried form, which
diff --git a/Mathlib/MeasureTheory/Measure/Prokhorov.lean b/Mathlib/MeasureTheory/Measure/Prokhorov.lean
index 3668103e9c3a36..42a8a0b8a738bc 100644
--- a/Mathlib/MeasureTheory/Measure/Prokhorov.lean
+++ b/Mathlib/MeasureTheory/Measure/Prokhorov.lean
@@ -106,14 +106,14 @@ theorem isCompact_setOf_finiteMeasure_le_of_compactSpace [CompactSpace E] (C : 
   { toFun := Λ
     map_add' g g' := by
       have : Tendsto (fun (μ : FiniteMeasure E) ↦ ∫ x, g x + g' x ∂μ) f (𝓝 (Λ g + Λ g')) := by
-        convert (hΛ g).add (hΛ g')
+        convert! (hΛ g).add (hΛ g')
         rw [integral_add]
         · exact g.continuous.integrable_of_hasCompactSupport g.hasCompactSupport
         · exact g'.continuous.integrable_of_hasCompactSupport g'.hasCompactSupport
       exact tendsto_nhds_unique (hΛ (g + g')) this
     map_smul' c g := by
       have : Tendsto (fun (μ : FiniteMeasure E) ↦ ∫ x, c • g x ∂μ) f (𝓝 (c • Λ g)) := by
-        convert (hΛ g).const_smul c
+        convert! (hΛ g).const_smul c
         rw [integral_smul]
       exact tendsto_nhds_unique (hΛ (c • g)) this
     monotone' g g' hgg' := by
@@ -142,7 +142,7 @@ theorem isCompact_setOf_finiteMeasure_le_of_compactSpace [CompactSpace E] (C : 
   let g' : C_c(E, ℝ) :=
   { toFun := g
     hasCompactSupport' := HasCompactSupport.of_compactSpace _ }
-  convert hΛ g'
+  convert! hΛ g'
   change ∫ (x : E), g' x ∂μlim' = Λ g'
   simp only [FiniteMeasure.toMeasure_mk, RealRMK.integral_rieszMeasure, μlim', μlim]
   rfl
@@ -249,7 +249,7 @@ lemma isCompact_setOf_finiteMeasure_mass_le_compl_isCompact_le
       simp only [restrict_mass, restrict_measure_eq,
         Measure.restrict_apply (A n).measurableSet.compl]
       refine ⟨(apply_le_mass ρ _).trans hρ.1, ?_⟩
-      convert measure_empty (μ := (ρ : Measure E))
+      convert! measure_empty (μ := (ρ : Measure E))
       apply disjoint_iff.1
       apply disjoint_compl_left.mono_right
       exact le_trans sdiff_le (le_partialSups _ _)
@@ -264,7 +264,7 @@ lemma isCompact_setOf_finiteMeasure_mass_le_compl_isCompact_le
     let μ : FiniteMeasure E := ⟨ν', ν'_fin⟩
     refine ⟨μ, ν'_reg, by simp [μ, ν'K], ?_⟩
     apply tendsto_of_forall_integral_tendsto (fun g ↦ ?_)
-    convert tendsto_iff_forall_integral_tendsto.1 ν_lim g using 2
+    convert! tendsto_iff_forall_integral_tendsto.1 ν_lim g using 2
     exact (hν' g).symm
   -- let `νₙ` be such nice limits on `disjointed K n`.
   choose! ν ν_reg νK hν using M
@@ -281,7 +281,7 @@ lemma isCompact_setOf_finiteMeasure_mass_le_compl_isCompact_le
         = (∑ i ∈ Finset.range (n + 1), ν i).toMeasure univ := by simp
     rw [this]
     suffices (∑ i ∈ Finset.range (n + 1), ν i).mass ≤ C by
-      convert ENNReal.coe_le_coe.2 this
+      convert! ENNReal.coe_le_coe.2 this
       simp
     have : Tendsto (fun (μ : FiniteMeasure E) ↦
         (∑ i ∈ Finset.range (n + 1), μ.restrict (disjointed K i)).mass) f
@@ -417,7 +417,7 @@ lemma isCompact_setOf_finiteMeasure_mass_le_compl_isCompact_le
     -- `ρ.restricted (K m \ K n)` is bounded by `ρ (Kₙᶜ) ≤ uₙ`.
     suffices (μ : Measure E) (K n)ᶜ ≤ u n by
       apply ENNReal.coe_le_coe.1
-      convert this
+      convert! this
       simp
     simp only [toMeasure_mk, (hK n).measurableSet.compl, Measure.sum_apply, μ]
     have : Tendsto (fun m ↦ ∑ i ∈ Finset.range (m + 1), (ν i : Measure E) (K n)ᶜ) atTop
@@ -441,7 +441,7 @@ lemma isCompact_setOf_finiteMeasure_mass_le_compl_isCompact_le
       gcongr
       simp
     suffices (∑ i ∈ Finset.Ioc n m, ν i).mass ≤ u n by
-      convert ENNReal.coe_le_coe.2 this
+      convert! ENNReal.coe_le_coe.2 this
       simp
     have : Tendsto (fun (μ : FiniteMeasure E) ↦
         (∑ i ∈ Finset.Ioc n m, μ.restrict (disjointed K i)).mass) f
diff --git a/Mathlib/MeasureTheory/Measure/QuasiMeasurePreserving.lean b/Mathlib/MeasureTheory/Measure/QuasiMeasurePreserving.lean
index 422a24f76b8021..b0cd4d56b46384 100644
--- a/Mathlib/MeasureTheory/Measure/QuasiMeasurePreserving.lean
+++ b/Mathlib/MeasureTheory/Measure/QuasiMeasurePreserving.lean
@@ -152,7 +152,7 @@ theorem image_zpow_ae_eq {s : Set α} {e : α ≃ α} (he : QuasiMeasurePreservi
     rwa [Equiv.Perm.iterate_eq_pow e⁻¹ k, inv_pow e k] at he'
   · rw [zpow_neg, zpow_natCast]
     replace hs : e ⁻¹' s =ᵐ[μ] s := by
-      convert he.preimage_ae_eq hs.symm
+      convert! he.preimage_ae_eq hs.symm
       rw [Equiv.preimage_image]
     replace he : (⇑e)^[k] ⁻¹' s =ᵐ[μ] s := he.preimage_iterate_ae_eq k hs
     rwa [Equiv.Perm.iterate_eq_pow e k] at he
diff --git a/Mathlib/MeasureTheory/Measure/Real.lean b/Mathlib/MeasureTheory/Measure/Real.lean
index 9e1c3f09c8fe3d..7178ed5b91de41 100644
--- a/Mathlib/MeasureTheory/Measure/Real.lean
+++ b/Mathlib/MeasureTheory/Measure/Real.lean
@@ -157,7 +157,7 @@ theorem measureReal_biUnion_finset_le (s : Finset β) (f : β → Set α) :
 
 theorem measureReal_iUnion_fintype_le [Fintype β] (f : β → Set α) :
     μ.real (⋃ b, f b) ≤ ∑ p, μ.real (f p) := by
-  convert measureReal_biUnion_finset_le Finset.univ f
+  convert! measureReal_biUnion_finset_le Finset.univ f
   simp
 
 theorem measureReal_iUnion_fintype [Fintype β] {f : β → Set α} (hn : Pairwise (Disjoint on f))
@@ -411,7 +411,7 @@ theorem exists_nonempty_inter_of_measureReal_univ_lt_sum_measureReal [IsFiniteMe
     (fun i mi ↦ (h i mi).nullMeasurableSet)
   simp only [Measure.real] at H
   apply (ENNReal.toReal_lt_toReal (by finiteness) _).1
-  · convert H
+  · convert! H
     rw [ENNReal.toReal_sum (by finiteness)]
   · exact (ENNReal.sum_lt_top.mpr (fun i hi ↦ measure_lt_top ..)).ne
 
diff --git a/Mathlib/MeasureTheory/Measure/Regular.lean b/Mathlib/MeasureTheory/Measure/Regular.lean
index a21d3d03757b73..6fa51d2ce28994 100644
--- a/Mathlib/MeasureTheory/Measure/Regular.lean
+++ b/Mathlib/MeasureTheory/Measure/Regular.lean
@@ -745,7 +745,7 @@ protected theorem map_iff [BorelSpace α] [MeasurableSpace β] [TopologicalSpace
     [BorelSpace β] (f : α ≃ₜ β) :
     InnerRegular (Measure.map f μ) ↔ InnerRegular μ := by
   refine ⟨fun h ↦ ?_, fun h ↦ h.map f⟩
-  convert h.map f.symm
+  convert! h.map f.symm
   rw [map_map f.symm.continuous.measurable f.continuous.measurable]
   simp
 
@@ -881,7 +881,7 @@ instance restrict [h : InnerRegularCompactLTTop μ] (A : Set α) :
 instance (priority := 50) [h : InnerRegularCompactLTTop μ] [IsFiniteMeasure μ] :
     InnerRegular μ := by
   constructor
-  convert h.innerRegular with s
+  convert! h.innerRegular with s
   simp [measure_ne_top μ s]
 
 instance (priority := 50) [BorelSpace α] [R1Space α] [InnerRegularCompactLTTop μ]
@@ -970,7 +970,7 @@ instance smul [h : InnerRegularCompactLTTop μ] (c : ℝ≥0∞) : InnerRegularC
     · simp [h's] at hr
     · simp [h'c, h's] at hs
   · constructor
-    convert InnerRegularWRT.smul h.innerRegular c using 2 with s
+    convert! InnerRegularWRT.smul h.innerRegular c using 2 with s
     have : (c • μ) s ≠ ∞ ↔ μ s ≠ ∞ := by simp [ENNReal.mul_eq_top, hc, h'c]
     simp only [this]
 
@@ -1122,7 +1122,7 @@ protected theorem map_iff [BorelSpace α] [MeasurableSpace β] [TopologicalSpace
     [BorelSpace β] (f : α ≃ₜ β) :
     Regular (Measure.map f μ) ↔ Regular μ := by
   refine ⟨fun h ↦ ?_, fun h ↦ h.map f⟩
-  convert h.map f.symm
+  convert! h.map f.symm
   rw [map_map f.symm.continuous.measurable f.continuous.measurable]
   simp
 
diff --git a/Mathlib/MeasureTheory/Measure/RegularityCompacts.lean b/Mathlib/MeasureTheory/Measure/RegularityCompacts.lean
index 189361037a6fd2..5f617b316ce066 100644
--- a/Mathlib/MeasureTheory/Measure/RegularityCompacts.lean
+++ b/Mathlib/MeasureTheory/Measure/RegularityCompacts.lean
@@ -208,7 +208,7 @@ theorem innerRegular_isCompact_isClosed_measurableSet_of_finite [TopologicalSpac
     P.InnerRegularWRT (fun s ↦ IsCompact s ∧ IsClosed s) MeasurableSet := by
   suffices P.InnerRegularWRT (fun s ↦ IsCompact s ∧ IsClosed s)
       fun s ↦ MeasurableSet s ∧ P s ≠ ∞ by
-    convert this
+    convert! this
     simp only [iff_self_and]
     exact fun _ ↦ measure_ne_top P _
   refine Measure.InnerRegularWRT.measurableSet_of_isOpen ?_ ?_
diff --git a/Mathlib/MeasureTheory/Measure/SeparableMeasure.lean b/Mathlib/MeasureTheory/Measure/SeparableMeasure.lean
index f7b837b27f2372..b4b3fa530b1330 100644
--- a/Mathlib/MeasureTheory/Measure/SeparableMeasure.lean
+++ b/Mathlib/MeasureTheory/Measure/SeparableMeasure.lean
@@ -101,7 +101,7 @@ theorem Measure.MeasureDense.nonempty' (h𝒜 : μ.MeasureDense 𝒜) :
     {s | s ∈ 𝒜 ∧ μ s ≠ ∞}.Nonempty := by
   rcases h𝒜.approx ∅ MeasurableSet.empty (by simp) 1 (by simp) with ⟨t, ht, hμt⟩
   refine ⟨t, ht, ?_⟩
-  convert ne_top_of_lt hμt
+  convert! ne_top_of_lt hμt
   rw [← bot_eq_empty, bot_symmDiff]
 
 /-- The set of measurable sets is measure-dense. -/
@@ -115,7 +115,7 @@ theorem Measure.MeasureDense.completion (h𝒜 : μ.MeasureDense 𝒜) : μ.comp
     obtain ⟨t, ht, hμst⟩ :=
       h𝒜.approx (toMeasurable μ s) (measurableSet_toMeasurable μ s) (by simpa) ε ε_pos
     refine ⟨t, ht, ?_⟩
-    convert hμst using 1
+    convert! hμst using 1
     rw [completion_apply]
     exact measure_congr <| ae_eq_set_symmDiff (NullMeasurableSet.toMeasurable_ae_eq hs).symm
       Filter.EventuallyEq.rfl
diff --git a/Mathlib/MeasureTheory/Measure/Support.lean b/Mathlib/MeasureTheory/Measure/Support.lean
index 9eca30b7825d69..57dd73eaaac971 100644
--- a/Mathlib/MeasureTheory/Measure/Support.lean
+++ b/Mathlib/MeasureTheory/Measure/Support.lean
@@ -130,7 +130,7 @@ lemma compl_support_eq_sUnion : μ.supportᶜ = ⋃₀ {t : Set X | IsOpen t ∧
     nhds_basis_opens x |>.notMem_measureSupport, fun t ↦ and_comm (b := x ∈ t)]
 
 lemma support_eq_sInter : μ.support = ⋂₀ {t : Set X | IsClosed t ∧ μ tᶜ = 0} := by
-  convert congr($(compl_support_eq_sUnion (μ := μ))ᶜ)
+  convert! congr($(compl_support_eq_sUnion (μ := μ))ᶜ)
   all_goals simp [Set.compl_sUnion, compl_involutive.image_eq_preimage_symm]
 
 section Lindelof
@@ -202,7 +202,7 @@ lemma support_restrict_subset {s : Set X} :
   refine Set.subset_inter (support_subset_of_isClosed isClosed_closure ?_)
     (support_mono restrict_le_self)
   rw [mem_ae_iff, μ.restrict_apply isClosed_closure.isOpen_compl.measurableSet]
-  convert μ.empty
+  convert! μ.empty
   exact subset_closure.disjoint_compl_left.eq_bot
 
 end Restrict
diff --git a/Mathlib/MeasureTheory/Measure/Tight.lean b/Mathlib/MeasureTheory/Measure/Tight.lean
index 775f0a2a0f58dc..9677fe44253823 100644
--- a/Mathlib/MeasureTheory/Measure/Tight.lean
+++ b/Mathlib/MeasureTheory/Measure/Tight.lean
@@ -123,7 +123,7 @@ protected lemma subset (hT : IsTightMeasureSet T) (hST : S ⊆ T) :
 protected lemma union (hS : IsTightMeasureSet S) (hT : IsTightMeasureSet T) :
     IsTightMeasureSet (S ∪ T) := by
   rw [IsTightMeasureSet, iSup_union]
-  convert Tendsto.sup_nhds hS hT
+  convert! Tendsto.sup_nhds hS hT
   simp
 
 protected lemma inter (hS : IsTightMeasureSet S) (T : Set (Measure 𝓧)) :
diff --git a/Mathlib/MeasureTheory/Measure/TightNormed.lean b/Mathlib/MeasureTheory/Measure/TightNormed.lean
index a7d24a8dd62afc..a97cdfcb30e1fd 100644
--- a/Mathlib/MeasureTheory/Measure/TightNormed.lean
+++ b/Mathlib/MeasureTheory/Measure/TightNormed.lean
@@ -49,7 +49,7 @@ variable [PseudoMetricSpace E]
 lemma tendsto_measure_compl_closedBall_of_isTightMeasureSet (hS : IsTightMeasureSet S) (x : E) :
     Tendsto (fun r : ℝ ↦ ⨆ μ ∈ S, μ (Metric.closedBall x r)ᶜ) atTop (𝓝 0) := by
   suffices Tendsto ((⨆ μ ∈ S, μ) ∘ (fun r ↦ (Metric.closedBall x r)ᶜ)) atTop (𝓝 0) by
-    convert this with r
+    convert! this with r
     simp
   refine hS.comp <| .mono_right ?_ <| monotone_smallSets Metric.cobounded_le_cocompact
   exact (Metric.hasAntitoneBasis_cobounded_compl_closedBall _).tendsto_smallSets
@@ -78,7 +78,7 @@ variable [NormedAddCommGroup E]
 lemma tendsto_measure_norm_gt_of_isTightMeasureSet (hS : IsTightMeasureSet S) :
     Tendsto (fun r : ℝ ↦ ⨆ μ ∈ S, μ {x | r < ‖x‖}) atTop (𝓝 0) := by
   have h := tendsto_measure_compl_closedBall_of_isTightMeasureSet hS 0
-  convert h using 6 with r
+  convert! h using 6 with r
   ext
   simp
 
@@ -86,7 +86,7 @@ lemma isTightMeasureSet_of_tendsto_measure_norm_gt [ProperSpace E]
     (h : Tendsto (fun r : ℝ ↦ ⨆ μ ∈ S, μ {x | r < ‖x‖}) atTop (𝓝 0)) :
     IsTightMeasureSet S := by
   refine isTightMeasureSet_of_tendsto_measure_compl_closedBall (x := 0) ?_
-  convert h using 6 with r
+  convert! h using 6 with r
   ext
   simp
 
@@ -139,7 +139,7 @@ lemma isTightMeasureSet_of_forall_basis_tendsto (b : OrthonormalBasis ι 𝕜 E)
     IsTightMeasureSet S := by
   rcases subsingleton_or_nontrivial E with hE | hE
   · simp only [IsTightMeasureSet, cocompact_eq_bot, smallSets_bot]
-    convert tendsto_pure_nhds (a := ∅) _
+    convert! tendsto_pure_nhds (a := ∅) _
     simp
   have h_rank : (0 : ℝ) < Fintype.card ι := by
     simpa [← Module.finrank_eq_card_basis b.toBasis, Module.finrank_pos_iff]
@@ -252,7 +252,7 @@ lemma isTightMeasureSet_range_of_tendsto_limsup_inner_of_norm_eq_one
     · simp only [norm_smul, norm_inv, norm_algebraMap', Real.norm_eq_abs, abs_norm]
       rw [inv_mul_cancel₀ (by positivity)]
     exact h.comp <| (tendsto_const_mul_atTop_of_pos (by positivity)).mpr tendsto_id
-  convert h' using 7 with r n x
+  convert! h' using 7 with r n x
   rw [inner_smul_left]
   simp only [map_inv₀, RCLike.conj_ofReal, norm_mul, norm_inv, norm_algebraMap', norm_norm]
   rw [mul_lt_mul_iff_right₀]
diff --git a/Mathlib/MeasureTheory/Measure/Typeclasses/Finite.lean b/Mathlib/MeasureTheory/Measure/Typeclasses/Finite.lean
index 0332eb77689970..c0cfa8c614f9ee 100644
--- a/Mathlib/MeasureTheory/Measure/Typeclasses/Finite.lean
+++ b/Mathlib/MeasureTheory/Measure/Typeclasses/Finite.lean
@@ -198,7 +198,7 @@ lemma tendsto_measure_biUnion_Ici_zero_of_pairwise_disjoint
   have key := tendsto_measure_iInter_atTop (μ := μ) (fun n ↦ by measurability)
     decr ⟨0, measure_ne_top _ _⟩
   simp only [nothing, measure_empty] at key
-  convert key
+  convert! key
 
 open scoped symmDiff
 
@@ -210,7 +210,7 @@ theorem abs_measureReal_sub_le_measureReal_symmDiff'
   have hts : μ (t \ s) ≠ ∞ := (measure_lt_top_of_subset diff_subset ht').ne
   suffices (μ s).toReal - (μ t).toReal = (μ (s \ t)).toReal - (μ (t \ s)).toReal by
     rw [this, measure_symmDiff_eq hs ht, ENNReal.toReal_add hst hts]
-    convert abs_sub (μ (s \ t)).toReal (μ (t \ s)).toReal <;> simp
+    convert! abs_sub (μ (s \ t)).toReal (μ (t \ s)).toReal <;> simp
   rw [measure_diff' s ht ht', measure_diff' t hs hs',
     ENNReal.toReal_sub_of_le measure_le_measure_union_right (by finiteness),
     ENNReal.toReal_sub_of_le measure_le_measure_union_right (by finiteness),
diff --git a/Mathlib/MeasureTheory/Measure/Typeclasses/Probability.lean b/Mathlib/MeasureTheory/Measure/Typeclasses/Probability.lean
index 3a88d1c217cdc9..3a4ceaa9cb3082 100644
--- a/Mathlib/MeasureTheory/Measure/Typeclasses/Probability.lean
+++ b/Mathlib/MeasureTheory/Measure/Typeclasses/Probability.lean
@@ -228,7 +228,7 @@ lemma prob_compl_lt_one_sub_of_lt_prob {p : ℝ≥0∞} (hμs : p < μ s) (s_mbl
   · simp at hμs
   · rw [prob_compl_eq_one_sub s_mble]
     apply ENNReal.sub_lt_of_sub_lt prob_le_one (Or.inl one_ne_top)
-    convert hμs
+    convert! hμs
     exact ENNReal.sub_sub_cancel one_ne_top (lt_of_lt_of_le hμs prob_le_one).le
 
 lemma prob_compl_le_one_sub_of_le_prob {p : ℝ≥0∞} (hμs : p ≤ μ s) (s_mble : MeasurableSet s) :
diff --git a/Mathlib/MeasureTheory/Measure/Typeclasses/SFinite.lean b/Mathlib/MeasureTheory/Measure/Typeclasses/SFinite.lean
index 6a5e3cb27ebc1f..2ce2bafbdcad01 100644
--- a/Mathlib/MeasureTheory/Measure/Typeclasses/SFinite.lean
+++ b/Mathlib/MeasureTheory/Measure/Typeclasses/SFinite.lean
@@ -160,7 +160,7 @@ theorem preimage_spanningSetsIndex_singleton (μ : Measure α) [SigmaFinite μ]
 
 theorem spanningSetsIndex_eq_iff (μ : Measure α) [SigmaFinite μ] {x : α} {n : ℕ} :
     spanningSetsIndex μ x = n ↔ x ∈ disjointed (spanningSets μ) n := by
-  convert Set.ext_iff.1 (preimage_spanningSetsIndex_singleton μ n) x
+  convert! Set.ext_iff.1 (preimage_spanningSetsIndex_singleton μ n) x
 
 theorem mem_disjointed_spanningSetsIndex (μ : Measure α) [SigmaFinite μ] (x : α) :
     x ∈ disjointed (spanningSets μ) (spanningSetsIndex μ x) :=
diff --git a/Mathlib/MeasureTheory/Measure/WithDensity.lean b/Mathlib/MeasureTheory/Measure/WithDensity.lean
index 06c802a4635846..c7202c88b472cb 100644
--- a/Mathlib/MeasureTheory/Measure/WithDensity.lean
+++ b/Mathlib/MeasureTheory/Measure/WithDensity.lean
@@ -252,7 +252,7 @@ theorem withDensity_apply_eq_zero' {f : α → ℝ≥0∞} {s : Set α} (hf : AE
     swap
     · simp only [measurableSet_toMeasurable, MeasurableSet.nullMeasurableSet]
     simp only [Pi.zero_apply] at A
-    convert A using 2
+    convert! A using 2
     ext x
     simp only [and_comm, exists_prop, mem_inter_iff, mem_setOf_eq,
       not_forall]
diff --git a/Mathlib/MeasureTheory/Order/Lattice.lean b/Mathlib/MeasureTheory/Order/Lattice.lean
index 04599857a97826..a699073554a52c 100644
--- a/Mathlib/MeasureTheory/Order/Lattice.lean
+++ b/Mathlib/MeasureTheory/Order/Lattice.lean
@@ -220,7 +220,7 @@ theorem Finset.measurable_range_sup' {f : ℕ → δ → α} {n : ℕ} (hf : ∀
 @[fun_prop]
 theorem Finset.measurable_range_sup'' {f : ℕ → δ → α} {n : ℕ} (hf : ∀ k ≤ n, Measurable (f k)) :
     Measurable fun x => (range (n + 1)).sup' nonempty_range_add_one fun k => f k x := by
-  convert Finset.measurable_range_sup' hf using 1
+  convert! Finset.measurable_range_sup' hf using 1
   ext x
   simp
 
diff --git a/Mathlib/MeasureTheory/OuterMeasure/AE.lean b/Mathlib/MeasureTheory/OuterMeasure/AE.lean
index 50f628fe48cbf8..62350704d6900c 100644
--- a/Mathlib/MeasureTheory/OuterMeasure/AE.lean
+++ b/Mathlib/MeasureTheory/OuterMeasure/AE.lean
@@ -205,33 +205,33 @@ theorem union_ae_eq_univ_of_ae_eq_univ_left (h : s =ᵐ[μ] univ) : (s ∪ t : S
   (ae_eq_set_union h (ae_eq_refl t)).trans <| by rw [univ_union]
 
 theorem union_ae_eq_univ_of_ae_eq_univ_right (h : t =ᵐ[μ] univ) : (s ∪ t : Set α) =ᵐ[μ] univ := by
-  convert ae_eq_set_union (ae_eq_refl s) h
+  convert! ae_eq_set_union (ae_eq_refl s) h
   rw [union_univ]
 
 theorem union_ae_eq_right_of_ae_eq_empty (h : s =ᵐ[μ] (∅ : Set α)) : (s ∪ t : Set α) =ᵐ[μ] t := by
-  convert ae_eq_set_union h (ae_eq_refl t)
+  convert! ae_eq_set_union h (ae_eq_refl t)
   rw [empty_union]
 
 theorem union_ae_eq_left_of_ae_eq_empty (h : t =ᵐ[μ] (∅ : Set α)) : (s ∪ t : Set α) =ᵐ[μ] s := by
-  convert ae_eq_set_union (ae_eq_refl s) h
+  convert! ae_eq_set_union (ae_eq_refl s) h
   rw [union_empty]
 
 theorem inter_ae_eq_right_of_ae_eq_univ (h : s =ᵐ[μ] univ) : (s ∩ t : Set α) =ᵐ[μ] t := by
-  convert ae_eq_set_inter h (ae_eq_refl t)
+  convert! ae_eq_set_inter h (ae_eq_refl t)
   rw [univ_inter]
 
 theorem inter_ae_eq_left_of_ae_eq_univ (h : t =ᵐ[μ] univ) : (s ∩ t : Set α) =ᵐ[μ] s := by
-  convert ae_eq_set_inter (ae_eq_refl s) h
+  convert! ae_eq_set_inter (ae_eq_refl s) h
   rw [inter_univ]
 
 theorem inter_ae_eq_empty_of_ae_eq_empty_left (h : s =ᵐ[μ] (∅ : Set α)) :
     (s ∩ t : Set α) =ᵐ[μ] (∅ : Set α) := by
-  convert ae_eq_set_inter h (ae_eq_refl t)
+  convert! ae_eq_set_inter h (ae_eq_refl t)
   rw [empty_inter]
 
 theorem inter_ae_eq_empty_of_ae_eq_empty_right (h : t =ᵐ[μ] (∅ : Set α)) :
     (s ∩ t : Set α) =ᵐ[μ] (∅ : Set α) := by
-  convert ae_eq_set_inter (ae_eq_refl s) h
+  convert! ae_eq_set_inter (ae_eq_refl s) h
   rw [inter_empty]
 
 theorem ae_eq_set_biInter {s : Set β} (hs : s.Countable) {t t' : β → Set α}
diff --git a/Mathlib/MeasureTheory/OuterMeasure/Caratheodory.lean b/Mathlib/MeasureTheory/OuterMeasure/Caratheodory.lean
index 2c6cbf77bef644..e20d3217288305 100644
--- a/Mathlib/MeasureTheory/OuterMeasure/Caratheodory.lean
+++ b/Mathlib/MeasureTheory/OuterMeasure/Caratheodory.lean
@@ -136,7 +136,7 @@ theorem isCaratheodory_iUnion_of_disjoint {s : ℕ → Set α} (h : ∀ i, IsCar
   apply (isCaratheodory_iff_le' m).mpr
   intro t
   have hp : m (t ∩ ⋃ i, s i) ≤ ⨆ n, m (t ∩ ⋃ i < n, s i) := by
-    convert measure_iUnion_le (μ := m) fun i => t ∩ s i using 1
+    convert! measure_iUnion_le (μ := m) fun i => t ∩ s i using 1
     · simp [inter_iUnion]
     · simp [ENNReal.tsum_eq_iSup_nat, isCaratheodory_sum m h hd]
   grw [hp, ENNReal.iSup_add]
@@ -214,7 +214,7 @@ theorem boundedBy_caratheodory {m : Set α → ℝ≥0∞} {s : Set α}
   apply ofFunction_caratheodory; intro t
   rcases t.eq_empty_or_nonempty with rfl | h
   · simp [Set.not_nonempty_empty]
-  · convert le_trans _ (hs t)
+  · convert! le_trans _ (hs t)
     · simp [h]
     exact add_le_add iSup_const_le iSup_const_le
 
diff --git a/Mathlib/MeasureTheory/PiSystem.lean b/Mathlib/MeasureTheory/PiSystem.lean
index df2010b2821d6a..1c6e968a10f640 100644
--- a/Mathlib/MeasureTheory/PiSystem.lean
+++ b/Mathlib/MeasureTheory/PiSystem.lean
@@ -591,7 +591,7 @@ inductive GenerateHas (s : Set (Set α)) : Set α → Prop
 theorem generateHas_compl {C : Set (Set α)} {s : Set α} : GenerateHas C sᶜ ↔ GenerateHas C s := by
   refine ⟨?_, GenerateHas.compl⟩
   intro h
-  convert GenerateHas.compl h
+  convert! GenerateHas.compl h
   simp
 
 /-- The least Dynkin system containing a collection of basic sets. -/
diff --git a/Mathlib/MeasureTheory/SetSemiring.lean b/Mathlib/MeasureTheory/SetSemiring.lean
index 3c9c34536d34d4..e024efd66574e6 100644
--- a/Mathlib/MeasureTheory/SetSemiring.lean
+++ b/Mathlib/MeasureTheory/SetSemiring.lean
@@ -270,7 +270,7 @@ lemma exists_disjoint_finset_diff_eq (hC : IsSetSemiring C) (hs : s ∈ C) (hI :
         refine hxy ?_
         refine Subtype.ext ?_
         exact h_dis.elim x.prop y.prop h_contra
-      convert hJu_disj' (x : Set α) (h_ss x.prop) y (h_ss y.prop) hxy_disj
+      convert! hJu_disj' (x : Set α) (h_ss x.prop) y (h_ss y.prop) hxy_disj
       · rw [sUnion_eq_biUnion]
         congr
       · rw [sUnion_eq_biUnion]
diff --git a/Mathlib/MeasureTheory/VectorMeasure/AddContent.lean b/Mathlib/MeasureTheory/VectorMeasure/AddContent.lean
index b296f2ba2d867e..fb2c6c1681039e 100644
--- a/Mathlib/MeasureTheory/VectorMeasure/AddContent.lean
+++ b/Mathlib/MeasureTheory/VectorMeasure/AddContent.lean
@@ -144,7 +144,7 @@ lemma exists_extension_of_isSetRing_of_le_measure_of_dense [IsFiniteMeasure μ]
       apply C'_dense.mono
       intro s hs
       simp only [Set.mem_setOf_eq]
-      convert hm s (C'C s hs)
+      convert! hm s (C'C s hs)
       exact C'_dense.extend_eq lip.continuous ⟨s, hs⟩
     simpa only [Dense, IsClosed.closure_eq, Set.mem_setOf_eq] using this
   /- Most involved technical step: show that the extension `m₁` of `m₀` is still finitely
diff --git a/Mathlib/MeasureTheory/VectorMeasure/Basic.lean b/Mathlib/MeasureTheory/VectorMeasure/Basic.lean
index e45965e0dbc9f6..4cf20ddf8f1627 100644
--- a/Mathlib/MeasureTheory/VectorMeasure/Basic.lean
+++ b/Mathlib/MeasureTheory/VectorMeasure/Basic.lean
@@ -129,7 +129,7 @@ theorem hasSum_of_disjoint_iUnion (hm : ∀ i, MeasurableSet (f i)) (hd : Pairwi
     HasSum (fun i => v (f i)) (v (⋃ i, f i)) := by
   rcases Countable.exists_injective_nat β with ⟨e, he⟩
   rw [← hasSum_extend_zero he]
-  convert m_iUnion v (f := Function.extend e f fun _ ↦ ∅) _ _
+  convert! m_iUnion v (f := Function.extend e f fun _ ↦ ∅) _ _
   · simp only [Pi.zero_def, Function.apply_extend v, Function.comp_def, empty]
   · exact (iSup_extend_bot he _).symm
   · simp [Function.apply_extend MeasurableSet, Function.comp_def, hm]
@@ -226,7 +226,7 @@ theorem tendsto_vectorMeasure_iUnion_atTop_nat
   have : HasSum (fun n ↦ v (t n)) (v (⋃ n, s n)) := by
     rw [← iUnion_disjointed]
     apply m_iUnion _ ht (disjoint_disjointed _)
-  convert (HasSum.tendsto_sum_nat this).comp (tendsto_add_atTop_nat 1) with n
+  convert! (HasSum.tendsto_sum_nat this).comp (tendsto_add_atTop_nat 1) with n
   dsimp
   rw [← of_biUnion_finset]
   · rw [biUnion_range_succ_disjointed, Monotone.partialSups_eq hm]
@@ -558,7 +558,7 @@ def map (v : VectorMeasure α M) (f : α → β) : VectorMeasure β M :=
       not_measurable' := fun _ hi => if_neg hi
       m_iUnion' := by
         intro g hg₁ hg₂
-        convert v.m_iUnion (fun i => hf (hg₁ i)) fun i j hij => (hg₂ hij).preimage _
+        convert! v.m_iUnion (fun i => hf (hg₁ i)) fun i j hij => (hg₂ hij).preimage _
         · rw [if_pos (hg₁ _)]
         · rw [Set.preimage_iUnion, if_pos (MeasurableSet.iUnion hg₁)] }
   else 0
@@ -656,7 +656,8 @@ def restrict (v : VectorMeasure α M) (i : Set α) : VectorMeasure α M :=
       not_measurable' := fun _ hi => if_neg hi
       m_iUnion' := by
         intro f hf₁ hf₂
-        convert v.m_iUnion (fun n => (hf₁ n).inter hi)
+        convert!
+          v.m_iUnion (fun n => (hf₁ n).inter hi)
             (hf₂.mono fun i j => Disjoint.mono inf_le_left inf_le_left)
         · rw [if_pos (hf₁ _)]
         · rw [Set.iUnion_inter, if_pos (MeasurableSet.iUnion hf₁)] }
@@ -1199,7 +1200,7 @@ def trim {m n : MeasurableSpace α} (v : VectorMeasure α M) (hle : m ≤ n) :
     (fun f hf₁ hf₂ => by
       dsimp only
       have hf₁' : ∀ k, MeasurableSet[n] (f k) := fun k => hle _ (hf₁ k)
-      convert v.m_iUnion hf₁' hf₂ using 1
+      convert! v.m_iUnion hf₁' hf₂ using 1
       · ext n
         rw [if_pos (hf₁ n)]
       · rw [if_pos (@MeasurableSet.iUnion _ _ m _ _ hf₁)])
diff --git a/Mathlib/MeasureTheory/VectorMeasure/BoundedVariation.lean b/Mathlib/MeasureTheory/VectorMeasure/BoundedVariation.lean
index 73cf1ce8eccf08..6cfb1d2441bbdf 100644
--- a/Mathlib/MeasureTheory/VectorMeasure/BoundedVariation.lean
+++ b/Mathlib/MeasureTheory/VectorMeasure/BoundedVariation.lean
@@ -96,7 +96,7 @@ private lemma exists_vectorMeasure_le_measureAux (hf : BoundedVariationOn f univ
     exact eVariationOn.edist_le _ (by grind) (by grind)
   have B : hα = generateFrom {s | ∃ u v, u ≤ v ∧ s = Ioc u v} := by
     borelize α
-    convert borel_eq_generateFrom_Ioc_le α using 2
+    convert! borel_eq_generateFrom_Ioc_le α using 2
     grind only
   rcases VectorMeasure.exists_extension_of_isSetSemiring_of_le_measure_of_generateFrom
     IsSetSemiring.Ioc A B with ⟨m', hm', h'm'⟩
@@ -164,7 +164,7 @@ lemma vectorMeasure_singleton (hf : BoundedVariationOn f univ) :
     apply tendsto_const_nhds.sub
     have : Tendsto u atTop (𝓝[<] a) := tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within _
       u_lim (Eventually.of_forall u_lt_a)
-    convert (hf.rightLim.tendsto_leftLim a).comp this using 2
+    convert! (hf.rightLim.tendsto_leftLim a).comp this using 2
     have : (𝓝[<] a).NeBot := by
       rw [← mem_closure_iff_nhdsWithin_neBot, closure_Iio' ⟨b, hb⟩]
       exact self_mem_Iic
diff --git a/Mathlib/MeasureTheory/VectorMeasure/Decomposition/Hahn.lean b/Mathlib/MeasureTheory/VectorMeasure/Decomposition/Hahn.lean
index b6cc5b8d51d598..892b8e9556e0a2 100644
--- a/Mathlib/MeasureTheory/VectorMeasure/Decomposition/Hahn.lean
+++ b/Mathlib/MeasureTheory/VectorMeasure/Decomposition/Hahn.lean
@@ -111,7 +111,7 @@ private def findExistsOneDivLT (s : SignedMeasure α) (i : Set α) : ℕ :=
 private theorem findExistsOneDivLT_spec (hi : ¬s ≤[i] 0) :
     ExistsOneDivLT s i (findExistsOneDivLT s i) := by
   rw [findExistsOneDivLT, dif_pos hi]
-  convert Nat.find_spec (existsNatOneDivLTMeasure_of_not_negative hi)
+  convert! Nat.find_spec (existsNatOneDivLTMeasure_of_not_negative hi)
 
 private theorem findExistsOneDivLT_min (hi : ¬s ≤[i] 0) {m : ℕ}
     (hm : m < findExistsOneDivLT s i) : ¬ExistsOneDivLT s i m := by
@@ -196,7 +196,7 @@ private theorem measure_of_restrictNonposSeq (hi₂ : ¬s ≤[i] 0) (n : ℕ)
     rw [restrictNonposSeq_succ]
     have h₁ : ¬s ≤[i \ ⋃ (k : ℕ) (_ : k ≤ n), restrictNonposSeq s i k] 0 := by
       refine mt (restrict_le_zero_subset _ ?_ (by simp)) hn
-      convert measurable_of_not_restrict_le_zero _ hn using 3
+      convert! measurable_of_not_restrict_le_zero _ hn using 3
       exact funext fun x => by rw [Nat.lt_succ_iff]
     rcases someExistsOneDivLT_spec h₁ with ⟨_, _, h⟩
     exact lt_trans Nat.one_div_pos_of_nat h
@@ -250,11 +250,11 @@ private theorem exists_subset_restrict_nonpos' (hi₁ : MeasurableSet i) (hi₂
       exact lt_of_lt_of_le hi₂ this
     refine tsum_nonneg ?_
     intro l; by_cases h : l < k
-    · convert h₁ _ h
+    · convert! h₁ _ h
       ext x
       rw [Set.mem_iUnion, exists_prop, and_iff_right_iff_imp]
       exact fun _ => h
-    · convert le_of_eq s.empty.symm
+    · convert! le_of_eq s.empty.symm
       ext; simp only [exists_prop, Set.mem_empty_iff_false, Set.mem_iUnion, not_and, iff_false]
       exact fun h' => False.elim (h h')
   · intro; exact MeasurableSet.iUnion fun _ => restrictNonposSeq_measurableSet _
@@ -279,7 +279,7 @@ theorem exists_subset_restrict_nonpos (hi : s i < 0) :
   set bdd : ℕ → ℕ := fun n => findExistsOneDivLT s (i \ ⋃ k ≤ n, restrictNonposSeq s i k)
   have hn' : ∀ n : ℕ, ¬s ≤[i \ ⋃ l ≤ n, restrictNonposSeq s i l] 0 := by
     intro n
-    convert hn (n + 1) using 5 <;>
+    convert! hn (n + 1) using 5 <;>
       · ext l
         simp only [exists_prop, Set.mem_iUnion, and_congr_left_iff]
         exact fun _ => Nat.lt_succ_iff.symm
@@ -304,7 +304,7 @@ theorem exists_subset_restrict_nonpos (hi : s i < 0) :
     simp only [one_div] at h₃'
     exact Summable.tendsto_atTop_of_pos h₃' fun n => Nat.cast_add_one_pos (bdd n)
   have h₄ : Tendsto (fun n => (bdd n : ℝ)) atTop atTop := by
-    convert atTop.tendsto_atTop_add_const_right (-1) h₃; simp
+    convert! atTop.tendsto_atTop_add_const_right (-1) h₃; simp
   have A_meas : MeasurableSet A :=
     hi₁.diff (MeasurableSet.iUnion fun _ => restrictNonposSeq_measurableSet _)
   refine ⟨A, A_meas, Set.diff_subset, ?_, h₂.trans_lt hi⟩
@@ -327,7 +327,7 @@ theorem exists_subset_restrict_nonpos (hi : s i < 0) :
   refine
     findExistsOneDivLT_min (hn' k) (Nat.sub_lt hk₁ Nat.zero_lt_one)
       ⟨E, Set.Subset.trans hE₂ hA', hE₁, ?_⟩
-  convert hk₂; norm_cast
+  convert! hk₂; norm_cast
   exact tsub_add_cancel_of_le hk₁
 
 end ExistsSubsetRestrictNonpos
diff --git a/Mathlib/MeasureTheory/VectorMeasure/Decomposition/Lebesgue.lean b/Mathlib/MeasureTheory/VectorMeasure/Decomposition/Lebesgue.lean
index 70f8dbd0485241..e86f35d52639ce 100644
--- a/Mathlib/MeasureTheory/VectorMeasure/Decomposition/Lebesgue.lean
+++ b/Mathlib/MeasureTheory/VectorMeasure/Decomposition/Lebesgue.lean
@@ -196,7 +196,7 @@ theorem singularPart_add_withDensity_rnDeriv_eq [s.HaveLebesgueDecomposition μ]
     add_assoc (-(s.toJordanDecomposition.negPart.singularPart μ).toSignedMeasure),
     ← toSignedMeasure_add, add_comm, ← add_assoc, ← neg_add, ← toSignedMeasure_add, add_comm,
     ← sub_eq_add_neg]
-  · convert rfl
+  · convert! rfl
     -- `convert rfl` much faster than `congr`
     · exact s.toJordanDecomposition.posPart.haveLebesgueDecomposition_add μ
     · rw [add_comm]
@@ -294,7 +294,7 @@ theorem eq_singularPart (t : SignedMeasure α) (f : α → ℝ) (htμ : t ⟂ᵥ
     (hadd : s = t + μ.withDensityᵥ f) : t = s.singularPart μ := by
   by_cases hfi : Integrable f μ
   · refine eq_singularPart' t hfi.1.measurable_mk (hfi.congr hfi.1.ae_eq_mk) htμ ?_
-    convert hadd using 2
+    convert! hadd using 2
     exact WithDensityᵥEq.congr_ae hfi.1.ae_eq_mk.symm
   · rw [withDensityᵥ, dif_neg hfi, add_zero] at hadd
     refine eq_singularPart' t measurable_zero (integrable_zero _ _ μ) htμ ?_
@@ -362,7 +362,7 @@ theorem eq_rnDeriv (t : SignedMeasure α) (f : α → ℝ) (hfi : Integrable f 
     f =ᵐ[μ] s.rnDeriv μ := by
   set f' := hfi.1.mk f
   have hadd' : s = t + μ.withDensityᵥ f' := by
-    convert hadd using 2
+    convert! hadd using 2
     exact WithDensityᵥEq.congr_ae hfi.1.ae_eq_mk.symm
   have := haveLebesgueDecomposition_mk μ hfi.1.measurable_mk htμ hadd'
   refine (Integrable.ae_eq_of_withDensityᵥ_eq (integrable_rnDeriv _ _) hfi ?_).symm
diff --git a/Mathlib/MeasureTheory/VectorMeasure/WithDensity.lean b/Mathlib/MeasureTheory/VectorMeasure/WithDensity.lean
index 6d4bca7b8207b9..88605419c9f9c4 100644
--- a/Mathlib/MeasureTheory/VectorMeasure/WithDensity.lean
+++ b/Mathlib/MeasureTheory/VectorMeasure/WithDensity.lean
@@ -48,7 +48,7 @@ def Measure.withDensityᵥ {m : MeasurableSpace α} (μ : Measure α) (f : α 
       empty' := by simp
       not_measurable' := fun _ hs => if_neg hs
       m_iUnion' := fun s hs₁ hs₂ => by
-        convert hasSum_integral_iUnion hs₁ hs₂ hf.integrableOn with n
+        convert! hasSum_integral_iUnion hs₁ hs₂ hf.integrableOn with n
         · rw [if_pos (hs₁ n)]
         · rw [if_pos (MeasurableSet.iUnion hs₁)] }
   else 0
diff --git a/Mathlib/ModelTheory/Arithmetic/Presburger/Definability.lean b/Mathlib/ModelTheory/Arithmetic/Presburger/Definability.lean
index 3e2b29a5a921d5..dbdb246371611b 100644
--- a/Mathlib/ModelTheory/Arithmetic/Presburger/Definability.lean
+++ b/Mathlib/ModelTheory/Arithmetic/Presburger/Definability.lean
@@ -116,17 +116,17 @@ lemma isSemilinearSet_boundedFormula_realize {n} (φ : presburger[[A]].BoundedFo
   | equal t₁ t₂ =>
     rcases term_realize_eq_add_dotProduct t₁ with ⟨k₁, u₁, ht₁⟩
     rcases term_realize_eq_add_dotProduct t₂ with ⟨k₂, u₂, ht₂⟩
-    convert Nat.isSemilinearSet_setOf_mulVec_eq ![k₁] ![k₂] (.of ![u₁]) (.of ![u₂])
+    convert! Nat.isSemilinearSet_setOf_mulVec_eq ![k₁] ![k₂] (.of ![u₁]) (.of ![u₂])
     simp [ht₁, ht₂]
   | rel f => nomatch f
   | falsum => exact .empty
   | imp _ _ ih₁ ih₂ =>
-    convert (ih₂.compl.inter ih₁).compl using 1
+    convert! (ih₂.compl.inter ih₁).compl using 1
     simp [setOf_inter_eq_sep, imp_iff_not_or, compl_setOf]
   | @all n φ ih =>
     let e := (Equiv.sumAssoc α (Fin n) (Fin 1)).trans (Equiv.sumCongr (.refl α) finSumFinEquiv)
     rw [← isSemilinearSet_image_iff (LinearEquiv.funCongrLeft ℕ ℕ e)] at ih
-    convert ih.compl.proj.compl using 1
+    convert! ih.compl.proj.compl using 1
     simp_rw [compl_setOf, not_exists, Fin.forall_fin_succ_pi, Fin.forall_fin_zero_pi,
       mem_compl_iff, mem_image, not_not, ← LinearEquiv.eq_symm_apply, LinearEquiv.funCongrLeft_symm,
       exists_eq_right, mem_setOf, LinearEquiv.funCongrLeft_apply, LinearMap.funLeft,
@@ -138,7 +138,7 @@ lemma isSemilinearSet_boundedFormula_realize {n} (φ : presburger[[A]].BoundedFo
 lemma isSemilinearSet_formula_realize_semilinear (φ : presburger[[A]].Formula α) :
     IsSemilinearSet (setOf φ.Realize : Set (α → ℕ)) := by
   let e := Equiv.sumEmpty α (Fin 0)
-  convert (isSemilinearSet_boundedFormula_realize φ).image (LinearMap.funLeft ℕ ℕ e.symm)
+  convert! (isSemilinearSet_boundedFormula_realize φ).image (LinearMap.funLeft ℕ ℕ e.symm)
   ext x
   simp only [mem_setOf_eq, mem_image]
   rw [(e.arrowCongr (.refl ℕ)).exists_congr_left]
@@ -163,7 +163,7 @@ theorem mul_not_definable : ¬ A.Definable presburger {v : Fin 3 → ℕ | v 0 =
   intro hmul
   have hsqr : A.Definable₁ presburger {x * x | x : ℕ} := by
     rw [Definable₁]
-    convert (hmul.preimage_comp (β := Fin 2) ![0, 1, 1]).image_comp ![0]
+    convert! (hmul.preimage_comp (β := Fin 2) ![0, 1, 1]).image_comp ![0]
     ext
     simpa [funext_iff, Fin.exists_fin_succ_pi] using exists_congr fun _ => Eq.comm
   rw [definable₁_iff_ultimately_periodic] at hsqr
diff --git a/Mathlib/ModelTheory/Arithmetic/Presburger/Semilinear/Basic.lean b/Mathlib/ModelTheory/Arithmetic/Presburger/Semilinear/Basic.lean
index 10f0b5bcd9c80a..0759840f7cca0c 100644
--- a/Mathlib/ModelTheory/Arithmetic/Presburger/Semilinear/Basic.lean
+++ b/Mathlib/ModelTheory/Arithmetic/Presburger/Semilinear/Basic.lean
@@ -209,8 +209,9 @@ private lemma Nat.isSemilinearSet_preimage_of_isLinearSet [Finite ι] {F : Type*
   change IsSemilinearSet { x | f x ∈ _ }
   simp only [mem_vadd_set, mem_range, vadd_eq_add, exists_exists_eq_and]
   apply IsSemilinearSet.proj'
-  convert isSemilinearSet_setOf_eq a 0 (g.comp (LinearMap.funLeft ℕ ℕ Sum.inr).toAddMonoidHom)
-    ((f : (ι → ℕ) →+ M).comp (LinearMap.funLeft ℕ ℕ Sum.inl).toAddMonoidHom)
+  convert!
+    isSemilinearSet_setOf_eq a 0 (g.comp (LinearMap.funLeft ℕ ℕ Sum.inr).toAddMonoidHom)
+      ((f : (ι → ℕ) →+ M).comp (LinearMap.funLeft ℕ ℕ Sum.inl).toAddMonoidHom)
   simp [LinearMap.funLeft]
 
 private theorem Nat.isSemilinearSet_preimage [Finite ι] {F : Type*}
@@ -275,8 +276,9 @@ private lemma Nat.isSemilinearSet_inter_of_isLinearSet [Finite ι] {s₁ s₂ :
   rcases hs₂ with ⟨v, m, B, rfl⟩
   simp_rw [← setOf_and, exists_and_exists_comm]
   refine IsSemilinearSet.proj' (IsSemilinearSet.proj' ?_)
-  convert isSemilinearSet_setOf_mulVec_eq (κ := (ι ⊕ Fin n) ⊕ Fin m) (Sum.elim u v) 0
-    (fromBlocks (fromCols 0 A) 0 0 B) (fromBlocks (fromCols 1 0) 0 (fromCols 1 0) 0)
+  convert!
+    isSemilinearSet_setOf_mulVec_eq (κ := (ι ⊕ Fin n) ⊕ Fin m) (Sum.elim u v) 0
+      (fromBlocks (fromCols 0 A) 0 0 B) (fromBlocks (fromCols 1 0) 0 (fromCols 1 0) 0)
   simp [fromBlocks_mulVec, fromCols_mulVec, ← Sum.elim_add_add, Sum.elim_eq_iff]
 
 private theorem Nat.isSemilinearSet_inter [Finite ι] {s₁ s₂ : Set (ι → ℕ)}
@@ -420,7 +422,7 @@ private theorem span_basisSet : span ℚ (toRatVec '' hs.basisSet) = ⊤ := by
     ← top_le_iff]
   apply (span_mono (image_mono subset_union_right)).trans'
   rw [top_le_iff]
-  convert (Pi.basisFun ℚ ι).span_eq
+  convert! (Pi.basisFun ℚ ι).span_eq
   ext
   simp only [mem_image, mem_range, exists_exists_eq_and]
   congr!
@@ -584,7 +586,7 @@ private theorem mem_iff_fract_eq_and_floor_nonneg (x) :
     rw [Finset.sum_filter, ← hx₁]
     conv_rhs =>
       rw [← add_zero x, ← Finset.sum_const_zero (ι := hs.basisSet) (s := Finset.univ)]
-    convert (hs.add_floor_neg_toNat_sum_eq x).symm using 3 with i _ i
+    convert! (hs.add_floor_neg_toNat_sum_eq x).symm using 3 with i _ i
     · split_ifs with hi
       · simp
       · simp [(hx₂ i).2 hi]
@@ -619,9 +621,10 @@ private theorem isSemilinearSet_setOfFractNe : IsSemilinearSet hs.setOfFractNe :
       (.closure_of_finite hs.finite_basisSet) (LinearMap.funLeft ℕ ℕ Sum.inr)
     classical
     haveI := Fintype.ofFinite ι
-    convert Nat.isSemilinearSet_setOf_mulVec_eq (κ := (ι ⊕ ι) ⊕ ι) 0 i
-      (Matrix.fromCols (Matrix.fromCols 1 0) 1) (Matrix.fromCols (Matrix.fromCols 0 1) 0)
-      using 4 <;> simp [fromCols_mulVec]
+    convert!
+      Nat.isSemilinearSet_setOf_mulVec_eq (κ := (ι ⊕ ι) ⊕ ι) 0 i
+        (Matrix.fromCols (Matrix.fromCols 1 0) 1) (Matrix.fromCols (Matrix.fromCols 0 1) 0) using
+      4 <;> simp [fromCols_mulVec]
 
 private noncomputable def setOfFloorNeg : Set (ι → ℕ) :=
   { x | hs.fract x = hs.base ∧ ∃ i, hs.floor x i < 0 }
@@ -680,9 +683,10 @@ private theorem isSemilinearSet_setOfFloorNeg : IsSemilinearSet hs.setOfFloorNeg
     apply Nat.isSemilinearSet_inter <| Nat.isSemilinearSet_preimage
       (.closure_of_finite hs.finite_basisSet.diff) (LinearMap.funLeft ℕ ℕ Sum.inr)
     haveI := Fintype.ofFinite ι
-    convert Nat.isSemilinearSet_setOf_mulVec_eq (κ := ((ι ⊕ ι) ⊕ ι) ⊕ ι) i.1 hs.base
-      (Matrix.fromCols (Matrix.fromCols (Matrix.fromCols 1 1) 0) 1)
-      (Matrix.fromCols (Matrix.fromCols (Matrix.fromCols 0 0) 1) 0) using 4
+    convert!
+      Nat.isSemilinearSet_setOf_mulVec_eq (κ := ((ι ⊕ ι) ⊕ ι) ⊕ ι) i.1 hs.base
+        (Matrix.fromCols (Matrix.fromCols (Matrix.fromCols 1 1) 0) 1)
+        (Matrix.fromCols (Matrix.fromCols (Matrix.fromCols 0 0) 1) 0) using 4
       <;> simp [add_comm _ i.1, add_assoc, fromCols_mulVec]
 
 private noncomputable def setOfFloorPos : Set (ι → ℕ) :=
@@ -740,7 +744,8 @@ private theorem isSemilinearSet_setOfFloorPos : IsSemilinearSet hs.setOfFloorPos
     apply Nat.isSemilinearSet_inter <| Nat.isSemilinearSet_preimage
       (.closure_of_finite hs.finite_basisSet.diff) (LinearMap.funLeft ℕ ℕ Sum.inr)
     haveI := Fintype.ofFinite ι
-    convert Nat.isSemilinearSet_setOf_mulVec_eq (κ := ((ι ⊕ ι) ⊕ ι) ⊕ ι) 0 (hs.base + i.1)
+    convert!
+      Nat.isSemilinearSet_setOf_mulVec_eq (κ := ((ι ⊕ ι) ⊕ ι) ⊕ ι) 0 (hs.base + i.1)
         (Matrix.fromCols (Matrix.fromCols (Matrix.fromCols 1 0) 0) 1)
         (Matrix.fromCols (Matrix.fromCols (Matrix.fromCols 0 1) 1) 0) using 4
       <;> simp [add_assoc, fromCols_mulVec]
@@ -749,8 +754,9 @@ end IsProperLinearSet
 
 private lemma Nat.isSemilinearSet_compl_of_isProperLinearSet [Finite ι] {s : Set (ι → ℕ)}
     (hs : IsProperLinearSet s) : IsSemilinearSet sᶜ := by
-  convert hs.isSemilinearSet_setOfFractNe.union <| hs.isSemilinearSet_setOfFloorNeg.union <|
-    hs.isSemilinearSet_setOfFloorPos using 1
+  convert!
+    hs.isSemilinearSet_setOfFractNe.union <|
+      hs.isSemilinearSet_setOfFloorNeg.union <| hs.isSemilinearSet_setOfFloorPos using 1
   ext
   simp only [mem_compl_iff, hs.mem_iff_fract_eq_and_floor_nonneg, IsProperLinearSet.setOfFractNe,
     IsProperLinearSet.setOfFloorNeg, IsProperLinearSet.setOfFloorPos, mem_union, mem_setOf_eq]
diff --git a/Mathlib/ModelTheory/Arithmetic/Presburger/Semilinear/Defs.lean b/Mathlib/ModelTheory/Arithmetic/Presburger/Semilinear/Defs.lean
index 5f5944cd3c0822..3cceccbb2e484a 100644
--- a/Mathlib/ModelTheory/Arithmetic/Presburger/Semilinear/Defs.lean
+++ b/Mathlib/ModelTheory/Arithmetic/Presburger/Semilinear/Defs.lean
@@ -203,7 +203,7 @@ theorem IsSemilinearSet.image (hs : IsSemilinearSet s) (f : F) : IsSemilinearSet
 theorem isSemilinearSet_image_iff {F : Type*} [EquivLike F M N] [AddEquivClass F M N] (f : F) :
     IsSemilinearSet (f '' s) ↔ IsSemilinearSet s := by
   constructor <;> intro h
-  · convert h.image (f : M ≃+ N).symm
+  · convert! h.image (f : M ≃+ N).symm
     simp [image_image]
   · exact h.image f
 
@@ -211,7 +211,7 @@ theorem isSemilinearSet_image_iff {F : Type*} [EquivLike F M N] [AddEquivClass F
 the index). It is a special case of `IsSemilinearSet.image`. -/
 theorem IsSemilinearSet.proj {s : Set (ι ⊕ κ → M)} (hs : IsSemilinearSet s) :
     IsSemilinearSet { x | ∃ y, Sum.elim x y ∈ s } := by
-  convert hs.image (LinearMap.funLeft ℕ M Sum.inl)
+  convert! hs.image (LinearMap.funLeft ℕ M Sum.inl)
   ext x
   constructor
   · intro ⟨y, hy⟩
@@ -227,7 +227,7 @@ theorem IsSemilinearSet.proj' {p : (ι → M) → (κ → M) → Prop} :
 
 protected lemma IsLinearSet.closure (hs : IsLinearSet s) : IsSemilinearSet (closure s : Set M) := by
   rcases hs with ⟨a, t, ht, rfl⟩
-  convert (IsSemilinearSet.singleton 0).union (isSemilinearSet ⟨a, {a} ∪ t, by simp [ht], rfl⟩)
+  convert! (IsSemilinearSet.singleton 0).union (isSemilinearSet ⟨a, { a } ∪ t, by simp [ht], rfl⟩)
   ext x
   simp only [SetLike.mem_coe, singleton_union, mem_insert_iff, mem_vadd_set, vadd_eq_add]
   constructor
@@ -356,7 +356,8 @@ lemma IsLinearSet.isProperSemilinearSet [IsCancelAdd M] (hs : IsLinearSet s) :
       induction hn : g i using Nat.strong_induction_on generalizing g with | _ n ih'
       subst hn
       by_cases! hfg : ∀ j ∈ t', f j ≤ g j
-      · convert ih' (g i - f i) (Nat.sub_lt_self hfi (hfg i hi))
+      · convert!
+        ih' (g i - f i) (Nat.sub_lt_self hfi (hfg i hi))
           (fun j => if j ∈ t' then g j - f j else g j + f j) (by simp [hi]) using 1
         conv_lhs => rw [← Finset.union_sdiff_of_subset ht']
         simp_rw [vadd_eq_add, add_left_cancel_iff, Finset.sum_union Finset.sdiff_disjoint.symm,
@@ -435,7 +436,7 @@ theorem Nat.isSemilinearSet_iff_ultimately_periodic {s : Set ℕ} :
     have h₁ : {x ∈ s | x < k}.Finite := (Set.finite_lt_nat k).subset (sep_subset_setOf _ _)
     have h₂ : {x ∈ s | k ≤ x ∧ x < k + p}.Finite :=
       (Set.finite_Ico k (k + p)).subset (sep_subset_setOf _ _)
-    convert (IsSemilinearSet.of_finite h₁).union (.add (.of_finite h₂) (.closure_finset {p}))
+    convert! (IsSemilinearSet.of_finite h₁).union (.add (.of_finite h₂) (.closure_finset { p }))
     ext x
     simp only [sep_and, Finset.coe_singleton, mem_union, mem_setOf_eq, mem_add, mem_inter_iff,
       SetLike.mem_coe, AddSubmonoid.mem_closure_singleton, smul_eq_mul, exists_exists_eq_and]
diff --git a/Mathlib/ModelTheory/Basic.lean b/Mathlib/ModelTheory/Basic.lean
index 2fbcc91b10a0c3..4d6a39769479f4 100644
--- a/Mathlib/ModelTheory/Basic.lean
+++ b/Mathlib/ModelTheory/Basic.lean
@@ -712,7 +712,7 @@ theorem comp_symm (f : M ≃[L] N) (g : N ≃[L] P) : (g.comp f).symm = f.symm.c
 theorem comp_right_injective (h : M ≃[L] N) :
     Function.Injective (fun f ↦ f.comp h : (N ≃[L] P) → (M ≃[L] P)) := by
   intro f g hfg
-  convert (congr_arg (fun r : (M ≃[L] P) ↦ r.comp h.symm) hfg) <;>
+  convert! (congr_arg (fun r : (M ≃[L] P) ↦ r.comp h.symm) hfg) <;>
     rw [comp_assoc, self_comp_symm, comp_refl]
 
 @[simp]
diff --git a/Mathlib/ModelTheory/Definability.lean b/Mathlib/ModelTheory/Definability.lean
index feeb69a8190509..11999fc7916854 100644
--- a/Mathlib/ModelTheory/Definability.lean
+++ b/Mathlib/ModelTheory/Definability.lean
@@ -150,13 +150,13 @@ theorem definable_biUnion_finset {ι : Type*} {f : ι → Set (α → M)}
 theorem definable_iInter_of_finite {ι : Type*} [Finite ι] {f : ι → Set (α → M)}
     (hf : ∀ i, A.Definable L (f i)) : A.Definable L (⋂ i, f i) := by
   haveI := Fintype.ofFinite ι
-  convert definable_finset_inf hf Finset.univ using 1
+  convert! definable_finset_inf hf Finset.univ using 1
   simp
 
 theorem definable_iUnion_of_finite {ι : Type*} [Finite ι] {f : ι → Set (α → M)}
     (hf : ∀ i, A.Definable L (f i)) : A.Definable L (⋃ i, f i) := by
   haveI := Fintype.ofFinite ι
-  convert definable_finset_sup hf Finset.univ using 1
+  convert! definable_finset_sup hf Finset.univ using 1
   simp
 
 @[simp]
@@ -523,7 +523,7 @@ lemma _root_.Set.Definable.preimage_map
       (hF i).preimage_comp (fun | none => Sum.inr i | some j => Sum.inl j)
   have h_cyl : A.Definable L { w : α ⊕ β → M | w ∘ Sum.inr ∈ S } :=
     hS.preimage_comp Sum.inr
-  convert Definable.exists_of_finite (Definable.inter h_graph h_cyl) using 1
+  convert! Definable.exists_of_finite (Definable.inter h_graph h_cyl) using 1
   ext v
   simp [← funext_iff]
 
@@ -551,7 +551,7 @@ theorem DefinableFun.ite {p : (α → M) → Prop} {g} [DecidablePred p]
   let P : Set (Option α → M) := {w | p (w ∘ some)}
   have hP : A.Definable L P := hp.preimage_comp some
   simp only [DefinableFun]
-  convert (hP.inter hf).union (hP.compl.inter hg)
+  convert! (hP.inter hf).union (hP.compl.inter hg)
   ext w
   by_cases h : p (w ∘ some) <;> simp [tupleGraph, P, h]
 
@@ -664,7 +664,7 @@ theorem TermDefinable₁.definable₂_graph {f : M → M} (h : A.TermDefinable
   obtain ⟨t, h⟩ := h.termDefinable.definable_tupleGraph A L
   use t.relabel (Option.elim · 1 (fun _ ↦ 0))
   ext v
-  convert Set.ext_iff.1 h (v ∘ (Option.elim · 1 (fun _ ↦ 0)))
+  convert! Set.ext_iff.1 h (v ∘ (Option.elim · 1 (fun _ ↦ 0)))
   simp
 
 /-- The identity function is `TermDefinable₁` -/
diff --git a/Mathlib/ModelTheory/ElementarySubstructures.lean b/Mathlib/ModelTheory/ElementarySubstructures.lean
index 8bd1396a441b9a..bebffda1987a1c 100644
--- a/Mathlib/ModelTheory/ElementarySubstructures.lean
+++ b/Mathlib/ModelTheory/ElementarySubstructures.lean
@@ -226,7 +226,7 @@ theorem meetsDefinable (S : L.ElementarySubstructure M) : L.MeetsDefinable (S :
     simp only [Formula.Realize, ← BoundedFormula.realize_constantsVarsEquiv,
       ← S.subtype.map_boundedFormula] at hv'
     simp only [Formula.Realize, ← BoundedFormula.realize_constantsVarsEquiv]
-    convert hv' using 1
+    convert! hv' using 1
     funext i
     cases i <;> rfl
   change (Subtype.val ∘ v') ∈ {x | x 0 ∈ D}
diff --git a/Mathlib/ModelTheory/Order.lean b/Mathlib/ModelTheory/Order.lean
index fc294f4a38219d..fc01bc4c2f53c7 100644
--- a/Mathlib/ModelTheory/Order.lean
+++ b/Mathlib/ModelTheory/Order.lean
@@ -485,9 +485,10 @@ lemma dlo_isExtensionPair
   let g' :
     ((Substructure.closure Language.order).toFun {m} ⊔ S : Language.order.Substructure M) ↪o N :=
     ((OrderIso.setCongr _ _ (by
-      convert LowerAdjoint.closure_eq_self_of_mem_closed _
-        (Substructure.mem_closed_of_isRelational Language.order
-        ((insert m hS.toFinset : Finset M) : Set M))
+      convert!
+        LowerAdjoint.closure_eq_self_of_mem_closed _
+          (Substructure.mem_closed_of_isRelational Language.order
+            ((insert m hS.toFinset : Finset M) : Set M))
       simp only [Finset.coe_insert, Set.Finite.coe_toFinset, Substructure.closure_insert,
         Substructure.closure_eq])).toOrderEmbedding.trans g)
   use StrongHomClass.toEmbedding g'
diff --git a/Mathlib/ModelTheory/PartialEquiv.lean b/Mathlib/ModelTheory/PartialEquiv.lean
index d06d3e3da704f5..972b174ab5080c 100644
--- a/Mathlib/ModelTheory/PartialEquiv.lean
+++ b/Mathlib/ModelTheory/PartialEquiv.lean
@@ -152,7 +152,7 @@ private theorem le_antisymm (f g : M ≃ₚ[L] N) (le_fg : f ≤ g) (le_gf : g 
   let ⟨dom_f, cod_f, equiv_f⟩ := f
   cases _root_.le_antisymm (dom_le_dom le_fg) (dom_le_dom le_gf)
   cases _root_.le_antisymm (cod_le_cod le_fg) (cod_le_cod le_gf)
-  convert rfl
+  convert! rfl
   exact Equiv.injective_toEmbedding ((subtype _).comp_injective (subtype_toEquiv_inclusion le_fg))
 
 instance : PartialOrder (M ≃ₚ[L] N) where
@@ -489,7 +489,7 @@ theorem embedding_from_cg (M_cg : Structure.CG L M) (g : L.FGEquiv M N)
       (le_partialEquivLimit S (Encodable.encode (⟨x, hx⟩ : X) + 1)) this
   have isTop : F.dom = ⊤ := by rwa [← top_le_iff, ← X_gen, Substructure.closure_le]
   exact ⟨toEmbeddingOfEqTop isTop,
-        by convert (le_partialEquivLimit S 0); apply Embedding.toPartialEquiv_toEmbedding⟩
+        by convert! (le_partialEquivLimit S 0); apply Embedding.toPartialEquiv_toEmbedding⟩
 
 /-- For two countably generated structure `M` and `N`, if any PartialEquiv
 between finitely generated substructures can be extended to any element in the domain and to
@@ -524,7 +524,7 @@ theorem equiv_between_cg (M_cg : Structure.CG L M) (N_cg : Structure.CG L N)
   have dom_top : F.dom = ⊤ := by rwa [← top_le_iff, ← X_gen, Substructure.closure_le]
   have cod_top : F.cod = ⊤ := by rwa [← top_le_iff, ← Y_gen, Substructure.closure_le]
   refine ⟨toEquivOfEqTop dom_top cod_top, ?_⟩
-  convert le_partialEquivLimit S 0
+  convert! le_partialEquivLimit S 0
   rw [toEquivOfEqTop_toEmbedding]
   apply Embedding.toPartialEquiv_toEmbedding
 
diff --git a/Mathlib/ModelTheory/Ultraproducts.lean b/Mathlib/ModelTheory/Ultraproducts.lean
index 98ed1cd4d6c9c0..e84d5b83c0aac8 100644
--- a/Mathlib/ModelTheory/Ultraproducts.lean
+++ b/Mathlib/ModelTheory/Ultraproducts.lean
@@ -82,7 +82,8 @@ theorem funMap_cast {n : ℕ} (f : L.Functions n) (x : Fin n → ∀ a, M a) :
 theorem term_realize_cast {β : Type*} (x : β → ∀ a, M a) (t : L.Term β) :
     (t.realize fun i => (x i : (u : Filter α).Product M)) =
       (fun a => t.realize fun i => x i a : (u : Filter α).Product M) := by
-  convert @Term.realize_quotient_mk' L _ ((u : Filter α).productSetoid M)
+  convert!
+    @Term.realize_quotient_mk' L _ ((u : Filter α).productSetoid M)
       (Ultraproduct.setoidPrestructure M u) _ t x using 2
   ext a
   induction t with
diff --git a/Mathlib/NumberTheory/AbelSummation.lean b/Mathlib/NumberTheory/AbelSummation.lean
index b0743d015285f1..af5755b62443ac 100644
--- a/Mathlib/NumberTheory/AbelSummation.lean
+++ b/Mathlib/NumberTheory/AbelSummation.lean
@@ -178,7 +178,7 @@ theorem _root_.sum_mul_eq_sub_sub_integral_mul' {n m : ℕ} (h : n ≤ m)
     ∑ k ∈ Ioc n m, f k * c k =
       f m * (∑ k ∈ Icc 0 m, c k) - f n * (∑ k ∈ Icc 0 n, c k) -
         ∫ t in Set.Ioc (n : ℝ) m, deriv f t * ∑ k ∈ Icc 0 ⌊t⌋₊, c k := by
-  convert sum_mul_eq_sub_sub_integral_mul c n.cast_nonneg (Nat.cast_le.mpr h) hf_diff hf_int
+  convert! sum_mul_eq_sub_sub_integral_mul c n.cast_nonneg (Nat.cast_le.mpr h) hf_diff hf_int
   all_goals rw [Nat.floor_natCast]
 
 end abelSummationProof
@@ -203,7 +203,7 @@ theorem sum_mul_eq_sub_integral_mul' (m : ℕ)
     ∑ k ∈ Icc 0 m, f k * c k =
       f m * (∑ k ∈ Icc 0 m, c k) -
         ∫ t in Set.Ioc (0 : ℝ) m, deriv f t * ∑ k ∈ Icc 0 ⌊t⌋₊, c k := by
-  convert sum_mul_eq_sub_integral_mul c m.cast_nonneg hf_diff hf_int
+  convert! sum_mul_eq_sub_integral_mul c m.cast_nonneg hf_diff hf_int
   all_goals rw [Nat.floor_natCast]
 
 /-- Specialized version of `sum_mul_eq_sub_integral_mul` when the first coefficient of the sequence
@@ -232,7 +232,7 @@ theorem sum_mul_eq_sub_integral_mul₀' (hc : c 0 = 0) (m : ℕ)
     ∑ k ∈ Icc 0 m, f k * c k =
       f m * (∑ k ∈ Icc 0 m, c k) -
         ∫ t in Set.Ioc (1 : ℝ) m, deriv f t * ∑ k ∈ Icc 0 ⌊t⌋₊, c k := by
-  convert sum_mul_eq_sub_integral_mul₀ c hc m hf_diff hf_int
+  convert! sum_mul_eq_sub_integral_mul₀ c hc m hf_diff hf_int
   all_goals rw [Nat.floor_natCast]
 
 /-- Specialized version of `sum_mul_eq_sub_integral_mul` when `c 0 = c 1 = 0`. -/
diff --git a/Mathlib/NumberTheory/ArithmeticFunction/Misc.lean b/Mathlib/NumberTheory/ArithmeticFunction/Misc.lean
index d65776f705c9d5..6b7c2d9b959adf 100644
--- a/Mathlib/NumberTheory/ArithmeticFunction/Misc.lean
+++ b/Mathlib/NumberTheory/ArithmeticFunction/Misc.lean
@@ -430,7 +430,7 @@ theorem sum_Ioc_mul_zeta_eq_sum (f : ArithmeticFunction R) (N : ℕ) :
 theorem sum_Ioc_sigma0_eq_sum_div (N : ℕ) :
     ∑ n ∈ Ioc 0 N, sigma 0 n = ∑ n ∈ Ioc 0 N, (N / n) := by
   rw [← zeta_mul_pow_eq_sigma, pow_zero_eq_zeta]
-  convert sum_Ioc_mul_zeta_eq_sum zeta N using 1
+  convert! sum_Ioc_mul_zeta_eq_sum zeta N using 1
   simpa using sum_congr rfl (by grind)
 
 end Sum
diff --git a/Mathlib/NumberTheory/Bernoulli.lean b/Mathlib/NumberTheory/Bernoulli.lean
index e89c502cc2c56d..feab7adab9a611 100644
--- a/Mathlib/NumberTheory/Bernoulli.lean
+++ b/Mathlib/NumberTheory/Bernoulli.lean
@@ -169,7 +169,7 @@ theorem bernoulli'PowerSeries_mul_exp_sub_one :
     simpa [map_sum, Nat.factorial] using congr_arg (algebraMap ℚ A) this
   apply eq_inv_of_mul_eq_one_left
   rw [sum_mul]
-  convert bernoulli'_spec' n using 1
+  convert! bernoulli'_spec' n using 1
   apply sum_congr rfl
   simp_rw [mem_antidiagonal]
   rintro ⟨i, j⟩ rfl
@@ -259,7 +259,7 @@ theorem bernoulli_spec' (n : ℕ) :
   -- massage it to match the structure of the goal, then convert piece by piece
   rw [sum_eq_add_sum_diff_singleton_of_mem h₁] at H ⊢
   apply add_eq_of_eq_sub'
-  convert eq_sub_of_add_eq' H using 1
+  convert! eq_sub_of_add_eq' H using 1
   · refine sum_congr rfl fun p h => ?_
     obtain ⟨h', h''⟩ : p ∈ _ ∧ p ≠ _ := by rwa [mem_sdiff, mem_singleton] at h
     simp [bernoulli_eq_bernoulli'_of_ne_one ((not_congr (antidiagonal_congr h' h₁)).mp h'')]
@@ -367,7 +367,8 @@ theorem sum_Ico_pow (n p : ℕ) :
   cases p with | zero => simp | succ p =>
   let f i := bernoulli i * p.succ.succ.choose i * (n : ℚ) ^ (p.succ.succ - i) / p.succ.succ
   let f' i := bernoulli' i * p.succ.succ.choose i * (n : ℚ) ^ (p.succ.succ - i) / p.succ.succ
-  suffices (∑ k ∈ Ico 1 n.succ, (k : ℚ) ^ p.succ) = ∑ i ∈ range p.succ.succ, f' i by convert this
+  suffices (∑ k ∈ Ico 1 n.succ, (k : ℚ) ^ p.succ) = ∑ i ∈ range p.succ.succ, f' i by convert!
+    this
   -- prove some algebraic facts that will make things easier for us later on
   have hle := Nat.le_add_left 1 n
   have hne : (p + 1 + 1 : ℚ) ≠ 0 := by norm_cast
diff --git a/Mathlib/NumberTheory/BernoulliPolynomials.lean b/Mathlib/NumberTheory/BernoulliPolynomials.lean
index 179175af32983a..6adffaddb78dfa 100644
--- a/Mathlib/NumberTheory/BernoulliPolynomials.lean
+++ b/Mathlib/NumberTheory/BernoulliPolynomials.lean
@@ -63,7 +63,7 @@ theorem coeff_bernoulli (n i : ℕ) :
     (bernoulli n).coeff i = if i ≤ n then (_root_.bernoulli (n - i) * choose n i) else 0 := by
   simp only [bernoulli, finsetSum_coeff, coeff_monomial]
   split_ifs with h
-  · convert sum_ite_eq_of_mem (range (n + 1)) (n - i) _ (by grind) using 3 <;> grind [choose_symm]
+  · convert! sum_ite_eq_of_mem (range (n + 1)) (n - i) _ (by grind) using 3 <;> grind [choose_symm]
   · exact Finset.sum_eq_zero <| by grind
 
 /-
diff --git a/Mathlib/NumberTheory/Bertrand.lean b/Mathlib/NumberTheory/Bertrand.lean
index dc809c44a95dbf..89e05cf1c9edb1 100644
--- a/Mathlib/NumberTheory/Bertrand.lean
+++ b/Mathlib/NumberTheory/Bertrand.lean
@@ -82,8 +82,9 @@ theorem real_main_inequality {x : ℝ} (x_large : (512 : ℝ) ≤ x) :
     · apply ConcaveOn.add
       · exact strictConcaveOn_log_Ioi.concaveOn.subset
           (Set.Ioi_subset_Ioi (by norm_num)) (convex_Ioi 0.5)
-      convert ((strictConcaveOn_sqrt_mul_log_Ioi.concaveOn.comp_linearMap
-        ((2 : ℝ) • LinearMap.id))) using 1
+      convert!
+        ((strictConcaveOn_sqrt_mul_log_Ioi.concaveOn.comp_linearMap ((2 : ℝ) • LinearMap.id)))
+        using 1
       ext x
       simp only [Set.mem_Ioi, Set.mem_preimage, LinearMap.smul_apply,
         LinearMap.id_coe, id_eq, smul_eq_mul]
diff --git a/Mathlib/NumberTheory/Chebyshev.lean b/Mathlib/NumberTheory/Chebyshev.lean
index 52c778e18bf6ae..f1d3c6c36c98fe 100644
--- a/Mathlib/NumberTheory/Chebyshev.lean
+++ b/Mathlib/NumberTheory/Chebyshev.lean
@@ -107,7 +107,7 @@ theorem theta_eq_sum_primesLE_log (n : ℕ) : θ n = ∑ p ∈ primesLE n, log p
 theorem psi_eq_zero_of_lt_two {x : ℝ} (hx : x < 2) : ψ x = 0 := by
   apply sum_eq_zero fun n hn ↦ ?_
   simp only [mem_Ioc] at hn
-  convert vonMangoldt_apply_one
+  convert! vonMangoldt_apply_one
   have := lt_of_le_of_lt (le_floor_iff' hn.1.ne' |>.mp hn.2) hx
   norm_cast at this
   linarith
@@ -120,7 +120,7 @@ theorem psi_one : ψ 1 = 0 := psi_eq_zero_of_lt_two one_lt_two
 
 theorem theta_eq_zero_of_lt_two {x : ℝ} (hx : x < 2) : θ x = 0 := by
   apply sum_eq_zero fun n hn ↦ ?_
-  convert log_one
+  convert! log_one
   simp only [mem_filter, mem_Ioc] at hn
   have := lt_of_le_of_lt (le_floor_iff' hn.1.1.ne' |>.mp hn.1.2) hx
   norm_cast at ⊢ this
diff --git a/Mathlib/NumberTheory/ClassNumber/AdmissibleAbsoluteValue.lean b/Mathlib/NumberTheory/ClassNumber/AdmissibleAbsoluteValue.lean
index 396b59116f50ac..681bb81828ef4f 100644
--- a/Mathlib/NumberTheory/ClassNumber/AdmissibleAbsoluteValue.lean
+++ b/Mathlib/NumberTheory/ClassNumber/AdmissibleAbsoluteValue.lean
@@ -62,8 +62,8 @@ theorem exists_partition {ι : Type*} [Finite ι] {ε : ℝ} (hε : 0 < ε) {b :
   rcases Finite.exists_equiv_fin ι with ⟨n, ⟨e⟩⟩
   obtain ⟨t, ht⟩ := h.exists_partition' n hε hb (A ∘ e.symm)
   refine ⟨t ∘ e, fun i₀ i₁ h ↦ ?_⟩
-  convert (config := { transparency := .default })
-    ht (e i₀) (e i₁) h <;> simp only [e.symm_apply_apply]
+  convert! (config := { transparency := .default }) ht (e i₀) (e i₁) h <;>
+    simp only [e.symm_apply_apply]
 
 set_option backward.isDefEq.respectTransparency false in
 /-- Any large enough family of vectors in `R^n` has a pair of elements
@@ -120,7 +120,7 @@ theorem exists_approx {ι : Type*} [Fintype ι] {ε : ℝ} (hε : 0 < ε) {b : R
   let e := Fintype.equivFin ι
   obtain ⟨i₀, i₁, ne, h⟩ := h.exists_approx_aux (Fintype.card ι) hε hb fun x y ↦ A x (e.symm y)
   refine ⟨i₀, i₁, ne, fun k ↦ ?_⟩
-  convert h (e k) <;> simp only [e.symm_apply_apply]
+  convert! h (e k) <;> simp only [e.symm_apply_apply]
 
 end IsAdmissible
 
diff --git a/Mathlib/NumberTheory/ClassNumber/AdmissibleCardPowDegree.lean b/Mathlib/NumberTheory/ClassNumber/AdmissibleCardPowDegree.lean
index 9fbf101be27466..32f9a6ee24962e 100644
--- a/Mathlib/NumberTheory/ClassNumber/AdmissibleCardPowDegree.lean
+++ b/Mathlib/NumberTheory/ClassNumber/AdmissibleCardPowDegree.lean
@@ -92,7 +92,7 @@ theorem exists_approx_polynomial_aux [Ring Fq] {d : ℕ} {m : ℕ} (hm : Fintype
       rwa [tsub_lt_iff_tsub_lt hd hbj] at this
   have : j = b.natDegree - (natDegree b - j.succ).succ := by
     rw [← Nat.succ_sub hbj, Nat.succ_sub_succ, tsub_tsub_cancel_of_le hbj.le]
-  convert congr_fun i_eq.symm ⟨natDegree b - j.succ, hj⟩
+  convert! congr_fun i_eq.symm ⟨natDegree b - j.succ, hj⟩
 
 variable [Field Fq]
 
@@ -136,7 +136,7 @@ theorem exists_approx_polynomial {b : Fq[X]} (hb : b ≠ 0) {ε : ℝ} (hε : 0
   -- to turn the `-⌈-stuff⌉₊` into `+ stuff`.
   apply lt_of_lt_of_le (Nat.cast_lt.mpr (WithBot.coe_lt_coe.mp _)) _
   swap
-  · convert deg_lt
+  · convert! deg_lt
     rw [degree_eq_natDegree h']; rfl
   rw [← sub_neg_eq_add, ← neg_div, Nat.cast_sub le_b.le]
   grw [← Nat.le_ceil]
@@ -160,7 +160,7 @@ theorem cardPowDegree_anti_archimedean {x y z : Fq[X]} {a : ℤ} (hxy : cardPowD
   refine Or.imp (pow_le_pow_right₀ this) (pow_le_pow_right₀ this) ?_
   rw [natDegree_le_iff_degree_le, natDegree_le_iff_degree_le, ← le_max_iff, ←
     degree_eq_natDegree hxy', ← degree_eq_natDegree hyz']
-  convert degree_add_le (x - y) (y - z) using 2
+  convert! degree_add_le (x - y) (y - z) using 2
   exact (sub_add_sub_cancel _ _ _).symm
 
 /-- A slightly stronger version of `exists_partition` on which we perform induction on `n`:
diff --git a/Mathlib/NumberTheory/ClassNumber/Finite.lean b/Mathlib/NumberTheory/ClassNumber/Finite.lean
index bcd6c61e51b97d..e4acead5a61378 100644
--- a/Mathlib/NumberTheory/ClassNumber/Finite.lean
+++ b/Mathlib/NumberTheory/ClassNumber/Finite.lean
@@ -77,7 +77,7 @@ theorem norm_le (a : S) {y : ℤ} (hy : ∀ k, abv (bS.repr a k) ≤ y) :
   rw [Algebra.norm_apply, ← LinearMap.det_toMatrix bS]
   simp only [map_sum, map_smul, map_sum, map_smul,
     normBound, smul_mul_assoc, ← mul_pow]
-  convert Matrix.det_sum_smul_le Finset.univ _ hy using 3
+  convert! Matrix.det_sum_smul_le Finset.univ _ hy using 3
   · rw [Finset.card_univ, smul_mul_assoc, mul_comm]
   · intro i j k
     apply Finset.le_max'
diff --git a/Mathlib/NumberTheory/Cyclotomic/Basic.lean b/Mathlib/NumberTheory/Cyclotomic/Basic.lean
index 64f9a5cb00b6d5..7d40aea828dbed 100644
--- a/Mathlib/NumberTheory/Cyclotomic/Basic.lean
+++ b/Mathlib/NumberTheory/Cyclotomic/Basic.lean
@@ -163,7 +163,7 @@ theorem subsingleton_iff [Subsingleton B] :
   · refine subset_pair_iff.mpr fun s hs ↦ or_iff_not_imp_left.mpr fun hs' ↦ ?_
     obtain ⟨ζ, hζ⟩ := hprim hs hs'
     exact mod_cast hζ.unique (IsPrimitiveRoot.of_subsingleton ζ)
-  · refine ⟨fun {s} hs hs' ↦ ?_, fun x ↦ by convert (mem_top (R := A) : x ∈ ⊤)⟩
+  · refine ⟨fun {s} hs hs' ↦ ?_, fun x ↦ by convert! (mem_top (R := A) : x ∈ ⊤)⟩
     · have : s = 1 := (subset_pair_iff.mp hS s hs).resolve_left hs'
       exact ⟨0, this ▸ IsPrimitiveRoot.of_subsingleton 0⟩
 
@@ -195,7 +195,7 @@ theorem union_left [h : IsCyclotomicExtension T A B] (hS : S ⊆ T) :
   · obtain ⟨b, hb⟩ := ((isCyclotomicExtension_iff _ _ _).1 h).1 (hS hn) hn'
     refine ⟨⟨b, subset_adjoin ⟨n, hn, hn', hb.pow_eq_one⟩⟩, ?_⟩
     rwa [← IsPrimitiveRoot.coe_submonoidClass_iff, Subtype.coe_mk]
-  · convert mem_top (R := A) (x := b)
+  · convert! mem_top (R := A) (x := b)
     rw [← adjoin_adjoin_coe_preimage, preimage_setOf_eq]
     norm_cast
 
@@ -275,8 +275,8 @@ variable {A B}
 /-- If `(⊥ : SubAlgebra A B) = ⊤`, then `IsCyclotomicExtension {1} A B`. -/
 theorem singleton_one_of_bot_eq_top (h : (⊥ : Subalgebra A B) = ⊤) :
     IsCyclotomicExtension {1} A B := by
-  convert eq_self_sdiff_zero _ A B ▸
-    (iff_union_singleton_one _ A _).1 (singleton_zero_of_bot_eq_top h)
+  convert!
+    eq_self_sdiff_zero _ A B ▸ (iff_union_singleton_one _ A _).1 (singleton_zero_of_bot_eq_top h)
   simp
 
 /-- If `Function.Surjective (algebraMap A B)`, then `IsCyclotomicExtension {1} A B`. -/
@@ -580,7 +580,7 @@ theorem isGalois [IsCyclotomicExtension S K L] : IsGalois K L := by
     use n, hn, h1
     rw [← map_pow, ← map_one f, h2]
   | algebraMap x =>
-    convert IntermediateField.algebraMap_mem _ x
+    convert! IntermediateField.algebraMap_mem _ x
     exact AlgHom.commutes _ x
   | add x y hx hy ihx ihy =>
     rw [map_add]
diff --git a/Mathlib/NumberTheory/Cyclotomic/Discriminant.lean b/Mathlib/NumberTheory/Cyclotomic/Discriminant.lean
index d2db272a7cfcb1..32a9e7294f057f 100644
--- a/Mathlib/NumberTheory/Cyclotomic/Discriminant.lean
+++ b/Mathlib/NumberTheory/Cyclotomic/Discriminant.lean
@@ -168,7 +168,7 @@ theorem discr_prime_pow [hcycl : IsCyclotomicExtension {p ^ k} K L] [hp : Fact p
         simp only [map_neg, map_one, Function.comp_apply, Fin.val_eq_zero, _root_.pow_zero]
         suffices (e.symm i : ℕ) = 0 by simp [this]
         rw [← Nat.lt_one_iff]
-        convert (e.symm i).2
+        convert! (e.symm i).2
         rw [this]
       · simp only [discr, traceMatrix_apply, Matrix.det_unique, Fin.default_eq_zero, Fin.val_zero,
           _root_.pow_zero, traceForm_apply, mul_one]
@@ -198,7 +198,7 @@ theorem discr_odd_prime [IsCyclotomicExtension {p} K L] [hp : Fact p.Prime]
     rw [zero_add, pow_one]
     infer_instance
   have hζ' : IsPrimitiveRoot ζ (p ^ (0 + 1)) := by simpa using hζ
-  convert discr_prime_pow_ne_two hζ' (by simpa [hirr]) (by simp [hodd]) using 2
+  convert! discr_prime_pow_ne_two hζ' (by simpa [hirr]) (by simp [hodd]) using 2
   · rw [zero_add, pow_one, totient_prime hp.out]
   · rw [_root_.pow_zero, one_mul, zero_add, mul_one, Nat.sub_sub]
 
diff --git a/Mathlib/NumberTheory/Cyclotomic/Gal.lean b/Mathlib/NumberTheory/Cyclotomic/Gal.lean
index 19bba50aa22431..a1953f31cffa15 100644
--- a/Mathlib/NumberTheory/Cyclotomic/Gal.lean
+++ b/Mathlib/NumberTheory/Cyclotomic/Gal.lean
@@ -123,7 +123,7 @@ theorem fromZetaAut_spec : fromZetaAut hμ h (zeta n K L) = μ := by
   generalize_proofs hζ h _ hμ _
   nth_rewrite 4 [← hζ.powerBasis_gen K]
   rw [PowerBasis.equivOfMinpoly_gen, hμ.powerBasis_gen K]
-  convert h.choose_spec.2
+  convert! h.choose_spec.2
   exact ZMod.val_cast_of_lt h.choose_spec.1
 
 end IsCyclotomicExtension
diff --git a/Mathlib/NumberTheory/Cyclotomic/PrimitiveRoots.lean b/Mathlib/NumberTheory/Cyclotomic/PrimitiveRoots.lean
index 89702f2373b5ee..a797e5e244fc44 100644
--- a/Mathlib/NumberTheory/Cyclotomic/PrimitiveRoots.lean
+++ b/Mathlib/NumberTheory/Cyclotomic/PrimitiveRoots.lean
@@ -99,7 +99,7 @@ theorem aeval_zeta [IsDomain B] [NeZero (n : B)] :
   exact zeta_spec n A B
 
 theorem zeta_isRoot [IsDomain B] [NeZero (n : B)] : IsRoot (cyclotomic n B) (zeta n A B) := by
-  convert aeval_zeta n A B using 0
+  convert! aeval_zeta n A B using 0
   rw [IsRoot.def, aeval_def, eval₂_eq_eval_map, map_cyclotomic]
 
 theorem zeta_pow : zeta n A B ^ n = 1 :=
@@ -197,7 +197,7 @@ theorem _root_.IsPrimitiveRoot.lcm_totient_le_finrank [FiniteDimensional K L] {p
   let k := PNat.lcm ⟨p, hppos⟩ ⟨q, hqpos⟩
   have : IsPrimitiveRoot z k := hx.pow_mul_pow_lcm hy hppos.ne' hqpos.ne'
   haveI := IsPrimitiveRoot.adjoin_isCyclotomicExtension K this
-  convert Submodule.finrank_le (Subalgebra.toSubmodule (adjoin K {z}))
+  convert! Submodule.finrank_le (Subalgebra.toSubmodule (adjoin K { z }))
   rw [show Nat.lcm p q = (k : ℕ) from rfl] at hirr
   simpa using (IsCyclotomicExtension.finrank (Algebra.adjoin K {z}) hirr).symm
 
@@ -245,7 +245,7 @@ theorem exists_neg_pow_of_isOfFinOrder [IsCyclotomicExtension {n} ℚ K]
     (hno : Odd n) {ζ x : K} (hζ : IsPrimitiveRoot ζ n) (hx : IsOfFinOrder x) :
     ∃ r : ℕ, x = (-ζ) ^ r := by
   have hnegζ : IsPrimitiveRoot (-ζ) (2 * n) := by
-    convert IsPrimitiveRoot.orderOf (-ζ)
+    convert! IsPrimitiveRoot.orderOf (-ζ)
     rw [neg_eq_neg_one_mul, (Commute.all _ _).orderOf_mul_eq_mul_orderOf_of_coprime]
     · simp [hζ.eq_orderOf]
     · simp [← hζ.eq_orderOf, hno]
@@ -413,11 +413,11 @@ theorem norm_pow_sub_one_of_prime_pow_ne_two {k s : ℕ} (hζ : IsPrimitiveRoot
     refine IsCyclotomicExtension.equiv _ _ _ (h := ?_) (.refl : K⟮η + 1⟯.toSubalgebra ≃ₐ[K] _)
     rw [H]
     have hη' : IsPrimitiveRoot (η + 1) (p ^ (k + 1 - s)) := by simpa using hη
-    convert hη'.adjoin_isCyclotomicExtension K using 1
+    convert! hη'.adjoin_isCyclotomicExtension K using 1
     rw [Nat.sub_add_comm hs]
   replace hη : IsPrimitiveRoot (η₁ + 1) (p ^ (k - s + 1)) := by
     apply coe_submonoidClass_iff.1
-    convert hη using 1
+    convert! hη using 1
     rw [Nat.sub_add_comm hs]
   have := IsCyclotomicExtension.finiteDimensional {p ^ (k + 1)} K L
   have := IsCyclotomicExtension.isGalois {p ^ (k + 1)} K L
diff --git a/Mathlib/NumberTheory/Dioph.lean b/Mathlib/NumberTheory/Dioph.lean
index bdbe351279c914..585cda8b56ae2d 100644
--- a/Mathlib/NumberTheory/Dioph.lean
+++ b/Mathlib/NumberTheory/Dioph.lean
@@ -342,7 +342,7 @@ def DiophFn (f : (α → ℕ) → ℕ) : Prop :=
   Dioph {v : Option α → ℕ | f (v ∘ some) = v none}
 
 theorem reindex_diophFn {f : (α → ℕ) → ℕ} (g : α → β) (d : DiophFn f) :
-    DiophFn fun v => f (v ∘ g) := by convert reindex_dioph (Option β) (Option.map g) d
+    DiophFn fun v => f (v ∘ g) := by convert! reindex_dioph (Option β) (Option.map g) d
 
 theorem ex_dioph {S : Set (α ⊕ β → ℕ)} : Dioph S → Dioph {v | ∃ x, v ⊗ x ∈ S}
   | ⟨γ, p, pe⟩ =>
diff --git a/Mathlib/NumberTheory/DiophantineApproximation/Basic.lean b/Mathlib/NumberTheory/DiophantineApproximation/Basic.lean
index 36b537a3a39ba9..756967cd86db87 100644
--- a/Mathlib/NumberTheory/DiophantineApproximation/Basic.lean
+++ b/Mathlib/NumberTheory/DiophantineApproximation/Basic.lean
@@ -149,7 +149,7 @@ theorem exists_rat_abs_sub_le_and_den_le (ξ : ℝ) {n : ℕ} (n_pos : 0 < n) :
   obtain ⟨j, k, hk₀, hk₁, h⟩ := exists_int_int_abs_mul_sub_le ξ n_pos
   have hk₀' : (0 : ℝ) < k := Int.cast_pos.mpr hk₀
   have hden : ((j / k : ℚ).den : ℤ) ≤ k := by
-    convert le_of_dvd hk₀ (Rat.den_dvd j k)
+    convert! le_of_dvd hk₀ (Rat.den_dvd j k)
     exact Rat.intCast_div_eq_divInt _ _
   refine ⟨j / k, ?_, Nat.cast_le.mp (hden.trans hk₁)⟩
   rw [← div_div, le_div_iff₀ (Nat.cast_pos.mpr <| Rat.pos _ : (0 : ℝ) < _)]
@@ -280,7 +280,7 @@ theorem Real.infinite_rat_abs_sub_lt_one_div_den_sq_iff_irrational (ξ : ℝ) :
     ⟨fun h => (irrational_iff_ne_rational ξ).mpr fun a b _ => ?_,
       Real.infinite_rat_abs_sub_lt_one_div_den_sq_of_irrational⟩
   contrapose! h
-  convert Rat.finite_rat_abs_sub_lt_one_div_den_sq ((a : ℚ) / b) with q
+  convert! Rat.finite_rat_abs_sub_lt_one_div_den_sq ((a : ℚ) / b) with q
   rw [h, (by (push_cast; rfl) : (1 : ℝ) / (q.den : ℝ) ^ 2 = (1 / (q.den : ℚ) ^ 2 : ℚ))]
   norm_cast
 
@@ -502,7 +502,7 @@ theorem exists_rat_eq_convergent' {v : ℕ} (h : ContfracLegendre.Ass ξ u v) :
     rcases le_or_gt (u : ℝ) ξ with ht | ht
     · use 0
       rw [convergent_zero, Rat.coe_int_inj, eq_comm, floor_eq_iff]
-      convert And.intro ht (sub_lt_iff_lt_add'.mp (abs_lt.mp h₂).2) <;> norm_num
+      convert! And.intro ht (sub_lt_iff_lt_add'.mp (abs_lt.mp h₂).2) <;> norm_num
     · replace h₁ := lt_sub_iff_add_lt'.mp (h₁ rfl)
       have hξ₁ : ⌊ξ⌋ = u - 1 := by
         rw [floor_eq_iff, cast_sub, cast_one, sub_add_cancel]
@@ -515,7 +515,7 @@ theorem exists_rat_eq_convergent' {v : ℕ} (h : ContfracLegendre.Ass ξ u v) :
             one_add_one_eq_two, inv_lt_comm₀ (fract_pos.mpr Hξ) zero_lt_two]
           refine ⟨(fract_lt_one ξ).le, ?_⟩
           rw [fract, hξ₁, cast_sub, cast_one, lt_sub_iff_add_lt', sub_add]
-          convert h₁ using 1
+          convert! h₁ using 1
           rw [sub_eq_add_neg]
           norm_num
         use 1
diff --git a/Mathlib/NumberTheory/DirichletCharacter/Basic.lean b/Mathlib/NumberTheory/DirichletCharacter/Basic.lean
index bd09cdc1f18200..3bbe311ee2e576 100644
--- a/Mathlib/NumberTheory/DirichletCharacter/Basic.lean
+++ b/Mathlib/NumberTheory/DirichletCharacter/Basic.lean
@@ -301,7 +301,7 @@ theorem changeLevel_primitiveCharacter :
 lemma primitiveCharacter_isPrimitive : IsPrimitive (χ.primitiveCharacter) := by
   by_cases h : χ.conductor = 0
   · rw [isPrimitive_def]
-    convert conductor_eq_zero_iff_level_eq_zero.mpr h
+    convert! conductor_eq_zero_iff_level_eq_zero.mpr h
   · exact le_antisymm (Nat.le_of_dvd (Nat.pos_of_ne_zero h) (conductor_dvd_level _)) <|
       conductor_le_conductor_mem_conductorSet <| conductor_mem_conductorSet χ
 
@@ -421,7 +421,7 @@ def Odd : Prop := ψ (-1) = -1
 def Even : Prop := ψ (-1) = 1
 
 lemma even_or_odd [NoZeroDivisors S] : ψ.Even ∨ ψ.Odd := by
-  suffices ψ (-1) ^ 2 = 1 by convert sq_eq_one_iff.mp this
+  suffices ψ (-1) ^ 2 = 1 by convert! sq_eq_one_iff.mp this
   rw [← map_pow _, neg_one_sq, map_one]
 
 lemma not_even_and_odd [NeZero (2 : S)] : ¬(ψ.Even ∧ ψ.Odd) := by
diff --git a/Mathlib/NumberTheory/EulerProduct/DirichletLSeries.lean b/Mathlib/NumberTheory/EulerProduct/DirichletLSeries.lean
index eead73829c8315..40581cddca34b2 100644
--- a/Mathlib/NumberTheory/EulerProduct/DirichletLSeries.lean
+++ b/Mathlib/NumberTheory/EulerProduct/DirichletLSeries.lean
@@ -57,7 +57,7 @@ def dirichletSummandHom {n : ℕ} (χ : DirichletCharacter ℂ n) (hs : s ≠ 0)
 lemma summable_riemannZetaSummand (hs : 1 < s.re) :
     Summable (fun n ↦ ‖riemannZetaSummandHom (ne_zero_of_one_lt_re hs) n‖) := by
   simp only [riemannZetaSummandHom, MonoidWithZeroHom.coe_mk, ZeroHom.coe_mk]
-  convert Real.summable_nat_rpow_inv.mpr hs with n
+  convert! Real.summable_nat_rpow_inv.mpr hs with n
   rw [← ofReal_natCast,
     norm_cpow_eq_rpow_re_of_nonneg (Nat.cast_nonneg n) <| re_neg_ne_zero_of_one_lt_re hs,
     neg_re, Real.rpow_neg <| Nat.cast_nonneg n]
@@ -113,7 +113,7 @@ theorem DirichletCharacter.LSeries_eulerProduct_hasProd {N : ℕ} (χ : Dirichle
     (hs : 1 < s.re) :
     HasProd (fun p : Primes ↦ (1 - χ p * (p : ℂ) ^ (-s))⁻¹) (L ↗χ s) := by
   rw [← tsum_dirichletSummand χ hs]
-  convert eulerProduct_completely_multiplicative_hasProd <| summable_dirichletSummand χ hs
+  convert! eulerProduct_completely_multiplicative_hasProd <| summable_dirichletSummand χ hs
 
 /-- The Euler product for Dirichlet L-series, valid for `s.re > 1`.
 This version is stated in terms of `tprod`. -/
@@ -151,8 +151,9 @@ open DirichletCharacter
 /-- A variant of the Euler product for the L-series of `ζ`. -/
 theorem ArithmeticFunction.LSeries_zeta_eulerProduct_exp_log {s : ℂ} (hs : 1 < s.re) :
     exp (∑' p : Nat.Primes, -Complex.log (1 - p ^ (-s))) = L 1 s := by
-  convert modOne_eq_one (R := ℂ) ▸
-    DirichletCharacter.LSeries_eulerProduct_exp_log (1 : DirichletCharacter ℂ 1) hs using 7
+  convert!
+    modOne_eq_one (R := ℂ) ▸
+      DirichletCharacter.LSeries_eulerProduct_exp_log (1 : DirichletCharacter ℂ 1) hs using 7
   rw [MulChar.one_apply <| isUnit_of_subsingleton _, one_mul]
 
 /-- A variant of the Euler product for the Riemann zeta function. -/
diff --git a/Mathlib/NumberTheory/FLT/MasonStothers.lean b/Mathlib/NumberTheory/FLT/MasonStothers.lean
index c8cd330d73caf1..bce9515a2ceef1 100644
--- a/Mathlib/NumberTheory/FLT/MasonStothers.lean
+++ b/Mathlib/NumberTheory/FLT/MasonStothers.lean
@@ -63,13 +63,13 @@ protected theorem Polynomial.abc
   have hbc : IsCoprime b c := by
     rw [add_eq_zero_iff_neg_eq] at hsum
     rw [← hsum, IsCoprime.neg_right_iff]
-    convert IsCoprime.add_mul_left_right hab.symm 1
+    convert! IsCoprime.add_mul_left_right hab.symm 1
     rw [mul_one]
   have hsum' : b + c + a = 0 := by rwa [add_rotate] at hsum
   have hca : IsCoprime c a := by
     rw [add_eq_zero_iff_neg_eq] at hsum'
     rw [← hsum', IsCoprime.neg_right_iff]
-    convert IsCoprime.add_mul_left_right hbc.symm 1
+    convert! IsCoprime.add_mul_left_right hbc.symm 1
     rw [mul_one]
   have wbc : w = wronskian b c := wronskian_eq_of_sum_zero hsum
   have wca : w = wronskian c a := by
diff --git a/Mathlib/NumberTheory/FLT/Polynomial.lean b/Mathlib/NumberTheory/FLT/Polynomial.lean
index b0a8332e0e8335..ff0cd99f2cd69a 100644
--- a/Mathlib/NumberTheory/FLT/Polynomial.lean
+++ b/Mathlib/NumberTheory/FLT/Polynomial.lean
@@ -53,7 +53,7 @@ private lemma rot_coprime
   rw [add_eq_zero_iff_neg_eq] at heq
   rw [← IsCoprime.pow_iff hq.bot_lt hr.bot_lt, ← isCoprime_mul_units_left hCv hCw,
     ← heq, IsCoprime.neg_right_iff]
-  convert IsCoprime.add_mul_left_right hab.symm 1 using 2
+  convert! IsCoprime.add_mul_left_right hab.symm 1 using 2
   rw [mul_one]
 
 private lemma ineq_pqr_contradiction {p q r a b c : ℕ}
@@ -266,7 +266,7 @@ theorem fermatLastTheoremWith'_polynomial {n : ℕ} (hn : 3 ≤ n) (chn : (n : k
     rw [← hc', C_ne_zero] at hc
     exact ⟨ha.right.isUnit_C, hb.right.isUnit_C, hc.right.isUnit_C⟩
   apply flt hn chn ha.right hb.right hc.right _ heq
-  convert isCoprime_div_gcd_div_gcd _
+  convert! isCoprime_div_gcd_div_gcd _
   · exact EuclideanDomain.eq_div_of_mul_eq_left ha.left eq_a.symm
   · exact EuclideanDomain.eq_div_of_mul_eq_left ha.left eq_b.symm
   · rw [eq_b]
diff --git a/Mathlib/NumberTheory/FLT/Three.lean b/Mathlib/NumberTheory/FLT/Three.lean
index 3452cacc0e72dd..711bf57d10cf26 100644
--- a/Mathlib/NumberTheory/FLT/Three.lean
+++ b/Mathlib/NumberTheory/FLT/Three.lean
@@ -86,7 +86,7 @@ lemma three_dvd_b_of_dvd_a_of_gcd_eq_one_of_case2 {a b c : ℤ} (ha : a ≠ 0)
     refine IsCoprime.neg_neg ?_
     rw [add_comm (a ^ 3), add_assoc, add_comm (a ^ 3), ← add_assoc] at HF
     refine isCoprime_of_gcd_eq_one_of_FLT ?_ HF
-    convert Hgcd using 2
+    convert! Hgcd using 2
     rw [Finset.pair_comm, Finset.insert_comm]
   by_contra! h3b
   by_cases h3c : 3 ∣ c
@@ -433,7 +433,7 @@ lemma associated_of_dvd_a_add_b_of_dvd_a_add_eta_sq_mul_b {p : 𝓞 K} (hp : Pri
   rw [← one_mul S.a] at hpaηsqb
   have := dvd_mul_sub_mul_mul_gcd_of_dvd hpab hpaηsqb
   rw [one_mul, mul_one, IsUnit.dvd_mul_right <| (gcd_isUnit_iff _ _).2 S.coprime, ← dvd_neg] at this
-  convert dvd_mul_of_dvd_left this η using 1
+  convert! dvd_mul_of_dvd_left this η using 1
   rw [eta_sq, neg_sub, sub_mul, sub_mul, neg_mul, ← pow_two, eta_sq, coe_eta]
   ring
 
@@ -446,7 +446,7 @@ lemma associated_of_dvd_a_add_eta_mul_b_of_dvd_a_add_eta_sq_mul_b {p : 𝓞 K} (
   rw [← one_mul S.a] at hpaηsqb
   have := dvd_mul_sub_mul_mul_gcd_of_dvd hpaηb hpaηsqb
   rw [one_mul, mul_one, IsUnit.dvd_mul_right <| (gcd_isUnit_iff _ _).2 S.coprime] at this
-  convert (dvd_mul_of_dvd_left (dvd_mul_of_dvd_left this η) η) using 1
+  convert! (dvd_mul_of_dvd_left (dvd_mul_of_dvd_left this η) η) using 1
   symm
   calc _ = (-η.1 - 1 - η) * (-η - 1) := by rw [eta_sq, mul_assoc, ← pow_two, eta_sq]
   _ = 2 * η.1 ^ 2 + 3 * η + 1 := by ring
@@ -557,7 +557,7 @@ lemma x_mul_y_mul_z_eq_u_mul_w_cube : S.x * S.y * S.z = S.u * S.w ^ 3 := by
       mul_assoc] at hh
     simp only [mul_eq_mul_left_iff, pow_eq_zero_iff', hζ.zeta_sub_one_prime'.ne_zero, ne_eq,
       mul_eq_zero, OfNat.ofNat_ne_zero, false_or, false_and, or_false] at hh
-    convert hh using 1
+    convert! hh using 1
     ring
   simp only [← x_spec, mul_assoc, ← y_spec, ← z_spec]
   rw [mul_comm 3, pow_mul, ← mul_pow, ← w_spec, ← S.H, a_cube_add_b_cube_eq_mul]
diff --git a/Mathlib/NumberTheory/FermatPsp.lean b/Mathlib/NumberTheory/FermatPsp.lean
index 35dd48f583eb42..dc610844384b41 100644
--- a/Mathlib/NumberTheory/FermatPsp.lean
+++ b/Mathlib/NumberTheory/FermatPsp.lean
@@ -149,7 +149,7 @@ private theorem AB_id_helper (b p : ℕ) (_ : 2 ≤ b) (hp : Odd p) :
     (b ^ p - 1) / (b - 1) * ((b ^ p + 1) / (b + 1)) = (b ^ (2 * p) - 1) / (b ^ 2 - 1) := by
   have q₁ : b - 1 ∣ b ^ p - 1 := by simpa only [one_pow] using Nat.sub_dvd_pow_sub_pow b 1 p
   have q₂ : b + 1 ∣ b ^ p + 1 := by simpa only [one_pow] using hp.nat_add_dvd_pow_add_pow b 1
-  convert Nat.div_mul_div_comm q₁ q₂ using 2 <;> rw [mul_comm (_ - 1), ← Nat.sq_sub_sq]
+  convert! Nat.div_mul_div_comm q₁ q₂ using 2 <;> rw [mul_comm (_ - 1), ← Nat.sq_sub_sq]
   ring_nf
 
 /-- Used in the proof of `psp_from_prime_psp`
diff --git a/Mathlib/NumberTheory/FrobeniusNumber.lean b/Mathlib/NumberTheory/FrobeniusNumber.lean
index 1d979ed8c5e948..5af9915fceace7 100644
--- a/Mathlib/NumberTheory/FrobeniusNumber.lean
+++ b/Mathlib/NumberTheory/FrobeniusNumber.lean
@@ -152,9 +152,10 @@ theorem exists_mem_span_nat_finset_of_ge :
   obtain ⟨rx, hrx⟩ : setGcd s ∣ r := (dvd_mod_iff (setGcd_dvd_of_mem hxs)).mpr <|
     (Nat.dvd_add_right <| dvd_mul_of_dvd_right (Finset.dvd_sum fun i _ ↦
       dvd_mul_of_dvd_right (setGcd_dvd_of_mem (hts i.2)) _) _).mp dvd
-  convert (sum_mem fun i _ ↦ mul_mem_left _ _ (subset_span i.2) :
-    -- an explicit ℕ-linear combination of elements of `t` that is equal to `r + n`
-    ∑ i : t, (if 0 ≤ a i then rx else x / setGcd s - rx) * (a i).natAbs * i ∈ span t)
+  convert!
+    (sum_mem fun i _ ↦ mul_mem_left _ _ (subset_span i.2) :
+      -- an explicit ℕ-linear combination of elements of `t` that is equal to `r + n`
+       ∑ i : t, (if 0 ≤ a i then rx else x / setGcd s - rx) * (a i).natAbs * i ∈ span t)
   simp_rw [← Int.natCast_inj, hrx, n, Finset.mul_sum, mul_comm _ rx, cast_add, cast_sum, cast_mul,
     ← eq, Finset.mul_sum, smul_eq_mul, ← mul_assoc, ← Finset.sum_add_distrib, ← add_mul]
   congr! 2 with i
diff --git a/Mathlib/NumberTheory/FunctionField.lean b/Mathlib/NumberTheory/FunctionField.lean
index 07f1fd03fff3ad..44f5f68e40d708 100644
--- a/Mathlib/NumberTheory/FunctionField.lean
+++ b/Mathlib/NumberTheory/FunctionField.lean
@@ -77,7 +77,7 @@ theorem functionField_iff (Ft : Type*) [Field Ft] [Algebra F[X] Ft]
     exact (b.mapCoeffs e this).finiteDimensional_of_finite
   · let b := Module.finBasis Ft K
     refine (b.mapCoeffs e.symm ?_).finiteDimensional_of_finite
-    intro c x; convert (this (e.symm c) x).symm; simp only [e.apply_symm_apply]
+    intro c x; convert! (this (e.symm c) x).symm; simp only [e.apply_symm_apply]
 
 namespace FunctionField
 
diff --git a/Mathlib/NumberTheory/GaussSum.lean b/Mathlib/NumberTheory/GaussSum.lean
index dfe725f1e1c7d2..546da839541209 100644
--- a/Mathlib/NumberTheory/GaussSum.lean
+++ b/Mathlib/NumberTheory/GaussSum.lean
@@ -297,7 +297,7 @@ theorem FiniteField.two_pow_card {F : Type*} [Fintype F] [Field F] (hF : ringCha
     exact mt FFp.dvd_of_dvd_pow hFF
   -- there is a primitive additive character `ℤ/8ℤ → FF`, sending `a + 8ℤ ↦ τ^a`
   -- with a primitive eighth root of unity `τ`
-  let ψ₈ := primitiveZModChar 8 F (by convert hp2 3 using 1; norm_cast)
+  let ψ₈ := primitiveZModChar 8 F (by convert! hp2 3 using 1; norm_cast)
   -- We cast from `AddChar (ZMod (8 : ℕ+)) FF` to `AddChar (ZMod 8) FF`
   -- This is needed to make `simp_rw [← h₁]` below work.
   let ψ₈char : AddChar (ZMod 8) FF := ψ₈.char
diff --git a/Mathlib/NumberTheory/Harmonic/Bounds.lean b/Mathlib/NumberTheory/Harmonic/Bounds.lean
index 16f920c6c765f4..9bf769b83daeb5 100644
--- a/Mathlib/NumberTheory/Harmonic/Bounds.lean
+++ b/Mathlib/NumberTheory/Harmonic/Bounds.lean
@@ -48,10 +48,10 @@ theorem harmonic_le_one_add_log (n : ℕ) :
   · simp_rw [Nat.cast_add, Nat.cast_one, add_sub_cancel_right]
   · exact @AntitoneOn.sum_le_integral_Ico 2 (n + 1) (fun x : ℝ ↦ (x - 1)⁻¹) (by linarith [hn]) <|
       sub_inv_antitoneOn_Icc_right (by simp)
-  · convert intervalIntegral.integral_comp_sub_right _ 1
+  · convert! intervalIntegral.integral_comp_sub_right _ 1
     · norm_num
     · simp only [Nat.cast_add, Nat.cast_one, add_sub_cancel_right]
-  · convert integral_inv _
+  · convert! integral_inv _
     · rw [div_one]
     · simp only [Nat.one_le_cast, hn, Set.uIcc_of_le, Set.mem_Icc, Nat.cast_nonneg,
         and_true, not_le, zero_lt_one]
diff --git a/Mathlib/NumberTheory/Harmonic/ZetaAsymp.lean b/Mathlib/NumberTheory/Harmonic/ZetaAsymp.lean
index 92452a06dcedcc..bdb7faa128cd5e 100644
--- a/Mathlib/NumberTheory/Harmonic/ZetaAsymp.lean
+++ b/Mathlib/NumberTheory/Harmonic/ZetaAsymp.lean
@@ -377,7 +377,7 @@ lemma tendsto_riemannZeta_sub_one_div_Gammaℝ :
     (𝓝 ((γ - Complex.log (4 * ↑π)) / 2)) := by
   have := tendsto_riemannZeta_sub_one_div.add tendsto_Gamma_term_aux
   simp_rw [sub_add_sub_cancel] at this
-  convert this using 2
+  convert! this using 2
   ring_nf
 
 /-- Formula for `ζ 1`. Note that mathematically `ζ 1` is undefined, but our construction ascribes
diff --git a/Mathlib/NumberTheory/Height/Basic.lean b/Mathlib/NumberTheory/Height/Basic.lean
index 9f7c92337d7549..ccb65f86701f3c 100644
--- a/Mathlib/NumberTheory/Height/Basic.lean
+++ b/Mathlib/NumberTheory/Height/Basic.lean
@@ -314,7 +314,7 @@ private lemma hasFiniteMulSupport_iSup_nonarchAbsVal {x : ι → K} (hx : x ≠
     (fun v : nonarchAbsVal ↦ ⨆ i, v.val (x i)).HasFiniteMulSupport := by
   have : Nonempty {j // x j ≠ 0} := nonempty_subtype.mpr <| ne_iff.mp hx
   suffices (fun v : nonarchAbsVal ↦ ⨆ i : {j // x j ≠ 0}, v.val (x i)).HasFiniteMulSupport by
-    convert this with v
+    convert! this with v
     obtain ⟨i, hi⟩ : ∃ j, x j ≠ 0 := Function.ne_iff.mp hx
     have : Nonempty ι := .intro i
     refine le_antisymm (ciSup_le fun j ↦ ?_) (ciSup_le fun ⟨j, hj⟩ ↦ Finite.le_ciSup_of_le j le_rfl)
@@ -437,7 +437,7 @@ lemma mulHeight_eq_one_of_subsingleton {ι : Type*} [Subsingleton ι] (x : ι 
   obtain ⟨i, hi⟩ := Function.ne_iff.mp hx
   have : Nonempty ι := .intro i
   rw [← mulHeight_smul_eq_mulHeight x (inv_ne_zero hi)]
-  convert mulHeight_one
+  convert! mulHeight_one
   ext1 j
   simpa [Subsingleton.elim j i] using inv_mul_cancel₀ hi
 
diff --git a/Mathlib/NumberTheory/Height/MvPolynomial.lean b/Mathlib/NumberTheory/Height/MvPolynomial.lean
index f495a646d1b2c8..0181f63aaff311 100644
--- a/Mathlib/NumberTheory/Height/MvPolynomial.lean
+++ b/Mathlib/NumberTheory/Height/MvPolynomial.lean
@@ -541,7 +541,7 @@ variable [AdmissibleAbsValues K]
 lemma mulHeight_mul_mulHeight {a b c d : K} (hab : ![a, b] ≠ 0) (hcd : ![c, d] ≠ 0) :
     mulHeight ![a, b] * mulHeight ![c, d] = mulHeight ![a * c, a * d, b * c, b * d] := by
   simp only [← mulHeight_fun_mul_eq hab hcd]
-  convert mulHeight_comp_equiv finProdFinEquiv _ with i
+  convert! mulHeight_comp_equiv finProdFinEquiv _ with i
   fin_cases i <;> simp [finProdFinEquiv]
 
 open MvPolynomial
@@ -571,7 +571,7 @@ lemma mulHeight_sym2_le :
     grind
   rw [mul_assoc, mulHeight_mul_mulHeight hab hcd]
   grw [← le_max_left C 1]
-  convert hC _ with i
+  convert! hC _ with i
   fin_cases i <;> simp [p]
 
 lemma mulHeight_sym2_ge :
@@ -586,7 +586,7 @@ lemma mulHeight_sym2_ge :
   simp only [pow_one] at hC
   refine ⟨C, hC₀, fun hab hcd ↦ ?_⟩
   rw [mul_assoc, mulHeight_mul_mulHeight hab hcd]
-  convert hC p fun j ↦ ?H with i
+  convert! hC p fun j ↦ ?H with i
   case H => fin_cases j <;> simp [p, q, Fin.sum_univ_three] <;> ring
   fin_cases i <;> simp [p]
 
diff --git a/Mathlib/NumberTheory/Height/NumberField.lean b/Mathlib/NumberTheory/Height/NumberField.lean
index 208e01048630ac..2af31064d5d207 100644
--- a/Mathlib/NumberTheory/Height/NumberField.lean
+++ b/Mathlib/NumberTheory/Height/NumberField.lean
@@ -121,7 +121,7 @@ lemma mulHeight_eq {ι : Type*} {x : ι → K} (hx : x ≠ 0) :
 variable (K) in
 lemma totalWeight_eq_sum_mult : totalWeight K = ∑ v : InfinitePlace K, v.mult := by
   simp only [totalWeight]
-  convert sum_archAbsVal_eq (fun _ ↦ (1 : ℕ))
+  convert! sum_archAbsVal_eq (fun _ ↦ (1 : ℕ))
   · rw [← Multiset.sum_map_toList, ← Fin.sum_univ_fun_getElem, ← Multiset.length_toList,
       Fin.sum_const, Multiset.length_toList, smul_eq_mul, mul_one]
   · simp
@@ -233,7 +233,7 @@ lemma mulHeight₁_eq_max (q : ℚ) : mulHeight₁ q = max q.num.natAbs q.den :=
   have : (.univ : Finset (Fin 2)).gcd ![q.num, q.den] = 1 := by
     simpa [Finset.univ_fin2, Int.normalize_coe_nat, ← Int.coe_gcd q.num q.den] using
       Int.isCoprime_iff_gcd_eq_one.mp <| isCoprime_num_den q
-  convert mulHeight_eq_max_abs_of_gcd_eq_one this
+  convert! mulHeight_eq_max_abs_of_gcd_eq_one this
   · ext i; fin_cases i <;> simp
   · rw [← Int.cast_natCast, Int.cast_inj]
     push_cast
diff --git a/Mathlib/NumberTheory/KummerDedekind.lean b/Mathlib/NumberTheory/KummerDedekind.lean
index c94ea99c074d1f..e5a45bb93d2bd9 100644
--- a/Mathlib/NumberTheory/KummerDedekind.lean
+++ b/Mathlib/NumberTheory/KummerDedekind.lean
@@ -91,7 +91,7 @@ lemma quotMapEquivQuotQuotMap_symm_apply (hx : (conductor R x).comap (algebraMap
     RingEquiv.symm_symm, RingEquiv.coe_trans, Function.comp_apply, RingEquiv.symm_apply_apply,
     RingEquiv.symm_trans_apply, quotEquivOfEq_symm, quotEquivOfEq_mk]
   congr
-  convert (adjoin.powerBasis' hx').quotientEquivQuotientMinpolyMap_symm_apply_mk I Q
+  convert! (adjoin.powerBasis' hx').quotientEquivQuotientMinpolyMap_symm_apply_mk I Q
   apply (quotAdjoinEquivQuotMap hx
     (FaithfulSMul.algebraMap_injective ((adjoin R {x})) S)).injective
   simp only [RingEquiv.apply_symm_apply, adjoin.powerBasis'_gen, quotAdjoinEquivQuotMap_apply_mk,
diff --git a/Mathlib/NumberTheory/LSeries/AbstractFuncEq.lean b/Mathlib/NumberTheory/LSeries/AbstractFuncEq.lean
index c0b6901f6252c4..d8bb638dfc19be 100644
--- a/Mathlib/NumberTheory/LSeries/AbstractFuncEq.lean
+++ b/Mathlib/NumberTheory/LSeries/AbstractFuncEq.lean
@@ -107,7 +107,7 @@ section symmetry
 lemma WeakFEPair.h_feq' (P : WeakFEPair E) (x : ℝ) (hx : 0 < x) :
     P.g (1 / x) = (P.ε⁻¹ * ↑(x ^ P.k)) • P.f x := by
   rw [(div_div_cancel₀ (one_ne_zero' ℝ) ▸ P.h_feq (1 / x) (one_div_pos.mpr hx) :), ← mul_smul]
-  convert (one_smul ℂ (P.g (1 / x))).symm using 2
+  convert! (one_smul ℂ (P.g (1 / x))).symm using 2
   rw [one_div, inv_rpow hx.le, ofReal_inv]
   field [P.hε, (rpow_pos_of_pos hx _).ne']
 
@@ -156,7 +156,7 @@ lemma hf_zero (P : WeakFEPair E) (r : ℝ) :
   simp_rw [Function.comp_apply, ← one_div, P.h_feq' _ hx] at hC'
   rw [← ((mul_inv_cancel₀ h_nv).symm ▸ one_smul ℂ P.g₀ :), mul_smul _ _ P.g₀, ← smul_sub, norm_smul,
     ← le_div_iff₀' (lt_of_le_of_ne (norm_nonneg _) (norm_ne_zero_iff.mpr h_nv).symm)] at hC'
-  convert hC' using 1
+  convert! hC' using 1
   · congr 3
     rw [rpow_neg hx.le]
     simp [field]
diff --git a/Mathlib/NumberTheory/LSeries/Basic.lean b/Mathlib/NumberTheory/LSeries/Basic.lean
index f4420b306c5be9..201842a7425e6d 100644
--- a/Mathlib/NumberTheory/LSeries/Basic.lean
+++ b/Mathlib/NumberTheory/LSeries/Basic.lean
@@ -333,7 +333,7 @@ lemma LSeriesSummable.isBigO_rpow {f : ℕ → ℂ} {s : ℂ} (h : LSeriesSummab
     f =O[atTop] fun n ↦ (n : ℝ) ^ s.re := by
   obtain ⟨C, hC⟩ := h.le_const_mul_rpow
   refine Asymptotics.IsBigO.of_bound C <| eventually_atTop.mpr ⟨1, fun n hn ↦ ?_⟩
-  convert hC n (Nat.pos_iff_ne_zero.mp hn) using 2
+  convert! hC n (Nat.pos_iff_ne_zero.mp hn) using 2
   rw [Real.norm_eq_abs, Real.abs_rpow_of_nonneg n.cast_nonneg, abs_of_nonneg n.cast_nonneg]
 
 /-- If `f n` is bounded in absolute value by a constant times `n^(x-1)` and `re s > x`,
diff --git a/Mathlib/NumberTheory/LSeries/DirichletContinuation.lean b/Mathlib/NumberTheory/LSeries/DirichletContinuation.lean
index b9766e4837dcac..54977f1f924112 100644
--- a/Mathlib/NumberTheory/LSeries/DirichletContinuation.lean
+++ b/Mathlib/NumberTheory/LSeries/DirichletContinuation.lean
@@ -174,7 +174,7 @@ zeta function by multiplying with `∏ p ∈ N.primeFactors, (1 - (p : ℂ) ^ (-
 lemma LFunctionTrivChar_eq_mul_riemannZeta {s : ℂ} (hs : s ≠ 1) :
     LFunctionTrivChar N s = (∏ p ∈ N.primeFactors, (1 - (p : ℂ) ^ (-s))) * riemannZeta s := by
   rw [← LFunction_modOne_eq (χ := 1), LFunctionTrivChar, ← changeLevel_one N.one_dvd, mul_comm]
-  convert LFunction_changeLevel N.one_dvd 1 (.inr hs) using 4 with p
+  convert! LFunction_changeLevel N.one_dvd 1 (.inr hs) using 4 with p
   rw [MulChar.one_apply <| isUnit_of_subsingleton _, one_mul]
 
 /-- The L function of the trivial Dirichlet character mod `N` has a simple pole with
diff --git a/Mathlib/NumberTheory/LSeries/HurwitzZeta.lean b/Mathlib/NumberTheory/LSeries/HurwitzZeta.lean
index bdbae9c2a0199c..1fd05c4f234bb2 100644
--- a/Mathlib/NumberTheory/LSeries/HurwitzZeta.lean
+++ b/Mathlib/NumberTheory/LSeries/HurwitzZeta.lean
@@ -71,8 +71,9 @@ lemma differentiableAt_hurwitzZeta (a : UnitAddCircle) {s : ℂ} (hs : s ≠ 1)
 restrict to `a ∈ Icc 0 1` to simplify the statement. -/
 lemma hasSum_hurwitzZeta_of_one_lt_re {a : ℝ} (ha : a ∈ Icc 0 1) {s : ℂ} (hs : 1 < re s) :
     HasSum (fun n : ℕ ↦ 1 / (n + a : ℂ) ^ s) (hurwitzZeta a s) := by
-  convert (hasSum_nat_hurwitzZetaEven_of_mem_Icc ha hs).add
-      (hasSum_nat_hurwitzZetaOdd_of_mem_Icc ha hs) using 1
+  convert!
+    (hasSum_nat_hurwitzZetaEven_of_mem_Icc ha hs).add (hasSum_nat_hurwitzZetaOdd_of_mem_Icc ha hs)
+    using 1
   ext1 n
   -- plain `ring_nf` works here, but the following is faster:
   apply show ∀ (x y : ℂ), x = (x + y) / 2 + (x - y) / 2 by intros; ring
@@ -126,7 +127,7 @@ lemma sinZeta_eq (a : UnitAddCircle) (s : ℂ) :
 
 lemma hasSum_expZeta_of_one_lt_re (a : ℝ) {s : ℂ} (hs : 1 < re s) :
     HasSum (fun n : ℕ ↦ cexp (2 * π * I * a * n) / n ^ s) (expZeta a s) := by
-  convert (hasSum_nat_cosZeta a hs).add ((hasSum_nat_sinZeta a hs).mul_left I) using 1
+  convert! (hasSum_nat_cosZeta a hs).add ((hasSum_nat_sinZeta a hs).mul_left I) using 1
   ext1 n
   simp only [mul_right_comm _ I, ← cos_add_sin_I, push_cast]
   rw [add_div, mul_div, mul_comm _ I]
@@ -172,7 +173,7 @@ lemma expZeta_one_sub (a : UnitAddCircle) {s : ℂ} (hs : ∀ (n : ℕ), s ≠ 1
     expZeta a (1 - s) = (2 * π) ^ (-s) * Gamma s *
     (exp (π * I * s / 2) * hurwitzZeta a s + exp (-π * I * s / 2) * hurwitzZeta (-a) s) := by
   have hs' (n : ℕ) : s ≠ -↑n := by
-    convert hs (n + 1) using 1
+    convert! hs (n + 1) using 1
     push_cast
     ring
   rw [expZeta, cosZeta_one_sub a hs, sinZeta_one_sub a hs', hurwitzZeta, hurwitzZeta,
diff --git a/Mathlib/NumberTheory/LSeries/HurwitzZetaEven.lean b/Mathlib/NumberTheory/LSeries/HurwitzZetaEven.lean
index 6080dca219724c..3d7e9817422f7c 100644
--- a/Mathlib/NumberTheory/LSeries/HurwitzZetaEven.lean
+++ b/Mathlib/NumberTheory/LSeries/HurwitzZetaEven.lean
@@ -654,8 +654,10 @@ lemma differentiable_hurwitzZetaEven_sub_hurwitzZetaEven (a b : UnitAddCircle) :
   intro z
   rcases ne_or_eq z 1 with hz | rfl
   · exact (differentiableAt_hurwitzZetaEven a hz).sub (differentiableAt_hurwitzZetaEven b hz)
-  · convert (differentiableAt_hurwitzZetaEven_sub_one_div a).fun_sub
-      (differentiableAt_hurwitzZetaEven_sub_one_div b) using 2 with s
+  · convert!
+    (differentiableAt_hurwitzZetaEven_sub_one_div a).fun_sub
+      (differentiableAt_hurwitzZetaEven_sub_one_div b) using
+    2 with s
     abel
 
 /--
diff --git a/Mathlib/NumberTheory/LSeries/HurwitzZetaValues.lean b/Mathlib/NumberTheory/LSeries/HurwitzZetaValues.lean
index 13ae1c3b20b822..c07e995dd8a709 100644
--- a/Mathlib/NumberTheory/LSeries/HurwitzZetaValues.lean
+++ b/Mathlib/NumberTheory/LSeries/HurwitzZetaValues.lean
@@ -206,19 +206,19 @@ the functional equation). -/
 theorem riemannZeta_two_mul_nat {k : ℕ} (hk : k ≠ 0) :
     riemannZeta (2 * k) = (-1) ^ (k + 1) * (2 : ℂ) ^ (2 * k - 1)
       * (π : ℂ) ^ (2 * k) * bernoulli (2 * k) / (2 * k)! := by
-  convert congr_arg ((↑) : ℝ → ℂ) (hasSum_zeta_nat hk).tsum_eq
+  convert! congr_arg ((↑) : ℝ → ℂ) (hasSum_zeta_nat hk).tsum_eq
   · rw [← Nat.cast_two, ← Nat.cast_mul, zeta_nat_eq_tsum_of_gt_one (by lia)]
     simp [push_cast]
   · norm_cast
 
 theorem riemannZeta_two : riemannZeta 2 = (π : ℂ) ^ 2 / 6 := by
-  convert congr_arg ((↑) : ℝ → ℂ) hasSum_zeta_two.tsum_eq
+  convert! congr_arg ((↑) : ℝ → ℂ) hasSum_zeta_two.tsum_eq
   · rw [← Nat.cast_two, zeta_nat_eq_tsum_of_gt_one one_lt_two]
     simp [push_cast]
   · norm_cast
 
 theorem riemannZeta_four : riemannZeta 4 = π ^ 4 / 90 := by
-  convert congr_arg ((↑) : ℝ → ℂ) hasSum_zeta_four.tsum_eq
+  convert! congr_arg ((↑) : ℝ → ℂ) hasSum_zeta_four.tsum_eq
   · rw [← Nat.cast_one, show (4 : ℂ) = (4 : ℕ) by simp,
       zeta_nat_eq_tsum_of_gt_one (by simp : 1 < 4)]
     simp only [push_cast]
diff --git a/Mathlib/NumberTheory/LSeries/Injectivity.lean b/Mathlib/NumberTheory/LSeries/Injectivity.lean
index c8fe047f96595e..24cf8a1930d8dd 100644
--- a/Mathlib/NumberTheory/LSeries/Injectivity.lean
+++ b/Mathlib/NumberTheory/LSeries/Injectivity.lean
@@ -127,7 +127,7 @@ lemma LSeries.tendsto_atTop {f : ℕ → ℂ} (ha : abscissaOfAbsConv f < ⊤) :
   have hF {n : ℕ} (hn : n ≠ 0) : F n = f n := if_neg hn
   have ha' : abscissaOfAbsConv F < ⊤ := (abscissaOfAbsConv_congr hF).symm ▸ ha
   simp_rw [← LSeries_congr hF]
-  convert LSeries.tendsto_cpow_mul_atTop (n := 0) (fun _ hm ↦ Nat.le_zero.mp hm ▸ hF₀) ha' using 1
+  convert! LSeries.tendsto_cpow_mul_atTop (n := 0) (fun _ hm ↦ Nat.le_zero.mp hm ▸ hF₀) ha' using 1
   simp
 
 lemma LSeries_eq_zero_of_abscissaOfAbsConv_eq_top {f : ℕ → ℂ} (h : abscissaOfAbsConv f = ⊤) :
@@ -180,7 +180,7 @@ lemma LSeries_eq_zero_iff {f : ℕ → ℂ} (hf : f 0 = 0) :
   · simpa [h] using LSeries_eq_zero_of_abscissaOfAbsConv_eq_top h
   · simp only [h, or_false]
     refine ⟨fun H ↦ ?_, fun H ↦ H ▸ LSeries_zero⟩
-    convert (LSeries_eventually_eq_zero_iff'.mp ?_).resolve_right h
+    convert! (LSeries_eventually_eq_zero_iff'.mp ?_).resolve_right h
     · refine ⟨fun H' _ _ ↦ by rw [H', Pi.zero_apply], fun H' ↦ ?_⟩
       ext (- | m)
       · simp [hf]
diff --git a/Mathlib/NumberTheory/LSeries/MellinEqDirichlet.lean b/Mathlib/NumberTheory/LSeries/MellinEqDirichlet.lean
index c88c068bee4af7..1d6b46e9c172a1 100644
--- a/Mathlib/NumberTheory/LSeries/MellinEqDirichlet.lean
+++ b/Mathlib/NumberTheory/LSeries/MellinEqDirichlet.lean
@@ -28,8 +28,10 @@ lemma hasSum_mellin {a : ι → ℂ} {p : ι → ℝ} {F : ℝ → ℂ} {s : ℂ
     HasSum (fun i ↦ Gamma s * a i / p i ^ s) (mellin F s) := by
   simp_rw [mellin, smul_eq_mul, ← setIntegral_congr_fun measurableSet_Ioi
     (fun t ht ↦ congr_arg _ (hF t ht).tsum_eq), ← tsum_mul_left]
-  convert hasSum_integral_of_summable_integral_norm
-    (F := fun i t ↦ t ^ (s - 1) * (a i * rexp (-p i * t))) (fun i ↦ ?_) ?_ using 2 with i
+  convert!
+    hasSum_integral_of_summable_integral_norm (F := fun i t ↦ t ^ (s - 1) * (a i * rexp (-p i * t)))
+      (fun i ↦ ?_) ?_ using
+    2 with i
   · simp_rw [← mul_assoc, mul_comm _ (a _), mul_assoc (a _), mul_div_assoc, integral_const_mul]
     rcases hp i with hai | hpi
     · rw [hai, zero_mul, zero_mul]
@@ -50,7 +52,7 @@ lemma hasSum_mellin {a : ι → ℂ} {p : ι → ℝ} {F : ℝ → ℂ} {s : ℂ
     exact Or.inl (ofReal_ne_zero.mpr hpi.ne')
   · -- summability of integrals of norms
     apply Summable.of_norm
-    convert h_sum.mul_left (Real.Gamma s.re) using 2 with i
+    convert! h_sum.mul_left (Real.Gamma s.re) using 2 with i
     simp_rw [← mul_assoc, mul_comm _ (a i), mul_assoc, norm_mul (a i), integral_const_mul]
     rw [← mul_div_assoc, mul_comm (Real.Gamma _), mul_div_assoc, norm_mul ‖a i‖, norm_norm]
     rcases hp i with hai | hpi
@@ -71,7 +73,7 @@ lemma hasSum_mellin_pi_mul {a : ι → ℂ} {q : ι → ℝ} {F : ℝ → ℂ} {
     (h_sum : Summable fun i ↦ ‖a i‖ / (q i) ^ s.re) :
     HasSum (fun i ↦ π ^ (-s) * Gamma s * a i / q i ^ s) (mellin F s) := by
   have hp i : a i = 0 ∨ 0 < π * q i := by rcases hq i with h | h <;> simp [h, pi_pos]
-  convert hasSum_mellin hp hs (by simpa using hF) ?_ using 2 with i
+  convert! hasSum_mellin hp hs (by simpa using hF) ?_ using 2 with i
   · have : a i / ↑(π * q i) ^ s = π ^ (-s) * a i / q i ^ s := by
       rcases hq i with h | h
       · simp [h]
@@ -101,7 +103,7 @@ lemma hasSum_mellin_pi_mul₀ {a : ι → ℂ} {p : ι → ℝ} {F : ℝ → ℂ
       a' i * rexp (-π * p i * t) := by
     simp [a']
   simp_rw [this] at hF
-  convert hasSum_mellin_pi_mul hp' hs hF ?_ using 2 with i
+  convert! hasSum_mellin_pi_mul hp' hs hF ?_ using 2 with i
   · rcases eq_or_ne (p i) 0 with h | h <;>
     simp [a', h, ofReal_zero, zero_cpow hs', div_zero]
   · refine h_sum.of_norm_bounded (fun i ↦ ?_)
@@ -119,12 +121,12 @@ lemma hasSum_mellin_pi_mul_sq {a : ι → ℂ} {r : ι → ℝ} {F : ℝ → ℂ
     HasSum (fun i ↦ Gammaℝ s * a i / |r i| ^ s) (mellin F (s / 2)) := by
   have hs' : 0 < (s / 2).re := by rw [div_ofNat_re]; positivity
   simp_rw [← sq_eq_zero_iff (a := r _)] at hF
-  convert hasSum_mellin_pi_mul₀ (fun i ↦ sq_nonneg (r i)) hs' hF ?_ using 3 with i
+  convert! hasSum_mellin_pi_mul₀ (fun i ↦ sq_nonneg (r i)) hs' hF ?_ using 3 with i
   · rw [← neg_div, Gammaℝ_def]
   · rw [← sq_abs, ofReal_pow, ← cpow_nat_mul']
     · ring_nf
     all_goals rw [arg_ofReal_of_nonneg (abs_nonneg _)]; linarith [pi_pos]
-  · convert h_sum using 3 with i
+  · convert! h_sum using 3 with i
     rw [← sq_abs, ← rpow_natCast_mul (abs_nonneg _), div_ofNat_re, Nat.cast_ofNat,
       mul_div_cancel₀ _ two_pos.ne']
 
@@ -141,14 +143,14 @@ lemma hasSum_mellin_pi_mul_sq' {a : ι → ℂ} {r : ι → ℝ} {F : ℝ → 
       if r i = 0 then 0 else (a i * r i * rexp (-π * r i ^ 2 * t)) := by
     split_ifs with h <;> simp [h]
   conv at hF => enter [t, ht, 1, i]; rw [this]
-  convert hasSum_mellin_pi_mul_sq hs₂ hF ?_ using 2 with i
+  convert! hasSum_mellin_pi_mul_sq hs₂ hF ?_ using 2 with i
   · rcases eq_or_ne (r i) 0 with h | h
     · rw [h, abs_zero, ofReal_zero, zero_cpow hs₁, zero_cpow hs₃, div_zero, div_zero]
     · rw [cpow_add _ _ (ofReal_ne_zero.mpr <| abs_ne_zero.mpr h), cpow_one]
       conv_rhs => enter [1]; rw [← sign_mul_abs (r i), ofReal_mul, ← ofRealHom_eq_coe,
         SignType.map_cast]
       field [h]
-  · convert h_sum using 2 with i
+  · convert! h_sum using 2 with i
     rcases eq_or_ne (r i) 0 with h | h
     · rw [h, abs_zero, ofReal_zero, zero_rpow hs₂.ne', zero_rpow hs.ne', div_zero, div_zero]
     · rw [add_re, one_re, rpow_add (abs_pos.mpr h), rpow_one, norm_mul, norm_real,
diff --git a/Mathlib/NumberTheory/LSeries/Nonvanishing.lean b/Mathlib/NumberTheory/LSeries/Nonvanishing.lean
index 88103232edbfaf..37c682c89a9bb9 100644
--- a/Mathlib/NumberTheory/LSeries/Nonvanishing.lean
+++ b/Mathlib/NumberTheory/LSeries/Nonvanishing.lean
@@ -234,7 +234,7 @@ private lemma re_log_comb_nonneg' {a : ℝ} (ha₀ : 0 ≤ a) (ha₁ : a < 1) {z
   · simp only [← mul_div_assoc, ← add_div]
     refine div_nonneg ?_ n.cast_nonneg
     rw [← pow_mul, pow_mul', sq, mul_re, ← sq, ← sq, ← sq_norm_sub_sq_re, norm_pow, hz]
-    convert (show 0 ≤ 2 * a ^ n * ((z ^ n).re + 1) ^ 2 by positivity) using 1
+    convert! (show 0 ≤ 2 * a ^ n * ((z ^ n).re + 1) ^ 2 by positivity) using 1
     ring
 
 -- This is the version of the technical positivity lemma for logarithms of Euler factors.
@@ -252,7 +252,7 @@ private lemma re_log_comb_nonneg {n : ℕ} (hn : 2 ≤ n) {x : ℝ} (hx : 1 < x)
       simp only [neg_re, mul_re, I_re, ofReal_re, zero_mul, I_im, ofReal_im, mul_zero, sub_self,
         neg_zero, Real.rpow_zero, one_mul]
     rw [MulChar.one_apply hn', one_mul]
-    convert re_log_comb_nonneg' (by positivity) hn hz using 6
+    convert! re_log_comb_nonneg' (by positivity) hn hz using 6
     · simp only [ofReal_cpow n.cast_nonneg (-x), ofReal_natCast, ofReal_neg]
     · congr 2
       rw [neg_add, cpow_add _ _ <| mod_cast by lia, ← ofReal_neg, ofReal_cpow n.cast_nonneg (-x),
@@ -317,7 +317,7 @@ lemma LFunctionTrivChar_isBigO_near_one_horizontal :
   have : (fun w : ℂ ↦ LFunctionTrivChar N (1 + w)) =O[𝓝[≠] 0] (1 / ·) := by
     have H : Tendsto (fun w ↦ w * LFunctionTrivChar N (1 + w)) (𝓝[≠] 0)
         (𝓝 <| ∏ p ∈ N.primeFactors, (1 - (p : ℂ)⁻¹)) := by
-      convert (LFunctionTrivChar_residue_one (N := N)).comp (f := fun w ↦ 1 + w) ?_ using 1
+      convert! (LFunctionTrivChar_residue_one (N := N)).comp (f := fun w ↦ 1 + w) ?_ using 1
       · simp only [Function.comp_def, add_sub_cancel_left]
       · simpa only [tendsto_iff_comap, Homeomorph.coe_addLeft, add_zero, map_le_iff_le_comap] using
           ((Homeomorph.addLeft (1 : ℂ)).map_punctured_nhds_eq 0).le
diff --git a/Mathlib/NumberTheory/LSeries/PrimesInAP.lean b/Mathlib/NumberTheory/LSeries/PrimesInAP.lean
index 83bb2032551436..49052a193032d6 100644
--- a/Mathlib/NumberTheory/LSeries/PrimesInAP.lean
+++ b/Mathlib/NumberTheory/LSeries/PrimesInAP.lean
@@ -148,7 +148,7 @@ lemma abscissaOfAbsConv_residueClass_le_one :
   refine abscissaOfAbsConv_le_of_forall_lt_LSeriesSummable fun y hy ↦ ?_
   unfold LSeriesSummable
   have := LSeriesSummable_vonMangoldt <| show 1 < (y : ℂ).re by simp only [ofReal_re, hy]
-  convert this.indicator {n : ℕ | (n : ZMod q) = a}
+  convert! this.indicator {n : ℕ | (n : ZMod q) = a}
   ext1 n
   by_cases hn : (n : ZMod q) = a
   · simp +contextual only [term, Set.indicator, Set.mem_setOf_eq, hn, ↓reduceIte, apply_ite,
@@ -424,7 +424,7 @@ lemma not_summable_residueClass_prime_div (ha : IsUnit a) :
     ¬ Summable fun n : ℕ ↦ (if n.Prime then residueClass a n else 0) / n := by
   intro H
   have key : Summable fun n : ℕ ↦ residueClass a n / n := by
-    convert (summable_residueClass_non_primes_div a).add H using 2 with n
+    convert! (summable_residueClass_non_primes_div a).add H using 2 with n
     simp only [← add_div, ite_add_ite, zero_add, add_zero, ite_self]
   let C := ∑' n, residueClass a n / n
   have H₁ {x : ℝ} (hx : 1 < x) : ∑' n, residueClass a n / (n : ℝ) ^ x ≤ C := by
diff --git a/Mathlib/NumberTheory/LSeries/SumCoeff.lean b/Mathlib/NumberTheory/LSeries/SumCoeff.lean
index 888336e0efc5ac..ca48f9fc96eca5 100644
--- a/Mathlib/NumberTheory/LSeries/SumCoeff.lean
+++ b/Mathlib/NumberTheory/LSeries/SumCoeff.lean
@@ -110,8 +110,9 @@ private theorem LSeries_eq_mul_integral_aux {f : ℕ → ℂ} (hf : f 0 = 0) {r
   rw [← integral_const_mul]
   refine tendsto_nhds_unique ((tendsto_add_atTop_iff_nat 1).mpr hS.hasSum.tendsto_sum_nat) ?_
   simp_rw [Nat.range_succ_eq_Icc_zero, LSeries.term_def₀ hf, mul_comm (f _)]
-  convert tendsto_sum_mul_atTop_nhds_one_sub_integral₀ (f := fun x ↦ (x : ℂ) ^ (-s)) (l := 0)
-    ?_ hf h₃ ?_ ?_ ?_ (integrableAtFilter_rpow_atTop_iff.mpr h₁)
+  convert!
+    tendsto_sum_mul_atTop_nhds_one_sub_integral₀ (f := fun x ↦ (x : ℂ) ^ (-s)) (l := 0) ?_ hf h₃ ?_
+      ?_ ?_ (integrableAtFilter_rpow_atTop_iff.mpr h₁)
   · rw [zero_sub, ← integral_neg]
     refine setIntegral_congr_fun measurableSet_Ioi fun t ht ↦ ?_
     rw [deriv_ofReal_cpow_const (zero_lt_one.trans ht).ne', h₄]
diff --git a/Mathlib/NumberTheory/LSeries/ZMod.lean b/Mathlib/NumberTheory/LSeries/ZMod.lean
index b525973a837ba5..0c52b1eb0d493d 100644
--- a/Mathlib/NumberTheory/LSeries/ZMod.lean
+++ b/Mathlib/NumberTheory/LSeries/ZMod.lean
@@ -478,7 +478,7 @@ theorem completedLFunction_one_sub_even (hΦ : Φ.Even) (s : ℂ)
       apply Countable.union <;>
       split_ifs <;>
       simp only [countable_singleton, countable_empty]
-    convert (this.isConnected_compl_of_one_lt_rank ?_).isPreconnected using 1
+    convert! (this.isConnected_compl_of_one_lt_rank ?_).isPreconnected using 1
     · ext x
       by_cases h : Φ 0 = 0 <;>
       by_cases h' : ∑ j, Φ j = 0 <;>
diff --git a/Mathlib/NumberTheory/LegendreSymbol/Basic.lean b/Mathlib/NumberTheory/LegendreSymbol/Basic.lean
index c6abf66a4691d4..d7a0950ee86474 100644
--- a/Mathlib/NumberTheory/LegendreSymbol/Basic.lean
+++ b/Mathlib/NumberTheory/LegendreSymbol/Basic.lean
@@ -128,7 +128,7 @@ theorem eq_pow (a : ℤ) : (legendreSym p a : ZMod p) = (a : ZMod p) ^ (p / 2) :
       generalize (a : ZMod 2) = b; fin_cases b
       · tauto
       · simp
-  · convert quadraticChar_eq_pow_of_char_ne_two' hc (a : ZMod p)
+  · convert! quadraticChar_eq_pow_of_char_ne_two' hc (a : ZMod p)
     exact (card p).symm
 
 /-- If `p ∤ a`, then `legendreSym p a` is `1` or `-1`. -/
diff --git a/Mathlib/NumberTheory/LegendreSymbol/JacobiSymbol.lean b/Mathlib/NumberTheory/LegendreSymbol/JacobiSymbol.lean
index 1c08757e918b68..b466522103763e 100644
--- a/Mathlib/NumberTheory/LegendreSymbol/JacobiSymbol.lean
+++ b/Mathlib/NumberTheory/LegendreSymbol/JacobiSymbol.lean
@@ -408,7 +408,7 @@ theorem quadratic_reciprocity' {a b : ℕ} (ha : Odd a) (hb : Odd b) :
   -- define the right-hand side for fixed `a` as a `ℕ →* ℤ`
   let rhs : ℕ → ℕ →* ℤ := fun a =>
     { toFun := fun x => qrSign x a * J(x | a)
-      map_one' := by convert ← mul_one (M := ℤ) _; (on_goal 1 => symm); all_goals apply one_left
+      map_one' := by convert! ← mul_one (M := ℤ) _; (on_goal 1 => symm); all_goals apply one_left
       map_mul' := fun x y => by
         simp_rw [qrSign.mul_left x y a, Nat.cast_mul, mul_left, mul_mul_mul_comm] }
   have rhs_apply : ∀ a b : ℕ, rhs a b = qrSign b a * J(b | a) := fun a b => rfl
diff --git a/Mathlib/NumberTheory/LocalField/Basic.lean b/Mathlib/NumberTheory/LocalField/Basic.lean
index 48bf6912f0d03c..dd9694d4d63bb9 100644
--- a/Mathlib/NumberTheory/LocalField/Basic.lean
+++ b/Mathlib/NumberTheory/LocalField/Basic.lean
@@ -88,8 +88,9 @@ lemma isCompact_closedBall (γ : ValueGroupWithZero K) : IsCompact { x | valuati
       dsimp at hx ⊢
       exact hx.trans_lt (hr.trans_le hr1)
   simp_rw [← (valuation K).restrict_le_iff] at H ⊢
-  convert (hs'.of_isClosed_subset (Valued.isClosed_closedBall K _) H).image
-    (Homeomorph.mulLeft₀ (γ / r) (by simp [hr, div_eq_zero_iff, hγ])).continuous using 1
+  convert!
+    (hs'.of_isClosed_subset (Valued.isClosed_closedBall K _) H).image
+      (Homeomorph.mulLeft₀ (γ / r) (by simp [hr, div_eq_zero_iff, hγ])).continuous using 1
   refine .trans ?_ (Equiv.image_eq_preimage_symm _ _).symm
   ext x
   simp only [Set.mem_setOf_eq, Homeomorph.coe_symm_toEquiv, Homeomorph.mulLeft₀_symm_apply, inv_div,
diff --git a/Mathlib/NumberTheory/LucasLehmer.lean b/Mathlib/NumberTheory/LucasLehmer.lean
index 84cc4da4548ac3..1294928b60e53c 100644
--- a/Mathlib/NumberTheory/LucasLehmer.lean
+++ b/Mathlib/NumberTheory/LucasLehmer.lean
@@ -391,7 +391,7 @@ lemma α_pow (i : ℕ) : (α : X q) ^ (2 * i + 1) = 3 ^ i * α := by
 
 instance : CharP (X q) q where
   cast_eq_zero_iff x := by
-    convert ZMod.natCast_eq_zero_iff _ _
+    convert! ZMod.natCast_eq_zero_iff _ _
     exact ⟨congr_arg Prod.fst, fun hx ↦ ext hx (by simp)⟩
 
 instance : Coe (ZMod ↑q) (X q) where
@@ -471,7 +471,7 @@ theorem card_eq : Fintype.card (X q) = q ^ 2 := by
 /-- There are strictly fewer than `q^2` units, since `0` is not a unit. -/
 nonrec theorem card_units_lt (w : 1 < q) : Fintype.card (X q)ˣ < q ^ 2 := by
   have : Fact (1 < (q : ℕ)) := ⟨w⟩
-  convert card_units_lt (X q)
+  convert! card_units_lt (X q)
   rw [card_eq]
 
 end X
diff --git a/Mathlib/NumberTheory/Modular.lean b/Mathlib/NumberTheory/Modular.lean
index 16b47375eac53a..8885ca638d2539 100644
--- a/Mathlib/NumberTheory/Modular.lean
+++ b/Mathlib/NumberTheory/Modular.lean
@@ -95,7 +95,7 @@ theorem bottom_row_surj {R : Type*} [CommRing R] :
   rintro cd ⟨b₀, a, gcd_eqn⟩
   let A := of ![![a, -b₀], cd]
   have det_A_1 : det A = 1 := by
-    convert gcd_eqn
+    convert! gcd_eqn
     rw [det_fin_two]
     simp [A, (by ring : a * cd 1 + b₀ * cd 0 = b₀ * cd 0 + a * cd 1)]
   refine ⟨⟨A, det_A_1⟩, Set.mem_univ _, ?_⟩
@@ -152,7 +152,7 @@ theorem tendsto_normSq_coprime_pair :
       simp only [ofReal_im, ofReal_re, mul_im, zero_add, mul_zero]
   have hf' : IsClosedEmbedding f := f.isClosedEmbedding_of_injective hf
   have h₂ : Tendsto (fun p : Fin 2 → ℤ => ((↑) : ℤ → ℝ) ∘ p) cofinite (cocompact _) := by
-    convert Tendsto.pi_map_coprodᵢ fun _ => Int.tendsto_coe_cofinite
+    convert! Tendsto.pi_map_coprodᵢ fun _ => Int.tendsto_coe_cofinite
     · rw [coprodᵢ_cofinite]
     · rw [coprodᵢ_cocompact]
   exact tendsto_normSq_cocompact_atTop.comp (hf'.tendsto_cocompact.comp h₂)
@@ -207,7 +207,7 @@ theorem tendsto_lcRow0 {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) :
     cocompact_ℝ_to_cofinite_ℤ_matrix.comp Subtype.coe_injective.tendsto_cofinite
   have hf₂ : IsClosedEmbedding (lcRow0Extend hcd) :=
     (lcRow0Extend hcd).toContinuousLinearEquiv.toHomeomorph.isClosedEmbedding
-  convert hf₂.tendsto_cocompact.comp (hf₁.comp Subtype.coe_injective.tendsto_cofinite) using 1
+  convert! hf₂.tendsto_cocompact.comp (hf₁.comp Subtype.coe_injective.tendsto_cofinite) using 1
   ext ⟨g, rfl⟩ i j : 3
   fin_cases i <;> [fin_cases j; skip]
   -- the following are proved by `simp`, but it is replaced by `simp only` to avoid timeouts.
@@ -217,7 +217,7 @@ theorem tendsto_lcRow0 {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) :
       LinearMap.GeneralLinearGroup.coeFn_generalLinearEquiv, GeneralLinearGroup.coe_toLin,
       val_planeConformalMatrix, neg_neg, mulVecLin_apply, mulVec, dotProduct, Fin.sum_univ_two,
       cons_val_one, mB, f₁]
-  · convert congr_arg (fun n : ℤ => (-n : ℝ)) g.det_coe.symm using 1
+  · convert! congr_arg (fun n : ℤ => (-n : ℝ)) g.det_coe.symm using 1
     simp only [Fin.zero_eta, Function.comp_apply, lcRow0Extend_apply, cons_val_zero,
       LinearMap.GeneralLinearGroup.coeFn_generalLinearEquiv, GeneralLinearGroup.coe_toLin,
       mulVecLin_apply, mulVec, dotProduct, det_fin_two, f₁]
@@ -239,7 +239,7 @@ theorem smul_eq_lcRow0_add {p : Fin 2 → ℤ} (hp : IsCoprime (p 0) (p 1)) (hg
   have nonZ2 : (p 0 : ℂ) * z + p 1 ≠ 0 := by simpa using linear_ne_zero z this
   subst hg
   rw [coe_specialLinearGroup_apply]
-  replace nonZ2 : z * (g 1 0 : ℂ) + g 1 1 ≠ 0 := by convert nonZ2 using 1; ring
+  replace nonZ2 : z * (g 1 0 : ℂ) + g 1 1 ≠ 0 := by convert! nonZ2 using 1; ring
   have H := congr(Int.cast (R := ℂ) $(det_fin_two g))
   simp at H
   simp [field]
@@ -259,7 +259,7 @@ theorem tendsto_abs_re_smul {p : Fin 2 → ℤ} (hp : IsCoprime (p 0) (p 1)) :
   let f := Homeomorph.mulRight₀ _ this
   let ff := Homeomorph.addRight
     (((p 1 : ℂ) * z - p 0) / (((p 0 : ℂ) ^ 2 + (p 1 : ℂ) ^ 2) * (p 0 * z + p 1))).re
-  convert (f.trans ff).isClosedEmbedding.tendsto_cocompact.comp (tendsto_lcRow0 hp) with _ _ g
+  convert! (f.trans ff).isClosedEmbedding.tendsto_cocompact.comp (tendsto_lcRow0 hp) with _ _ g
   change
     ((g : SL(2, ℤ)) • z).re =
       lcRow0 p ↑(↑g : SL(2, ℝ)) / ((p 0 : ℝ) ^ 2 + (p 1 : ℝ) ^ 2) +
@@ -487,7 +487,7 @@ private lemma cases_c_zero (hz : z ∈ 𝒟) (hg : g • z ∈ 𝒟) (hc : g 1 0
   wlog hd : 0 ≤ g 1 1
   · specialize this hz (g := -g) (SL_neg_smul g z ▸ hg) (by simpa using hc) ?_
     · simpa using (not_le.mp hd).le
-    convert this using 2 <;> simp [neg_eq_iff_eq_neg, or_comm]
+    convert! this using 2 <;> simp [neg_eq_iff_eq_neg, or_comm]
   have hd' : g 1 1 = 1 ∨ g 1 1 = -1 := by
     simpa [hc, isCoprime_zero_left, Int.isUnit_iff] using bottom_row_coprime g
   replace hd : g 1 1 = 1 := by grind
@@ -523,7 +523,7 @@ private lemma cases_d_of_c_eq_one (hz : z ∈ 𝒟) (hg' : ‖denom g z‖ ≤ 1
   rw [add_re, intCast_re, add_comm, coe_re] at this
   have := (abs_sub_abs_le_abs_add ..).trans this
   grw [sub_le_iff_le_add, hz.2, ← Int.cast_abs, ← Int.le_floor] at this
-  convert this
+  convert! this
   rw [eq_comm, Int.floor_eq_iff]
   norm_num
 
@@ -616,7 +616,7 @@ private lemma case_c_one_d_neg_one (hz : z ∈ 𝒟) (hg : g • z ∈ 𝒟) (hg
     simp [this]
     ring_nf
   have hnorm : ‖(z : ℂ) - 1‖ ≤ 1 := by
-    convert hg' using 2
+    convert! hg' using 2
     simp [denom, hc, hd, sub_eq_add_neg]
   rw [norm_def, Real.sqrt_le_one] at hnorm
   have : normSq (z - 1) = normSq z + (-2 * z.re + 1) := by
@@ -842,7 +842,7 @@ lemma isClosed_coe_fd : IsClosed ((↑) '' 𝒟 : Set ℂ) := by
     · exact isClosed_le continuous_const Complex.continuous_im
     · exact isClosed_le continuous_const continuous_norm
     · exact isClosed_le (continuous_abs.comp Complex.continuous_re) continuous_const
-  convert this using 1
+  convert! this using 1
   ext x
   refine ⟨fun ⟨him, hre, hnorm⟩ ↦ ⟨him.le, hre, hnorm⟩, fun ⟨him, hre, hnorm⟩ ↦ ⟨?_, hre, hnorm⟩⟩
   exact him.lt_of_ne' <| by grind [abs_re_eq_norm]
@@ -896,7 +896,7 @@ private lemma mem_closure_of_arc {x : ℍ} (hxnorm : ‖(x : ℂ)‖ = 1) (hxre
     refine mem_closure_of_one_lt_norm ?_ (by simpa using hxre)
     suffices 1 < ‖(x : ℂ)‖ ^ 2 + a ^ 2 + 2 * a * x.im by
       rw [← one_lt_normSq_iff]
-      convert this
+      convert! this
       simp [← normSq_eq_norm_sq, normSq_apply]
       ring
     rw [hxnorm, one_pow, add_assoc, lt_add_iff_pos_right]
diff --git a/Mathlib/NumberTheory/ModularForms/ArithmeticSubgroups.lean b/Mathlib/NumberTheory/ModularForms/ArithmeticSubgroups.lean
index 46cc5675389c54..eba88f2176e2fc 100644
--- a/Mathlib/NumberTheory/ModularForms/ArithmeticSubgroups.lean
+++ b/Mathlib/NumberTheory/ModularForms/ArithmeticSubgroups.lean
@@ -220,9 +220,9 @@ variable {R : Type*} [CommRing R]
   rintro g (hg | hg)
   · exact HasDetPlusMinusOne.det_eq hg
   · by_cases hn : Even (Fintype.card n)
-    · convert HasDetPlusMinusOne.det_eq hg using 1 <;>
+    · convert! HasDetPlusMinusOne.det_eq hg using 1 <;>
         simp [Units.ext_iff, det_neg, hn]
-    · convert (HasDetPlusMinusOne.det_eq hg).symm using 1 <;>
+    · convert! (HasDetPlusMinusOne.det_eq hg).symm using 1 <;>
         simp [Units.ext_iff, det_neg, Nat.not_even_iff_odd.mp hn, neg_eq_iff_eq_neg]
 
 lemma Subgroup.hasDetOne_adjoinNegOne_iff {𝒢 : Subgroup (GL n R)} (hn : Even (Fintype.card n)) :
diff --git a/Mathlib/NumberTheory/ModularForms/CongruenceSubgroups.lean b/Mathlib/NumberTheory/ModularForms/CongruenceSubgroups.lean
index cbf6289c785ee8..7fd1f98ac389c4 100644
--- a/Mathlib/NumberTheory/ModularForms/CongruenceSubgroups.lean
+++ b/Mathlib/NumberTheory/ModularForms/CongruenceSubgroups.lean
@@ -160,7 +160,7 @@ theorem Gamma1_mem (N : ℕ) (A : SL(2, ℤ)) : A ∈ Gamma1 N ↔
     rw [Gamma1_to_Gamma0_mem] at hx
     simp only [Subgroup.mem_top, true_and] at hxx
     rw [← hxx]
-    convert hx
+    convert! hx
   · intro ha
     simp_rw [Gamma1, Subgroup.mem_map]
     have hA : A ∈ Gamma0 N := by simp [ha.right.right, Gamma0_mem]
diff --git a/Mathlib/NumberTheory/ModularForms/Cusps.lean b/Mathlib/NumberTheory/ModularForms/Cusps.lean
index 6703ae93f68c74..102372815d0acd 100644
--- a/Mathlib/NumberTheory/ModularForms/Cusps.lean
+++ b/Mathlib/NumberTheory/ModularForms/Cusps.lean
@@ -68,7 +68,7 @@ lemma IsCusp.smul {c : OnePoint ℝ} {𝒢 : Subgroup (GL (Fin 2) ℝ)} (hc : Is
 
 lemma IsCusp.smul_of_mem {c : OnePoint ℝ} {𝒢 : Subgroup (GL (Fin 2) ℝ)} (hc : IsCusp c 𝒢)
     {g : GL (Fin 2) ℝ} (hg : g ∈ 𝒢) : IsCusp (g • c) 𝒢 := by
-  convert hc.smul g
+  convert! hc.smul g
   ext x
   rw [Subgroup.mem_pointwise_smul_iff_inv_smul_mem, ← ConjAct.toConjAct_inv,
     ConjAct.toConjAct_smul, inv_inv, Subgroup.mul_mem_cancel_right _ hg,
diff --git a/Mathlib/NumberTheory/ModularForms/DedekindEta.lean b/Mathlib/NumberTheory/ModularForms/DedekindEta.lean
index b8b69cf7e4c144..ca869fb317bc52 100644
--- a/Mathlib/NumberTheory/ModularForms/DedekindEta.lean
+++ b/Mathlib/NumberTheory/ModularForms/DedekindEta.lean
@@ -162,7 +162,7 @@ lemma logDeriv_qParam (h : ℝ) (z : ℂ) : logDeriv (𝕢 h) z = 2 * π * I / h
 lemma summable_logDeriv_one_sub_eta_q {z : ℂ} (hz : z ∈ ℍₒ) :
     Summable fun i ↦ logDeriv (1 - eta_q i ·) z := by
   have := summable_norm_pow_mul_geometric_div_one_sub 1 (norm_qParam_lt_one 1 ⟨z, hz⟩)
-  convert ((summable_nat_add_iff 1).mpr this).mul_left (-2 * π * I) using 1 with n
+  convert! ((summable_nat_add_iff 1).mpr this).mul_left (-2 * π * I) using 1 with n
   grind [one_sub_eta_logDeriv_eq]
 
 open EisensteinSeries in
diff --git a/Mathlib/NumberTheory/ModularForms/Derivative.lean b/Mathlib/NumberTheory/ModularForms/Derivative.lean
index b557c4adfb676e..e7f4df6c11143a 100644
--- a/Mathlib/NumberTheory/ModularForms/Derivative.lean
+++ b/Mathlib/NumberTheory/ModularForms/Derivative.lean
@@ -164,7 +164,7 @@ If `F : ℍ → ℂ` is MDifferentiable, then `serreDerivative k F` is also MDif
 theorem serreDerivative_mdifferentiable {F : ℍ → ℂ} (k : ℂ) (hF : MDiff F) :
     MDiff (serreDerivative k F) := by
   refine (normalizedDerivOfComplex_mdifferentiable hF).sub ?_
-  convert
+  convert!
     (MDifferentiable.mul mdifferentiable_const (E2_mdifferentiable.mul hF) :
       MDiff (fun z ↦ (k * 12⁻¹) * (EisensteinSeries.E2 z * F z)))
   simp [Pi.mul_apply, mul_assoc, mul_left_comm, mul_comm]
diff --git a/Mathlib/NumberTheory/ModularForms/Discriminant.lean b/Mathlib/NumberTheory/ModularForms/Discriminant.lean
index 8a2a1636a7e81f..1e71c038af3f95 100644
--- a/Mathlib/NumberTheory/ModularForms/Discriminant.lean
+++ b/Mathlib/NumberTheory/ModularForms/Discriminant.lean
@@ -164,7 +164,7 @@ lemma tendsto_atImInfty_tprod_one_sub_eta_q_pow :
     exact pow_le_pow_left₀ (norm_nonneg _) (mem_ball_zero_iff.mp hq).le _
   have := (htprod.comp (UpperHalfPlane.qParam_tendsto_atImInfty zero_lt_one)).pow 24
   simp only [Periodic.qParam, ofReal_one, div_one, comp_apply, one_pow, eta_q] at *
-  convert this using 2 with τ
+  convert! this using 2 with τ
   rw [Multipliable.tprod_pow]
   apply (multipliableLocallyUniformlyOn_eta.multipliable τ.2).congr
   simp [eta_q, Periodic.qParam, ← exp_nat_mul]
diff --git a/Mathlib/NumberTheory/ModularForms/EisensteinSeries/Defs.lean b/Mathlib/NumberTheory/ModularForms/EisensteinSeries/Defs.lean
index 9e3b16905ff965..510b6f87e8faaa 100644
--- a/Mathlib/NumberTheory/ModularForms/EisensteinSeries/Defs.lean
+++ b/Mathlib/NumberTheory/ModularForms/EisensteinSeries/Defs.lean
@@ -191,7 +191,7 @@ theorem eisSummand_SL2_apply (k : ℤ) (i : (Fin 2 → ℤ)) (A : SL(2, ℤ)) (z
   simp only [eisSummand, vecMul, vec2_dotProduct, denom, UpperHalfPlane.specialLinearGroup_apply]
   have h (a b c d u v : ℂ) (hc : c * z + d ≠ 0) : (u * ((a * z + b) / (c * z + d)) + v) ^ (-k) =
       (c * z + d) ^ k * ((u * a + v * c) * z + (u * b + v * d)) ^ (-k) := by
-    replace hc : z * c + d ≠ 0 := by convert hc using 1; ring
+    replace hc : z * c + d ≠ 0 := by convert! hc using 1; ring
     field_simp
     simp [div_zpow]
     ring_nf
diff --git a/Mathlib/NumberTheory/ModularForms/EisensteinSeries/E2/Summable.lean b/Mathlib/NumberTheory/ModularForms/EisensteinSeries/E2/Summable.lean
index 1ed2d8d1bea48b..24a842b2385077 100644
--- a/Mathlib/NumberTheory/ModularForms/EisensteinSeries/E2/Summable.lean
+++ b/Mathlib/NumberTheory/ModularForms/EisensteinSeries/E2/Summable.lean
@@ -178,7 +178,7 @@ lemma tsum_symmetricIco_tsum_eq_S_act :
 private lemma telescope_aux (z : ℂ) (m : ℤ) (b : ℕ) :
     ∑ n ∈ Ico (-b : ℤ) b, (1 / ((m : ℂ) * z + n) - 1 / (m * z + n + 1)) =
     1 / (m * z - b) - 1 / (m * z + b) := by
-  convert sum_Ico_int_sub b (fun n ↦ 1 / ((m : ℂ) * z + n)) using 2 <;>
+  convert! sum_Ico_int_sub b (fun n ↦ 1 / ((m : ℂ) * z + n)) using 2 <;>
   simp [add_assoc, sub_eq_add_neg]
 
 lemma tsum_symmetricIco_linear_sub_linear_add_one_eq_zero (m : ℤ) :
@@ -272,7 +272,7 @@ lemma tsum_symmetricIco_tsum_sub_eq :
 
 lemma tsum_tsum_symmetricIco_sub_eq :
     ∑' m : ℤ, ∑'[symmetricIco ℤ] n : ℤ, (1 / ((m : ℂ) * z + n) - 1 / (m * z + n + 1)) = 0 := by
-  convert tsum_zero
+  convert! tsum_zero
   exact tsum_symmetricIco_linear_sub_linear_add_one_eq_zero z _
 
 end Auxiliary
diff --git a/Mathlib/NumberTheory/ModularForms/EisensteinSeries/MDifferentiable.lean b/Mathlib/NumberTheory/ModularForms/EisensteinSeries/MDifferentiable.lean
index aefab5b501e602..d56d84dbb2c919 100644
--- a/Mathlib/NumberTheory/ModularForms/EisensteinSeries/MDifferentiable.lean
+++ b/Mathlib/NumberTheory/ModularForms/EisensteinSeries/MDifferentiable.lean
@@ -54,7 +54,8 @@ theorem eisensteinSeriesSIF_mdifferentiable {k : ℤ} {N : ℕ} (hk : 3 ≤ k) (
     MDiff (eisensteinSeriesSIF a k) := by
   intro τ
   suffices DifferentiableAt ℂ (↑ₕeisensteinSeriesSIF a k) τ.1 by
-    convert MDifferentiableAt.comp τ (DifferentiableAt.mdifferentiableAt this) τ.mdifferentiable_coe
+    convert!
+      MDifferentiableAt.comp τ (DifferentiableAt.mdifferentiableAt this) τ.mdifferentiable_coe
     exact funext fun z ↦ (comp_ofComplex (eisensteinSeriesSIF a k) z).symm
   refine DifferentiableOn.differentiableAt ?_ (isOpen_upperHalfPlaneSet.mem_nhds τ.2)
   exact (eisensteinSeries_tendstoLocallyUniformlyOn hk a).differentiableOn
diff --git a/Mathlib/NumberTheory/ModularForms/EisensteinSeries/QExpansion.lean b/Mathlib/NumberTheory/ModularForms/EisensteinSeries/QExpansion.lean
index b6d65d4acfecab..00915ba0ddc93d 100644
--- a/Mathlib/NumberTheory/ModularForms/EisensteinSeries/QExpansion.lean
+++ b/Mathlib/NumberTheory/ModularForms/EisensteinSeries/QExpansion.lean
@@ -71,7 +71,7 @@ private lemma aux_IsBigO_mul (k l : ℕ) (p : ℝ) {f : ℕ → ℂ}
     simpa [h1] using isBigO_ofReal_right.mp (Asymptotics.isBigO_const_mul_self
       ((2 * π * I / p) ^ k) (fun (n : ℕ) ↦ (↑(n ^ k) : ℝ)) atTop)
   push_cast
-  convert hf.mul h0
+  convert! hf.mul h0
   ring
 
 open BoundedContinuousFunction in
@@ -102,7 +102,7 @@ theorem summableLocallyUniformlyOn_iteratedDerivWithin_smul_cexp (k l : ℕ) {f
     norm_natCast, abs_norm, ge_iff_le, r, c] at *
   rw [← mul_assoc]
   gcongr
-  convert h0
+  convert! h0
   rw [← norm_pow, ← exp_nsmul']
 
 /-- This is a version of `summableLocallyUniformlyOn_iteratedDerivWithin_smul_cexp` for level one
@@ -299,7 +299,7 @@ private lemma eisensteinSeries_coeff_identity {k : ℕ} (hk2 : Even k) (hkn0 : k
 lemma EisensteinSeries.q_expansion_bernoulli {k : ℕ} (hk : 3 ≤ k) (hk2 : Even k) (z : ℍ) :
     E hk z = 1 - (2 * k / bernoulli k) *
     ∑' n : ℕ+, σ (k - 1) n * cexp (2 * π * I * z) ^ (n : ℤ) := by
-  convert q_expansion_riemannZeta hk hk2 z using 1
+  convert! q_expansion_riemannZeta hk hk2 z using 1
   rw [eisensteinSeries_coeff_identity hk2 (by grind), neg_mul, ← sub_eq_add_neg]
 
 section NonZero
@@ -340,7 +340,7 @@ lemma EisensteinSeries.E_qExpansion_coeff {k : ℕ} (hk : 3 ≤ k) (hk2 : Even k
     rw [this, ← tsum_pnat_eq_tsum_succ (f := fun n ↦ (σ (k - 1) n : ℂ) * cexp (2 * π * I * τ) ^ n)]
     ring
   rw [hval]
-  convert (hS.mul_left β).hasSum using 1
+  convert! (hS.mul_left β).hasSum using 1
   · grind [Periodic.qParam, ofReal_one, div_one]
   · rw [tsum_mul_left]
 
diff --git a/Mathlib/NumberTheory/ModularForms/JacobiTheta/Bounds.lean b/Mathlib/NumberTheory/ModularForms/JacobiTheta/Bounds.lean
index 3013528e320515..ebe1e446cc64db 100644
--- a/Mathlib/NumberTheory/ModularForms/JacobiTheta/Bounds.lean
+++ b/Mathlib/NumberTheory/ModularForms/JacobiTheta/Bounds.lean
@@ -115,7 +115,7 @@ Here we use direct comparison with a geometric series.
 lemma F_nat_zero_le {a : ℝ} (ha : 0 ≤ a) {t : ℝ} (ht : 0 < t) :
     ‖F_nat 0 a t‖ ≤ rexp (-π * a ^ 2 * t) / (1 - rexp (-π * t)) := by
   refine tsum_of_norm_bounded ?_ (f_le_g_nat 0 ha ht)
-  convert (hasSum_geometric_of_lt_one (exp_pos _).le <| exp_lt_aux ht).mul_left _ using 1
+  convert! (hasSum_geometric_of_lt_one (exp_pos _).le <| exp_lt_aux ht).mul_left _ using 1
   ext1 n
   simp only [g_nat]
   rw [← Real.exp_nat_mul, ← Real.exp_add]
@@ -123,7 +123,7 @@ lemma F_nat_zero_le {a : ℝ} (ha : 0 ≤ a) {t : ℝ} (ht : 0 < t) :
 
 lemma F_nat_zero_zero_sub_le {t : ℝ} (ht : 0 < t) :
     ‖F_nat 0 0 t - 1‖ ≤ rexp (-π * t) / (1 - rexp (-π * t)) := by
-  convert F_nat_zero_le zero_le_one ht using 2
+  convert! F_nat_zero_le zero_le_one ht using 2
   · rw [F_nat, (summable_f_nat 0 0 ht).tsum_eq_zero_add, f_nat, Nat.cast_zero, add_zero, pow_zero,
       one_mul, pow_two, mul_zero, mul_zero, zero_mul, exp_zero, add_comm, add_sub_cancel_right]
     simp_rw [F_nat, f_nat, Nat.cast_add, Nat.cast_one, add_zero]
@@ -166,12 +166,12 @@ lemma F_nat_one_le {a : ℝ} (ha : 0 ≤ a) {t : ℝ} (ht : 0 < t) :
   apply HasSum.add
   · have h0' : ‖rexp (-π * t)‖ < 1 := by
       simpa only [norm_eq_abs, abs_exp] using exp_lt_aux ht
-    convert (hasSum_coe_mul_geometric_of_norm_lt_one h0').mul_left (exp (-π * a ^ 2 * t)) using 1
+    convert! (hasSum_coe_mul_geometric_of_norm_lt_one h0').mul_left (exp (-π * a ^ 2 * t)) using 1
     · ext1 n
       rw [mul_comm (exp _), ← Real.exp_nat_mul, mul_assoc (n : ℝ), ← Real.exp_add]
       ring_nf
     · rw [mul_add, add_mul, mul_one, exp_add, mul_div_assoc]
-  · convert (hasSum_geometric_of_lt_one (exp_pos _).le <| exp_lt_aux ht).mul_left _ using 1
+  · convert! (hasSum_geometric_of_lt_one (exp_pos _).le <| exp_lt_aux ht).mul_left _ using 1
     ext1 n
     rw [← Real.exp_nat_mul, mul_assoc _ (exp _), ← Real.exp_add]
     ring_nf
@@ -239,8 +239,9 @@ def F_int (k : ℕ) (a : UnitAddCircle) (t : ℝ) : ℝ :=
 lemma F_int_eq_of_mem_Icc (k : ℕ) {a : ℝ} (ha : a ∈ Icc 0 1) {t : ℝ} (ht : 0 < t) :
     F_int k a t = (F_nat k a t) + (F_nat k (1 - a) t) := by
   simp only [F_int, F_nat, Function.Periodic.lift_coe]
-  convert ((summable_f_nat k a ht).hasSum.int_rec (summable_f_nat k (1 - a) ht).hasSum).tsum_eq
-    using 3 with n
+  convert!
+    ((summable_f_nat k a ht).hasSum.int_rec (summable_f_nat k (1 - a) ht).hasSum).tsum_eq using
+    3 with n
   cases n
   · rw [f_int_ofNat _ ha.1]
   · rw [f_int_negSucc _ ha.2]
diff --git a/Mathlib/NumberTheory/ModularForms/JacobiTheta/OneVariable.lean b/Mathlib/NumberTheory/ModularForms/JacobiTheta/OneVariable.lean
index 868715865e478b..71fbd1eab9241f 100644
--- a/Mathlib/NumberTheory/ModularForms/JacobiTheta/OneVariable.lean
+++ b/Mathlib/NumberTheory/ModularForms/JacobiTheta/OneVariable.lean
@@ -78,7 +78,7 @@ theorem hasSum_nat_jacobiTheta {τ : ℂ} (hτ : 0 < im τ) :
     Int.cast_zero, sq (0 : ℂ), mul_zero, zero_mul, neg_sq, ← mul_two,
     Complex.exp_zero, add_sub_assoc, (by norm_num : (1 : ℂ) - 1 * 2 = -1), ← sub_eq_add_neg,
     Nat.cast_add, Nat.cast_one] at this
-  convert this.div_const 2 using 1
+  convert! this.div_const 2 using 1
   simp_rw [mul_div_cancel_right₀ _ (two_ne_zero' ℂ)]
 
 theorem jacobiTheta_eq_tsum_nat {τ : ℂ} (hτ : 0 < im τ) :
diff --git a/Mathlib/NumberTheory/ModularForms/LevelOne/DimensionFormula.lean b/Mathlib/NumberTheory/ModularForms/LevelOne/DimensionFormula.lean
index 493714e6aa38f0..3554333ba845cc 100644
--- a/Mathlib/NumberTheory/ModularForms/LevelOne/DimensionFormula.lean
+++ b/Mathlib/NumberTheory/ModularForms/LevelOne/DimensionFormula.lean
@@ -212,7 +212,7 @@ theorem dimension_level_one (k : ℕ) (hk2 : Even k) :
     interval_cases k
     · simpa using levelOne_weight_zero_rank_one
     · grind
-    · convert levelOne_weight_two_rank_zero
+    · convert! levelOne_weight_two_rank_zero
       norm_num
   · -- `3 ≤ k < 12`: the lemma `rank_eq_one_add_rank_cuspForm` applies
     -- and the mod form space of weight `k - 12` is zero
diff --git a/Mathlib/NumberTheory/ModularForms/QExpansion.lean b/Mathlib/NumberTheory/ModularForms/QExpansion.lean
index cd17cb79e09172..61f4a9a1817730 100644
--- a/Mathlib/NumberTheory/ModularForms/QExpansion.lean
+++ b/Mathlib/NumberTheory/ModularForms/QExpansion.lean
@@ -123,7 +123,7 @@ theorem periodic_comp_ofComplex [SlashInvariantFormClass F Γ k] (hΓ : h ∈ Γ
   by_cases! hw : 0 < im w
   · have : 0 < im (w + h) := by simp [hw]
     simp only [comp_apply, ofComplex_apply_of_im_pos this, ofComplex_apply_of_im_pos hw]
-    convert SlashInvariantForm.vAdd_apply_of_mem_strictPeriods f ⟨w, hw⟩ hΓ using 2
+    convert! SlashInvariantForm.vAdd_apply_of_mem_strictPeriods f ⟨w, hw⟩ hΓ using 2
     ext
     simp [add_comm]
   · have : im (w + h) ≤ 0 := by simpa using hw
@@ -180,8 +180,10 @@ lemma hasSum_qExpansion_of_norm_lt {f : ℍ → ℂ} (hh : 0 < h)
     (hfper : Periodic (f ∘ ofComplex) h) (hfhol : MDiff f) (hfbdd : IsBoundedAtImInfty f)
     {q : ℂ} (hq : ‖q‖ < 1) :
     HasSum (fun m : ℕ ↦ (qExpansion h f).coeff m • q ^ m) (cuspFunction h f q) := by
-  convert hasSum_taylorSeries_on_ball (differentiableOn_cuspFunction_ball hh hfper hfhol hfbdd)
-      (by simpa using hq) using 2 with m
+  convert!
+    hasSum_taylorSeries_on_ball (differentiableOn_cuspFunction_ball hh hfper hfhol hfbdd)
+      (by simpa using hq) using
+    2 with m
   grind [qExpansion_coeff, sub_zero, smul_eq_mul]
 
 lemma hasSum_qExpansion {f : ℍ → ℂ} (hh : 0 < h)
@@ -327,10 +329,12 @@ theorem exp_decay_sub_atImInfty {f : ℍ → ℂ} (hh : 0 < h)
     (hfper : Periodic (f ∘ ofComplex) h) (hfhol : MDiff f) (hfbdd : IsBoundedAtImInfty f) :
     (fun τ ↦ f τ - valueAtInfty f) =O[atImInfty] fun τ ↦ Real.exp (-2 * π * τ.im / h) := by
   have := hfbdd.comp_tendsto tendsto_comap_im_ofComplex
-  convert (hfper.exp_decay_sub_of_bounded_at_inf hh
-    (eventually_of_mem (preimage_mem_comap (Ioi_mem_atTop 0))
-      fun z hz ↦ by simpa using (UpperHalfPlane.mdifferentiableAt_iff.mp <| hfhol ⟨z, hz⟩))
-        this).comp_tendsto tendsto_coe_atImInfty
+  convert!
+    (hfper.exp_decay_sub_of_bounded_at_inf hh
+          (eventually_of_mem (preimage_mem_comap (Ioi_mem_atTop 0)) fun z hz ↦ by
+            simpa using (UpperHalfPlane.mdifferentiableAt_iff.mp <| hfhol ⟨z, hz⟩))
+          this).comp_tendsto
+      tendsto_coe_atImInfty
   simpa [cuspFunction] using
     (cuspFunction_apply_zero hh (analyticAt_cuspFunction_zero hh hfper hfhol hfbdd) hfper).symm
 
@@ -374,8 +378,8 @@ theorem exp_decay_sub_atImInfty' [ModularFormClass F Γ k] [Γ.HasDetPlusMinusOn
   have hh : 0 < Γ.strictWidthInfty := Γ.strictWidthInfty_pos_iff.mpr Fact.out
   have hΓ : Γ.strictWidthInfty ∈ Γ.strictPeriods := Γ.strictWidthInfty_mem_strictPeriods
   refine ⟨2 * π / Γ.strictWidthInfty, div_pos Real.two_pi_pos hh, ?_⟩
-  convert exp_decay_sub_atImInfty hh (periodic_comp_ofComplex f hΓ) (holo f)
-    (bdd_at_infty f) using 3 with τ
+  convert! exp_decay_sub_atImInfty hh (periodic_comp_ofComplex f hΓ) (holo f) (bdd_at_infty f) using
+    3 with τ
   ring_nf
 
 /-- Version of `exp_decay_atImInfty` stating a less precise result but easier to apply in practice
diff --git a/Mathlib/NumberTheory/ModularForms/SlashActions.lean b/Mathlib/NumberTheory/ModularForms/SlashActions.lean
index cc5ea689cef059..f857faba9a4e9e 100644
--- a/Mathlib/NumberTheory/ModularForms/SlashActions.lean
+++ b/Mathlib/NumberTheory/ModularForms/SlashActions.lean
@@ -190,7 +190,7 @@ theorem is_invariant_one' (A : SL(2, ℤ)) : (1 : ℍ → ℂ) ∣[(0 : ℤ)] (A
 theorem slash_action_eq'_iff (k : ℤ) (f : ℍ → ℂ) (γ : SL(2, ℤ)) (z : ℍ) :
     (f ∣[k] γ) z = f z ↔ f (γ • z) = ((γ 1 0 : ℂ) * z + (γ 1 1 : ℂ)) ^ k * f z := by
   simp only [SL_slash_apply]
-  convert inv_mul_eq_iff_eq_mul₀ (G₀ := ℂ) _ using 2
+  convert! inv_mul_eq_iff_eq_mul₀ (G₀ := ℂ) _ using 2
   · simp only [mul_comm (f _), denom, zpow_neg]
     rfl
   · exact zpow_ne_zero k (denom_ne_zero γ z)
diff --git a/Mathlib/NumberTheory/Multiplicity.lean b/Mathlib/NumberTheory/Multiplicity.lean
index 560e050d58115f..24ddc415029939 100644
--- a/Mathlib/NumberTheory/Multiplicity.lean
+++ b/Mathlib/NumberTheory/Multiplicity.lean
@@ -58,7 +58,7 @@ theorem sq_dvd_add_pow_sub_sub (p x : R) (n : ℕ) :
       Nat.cast_succ, tsub_self, pow_zero, mul_one, Nat.choose_self, Nat.cast_zero, zero_add,
       Nat.succ_sub_succ_eq_sub, Nat.sub_zero]
     suffices p ^ 2 ∣ ∑ i ∈ range n, x ^ i * p ^ (n + 1 - i) * ↑((n + 1).choose i) by
-      convert this; abel
+      convert! this; abel
     apply Finset.dvd_sum
     intro y hy
     calc
@@ -318,7 +318,7 @@ theorem Int.two_pow_sub_pow {x y : ℤ} {n : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2
   have hy : Odd y := by
     rw [← even_iff_two_dvd, Int.not_even_iff_odd] at hx
     replace hxy := (@even_neg _ _ (x - y)).mpr (even_iff_two_dvd.mpr hxy)
-    convert Even.add_odd hxy hx
+    convert! Even.add_odd hxy hx
     abel
   obtain ⟨d, rfl⟩ := hn
   simp only [← two_mul, pow_mul]
@@ -347,7 +347,7 @@ theorem Nat.two_pow_sub_pow {x y : ℕ} (hxy : 2 ∣ x - y) (hx : ¬2 ∣ x) {n
       Int.natCast_pow]
     rw [← Int.natCast_dvd_natCast] at hx
     rw [← Int.natCast_dvd_natCast, Int.ofNat_sub hyx] at hxy
-    convert Int.two_pow_sub_pow hxy hx hn using 2
+    convert! Int.two_pow_sub_pow hxy hx hn using 2
     rw [← Int.natCast_emultiplicity]
     rfl
   · simp only [Nat.sub_eq_zero_iff_le.mpr hyx,
diff --git a/Mathlib/NumberTheory/Niven.lean b/Mathlib/NumberTheory/Niven.lean
index dc805dc12cc65a..68444271f6f6ac 100644
--- a/Mathlib/NumberTheory/Niven.lean
+++ b/Mathlib/NumberTheory/Niven.lean
@@ -139,7 +139,7 @@ theorem niven (hθ : ∃ r : ℚ, θ = r * π) (hcos : ∃ q : ℚ, cos θ = q)
 /-- Niven's theorem, but stated for `sin` instead of `cos`. -/
 theorem niven_sin (hθ : ∃ r : ℚ, θ = r * π) (hcos : ∃ q : ℚ, sin θ = q) :
     sin θ ∈ ({-1, -1 / 2, 0, 1 / 2, 1} : Set ℝ) := by
-  convert ← niven (θ := θ - π / 2) ?_ ?_ using 1
+  convert! ← niven (θ := θ - π / 2) ?_ ?_ using 1
   · exact cos_sub_pi_div_two θ
   · exact hθ.imp' (· - 1 / 2) (by intros; push_cast; linarith)
   · simpa [cos_sub_pi_div_two]
diff --git a/Mathlib/NumberTheory/NumberField/Basic.lean b/Mathlib/NumberTheory/NumberField/Basic.lean
index f3db9fc17bbe68..14a4d13f5d746f 100644
--- a/Mathlib/NumberTheory/NumberField/Basic.lean
+++ b/Mathlib/NumberTheory/NumberField/Basic.lean
@@ -441,6 +441,6 @@ namespace AdjoinRoot
 is a number field. -/
 instance {f : Polynomial ℚ} [hf : Fact (Irreducible f)] : NumberField (AdjoinRoot f) where
   to_charZero := charZero_of_injective_algebraMap (algebraMap ℚ _).injective
-  to_finiteDimensional := by convert (AdjoinRoot.powerBasis hf.out.ne_zero).finite
+  to_finiteDimensional := by convert! (AdjoinRoot.powerBasis hf.out.ne_zero).finite
 
 end AdjoinRoot
diff --git a/Mathlib/NumberTheory/NumberField/CMField.lean b/Mathlib/NumberTheory/NumberField/CMField.lean
index 63d3e447624c0b..d69e78e577e231 100644
--- a/Mathlib/NumberTheory/NumberField/CMField.lean
+++ b/Mathlib/NumberTheory/NumberField/CMField.lean
@@ -198,7 +198,7 @@ An element of `K` is fixed by the complex conjugation iff it lies in `K⁺`.
 @[simp]
 theorem complexConj_eq_self_iff (x : K) :
     complexConj K x = x ↔ x ∈ K⁺ := by
-  convert (IntermediateField.mem_fixedField_iff (⊤ : Subgroup (K ≃ₐ[K⁺] K)) x).symm using 1
+  convert! (IntermediateField.mem_fixedField_iff (⊤ : Subgroup (K ≃ₐ[K⁺] K)) x).symm using 1
   · rw [← zpowers_complexConj_eq_top, Subgroup.forall_mem_zpowers]
     exact (MulAction.mem_fixedBy_zpowers_iff_mem_fixedBy (g := (complexConj K))).symm
   · rw [IsGalois.fixedField_top, IntermediateField.mem_bot]
@@ -361,7 +361,7 @@ noncomputable abbrev indexRealUnits : ℕ := (realUnits K ⊔ torsion K).index
 theorem indexRealUnits_mul_eq :
     indexRealUnits K * (unitsMulComplexConjInv K).range.index = 2 := by
   rw [indexRealUnits, sup_comm]
-  convert (Subgroup.index_map (torsion K) (unitsMulComplexConjInv K)).symm
+  convert! (Subgroup.index_map (torsion K) (unitsMulComplexConjInv K)).symm
   · rw [unitsMulComplexConjInv_ker]
   · rw [map_unitsMulComplexConjInv_torsion, IsCyclic.index_powMonoidHom_range, Nat.gcd_eq_right]
     rw [Nat.card_eq_fintype_card]
diff --git a/Mathlib/NumberTheory/NumberField/CanonicalEmbedding/Basic.lean b/Mathlib/NumberTheory/NumberField/CanonicalEmbedding/Basic.lean
index 28955e324bc829..fca12cda01748c 100644
--- a/Mathlib/NumberTheory/NumberField/CanonicalEmbedding/Basic.lean
+++ b/Mathlib/NumberTheory/NumberField/CanonicalEmbedding/Basic.lean
@@ -101,7 +101,7 @@ theorem integerLattice.inter_ball_finite [NumberField K] (r : ℝ) :
   · have heq : ∀ x, canonicalEmbedding K x ∈ Metric.closedBall 0 r ↔
         ∀ φ : K →+* ℂ, ‖φ x‖ ≤ r := by
       intro x; rw [← norm_le_iff, mem_closedBall_zero_iff]
-    convert (Embeddings.finite_of_norm_le K ℂ r).image (canonicalEmbedding K)
+    convert! (Embeddings.finite_of_norm_le K ℂ r).image (canonicalEmbedding K)
     ext; constructor
     · rintro ⟨⟨_, ⟨x, rfl⟩, rfl⟩, hx⟩
       exact ⟨x, ⟨SetLike.coe_mem x, fun φ => (heq _).mp hx φ⟩, rfl⟩
@@ -128,8 +128,9 @@ noncomputable def latticeBasis [NumberField K] :
       RingHom.equivRatAlgHom
     rw [show M = N.transpose by { ext : 2; rfl }]
     rw [Matrix.det_transpose, ← pow_ne_zero_iff two_ne_zero]
-    convert (map_ne_zero_iff _ (algebraMap ℚ ℂ).injective).mpr
-      (Algebra.discr_not_zero_of_basis ℚ (integralBasis K))
+    convert!
+      (map_ne_zero_iff _ (algebraMap ℚ ℂ).injective).mpr
+        (Algebra.discr_not_zero_of_basis ℚ (integralBasis K))
     rw [← Algebra.discr_reindex ℚ (integralBasis K) e.symm]
     exact (Algebra.discr_eq_det_embeddingsMatrixReindex_pow_two ℚ ℂ
       (fun i => integralBasis K (e i)) RingHom.equivRatAlgHom).symm
@@ -247,7 +248,7 @@ theorem volume_eq_zero (w : {w // IsReal w}) :
     volume ({x : mixedSpace K | x.1 w = 0}) = 0 := by
   let A : AffineSubspace ℝ (mixedSpace K) :=
     Submodule.toAffineSubspace (Submodule.mk ⟨⟨{x | x.1 w = 0}, by simp_all⟩, rfl⟩ (by simp_all))
-  convert Measure.addHaar_affineSubspace volume A fun h ↦ ?_
+  convert! Measure.addHaar_affineSubspace volume A fun h ↦ ?_
   simpa [A] using (h ▸ Set.mem_univ _ : 1 ∈ A)
 
 end Measure
@@ -1107,7 +1108,7 @@ theorem realSpace.volume_eq_zero [NumberField K] (w : InfinitePlace K) :
     volume ({x : realSpace K | x w = 0}) = 0 := by
   let A : AffineSubspace ℝ (realSpace K) :=
     Submodule.toAffineSubspace (Submodule.mk ⟨⟨{x | x w = 0}, by simp_all⟩, rfl⟩ (by simp_all))
-  convert Measure.addHaar_affineSubspace volume A fun h ↦ ?_
+  convert! Measure.addHaar_affineSubspace volume A fun h ↦ ?_
   simpa [A] using (h ▸ Set.mem_univ _ : 1 ∈ A)
 
 /--
diff --git a/Mathlib/NumberTheory/NumberField/CanonicalEmbedding/ConvexBody.lean b/Mathlib/NumberTheory/NumberField/CanonicalEmbedding/ConvexBody.lean
index f6f2c0eeb62df3..aafac0226dbf57 100644
--- a/Mathlib/NumberTheory/NumberField/CanonicalEmbedding/ConvexBody.lean
+++ b/Mathlib/NumberTheory/NumberField/CanonicalEmbedding/ConvexBody.lean
@@ -176,7 +176,7 @@ theorem convexBodyLT'_neg_mem (x : mixedSpace K) (hx : x ∈ convexBodyLT' K f w
     -x ∈ convexBodyLT' K f w₀ := by
   simp only [Set.mem_prod, Set.mem_pi, Set.mem_univ, mem_ball, dist_zero_right, Real.norm_eq_abs,
     true_implies, Subtype.forall, Prod.fst_neg, Pi.neg_apply, norm_neg, Prod.snd_neg] at hx ⊢
-  convert hx using 3
+  convert! hx using 3
   split_ifs <;> simp
 
 theorem convexBodyLT'_convex : Convex ℝ (convexBodyLT' K f w₀) := by
@@ -340,7 +340,7 @@ theorem convexBodySum_neg_mem {x : mixedSpace K} (hx : x ∈ (convexBodySum K B)
 
 theorem convexBodySum_convex : Convex ℝ (convexBodySum K B) := by
   refine Convex_subadditive_le (fun _ _ => convexBodySumFun_add_le _ _) (fun c x h => ?_) B
-  convert le_of_eq (convexBodySumFun_smul c x)
+  convert! le_of_eq (convexBodySumFun_smul c x)
   exact (abs_eq_self.mpr h).symm
 
 theorem convexBodySum_isBounded : Bornology.IsBounded (convexBodySum K B) := by
@@ -355,7 +355,7 @@ theorem convexBodySum_compact : IsCompact (convexBodySum K B) := by
   classical
   rw [Metric.isCompact_iff_isClosed_bounded]
   refine ⟨?_, convexBodySum_isBounded K B⟩
-  convert IsClosed.preimage (convexBodySumFun_continuous K) (isClosed_Icc : IsClosed (Set.Icc 0 B))
+  convert! IsClosed.preimage (convexBodySumFun_continuous K) (isClosed_Icc : IsClosed (Set.Icc 0 B))
   ext
   simp [convexBodySumFun_nonneg]
 
@@ -377,7 +377,7 @@ theorem convexBodySum_volume :
     exact finrank_pos.ne'
   · suffices volume (convexBodySum K 1) = (convexBodySumFactor K) by
       rw [mul_comm]
-      convert addHaar_smul volume B (convexBodySum K 1)
+      convert! addHaar_smul volume B (convexBodySum K 1)
       · simp_rw [← Set.preimage_smul_inv₀ (ne_of_gt hB), Set.preimage_setOf_eq, convexBodySumFun,
         normAtPlace_smul, abs_inv, abs_eq_self.mpr (le_of_lt hB), ← mul_assoc, mul_comm, mul_assoc,
         ← Finset.mul_sum, inv_mul_le_iff₀ hB, mul_one]
@@ -536,7 +536,7 @@ theorem exists_primitive_element_lt_of_isReal {w₀ : InfinitePlace K} (hw₀ :
   obtain ⟨a, h_nz, h_le⟩ := exists_ne_zero_mem_ringOfIntegers_lt K this
   refine ⟨a, ?_, fun w ↦ lt_of_lt_of_le (h_le w) ?_⟩
   · exact is_primitive_element_of_infinitePlace_lt h_nz
-      (fun w h_ne ↦ by convert (if_neg h_ne) ▸ h_le w) (Or.inl hw₀)
+      (fun w h_ne ↦ by convert! (if_neg h_ne) ▸ h_le w) (Or.inl hw₀)
   · split_ifs <;> simp
 
 theorem exists_primitive_element_lt_of_isComplex {w₀ : InfinitePlace K} (hw₀ : IsComplex w₀)
@@ -555,7 +555,7 @@ theorem exists_primitive_element_lt_of_isComplex {w₀ : InfinitePlace K} (hw₀
   obtain ⟨a, h_nz, h_le, h_le₀⟩ := exists_ne_zero_mem_ringOfIntegers_lt' K ⟨w₀, hw₀⟩ this
   refine ⟨a, ?_, fun w ↦ ?_⟩
   · exact is_primitive_element_of_infinitePlace_lt h_nz
-      (fun w h_ne ↦ by convert if_neg h_ne ▸ h_le w h_ne) (Or.inr h_le₀.1)
+      (fun w h_ne ↦ by convert! if_neg h_ne ▸ h_le w h_ne) (Or.inr h_le₀.1)
   · by_cases h_eq : w = w₀
     · rw [if_pos rfl] at h_le₀
       dsimp only at h_le₀
diff --git a/Mathlib/NumberTheory/NumberField/CanonicalEmbedding/FundamentalCone.lean b/Mathlib/NumberTheory/NumberField/CanonicalEmbedding/FundamentalCone.lean
index 173447bdf6699d..bea0228933450b 100644
--- a/Mathlib/NumberTheory/NumberField/CanonicalEmbedding/FundamentalCone.lean
+++ b/Mathlib/NumberTheory/NumberField/CanonicalEmbedding/FundamentalCone.lean
@@ -223,7 +223,7 @@ theorem smul_mem_of_mem (hx : x ∈ fundamentalCone K) (hc : c ≠ 0) :
 theorem smul_mem_iff_mem (hc : c ≠ 0) :
     c • x ∈ fundamentalCone K ↔ x ∈ fundamentalCone K := by
   refine ⟨fun h ↦ ?_, fun h ↦ smul_mem_of_mem h hc⟩
-  convert smul_mem_of_mem h (inv_ne_zero hc)
+  convert! smul_mem_of_mem h (inv_ne_zero hc)
   rw [eq_inv_smul_iff₀ hc]
 
 theorem exists_unit_smul_mem (hx : mixedEmbedding.norm x ≠ 0) :
@@ -543,7 +543,7 @@ def idealSetEquivNorm (n : ℕ) :
   calc
     _ ≃ {a : {a : integerSet K // (preimageOfMemIntegerSet a).1 ∈ J.1} //
             mixedEmbedding.norm a.1.1 = n} := by
-        convert (Equiv.subtypeEquivOfSubtype (idealSetEquiv K J).symm).symm using 3
+        convert! (Equiv.subtypeEquivOfSubtype (idealSetEquiv K J).symm).symm using 3
         rw [idealSetEquiv_symm_apply]
     _ ≃ {a : integerSet K // (preimageOfMemIntegerSet a).1 ∈ J.1 ∧
           mixedEmbedding.norm a.1 = n} := Equiv.subtypeSubtypeEquivSubtypeInter
@@ -556,7 +556,7 @@ def idealSetEquivNorm (n : ℕ) :
         (Equiv.subtypeEquivRight (fun _ ↦ by simp [and_comm]))).symm
     _ ≃ {I : {I : (Ideal (𝓞 K))⁰ // IsPrincipal I.1 ∧ absNorm I.1 = n} × (torsion K) //
           J.1 ∣ I.1.1} := by
-      convert Equiv.subtypeEquivOfSubtype (p := fun I ↦ J.1 ∣ I.1) (integerSetEquivNorm K n)
+      convert! Equiv.subtypeEquivOfSubtype (p := fun I ↦ J.1 ∣ I.1) (integerSetEquivNorm K n)
       rw [integerSetEquivNorm_apply_fst, dvd_span_singleton]
     _ ≃ {I : {I : (Ideal (𝓞 K))⁰ // IsPrincipal I.1 ∧ absNorm I.1 = n} // J.1 ∣ I.1} ×
         (torsion K) := Equiv.prodSubtypeFstEquivSubtypeProd
diff --git a/Mathlib/NumberTheory/NumberField/CanonicalEmbedding/NormLeOne.lean b/Mathlib/NumberTheory/NumberField/CanonicalEmbedding/NormLeOne.lean
index 0a68997e52752f..393d75f502a4f1 100644
--- a/Mathlib/NumberTheory/NumberField/CanonicalEmbedding/NormLeOne.lean
+++ b/Mathlib/NumberTheory/NumberField/CanonicalEmbedding/NormLeOne.lean
@@ -395,7 +395,7 @@ theorem linearIndependent_completeFamily :
   have h₁ : LinearIndependent ℝ (fun w : {w // w ≠ w₀} ↦ completeFamily K w.1) := by
     refine LinearIndependent.of_comp realSpaceToLogSpace ?_
     simp_rw [Function.comp_def, realSpaceToLogSpace_completeFamily_of_ne]
-    convert (((basisUnitLattice K).ofZLatticeBasis ℝ _).reindex equivFinRank).linearIndependent
+    convert! (((basisUnitLattice K).ofZLatticeBasis ℝ _).reindex equivFinRank).linearIndependent
     simp
   have h₂ : completeFamily K w₀ ∉ Submodule.span ℝ
       (Set.range (fun w : {w // w ≠ w₀} ↦ completeFamily K w.1)) := by
diff --git a/Mathlib/NumberTheory/NumberField/CanonicalEmbedding/PolarCoord.lean b/Mathlib/NumberTheory/NumberField/CanonicalEmbedding/PolarCoord.lean
index 11cef1f786bc7a..a01452ffe40947 100644
--- a/Mathlib/NumberTheory/NumberField/CanonicalEmbedding/PolarCoord.lean
+++ b/Mathlib/NumberTheory/NumberField/CanonicalEmbedding/PolarCoord.lean
@@ -401,7 +401,7 @@ theorem volume_eq_two_pi_pow_mul_integral [NumberField K]
       ← two_mul, Finset.prod_const, Finset.card_univ, ← Set.indicator_const_mul,
       ← Set.indicator_comp_right, Function.comp_def, Pi.one_apply, mul_one]
     rw [lintegral_mul_const' _ _ (ne_of_beq_false rfl).symm, mul_comm]
-    erw [setLIntegral_indicator (by convert hm.preimage mixedSpaceOfRealSpace.measurable)]
+    erw [setLIntegral_indicator (by convert! hm.preimage mixedSpaceOfRealSpace.measurable)]
     rw [hA, volume_eq_two_pi_pow_mul_integral_aux hA]
     congr 1
     refine setLIntegral_congr (ae_eq_set_inter (by rfl) (Measure.ae_eq_set_pi fun w _ ↦ ?_))
diff --git a/Mathlib/NumberTheory/NumberField/Cyclotomic/Basic.lean b/Mathlib/NumberTheory/NumberField/Cyclotomic/Basic.lean
index 6018628ba7f466..78dd359f80277c 100644
--- a/Mathlib/NumberTheory/NumberField/Cyclotomic/Basic.lean
+++ b/Mathlib/NumberTheory/NumberField/Cyclotomic/Basic.lean
@@ -236,7 +236,7 @@ noncomputable def subOneIntegralPowerBasisOfPrimePow [IsCyclotomicExtension {p ^
   PowerBasis.ofAdjoinEqTop'
     (RingOfIntegers.isIntegral ⟨ζ- 1, (hζ.isIntegral (NeZero.pos _)).sub isIntegral_one⟩) (by
     refine hζ.integralPowerBasisOfPrimePow.adjoin_eq_top_of_gen_mem_adjoin ?_
-    convert Subalgebra.add_mem _ (self_mem_adjoin_singleton ℤ _) (Subalgebra.one_mem _)
+    convert! Subalgebra.add_mem _ (self_mem_adjoin_singleton ℤ _) (Subalgebra.one_mem _)
     simp [RingOfIntegers.ext_iff, integralPowerBasisOfPrimePow_gen, toInteger])
 
 @[simp]
@@ -258,7 +258,7 @@ theorem zeta_sub_one_prime_of_ne_two [IsCyclotomicExtension {p ^ (k + 1)} ℚ K]
     simpa using congrArg (algebraMap _ K) h
   rw [Nat.irreducible_iff_prime, Ideal.absNorm_span_singleton, ← Nat.prime_iff,
     ← Int.prime_iff_natAbs_prime]
-  convert Nat.prime_iff_prime_int.1 hp.out
+  convert! Nat.prime_iff_prime_int.1 hp.out
   apply RingHom.injective_int (algebraMap ℤ ℚ)
   rw [← Algebra.norm_localization (Sₘ := K) ℤ (nonZeroDivisors ℤ)]
   simp only [algebraMap_int_eq, map_natCast]
@@ -277,7 +277,7 @@ theorem zeta_sub_one_prime_of_two_pow [IsCyclotomicExtension {2 ^ (k + 1)} ℚ K
   rw [Nat.irreducible_iff_prime, Ideal.absNorm_span_singleton, ← Nat.prime_iff,
     ← Int.prime_iff_natAbs_prime]
   cases k
-  · convert Prime.neg Int.prime_two
+  · convert! Prime.neg Int.prime_two
     apply RingHom.injective_int (algebraMap ℤ ℚ)
     rw [← Algebra.norm_localization (Sₘ := K) ℤ (nonZeroDivisors ℤ)]
     simp only [algebraMap_int_eq, map_neg, map_ofNat]
@@ -285,7 +285,7 @@ theorem zeta_sub_one_prime_of_two_pow [IsCyclotomicExtension {2 ^ (k + 1)} ℚ K
         pow_zero]
       using hζ.norm_pow_sub_one_two (cyclotomic.irreducible_rat
         (by simp only [zero_add, pow_one, Nat.ofNat_pos]))
-  convert Int.prime_two
+  convert! Int.prime_two
   apply RingHom.injective_int (algebraMap ℤ ℚ)
   rw [← Algebra.norm_localization (Sₘ := K) ℤ (nonZeroDivisors ℤ), algebraMap_int_eq]
   exact hζ.norm_sub_one_two Nat.AtLeastTwo.prop (cyclotomic.irreducible_rat (by simp))
@@ -301,7 +301,7 @@ theorem zeta_sub_one_prime [IsCyclotomicExtension {p ^ (k + 1)} ℚ K]
 /-- `ζ - 1` is prime if `ζ` is a primitive `p`-th root of unity. -/
 theorem zeta_sub_one_prime' [h : IsCyclotomicExtension {p} ℚ K] (hζ : IsPrimitiveRoot ζ p) :
     Prime ((hζ.toInteger - 1)) := by
-  convert zeta_sub_one_prime (k := 0) (by simpa only [zero_add, pow_one])
+  convert! zeta_sub_one_prime (k := 0) (by simpa only [zero_add, pow_one])
   simpa only [zero_add, pow_one]
 
 theorem subOneIntegralPowerBasisOfPrimePow_gen_prime [IsCyclotomicExtension {p ^ (k + 1)} ℚ K]
@@ -612,8 +612,8 @@ theorem discr_prime_pow [IsCyclotomicExtension {p ^ k} ℚ K] :
   let pB₁ := integralPowerBasisOfPrimePow hζ
   apply (algebraMap ℤ ℚ).injective_int
   rw [← NumberField.discr_eq_discr _ pB₁.basis, ← Algebra.discr_localizationLocalization ℤ ℤ⁰ K]
-  convert IsCyclotomicExtension.discr_prime_pow hζ
-    (cyclotomic.irreducible_rat (NeZero.pos _)) using 1
+  convert!
+    IsCyclotomicExtension.discr_prime_pow hζ (cyclotomic.irreducible_rat (NeZero.pos _)) using 1
   · have : pB₁.dim = (IsPrimitiveRoot.powerBasis ℚ hζ).dim := by
       rw [← PowerBasis.finrank, ← PowerBasis.finrank]
       exact RingOfIntegers.rank K
@@ -622,7 +622,7 @@ theorem discr_prime_pow [IsCyclotomicExtension {p ^ k} ℚ K] :
     ext i
     simp_rw [Function.comp_apply, Module.Basis.localizationLocalization_apply, powerBasis_dim,
       PowerBasis.coe_basis, pB₁, integralPowerBasisOfPrimePow_gen]
-    convert ← ((IsPrimitiveRoot.powerBasis ℚ hζ).basis_eq_pow i).symm using 1
+    convert! ← ((IsPrimitiveRoot.powerBasis ℚ hζ).basis_eq_pow i).symm using 1
   · simp_rw [algebraMap_int_eq, map_mul, map_pow, map_neg, map_one, map_natCast]
 
 @[deprecated (since := "2025-11-24")] alias absdiscr_prime_pow := discr_prime_pow
@@ -868,7 +868,7 @@ noncomputable def subOneIntegralPowerBasis [IsCyclotomicExtension {n} ℚ K]
   PowerBasis.ofAdjoinEqTop'
     (RingOfIntegers.isIntegral ⟨ζ- 1, (hζ.isIntegral (NeZero.pos _)).sub isIntegral_one⟩) (by
     refine hζ.integralPowerBasis.adjoin_eq_top_of_gen_mem_adjoin ?_
-    convert Subalgebra.add_mem _ (self_mem_adjoin_singleton ℤ _) (Subalgebra.one_mem _)
+    convert! Subalgebra.add_mem _ (self_mem_adjoin_singleton ℤ _) (Subalgebra.one_mem _)
     simp [RingOfIntegers.ext_iff, integralPowerBasis_gen, toInteger])
 
 @[simp]
@@ -903,7 +903,7 @@ theorem NumberField.Units.dvd_torsionOrder_of_isPrimitiveRoot [NeZero n] [Number
     (hζ : IsPrimitiveRoot ζ n) : n ∣ torsionOrder K := by
   rw [torsionOrder, Fintype.card_eq_nat_card]
   replace hζ := (hζ.toInteger_isPrimitiveRoot).isUnit_unit (NeZero.ne n)
-  convert orderOf_dvd_natCard (⟨(hζ.isUnit (NeZero.ne n)).unit, ?_⟩ : torsion K)
+  convert! orderOf_dvd_natCard (⟨(hζ.isUnit (NeZero.ne n)).unit, ?_⟩ : torsion K)
   · rw [Subgroup.orderOf_mk]
     exact hζ.eq_orderOf
   · refine (CommGroup.mem_torsion _ _).mpr ⟨n, NeZero.pos n, ?_⟩
diff --git a/Mathlib/NumberTheory/NumberField/Cyclotomic/Embeddings.lean b/Mathlib/NumberTheory/NumberField/Cyclotomic/Embeddings.lean
index 50e9330959db0f..da237c16e2618c 100644
--- a/Mathlib/NumberTheory/NumberField/Cyclotomic/Embeddings.lean
+++ b/Mathlib/NumberTheory/NumberField/Cyclotomic/Embeddings.lean
@@ -58,9 +58,9 @@ theorem nrComplexPlaces_eq_totient_div_two [h : IsCyclotomicExtension {n} ℚ K]
     simp [hk, key, ← two_mul]
   · have : φ n = 1 := by
       by_cases h1 : 1 < n
-      · convert totient_two
+      · convert! totient_two
         exact (eq_of_le_of_not_lt (succ_le_of_lt h1) hn).symm
-      · convert totient_one
+      · convert! totient_one
         exact eq_of_le_of_not_lt (not_lt.mp h1) (by simp [NeZero.ne _])
     rw [this]
     apply nrComplexPlaces_eq_zero_of_finrank_eq_one
diff --git a/Mathlib/NumberTheory/NumberField/Cyclotomic/Ideal.lean b/Mathlib/NumberTheory/NumberField/Cyclotomic/Ideal.lean
index 1b4f30d93b418a..6a23ec72c2d291 100644
--- a/Mathlib/NumberTheory/NumberField/Cyclotomic/Ideal.lean
+++ b/Mathlib/NumberTheory/NumberField/Cyclotomic/Ideal.lean
@@ -77,7 +77,7 @@ theorem absNorm_span_zeta_sub_one : absNorm (span {hζ.toInteger - 1}) = p := by
     span_singleton_eq_span_singleton.mpr <| associated_norm_zeta_sub_one p k hζ
 
 theorem p_mem_span_zeta_sub_one : (p : 𝓞 K) ∈ span {hζ.toInteger - 1} := by
-  convert Ideal.absNorm_mem _
+  convert! Ideal.absNorm_mem _
   exact (absNorm_span_zeta_sub_one ..).symm
 
 theorem span_zeta_sub_one_ne_bot : span {hζ.toInteger - 1} ≠ ⊥ :=
diff --git a/Mathlib/NumberTheory/NumberField/Cyclotomic/Three.lean b/Mathlib/NumberTheory/NumberField/Cyclotomic/Three.lean
index f21a211715a384..f8a4a423754978 100644
--- a/Mathlib/NumberTheory/NumberField/Cyclotomic/Three.lean
+++ b/Mathlib/NumberTheory/NumberField/Cyclotomic/Three.lean
@@ -65,7 +65,7 @@ theorem Units.mem [NumberField K] [IsCyclotomicExtension {3} ℚ K] :
   obtain ⟨n, hnpos, hn⟩ := isOfFinOrder_iff_pow_eq_one.1 <| (CommGroup.mem_torsion _ _).1 x.2
   replace hn : (↑u : K) ^ ((⟨n, hnpos⟩ : ℕ+) : ℕ) = 1 := by
     rw [← map_pow]
-    convert map_one (algebraMap (𝓞 K) K)
+    convert! map_one (algebraMap (𝓞 K) K)
     rw_mod_cast [hxu, hn]
     simp
   obtain ⟨r, hr3, hru⟩ := hζ.exists_pow_or_neg_mul_pow_of_isOfFinOrder (by decide)
@@ -187,9 +187,9 @@ lemma lambda_pow_four_dvd_cube_sub_one_of_dvd_sub_one {x : 𝓞 K} (h : λ ∣ x
 lemma lambda_pow_four_dvd_cube_add_one_of_dvd_add_one {x : 𝓞 K} (h : λ ∣ x + 1) :
     λ ^ 4 ∣ x ^ 3 + 1 := by
   replace h : λ ∣ -x - 1 := by
-    convert h.neg_right using 1
+    convert! h.neg_right using 1
     exact (neg_add' x 1).symm
-  convert (lambda_pow_four_dvd_cube_sub_one_of_dvd_sub_one hζ h).neg_right using 1
+  convert! (lambda_pow_four_dvd_cube_sub_one_of_dvd_sub_one hζ h).neg_right using 1
   ring
 
 /-- If `λ` does not divide `x`, then `λ ^ 4` divides `x ^ 3 - 1` or `x ^ 3 + 1`. -/
diff --git a/Mathlib/NumberTheory/NumberField/Discriminant/Basic.lean b/Mathlib/NumberTheory/NumberField/Discriminant/Basic.lean
index 78257f2feb9537..d144b529ff71ee 100644
--- a/Mathlib/NumberTheory/NumberField/Discriminant/Basic.lean
+++ b/Mathlib/NumberTheory/NumberField/Discriminant/Basic.lean
@@ -157,7 +157,7 @@ theorem exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr (I : (FractionalIdeal
       mul_one]
     · exact mul_ne_top (ne_of_lt (minkowskiBound_lt_top K I)) coe_ne_top
     · exact (Nat.cast_ne_zero.mpr (ne_of_gt finrank_pos))
-  convert exists_ne_zero_mem_ideal_of_norm_le K I h_le
+  convert! exists_ne_zero_mem_ideal_of_norm_le K I h_le
   rw [div_pow B, ← Real.rpow_natCast B, ← Real.rpow_mul (by positivity), div_mul_cancel₀ _
     (Nat.cast_ne_zero.mpr <| ne_of_gt finrank_pos), Real.rpow_one, mul_comm_div, mul_div_assoc']
   congr 1
@@ -264,7 +264,7 @@ theorem abs_discr_ge (h : 1 < finrank ℚ K) :
           simp [field, div_pow]
           ring
         · rw [_root_.le_div_iff₀ (by positivity), pow_succ]
-          convert (mul_le_mul h_m this (by positivity) (by positivity)) using 1
+          convert! (mul_le_mul h_m this (by positivity) (by positivity)) using 1
           field
       refine le_trans (le_of_eq (by simp [field]; norm_num)) (one_add_mul_le_pow ?_ (2 * m))
       exact le_trans (by norm_num : (-2 : ℝ) ≤ 0) (by positivity)
@@ -322,7 +322,7 @@ theorem finite_of_finite_generating_set {p : IntermediateField ℚ A → Prop}
   refine Set.finite_coe_iff.mp <| Finite.of_injective
     (fun ⟨F, hF⟩ ↦ (⟨(h F hF).choose, (h F hF).choose_spec.1⟩ : T)) (fun _ _ h_eq ↦ ?_)
   rw [Subtype.ext_iff, Subtype.ext_iff]
-  convert congr_arg (ℚ⟮·⟯) (Subtype.mk_eq_mk.mp h_eq)
+  convert! congr_arg (ℚ⟮·⟯) (Subtype.mk_eq_mk.mp h_eq)
   all_goals exact (h _ (Subtype.mem _)).choose_spec.2
 
 variable (N : ℕ)
@@ -433,7 +433,7 @@ theorem finite_of_discr_bdd_of_isReal :
     · refine mem_rootSet.mpr ⟨minpoly.ne_zero hx, ?_⟩
       exact (aeval_algebraMap_eq_zero_iff A (x : K) _).mpr (minpoly.aeval ℤ (x : K))
     · rw [← (IntermediateField.lift_injective _).eq_iff, eq_comm] at hx₁
-      convert hx₁
+      convert! hx₁
       · simp only [IntermediateField.lift_top]
       · simp only [IntermediateField.lift_adjoin, Set.image_singleton]
   calc
@@ -483,7 +483,7 @@ theorem finite_of_discr_bdd_of_isComplex :
     · refine mem_rootSet.mpr ⟨minpoly.ne_zero hx, ?_⟩
       exact (aeval_algebraMap_eq_zero_iff A (x : K) _).mpr (minpoly.aeval ℤ (x : K))
     · rw [← (IntermediateField.lift_injective _).eq_iff, eq_comm] at hx₁
-      convert hx₁
+      convert! hx₁
       · simp only [IntermediateField.lift_top]
       · simp only [IntermediateField.lift_adjoin, Set.image_singleton]
   calc
diff --git a/Mathlib/NumberTheory/NumberField/Discriminant/Defs.lean b/Mathlib/NumberTheory/NumberField/Discriminant/Defs.lean
index a04ad7fb371ba6..89170f562592ec 100644
--- a/Mathlib/NumberTheory/NumberField/Discriminant/Defs.lean
+++ b/Mathlib/NumberTheory/NumberField/Discriminant/Defs.lean
@@ -79,7 +79,7 @@ theorem numberField_discr : discr ℚ = 1 := by
   let b : Basis (Fin 1) ℤ (𝓞 ℚ) :=
     Basis.map (Basis.singleton (Fin 1) ℤ) ringOfIntegersEquiv.toAddEquiv.toIntLinearEquiv.symm
   calc NumberField.discr ℚ
-    _ = Algebra.discr ℤ b := by convert (discr_eq_discr ℚ b).symm
+    _ = Algebra.discr ℤ b := by convert! (discr_eq_discr ℚ b).symm
     _ = Algebra.trace ℤ (𝓞 ℚ) (b default * b default) := by
       rw [Algebra.discr_def, Matrix.det_unique, Algebra.traceMatrix_apply, Algebra.traceForm_apply]
     _ = Algebra.trace ℤ (𝓞 ℚ) 1 := by
@@ -103,7 +103,7 @@ theorem Algebra.discr_eq_discr_of_toMatrix_coeff_isIntegral [NumberField K]
     (h' : ∀ i j, IsIntegral ℤ (b'.toMatrix b i j)) : discr ℚ b = discr ℚ b' := by
   replace h' : ∀ i j, IsIntegral ℤ (b'.toMatrix (b.reindex (b.indexEquiv b')) i j) := by
     intro i j
-    convert h' i ((b.indexEquiv b').symm j)
+    convert! h' i ((b.indexEquiv b').symm j)
     simp [Basis.toMatrix_apply]
   classical
   rw [← (b.reindex (b.indexEquiv b')).toMatrix_map_vecMul b', discr_of_matrix_vecMul,
diff --git a/Mathlib/NumberTheory/NumberField/EquivReindex.lean b/Mathlib/NumberTheory/NumberField/EquivReindex.lean
index ff300249c4bdb5..c2ac127cc3b9b0 100644
--- a/Mathlib/NumberTheory/NumberField/EquivReindex.lean
+++ b/Mathlib/NumberTheory/NumberField/EquivReindex.lean
@@ -53,8 +53,9 @@ theorem conj_basisMatrix :
 
 theorem det_of_basisMatrix_non_zero [DecidableEq (K →+* ℂ)] : (basisMatrix K).det ≠ 0 := by
   rw [basisMatrix_eq_embeddingsMatrixReindex, ← pow_ne_zero_iff two_ne_zero]
-  convert (map_ne_zero_iff _ (algebraMap ℚ ℂ).injective).mpr
-    (Algebra.discr_not_zero_of_basis ℚ (integralBasis K))
+  convert!
+    (map_ne_zero_iff _ (algebraMap ℚ ℂ).injective).mpr
+      (Algebra.discr_not_zero_of_basis ℚ (integralBasis K))
   rw [← Algebra.discr_reindex ℚ (integralBasis K) (equivReindex K).symm]
   exact (Algebra.discr_eq_det_embeddingsMatrixReindex_pow_two ℚ ℂ
     (integralBasis K ∘ (equivReindex K)) RingHom.equivRatAlgHom).symm
diff --git a/Mathlib/NumberTheory/NumberField/House.lean b/Mathlib/NumberTheory/NumberField/House.lean
index cdeb09cbcaaed2..403ac21e762d0f 100644
--- a/Mathlib/NumberTheory/NumberField/House.lean
+++ b/Mathlib/NumberTheory/NumberField/House.lean
@@ -319,7 +319,7 @@ private theorem house_le_bound : ∀ l, house (ξ K x l).1 ≤ (c₁ K) *
        _ ≤ h * (c₂ K) * ((q * c₁ K * A) ^ ((p : ℝ) / (q - p))) := ?_
        _ ≤ c₁ K * ((c₁ K * ↑q * A) ^ ((p : ℝ) / (q - p))) := ?_
   · simp_rw [← map_mul, map_sum]; apply house_sum_le_sum_house
-  · gcongr with r _; convert house_mul_le ..
+  · gcongr with r _; convert! house_mul_le ..
     simp only [map_intCast, house_intCast, Int.cast_abs, Int.norm_eq_abs]
   · unfold supOfBasis
     gcongr with r _
diff --git a/Mathlib/NumberTheory/NumberField/Ideal/Asymptotics.lean b/Mathlib/NumberTheory/NumberField/Ideal/Asymptotics.lean
index c6b0a1338f5ee9..9a9c6ecfa906f7 100644
--- a/Mathlib/NumberTheory/NumberField/Ideal/Asymptotics.lean
+++ b/Mathlib/NumberTheory/NumberField/Ideal/Asymptotics.lean
@@ -87,15 +87,16 @@ theorem tendsto_norm_le_and_mk_eq_div_atTop :
   have h₂ : {x | x ∈ fundamentalCone K ∧ mixedEmbedding.norm x ≤ 1} = normLeOne K := by ext; simp
   obtain ⟨J, hJ⟩ := ClassGroup.mk0_surjective C⁻¹
   have h₃ : (absNorm J.1 : ℝ) ≠ 0 := (Nat.cast_ne_zero.mpr (absNorm_ne_zero_of_nonZeroDivisors J))
-  convert ((ZLattice.covolume.tendsto_card_le_div'
-    (ZLattice.comap ℝ (mixedEmbedding.idealLattice K (FractionalIdeal.mk0 K J))
-      (toMixed K).toLinearMap)
-    (F := fun x ↦ mixedEmbedding.norm (toMixed K x))
-    (X := (toMixed K) ⁻¹' (fundamentalCone K)) (fun _ _ _ h ↦ ?_) (fun _ _ h ↦ ?_)
-    ((toMixed K).antilipschitz.isBounded_preimage (isBounded_normLeOne K)) ?_ ?_).mul
-      (tendsto_const_nhds (x := (absNorm (J : Ideal (𝓞 K)) : ℝ) * (torsionOrder K : ℝ)⁻¹))).comp
-    (tendsto_id.atTop_mul_const' <| Nat.cast_pos.mpr (absNorm_pos_of_nonZeroDivisors J))
-    using 2 with s
+  convert!
+    ((ZLattice.covolume.tendsto_card_le_div'
+              (ZLattice.comap ℝ (mixedEmbedding.idealLattice K (FractionalIdeal.mk0 K J))
+                (toMixed K).toLinearMap)
+              (F := fun x ↦ mixedEmbedding.norm (toMixed K x)) (X :=
+              (toMixed K) ⁻¹' (fundamentalCone K)) (fun _ _ _ h ↦ ?_) (fun _ _ h ↦ ?_)
+              ((toMixed K).antilipschitz.isBounded_preimage (isBounded_normLeOne K)) ?_ ?_).mul
+          (tendsto_const_nhds (x := (absNorm (J : Ideal (𝓞 K)) : ℝ) * (torsionOrder K : ℝ)⁻¹))).comp
+      (tendsto_id.atTop_mul_const' <| Nat.cast_pos.mpr (absNorm_pos_of_nonZeroDivisors J)) using
+    2 with s
   · simp_rw [Ideal.tendsto_norm_le_and_mk_eq_div_atTop_aux₁ K hJ, id_eq,
       Nat.card_congr (Ideal.tendsto_norm_le_and_mk_eq_div_atTop_aux₂ K),
       ← card_isPrincipal_dvd_norm_le, Function.comp_def, Nat.cast_mul, div_eq_mul_inv, mul_inv,
@@ -128,8 +129,9 @@ theorem tendsto_norm_le_div_atTop₀ :
           (𝓝 ((2 ^ nrRealPlaces K * (2 * π) ^ nrComplexPlaces K * regulator K * classNumber K) /
             (torsionOrder K * Real.sqrt |discr K|))) := by
   classical
-  convert Filter.Tendsto.congr' ?_
-    (tendsto_finsetSum Finset.univ (fun C _ ↦ tendsto_norm_le_and_mk_eq_div_atTop K C))
+  convert!
+    Filter.Tendsto.congr' ?_
+      (tendsto_finsetSum Finset.univ (fun C _ ↦ tendsto_norm_le_and_mk_eq_div_atTop K C))
   · rw [Finset.sum_const, Finset.card_univ, nsmul_eq_mul, classNumber]
     ring
   · filter_upwards [eventually_ge_atTop 0] with s hs
diff --git a/Mathlib/NumberTheory/NumberField/InfinitePlace/Basic.lean b/Mathlib/NumberTheory/NumberField/InfinitePlace/Basic.lean
index 4498f40aff6de5..d10cf85e3932c9 100644
--- a/Mathlib/NumberTheory/NumberField/InfinitePlace/Basic.lean
+++ b/Mathlib/NumberTheory/NumberField/InfinitePlace/Basic.lean
@@ -353,7 +353,7 @@ variable [NumberField K]
 theorem prod_eq_abs_norm (x : K) :
     ∏ w : InfinitePlace K, w x ^ mult w = abs (Algebra.norm ℚ x) := by
   classical
-  convert (congr_arg (‖·‖) (Algebra.norm_eq_prod_embeddings ℚ ℂ x)).symm
+  convert! (congr_arg (‖·‖) (Algebra.norm_eq_prod_embeddings ℚ ℂ x)).symm
   · rw [norm_prod, ← Fintype.prod_equiv RingHom.equivRatAlgHom (fun f => ‖f x‖)
       (fun φ => ‖φ x‖) fun _ => by simp [RingHom.equivRatAlgHom_apply]]
     rw [← Finset.prod_fiberwise Finset.univ mk (fun φ => ‖φ x‖)]
@@ -430,8 +430,9 @@ theorem card_real_embeddings :
 theorem card_eq_nrRealPlaces_add_nrComplexPlaces :
     Fintype.card (InfinitePlace K) = nrRealPlaces K + nrComplexPlaces K := by
   classical
-  convert Fintype.card_subtype_or_disjoint (IsReal (K := K)) (IsComplex (K := K))
-    (disjoint_isReal_isComplex K) using 1
+  convert!
+    Fintype.card_subtype_or_disjoint (IsReal (K := K)) (IsComplex (K := K))
+      (disjoint_isReal_isComplex K) using 1
   exact (Fintype.card_of_subtype _ (fun w ↦ ⟨fun _ ↦ isReal_or_isComplex w, fun _ ↦ by simp⟩)).symm
 
 open scoped Classical in
@@ -443,7 +444,7 @@ theorem card_complex_embeddings :
     simp_rw [Finset.sum_const, this, smul_eq_mul, mul_one, Fintype.card, Finset.card_eq_sum_ones,
       Finset.mul_sum, Finset.sum_const, smul_eq_mul, mul_one]
   rintro ⟨w, hw⟩
-  convert card_filter_mk_eq w
+  convert! card_filter_mk_eq w
   · rw [← Fintype.card_subtype, ← Fintype.card_subtype]
     refine Fintype.card_congr (Equiv.ofBijective ?_ ⟨fun _ _ h => ?_, fun ⟨φ, hφ⟩ => ?_⟩)
     · exact fun ⟨φ, hφ⟩ => ⟨φ.val, by rwa [Subtype.ext_iff] at hφ⟩
diff --git a/Mathlib/NumberTheory/NumberField/InfinitePlace/Embeddings.lean b/Mathlib/NumberTheory/NumberField/InfinitePlace/Embeddings.lean
index ea6a83b45f797e..16feaf41197085 100644
--- a/Mathlib/NumberTheory/NumberField/InfinitePlace/Embeddings.lean
+++ b/Mathlib/NumberTheory/NumberField/InfinitePlace/Embeddings.lean
@@ -78,7 +78,7 @@ The images of `x` by the embeddings of `K` in `A` are exactly the roots in `A` o
 the minimal polynomial of `x` over `ℚ`. -/
 theorem range_eval_eq_rootSet_minpoly :
     (range fun φ : K →+* A => φ x) = (minpoly ℚ x).rootSet A := by
-  convert (NumberField.isAlgebraic K).range_eval_eq_rootSet_minpoly A x using 1
+  convert! (NumberField.isAlgebraic K).range_eval_eq_rootSet_minpoly A x using 1
   ext a
   exact ⟨fun ⟨φ, hφ⟩ => ⟨φ.toRatAlgHom, hφ⟩, fun ⟨φ, hφ⟩ => ⟨φ.toRingHom, hφ⟩⟩
 
@@ -238,7 +238,7 @@ lemma IsReal.comp (f : k →+* K) {φ : K →+* ℂ} (hφ : IsReal φ) :
 
 lemma isReal_comp_iff {f : k ≃+* K} {φ : K →+* ℂ} :
     IsReal (φ.comp (f : k →+* K)) ↔ IsReal φ :=
-  ⟨fun H ↦ by convert H.comp f.symm.toRingHom; ext1; simp, IsReal.comp _⟩
+  ⟨fun H ↦ by convert! H.comp f.symm.toRingHom; ext1; simp, IsReal.comp _⟩
 
 lemma exists_comp_symm_eq_of_comp_eq [Algebra k K] [IsGalois k K] (φ ψ : K →+* ℂ)
     (h : φ.comp (algebraMap k K) = ψ.comp (algebraMap k K)) :
diff --git a/Mathlib/NumberTheory/NumberField/InfinitePlace/Ramification.lean b/Mathlib/NumberTheory/NumberField/InfinitePlace/Ramification.lean
index a9ba9a5f4335cf..895e14943b6c9d 100644
--- a/Mathlib/NumberTheory/NumberField/InfinitePlace/Ramification.lean
+++ b/Mathlib/NumberTheory/NumberField/InfinitePlace/Ramification.lean
@@ -418,7 +418,7 @@ lemma even_nat_card_aut_of_not_isUnramified [IsGalois k K] (hw : ¬ IsUnramified
   · cases nonempty_fintype Gal(K/k)
     rw [even_iff_two_dvd, ← not_isUnramified_iff_card_stabilizer_eq_two.mp hw]
     exact Subgroup.card_subgroup_dvd_card (Stab w)
-  · convert Even.zero
+  · convert! Even.zero
     by_contra e
     exact H (Nat.finite_of_card_ne_zero e)
 
diff --git a/Mathlib/NumberTheory/NumberField/Units/Basic.lean b/Mathlib/NumberTheory/NumberField/Units/Basic.lean
index 2a16846f0e3ff0..2bf76b76253608 100644
--- a/Mathlib/NumberTheory/NumberField/Units/Basic.lean
+++ b/Mathlib/NumberTheory/NumberField/Units/Basic.lean
@@ -58,7 +58,7 @@ variable {K}
 
 theorem NumberField.isUnit_iff_norm [NumberField K] {x : 𝓞 K} :
     IsUnit x ↔ |(RingOfIntegers.norm ℚ x : ℚ)| = 1 := by
-  convert (RingOfIntegers.isUnit_norm ℚ (F := K)).symm
+  convert! (RingOfIntegers.isUnit_norm ℚ (F := K)).symm
   rw [← abs_one, abs_eq_abs, ← Rat.RingOfIntegers.isUnit_iff]
 
 end IsUnit
diff --git a/Mathlib/NumberTheory/NumberField/Units/DirichletTheorem.lean b/Mathlib/NumberTheory/NumberField/Units/DirichletTheorem.lean
index ec4f090dfea07d..0fa198ba66bf59 100644
--- a/Mathlib/NumberTheory/NumberField/Units/DirichletTheorem.lean
+++ b/Mathlib/NumberTheory/NumberField/Units/DirichletTheorem.lean
@@ -176,7 +176,7 @@ open scoped Classical in
 theorem unitLattice_inter_ball_finite (r : ℝ) :
     ((unitLattice K : Set (logSpace K)) ∩ Metric.closedBall 0 r).Finite := by
   obtain hr | hr := lt_or_ge r 0
-  · convert Set.finite_empty
+  · convert! Set.finite_empty
     rw [Metric.closedBall_eq_empty.mpr hr]
     exact Set.inter_empty _
   · suffices {x : (𝓞 K)ˣ | IsIntegral ℤ (x : K) ∧
@@ -226,7 +226,7 @@ theorem seq_next {x : 𝓞 K} (hx : x ≠ 0) :
   suffices ∀ w, w ≠ w₁ → f w ≠ 0 by
     obtain ⟨g, h_geqf, h_gprod⟩ := adjust_f K B this
     obtain ⟨y, h_ynz, h_yle⟩ := exists_ne_zero_mem_ringOfIntegers_lt K (f := g)
-      (by rw [convexBodyLT_volume]; convert hB; exact congr_arg ((↑) : NNReal → ENNReal) h_gprod)
+      (by rw [convexBodyLT_volume]; convert! hB; exact congr_arg ((↑) : NNReal → ENNReal) h_gprod)
     refine ⟨y, h_ynz, fun w hw ↦ (h_geqf w hw ▸ h_yle w).trans ?_, ?_⟩
     · rw [← Rat.cast_le (K := ℝ), Rat.cast_natCast]
       calc
@@ -360,7 +360,7 @@ instance instDiscrete_unitLattice : DiscreteTopology (unitLattice K) := by
   refine isOpen_singleton_of_finite_mem_nhds 0 (s := Metric.closedBall 0 1) ?_ ?_
   · exact Metric.closedBall_mem_nhds _ (by simp)
   · refine Set.Finite.of_finite_image ?_ (Set.injOn_of_injective Subtype.val_injective)
-    convert unitLattice_inter_ball_finite K 1
+    convert! unitLattice_inter_ball_finite K 1
     ext x
     refine ⟨?_, fun ⟨hx1, hx2⟩ ↦ ⟨⟨x, hx1⟩, hx2, rfl⟩⟩
     rintro ⟨x, hx, rfl⟩
diff --git a/Mathlib/NumberTheory/NumberField/Units/Regulator.lean b/Mathlib/NumberTheory/NumberField/Units/Regulator.lean
index 806dd2712f16fa..cc03550c708700 100644
--- a/Mathlib/NumberTheory/NumberField/Units/Regulator.lean
+++ b/Mathlib/NumberTheory/NumberField/Units/Regulator.lean
@@ -204,7 +204,7 @@ theorem abs_det_eq_abs_det (u : Fin (rank K) → (𝓞 K)ˣ)
     (of fun i w ↦ (mult (f w) : ℝ) * ((f w) (u i)).log) ?_ 0 (f.symm w₂)
   · rw [← det_reindex_self e₁, ← det_reindex_self g]
     · rw [Units.smul_def, abs_zsmul, Int.abs_negOnePow, one_smul] at h
-      convert h
+      convert! h
       · ext; simp only [ne_eq, reindex_apply, submatrix_apply, of_apply, Equiv.apply_symm_apply,
           Equiv.trans_apply, Fin.succAbove_zero, id_eq, finSuccEquiv_succ,
           Equiv.optionSubtype_symm_apply_apply_coe, f]
@@ -268,7 +268,7 @@ def regulator : ℝ := ZLattice.covolume (unitLattice K)
 theorem isMaxRank_fundSystem :
     IsMaxRank (fundSystem K) := by
   classical
-  convert ((basisUnitLattice K).ofZLatticeBasis ℝ (unitLattice K)).linearIndependent
+  convert! ((basisUnitLattice K).ofZLatticeBasis ℝ (unitLattice K)).linearIndependent
   rw [logEmbedding_fundSystem, Basis.ofZLatticeBasis_apply]
 
 open scoped Classical in
diff --git a/Mathlib/NumberTheory/Padics/Hensel.lean b/Mathlib/NumberTheory/Padics/Hensel.lean
index 970b05c8b30a6a..98571de58969ce 100644
--- a/Mathlib/NumberTheory/Padics/Hensel.lean
+++ b/Mathlib/NumberTheory/Padics/Hensel.lean
@@ -74,7 +74,7 @@ include ncs_der_val
 
 private theorem ncs_tendsto_const :
     Tendsto (fun i => ‖F.derivative.aeval (ncs i)‖) atTop (𝓝 ‖F.derivative.aeval a‖) := by
-  convert @tendsto_const_nhds ℝ _ ℕ _ _; rw [ncs_der_val]
+  convert! @tendsto_const_nhds ℝ _ ℕ _ _; rw [ncs_der_val]
 
 private theorem norm_deriv_eq : ‖F.derivative.aeval ncs.lim‖ = ‖F.derivative.aeval a‖ :=
   tendsto_nhds_unique ncs_tendsto_lim (ncs_tendsto_const ncs_der_val)
diff --git a/Mathlib/NumberTheory/Padics/MahlerBasis.lean b/Mathlib/NumberTheory/Padics/MahlerBasis.lean
index a0916015af130c..a6a125ff8d4a35 100644
--- a/Mathlib/NumberTheory/Padics/MahlerBasis.lean
+++ b/Mathlib/NumberTheory/Padics/MahlerBasis.lean
@@ -342,7 +342,7 @@ lemma hasSum_mahler (f : C(ℤ_[p], E)) : HasSum (fun n ↦ mahlerTerm (Δ_[1]^[
       (mahlerSeries (Δ_[1]^[·] f 0) : C(ℤ_[p], E)) :=
     hasSum_mahlerSeries (fwdDiff_tendsto_zero f)
   -- Now show that the sum of the Mahler terms must equal `f` on a dense set, so it is actually `f`.
-  convert this using 1
+  convert! this using 1
   refine ContinuousMap.coe_injective (denseRange_natCast.equalizer
     (map_continuous f) (map_continuous _) (funext fun n ↦ ?_))
   simpa [mahlerSeries_apply_nat (fwdDiff_tendsto_zero f) le_rfl]
diff --git a/Mathlib/NumberTheory/Padics/PadicIntegers.lean b/Mathlib/NumberTheory/Padics/PadicIntegers.lean
index bb26b5291c7eab..a1ff8136d77779 100644
--- a/Mathlib/NumberTheory/Padics/PadicIntegers.lean
+++ b/Mathlib/NumberTheory/Padics/PadicIntegers.lean
@@ -265,7 +265,7 @@ theorem exists_pow_neg_lt {ε : ℝ} (hε : 0 < ε) : ∃ k : ℕ, (p : ℝ) ^ (
     apply lt_of_lt_of_le hk
     norm_cast
     apply le_of_lt
-    convert Nat.lt_pow_self _ using 1
+    convert! Nat.lt_pow_self _ using 1
     exact hp.1.one_lt
   · exact mod_cast hp.1.pos
 
diff --git a/Mathlib/NumberTheory/Padics/PadicVal/Basic.lean b/Mathlib/NumberTheory/Padics/PadicVal/Basic.lean
index 2d99b6821f97c2..18333fad51b625 100644
--- a/Mathlib/NumberTheory/Padics/PadicVal/Basic.lean
+++ b/Mathlib/NumberTheory/Padics/PadicVal/Basic.lean
@@ -647,7 +647,7 @@ digits of `k` plus the sum of the digits of `n - k` minus the sum of digits of `
 theorem sub_one_mul_padicValNat_choose_eq_sub_sum_digits {k n : ℕ} [hp : Fact p.Prime]
     (h : k ≤ n) : (p - 1) * padicValNat p (choose n k) =
     (p.digits k).sum + (p.digits (n - k)).sum - (p.digits n).sum := by
-  convert @sub_one_mul_padicValNat_choose_eq_sub_sum_digits' _ _ _ ‹_›
+  convert! @sub_one_mul_padicValNat_choose_eq_sub_sum_digits' _ _ _ ‹_›
   all_goals lia
 
 end padicValNat
diff --git a/Mathlib/NumberTheory/Padics/RingHoms.lean b/Mathlib/NumberTheory/Padics/RingHoms.lean
index 126f17140c5ddf..7a27105295d93f 100644
--- a/Mathlib/NumberTheory/Padics/RingHoms.lean
+++ b/Mathlib/NumberTheory/Padics/RingHoms.lean
@@ -73,7 +73,7 @@ def modPart : ℤ :=
 variable {p}
 
 theorem modPart_lt_p : modPart p r < p := by
-  convert Int.emod_lt_abs _ _
+  convert! Int.emod_lt_abs _ _
   · simp
   · exact mod_cast hp_prime.1.ne_zero
 
@@ -103,7 +103,7 @@ theorem norm_sub_modPart (h : ‖(r : ℚ_[p])‖ ≤ 1) : ‖(⟨r, h⟩ - modP
   let n := modPart p r
   rw [norm_lt_one_iff_dvd, ← (isUnit_den r h).dvd_mul_right]
   suffices ↑p ∣ r.num - n * r.den by
-    convert (map_dvd (Int.castRingHom ℤ_[p])) this
+    convert! (map_dvd (Int.castRingHom ℤ_[p])) this
     simp only [n, sub_mul, Int.cast_natCast, eq_intCast, Int.cast_mul, sub_left_inj,
       Int.cast_sub]
     apply Subtype.coe_injective
@@ -252,7 +252,7 @@ lemma zmodRepr_natCast_of_lt {n : ℕ} (hn : n < p) :
 
 lemma zmodRepr_natCast_ofNat {n : ℕ} (hn : ofNat(n) < p) :
     zmodRepr (ofNat(n) : ℤ_[p]) = ofNat(n) := by
-  convert zmodRepr_natCast_of_lt hn
+  convert! zmodRepr_natCast_of_lt hn
   rcases n with _ | _ | n <;> simp
 
 lemma zmodRepr_units_ne_zero (x : ℤ_[p]ˣ) : x.val.zmodRepr ≠ 0 := by
@@ -280,7 +280,7 @@ def toZModHom (v : ℕ) (f : ℤ_[p] → ℕ) (f_spec : ∀ x, x - f x ∈ (Idea
     intro x y
     rw [f_congr (x + y) _ (f x + f y), cast_add]
     · exact f_spec _
-    · convert Ideal.add_mem _ (f_spec x) (f_spec y) using 1
+    · convert! Ideal.add_mem _ (f_spec x) (f_spec y) using 1
       rw [cast_add]
       ring
   map_mul' := by
@@ -288,7 +288,7 @@ def toZModHom (v : ℕ) (f : ℤ_[p] → ℕ) (f_spec : ∀ x, x - f x ∈ (Idea
     rw [f_congr (x * y) _ (f x * f y), cast_mul]
     · exact f_spec _
     · let I : Ideal ℤ_[p] := Ideal.span {↑v}
-      convert I.add_mem (I.mul_mem_left x (f_spec y)) (I.mul_mem_right ↑(f y) (f_spec x)) using 1
+      convert! I.add_mem (I.mul_mem_left x (f_spec y)) (I.mul_mem_right ↑(f y) (f_spec x)) using 1
       rw [cast_mul]
       ring
 
@@ -314,7 +314,7 @@ This coercion is only a ring homomorphism if it coerces into a ring whose charac
 `p`. While this is not the case here we can still make use of the coercion.
 -/
 theorem toZMod_spec : x - (ZMod.cast (toZMod x) : ℤ_[p]) ∈ maximalIdeal ℤ_[p] := by
-  convert sub_zmodRepr_mem x using 2
+  convert! sub_zmodRepr_mem x using 2
   dsimp [toZMod, toZModHom]
   rcases Nat.exists_eq_add_of_lt hp_prime.1.pos with ⟨p', rfl⟩
   change ↑((_ : ZMod (0 + p' + 1)).val) = (_ : ℤ_[0 + p' + 1])
@@ -331,7 +331,7 @@ theorem ker_toZMod : RingHom.ker (toZMod : ℤ_[p] →+* ZMod p) = maximalIdeal
   · intro h
     rw [← sub_zero x] at h
     dsimp [toZMod, toZModHom]
-    convert zmod_congr_of_sub_mem_max_ideal x _ 0 _ h
+    convert! zmod_congr_of_sub_mem_max_ideal x _ 0 _ h
     · norm_cast
     · apply sub_zmodRepr_mem
 
@@ -461,7 +461,7 @@ theorem ker_toZModPow (n : ℕ) :
   constructor
   · intro h
     suffices x.appr n = 0 by
-      convert appr_spec n x
+      convert! appr_spec n x
       simp only [this, sub_zero, cast_zero]
     dsimp [toZModPow, toZModHom] at h
     rw [ZMod.natCast_eq_zero_iff] at h
@@ -668,7 +668,7 @@ theorem lift_sub_val_mem_span (r : R) (n : ℕ) :
   rw [sub_eq_sub_add_sub (limNthHom f_compat r) _ ↑(nthHom f r (max n k))]
   apply Ideal.add_mem _ _ this
   rw [Ideal.mem_span_singleton]
-  convert
+  convert!
     map_dvd (Int.castRingHom ℤ_[p]) (pow_dvd_nthHom_sub f_compat r n (max n k) (le_max_left _ _))
   · simp
   · simp [nthHom]
diff --git a/Mathlib/NumberTheory/Pell.lean b/Mathlib/NumberTheory/Pell.lean
index d12baab84524cc..b5df88679627e2 100644
--- a/Mathlib/NumberTheory/Pell.lean
+++ b/Mathlib/NumberTheory/Pell.lean
@@ -575,7 +575,7 @@ theorem mul_inv_x_lt_x {a₁ : Solution₁ d} (h : IsFundamental a₁) {a : Solu
     _ = a.x * a₁.y * a₁.x := by ring
     _ ≤ a.y * a₁.x * a₁.x := by have := h.1; have := x_mul_y_le_y_mul_x h hax hay; gcongr
   rw [mul_assoc, ← sq, a₁.prop_x, ← sub_neg]
-  suffices a.y - a.x * a₁.y < 0 by convert this using 1; ring
+  suffices a.y - a.x * a₁.y < 0 by convert! this using 1; ring
   rw [sub_neg, ← abs_of_pos hay, ← abs_of_pos h.2.1, ← abs_of_pos <| zero_lt_one.trans hax, ←
     abs_mul, ← sq_lt_sq, mul_pow, a.prop_x]
   calc
diff --git a/Mathlib/NumberTheory/PrimeCounting.lean b/Mathlib/NumberTheory/PrimeCounting.lean
index 17a41190196bc0..b88f94d8aa0873 100644
--- a/Mathlib/NumberTheory/PrimeCounting.lean
+++ b/Mathlib/NumberTheory/PrimeCounting.lean
@@ -88,7 +88,7 @@ theorem surjective_primeCounting' : Function.Surjective π' :=
 
 theorem surjective_primeCounting : Function.Surjective π := by
   suffices Function.Surjective (π ∘ fun n => n - 1) from this.of_comp
-  convert surjective_primeCounting'
+  convert! surjective_primeCounting'
   ext
   exact primeCounting_sub_one _
 
@@ -266,7 +266,7 @@ theorem primeCounting'_add_le {a k : ℕ} (h0 : a ≠ 0) (h1 : a < k) (n : ℕ)
 theorem primeCounting_add_le {a k : ℕ} (h0 : a ≠ 0) (h1 : a ≤ k) (n : ℕ) :
     π (k + n) ≤ π k + totient a * (n / a + 1) := by
   rw [primeCounting_eq_primeCounting'_succ]
-  convert primeCounting'_add_le h0 (Order.lt_add_one_iff.mpr h1) n using 2
+  convert! primeCounting'_add_le h0 (Order.lt_add_one_iff.mpr h1) n using 2
   omega
 
 end Nat
diff --git a/Mathlib/NumberTheory/PythagoreanTriples.lean b/Mathlib/NumberTheory/PythagoreanTriples.lean
index 4b01469bd7a972..062bb6e1941f47 100644
--- a/Mathlib/NumberTheory/PythagoreanTriples.lean
+++ b/Mathlib/NumberTheory/PythagoreanTriples.lean
@@ -80,7 +80,7 @@ theorem mul_iff (k : ℤ) (hk : k ≠ 0) :
   simp only [PythagoreanTriple]
   intro h
   rw [← mul_left_inj' (mul_ne_zero hk hk)]
-  convert h using 1 <;> ring
+  convert! h using 1 <;> ring
 
 /-- A Pythagorean triple `x, y, z` is “classified” if there exist integers `k, m, n` such that
 either
@@ -181,8 +181,9 @@ theorem isClassified_of_isPrimitiveClassified (hp : h.IsPrimitiveClassified) : h
 
 theorem isClassified_of_normalize_isPrimitiveClassified (hc : h.normalize.IsPrimitiveClassified) :
     h.IsClassified := by
-  convert h.normalize.mul_isClassified (Int.gcd x y)
-        (isClassified_of_isPrimitiveClassified h.normalize hc) <;>
+  convert!
+    h.normalize.mul_isClassified (Int.gcd x y)
+      (isClassified_of_isPrimitiveClassified h.normalize hc) <;>
     rw [Int.mul_ediv_cancel']
   · exact Int.gcd_dvd_left ..
   · exact Int.gcd_dvd_right ..
@@ -252,7 +253,7 @@ def circleEquivGen (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) :
   left_inv x := by
     have h2 : (1 + 1 : K) = 2 := by norm_num
     have h3 : (2 : K) ≠ 0 := by
-      convert hk 1
+      convert! hk 1
       rw [one_pow 2, h2]
     simp [field, hk x, h2, add_assoc, add_comm, add_sub_cancel, mul_comm]
   right_inv := fun ⟨⟨x, y⟩, hxy, hy⟩ => by
@@ -262,7 +263,7 @@ def circleEquivGen (hk : ∀ x : K, 1 + x ^ 2 ≠ 0) :
       rw [(add_neg_eq_iff_eq_add.mpr hxy.symm).symm]
       ring
     have h4 : (2 : K) ≠ 0 := by
-      convert hk 1
+      convert! hk 1
       rw [one_pow 2]
       ring
     simp only [Prod.mk_inj, Subtype.mk_eq_mk]
@@ -291,10 +292,10 @@ private theorem coprime_sq_sub_sq_add_of_even_odd {m n : ℤ} (h : Int.gcd m n =
   obtain ⟨p, hp, hp1, hp2⟩ := Nat.Prime.not_coprime_iff_dvd.mp H
   rw [← Int.natCast_dvd] at hp1 hp2
   have h2m : (p : ℤ) ∣ 2 * m ^ 2 := by
-    convert dvd_add hp2 hp1 using 1
+    convert! dvd_add hp2 hp1 using 1
     ring
   have h2n : (p : ℤ) ∣ 2 * n ^ 2 := by
-    convert dvd_sub hp2 hp1 using 1
+    convert! dvd_sub hp2 hp1 using 1
     ring
   have hmc : p = 2 ∨ p ∣ Int.natAbs m := prime_two_or_dvd_of_dvd_two_mul_pow_self_two hp h2m
   have hnc : p = 2 ∨ p ∣ Int.natAbs n := prime_two_or_dvd_of_dvd_two_mul_pow_self_two hp h2n
@@ -388,10 +389,10 @@ private theorem coprime_sq_sub_sq_sum_of_odd_odd {m n : ℤ} (h : Int.gcd m n =
   rw [← Int.natCast_dvd] at hp1 hp2
   apply Nat.dvd_gcd
   · apply Int.Prime.dvd_natAbs_of_coe_dvd_sq hp
-    convert dvd_add hp1 hp2
+    convert! dvd_add hp1 hp2
     ring
   · apply Int.Prime.dvd_natAbs_of_coe_dvd_sq hp
-    convert dvd_sub hp2 hp1
+    convert! dvd_sub hp2 hp1
     ring
 
 namespace PythagoreanTriple
diff --git a/Mathlib/NumberTheory/RamificationInertia/Basic.lean b/Mathlib/NumberTheory/RamificationInertia/Basic.lean
index 05e2ed79846948..7a88c4a6d1dee8 100644
--- a/Mathlib/NumberTheory/RamificationInertia/Basic.lean
+++ b/Mathlib/NumberTheory/RamificationInertia/Basic.lean
@@ -260,7 +260,8 @@ theorem finrank_quotient_map [IsDomain S] [IsDedekindDomain R] [Algebra K L]
         Submodule.Quotient.eq] at y_eq
       exact add_mem (Submodule.mem_sup_left y_mem) (neg_mem <| Submodule.mem_sup_right y_eq)
   · have := b.linearIndependent; rw [b_eq_b'] at this
-    convert FinrankQuotientMap.linearIndependent_of_nontrivial K _
+    convert!
+      FinrankQuotientMap.linearIndependent_of_nontrivial K _
         ((Algebra.linearMap S L).restrictScalars R) _ ((Submodule.mkQ _).restrictScalars R) this
     · rw [Quotient.algebraMap_eq, Ideal.mk_ker]
       exact hp.ne_top
diff --git a/Mathlib/NumberTheory/RamificationInertia/Ramification.lean b/Mathlib/NumberTheory/RamificationInertia/Ramification.lean
index 7f2015f426cce7..7013facf35c31a 100644
--- a/Mathlib/NumberTheory/RamificationInertia/Ramification.lean
+++ b/Mathlib/NumberTheory/RamificationInertia/Ramification.lean
@@ -71,7 +71,7 @@ variable {p P}
 theorem ramificationIdx_eq_find [DecidablePred fun n ↦ ∀ (k : ℕ), map f p ≤ P ^ k → k ≤ n]
     (h : ∃ n, ∀ k, map f p ≤ P ^ k → k ≤ n) :
     ramificationIdx p P = Nat.find h := by
-  convert Nat.sSup_def h
+  convert! Nat.sSup_def h
 
 theorem ramificationIdx_eq_zero (h : ∀ n : ℕ, ∃ k, map f p ≤ P ^ k ∧ n < k) :
     ramificationIdx p P = 0 :=
@@ -270,7 +270,7 @@ lemma ramificationIdx_eq_one_iff
   have ha' : ¬ a ≤ P := fun h ↦ H₁ (ha.trans_le (Ideal.mul_mono_right h))
   rw [IsScalarTower.algebraMap_eq _ S, ← Ideal.map_map, ha, Ideal.map_mul,
     Localization.AtPrime.map_eq_maximalIdeal]
-  convert Ideal.mul_top _
+  convert! Ideal.mul_top _
   on_goal 2 => infer_instance
   rw [← not_ne_iff, IsLocalization.map_algebraMap_ne_top_iff_disjoint P.primeCompl]
   simpa [primeCompl, Set.disjoint_compl_left_iff_subset]
diff --git a/Mathlib/NumberTheory/Real/GoldenRatio.lean b/Mathlib/NumberTheory/Real/GoldenRatio.lean
index 81d8de91d46b21..2b6c97d2d59bdf 100644
--- a/Mathlib/NumberTheory/Real/GoldenRatio.lean
+++ b/Mathlib/NumberTheory/Real/GoldenRatio.lean
@@ -120,7 +120,7 @@ theorem neg_one_lt_goldenConj : -1 < ψ := by
 theorem goldenRatio_irrational : Irrational φ := by
   have := Nat.Prime.irrational_sqrt (show Nat.Prime 5 by norm_num)
   have := this.ratCast_add 1
-  convert this.ratCast_mul (show (0.5 : ℚ) ≠ 0 by norm_num)
+  convert! this.ratCast_mul (show (0.5 : ℚ) ≠ 0 by norm_num)
   simp
   ring
 
@@ -128,7 +128,7 @@ theorem goldenRatio_irrational : Irrational φ := by
 theorem goldenConj_irrational : Irrational ψ := by
   have := Nat.Prime.irrational_sqrt (show Nat.Prime 5 by norm_num)
   have := this.ratCast_sub 1
-  convert this.ratCast_mul (show (0.5 : ℚ) ≠ 0 by norm_num)
+  convert! this.ratCast_mul (show (0.5 : ℚ) ≠ 0 by norm_num)
   simp
   ring
 
@@ -187,7 +187,7 @@ theorem coe_fib_eq' :
   · exact fib_isSol_fibRec
   · suffices LinearRecurrence.IsSolution fibRec
         ((fun n ↦ (√5)⁻¹ * φ ^ n) - (fun n ↦ (√5)⁻¹ * ψ ^ n)) by
-      convert this
+      convert! this
       rw [Pi.sub_apply]
       ring
     apply (@fibRec ℝ _).solSpace.sub_mem
diff --git a/Mathlib/NumberTheory/SmoothNumbers.lean b/Mathlib/NumberTheory/SmoothNumbers.lean
index 56d8ee820b5e11..74aac9f56b95f8 100644
--- a/Mathlib/NumberTheory/SmoothNumbers.lean
+++ b/Mathlib/NumberTheory/SmoothNumbers.lean
@@ -461,8 +461,7 @@ lemma smoothNumbersUpTo_subset_image (N k : ℕ) :
 /-- The cardinality of the set of `k`-smooth numbers `≤ N` is bounded by `2^π(k-1) * √N`. -/
 lemma smoothNumbersUpTo_card_le (N k : ℕ) :
     #(smoothNumbersUpTo N k) ≤ 2 ^ #k.primesBelow * N.sqrt := by
-  convert (Finset.card_le_card <| smoothNumbersUpTo_subset_image N k).trans <|
-    Finset.card_image_le
+  convert! (Finset.card_le_card <| smoothNumbersUpTo_subset_image N k).trans <| Finset.card_image_le
   simp only [Finset.card_product, Finset.card_powerset, Finset.mem_range, zero_lt_succ,
     Finset.card_erase_of_mem, Finset.card_range, succ_sub_succ_eq_sub, Nat.sub_zero]
 
diff --git a/Mathlib/NumberTheory/SumPrimeReciprocals.lean b/Mathlib/NumberTheory/SumPrimeReciprocals.lean
index 94e4d257368527..5811222e1cb395 100644
--- a/Mathlib/NumberTheory/SumPrimeReciprocals.lean
+++ b/Mathlib/NumberTheory/SumPrimeReciprocals.lean
@@ -49,7 +49,7 @@ lemma one_half_le_sum_primes_ge_one_div (k : ℕ) :
   set N₀ : ℕ := 2 * m ^ 2 with hN₀
   let S : ℝ := ((2 * N₀).succ.primesBelow \ k.primesBelow).sum (fun p ↦ (1 / p : ℝ))
   suffices 1 / 2 ≤ S by
-    convert this using 5
+    convert! this using 5
     rw [show 4 = 2 ^ 2 by simp, pow_right_comm]
     ring
   suffices 2 * N₀ ≤ m * (2 * N₀).sqrt + 2 * N₀ * S by
@@ -72,11 +72,13 @@ theorem not_summable_one_div_on_primes :
   specialize hk ({p | Nat.Prime p} ∩ {p | k ≤ p}) inter_subset_right
   rw [tsum_subtype, indicator_indicator, inter_eq_left.mpr fun n hn ↦ hn.1, mem_Iio] at hk
   have h' : Summable (indicator ({p | Nat.Prime p} ∩ {p | k ≤ p}) fun n ↦ (1 : ℝ) / n) := by
-    convert h.indicator {n : ℕ | k ≤ n} using 1
+    convert! h.indicator {n : ℕ | k ≤ n} using 1
     simp only [indicator_indicator, inter_comm]
   refine ((one_half_le_sum_primes_ge_one_div k).trans_lt <| LE.le.trans_lt ?_ hk).false
-  convert Summable.sum_le_tsum (primesBelow ((4 ^ (k.primesBelow.card + 1)).succ) \ primesBelow k)
-    (fun n _ ↦ indicator_nonneg (fun p _ ↦ by positivity) _) h' using 2 with p hp
+  convert!
+    Summable.sum_le_tsum (primesBelow ((4 ^ (k.primesBelow.card + 1)).succ) \ primesBelow k)
+      (fun n _ ↦ indicator_nonneg (fun p _ ↦ by positivity) _) h' using
+    2 with p hp
   obtain ⟨hp₁, hp₂⟩ := mem_setOf_eq ▸ Finset.mem_sdiff.mp hp
   have hpp := prime_of_mem_primesBelow hp₁
   refine (indicator_of_mem ?_ fun n : ℕ ↦ (1 / n : ℝ)).symm
@@ -85,7 +87,7 @@ theorem not_summable_one_div_on_primes :
 set_option backward.isDefEq.respectTransparency false in
 /-- The sum over the reciprocals of the primes diverges. -/
 theorem Nat.Primes.not_summable_one_div : ¬ Summable (fun p : Nat.Primes ↦ (1 / p : ℝ)) := by
-  convert summable_subtype_iff_indicator.mp.mt not_summable_one_div_on_primes
+  convert! summable_subtype_iff_indicator.mp.mt not_summable_one_div_on_primes
 
 /-- The series over `p^r` for primes `p` converges if and only if `r < -1`. -/
 theorem Nat.Primes.summable_rpow {r : ℝ} :
diff --git a/Mathlib/NumberTheory/Transcendental/Lindemann/AnalyticalPart.lean b/Mathlib/NumberTheory/Transcendental/Lindemann/AnalyticalPart.lean
index 2cf8a8492ee505..f25063e0c90276 100644
--- a/Mathlib/NumberTheory/Transcendental/Lindemann/AnalyticalPart.lean
+++ b/Mathlib/NumberTheory/Transcendental/Lindemann/AnalyticalPart.lean
@@ -31,7 +31,7 @@ theorem hasDerivAt_cexp_mul_sumIDeriv (p : ℂ[X]) (s : ℂ) (x : ℝ) :
   have h₀ := (hasDerivAt_id' x).smul_const s
   have h₁ := h₀.fun_neg.cexp
   have h₂ := ((sumIDeriv p).hasDerivAt (x • s)).comp x h₀
-  convert (h₁.mul h₂).fun_neg using 1
+  convert! (h₁.mul h₂).fun_neg using 1
   nth_rw 1 [sumIDeriv_eq_self_add p]
   simp only [one_smul, eval_add, Function.comp_apply]
   ring
@@ -72,7 +72,7 @@ private theorem P_le_aux (f : ℕ → ℂ[X]) (s : ℂ) (c : ℝ)
   rw [P_eq_integral_exp_mul_eval (f p) s, mul_comm s, norm_mul, norm_mul, norm_exp]
   gcongr
   rw [intervalIntegral.integral_of_le zero_le_one, ← mul_one (_ * _)]
-  convert MeasureTheory.norm_setIntegral_le_of_norm_le_const _ _
+  convert! MeasureTheory.norm_setIntegral_le_of_norm_le_const _ _
   · rw [Real.volume_real_Ioc_of_le zero_le_one, sub_zero]
   · rw [Real.volume_Ioc, sub_zero]; exact ENNReal.ofReal_lt_top
   intro x hx
diff --git a/Mathlib/NumberTheory/Transcendental/Liouville/LiouvilleNumber.lean b/Mathlib/NumberTheory/Transcendental/Liouville/LiouvilleNumber.lean
index 42ffe3c7473802..2242416cd8e260 100644
--- a/Mathlib/NumberTheory/Transcendental/Liouville/LiouvilleNumber.lean
+++ b/Mathlib/NumberTheory/Transcendental/Liouville/LiouvilleNumber.lean
@@ -81,7 +81,7 @@ protected theorem summable {m : ℝ} (hm : 1 < m) : Summable fun i : ℕ => 1 /
 
 theorem remainder_summable {m : ℝ} (hm : 1 < m) (k : ℕ) :
     Summable fun i : ℕ => 1 / m ^ (i + (k + 1))! := by
-  convert (summable_nat_add_iff (k + 1)).2 (LiouvilleNumber.summable hm)
+  convert! (summable_nat_add_iff (k + 1)).2 (LiouvilleNumber.summable hm)
 
 theorem remainder_pos {m : ℝ} (hm : 1 < m) (k : ℕ) : 0 < remainder m k :=
   (remainder_summable hm k).tsum_pos (fun _ => by positivity) 0 (by positivity)
diff --git a/Mathlib/NumberTheory/Transcendental/Liouville/LiouvilleWith.lean b/Mathlib/NumberTheory/Transcendental/Liouville/LiouvilleWith.lean
index 9c603876f5cce2..682e83ab6f38d2 100644
--- a/Mathlib/NumberTheory/Transcendental/Liouville/LiouvilleWith.lean
+++ b/Mathlib/NumberTheory/Transcendental/Liouville/LiouvilleWith.lean
@@ -219,7 +219,7 @@ protected theorem neg (h : LiouvilleWith p x) : LiouvilleWith p (-x) := by
   refine ⟨C, hC.mono ?_⟩
   rintro n ⟨m, hne, hlt⟩
   refine ⟨-m, by simp [neg_div, hne], ?_⟩
-  convert hlt using 1
+  convert! hlt using 1
   rw [abs_sub_comm]
   congr! 1; push_cast; ring
 
diff --git a/Mathlib/NumberTheory/Transcendental/Liouville/Residual.lean b/Mathlib/NumberTheory/Transcendental/Liouville/Residual.lean
index 970a8e420ede92..c3d05833f12589 100644
--- a/Mathlib/NumberTheory/Transcendental/Liouville/Residual.lean
+++ b/Mathlib/NumberTheory/Transcendental/Liouville/Residual.lean
@@ -63,7 +63,7 @@ theorem eventually_residual_liouville : ∀ᶠ x in residual ℝ, Liouville x :=
     simp only [mem_iInter, mem_iUnion]
     refine fun n => ⟨r.num * 2, r.den * 2, ?_, ?_⟩
     · have := r.pos; lia
-    · convert @mem_ball_self ℝ _ (r : ℝ) _ _
+    · convert! @mem_ball_self ℝ _ (r : ℝ) _ _
       · push_cast
         -- Workaround for https://github.com/leanprover/lean4/pull/6438; this eliminates an
         -- `Expr.mdata` that would cause `norm_cast` to skip a numeral.
diff --git a/Mathlib/NumberTheory/WellApproximable.lean b/Mathlib/NumberTheory/WellApproximable.lean
index 0d6bafe84f0dd4..51f2d6e1ac8f88 100644
--- a/Mathlib/NumberTheory/WellApproximable.lean
+++ b/Mathlib/NumberTheory/WellApproximable.lean
@@ -106,7 +106,7 @@ theorem image_pow_subset_of_coprime (hm : 0 < m) (hmn : n.Coprime m) :
   replace hb : b ^ m ∈ {u : A | orderOf u = n} := by
     rw [← hb] at hmn ⊢; exact hmn.orderOf_pow
   apply ball_subset_thickening hb ((m : ℝ) • δ)
-  convert pow_mem_ball hm hab using 1
+  convert! pow_mem_ball hm hab using 1
   simp only [nsmul_eq_mul, smul_eq_mul]
 
 @[to_additive]
@@ -117,7 +117,7 @@ theorem image_pow_subset (n : ℕ) (hm : 0 < m) :
   replace hb : b ^ m ∈ {y : A | orderOf y = n} := by
     rw [mem_setOf_eq, orderOf_pow' b hm.ne', hb, Nat.gcd_mul_left_left, n.mul_div_cancel hm]
   apply ball_subset_thickening hb (m * δ)
-  convert pow_mem_ball hm hab using 1
+  convert! pow_mem_ball hm hab using 1
   simp only [nsmul_eq_mul]
 
 @[to_additive]
@@ -285,7 +285,7 @@ theorem addWellApproximable_ae_empty_or_univ (δ : ℕ → ℝ) (hδ : Tendsto 
     specialize this (approxAddOrderOf.image_nsmul_subset (δ n) (n / p) hp.pos)
     simp only [h_div] at this ⊢
     refine this.trans ?_
-    convert approxAddOrderOf.vadd_subset_of_coprime (p * δ n) h_cop
+    convert! approxAddOrderOf.vadd_subset_of_coprime (p * δ n) h_cop
     rw [hu₀, Subtype.coe_mk, mul_comm p, h_div]
   change (∀ᵐ x, x ∉ E) ∨ E ∈ ae volume
   rw [← eventuallyEq_empty, ← eventuallyEq_univ]
diff --git a/Mathlib/NumberTheory/ZetaValues.lean b/Mathlib/NumberTheory/ZetaValues.lean
index 7cc9d44990bfcd..40bb5b8d8cd850 100644
--- a/Mathlib/NumberTheory/ZetaValues.lean
+++ b/Mathlib/NumberTheory/ZetaValues.lean
@@ -85,7 +85,7 @@ section Calculus
 
 theorem hasDerivAt_bernoulliFun (k : ℕ) (x : ℝ) :
     HasDerivAt (bernoulliFun k) (k * bernoulliFun (k - 1) x) x := by
-  convert ((Polynomial.bernoulli k).map <| algebraMap ℚ ℝ).hasDerivAt x using 1
+  convert! ((Polynomial.bernoulli k).map <| algebraMap ℚ ℝ).hasDerivAt x using 1
   simp only [bernoulliFun, Polynomial.derivative_map, Polynomial.derivative_bernoulli k,
     Polynomial.map_mul, Polynomial.map_natCast, Polynomial.eval_mul, Polynomial.eval_natCast]
 
@@ -109,7 +109,7 @@ theorem deriv_bernoulliFun :
 
 theorem antideriv_bernoulliFun (k : ℕ) (x : ℝ) :
     HasDerivAt (fun x => bernoulliFun (k + 1) x / (k + 1)) (bernoulliFun k x) x := by
-  convert (hasDerivAt_bernoulliFun (k + 1) x).div_const _ using 1
+  convert! (hasDerivAt_bernoulliFun (k + 1) x).div_const _ using 1
   simp [Nat.cast_add_one_ne_zero k]
 
 theorem integral_bernoulliFun : ∫ x : ℝ in 0..1, bernoulliFun k x = if k = 0 then 1 else 0 := by
@@ -309,7 +309,7 @@ theorem hasSum_one_div_pow_mul_fourier_mul_bernoulliFun {k : ℕ} (hk : 2 ≤ k)
     rw [← Ico_insert_right (zero_le_one' ℝ), mem_insert_iff, or_comm] at hx
     rcases hx with (hx | rfl)
     · exact this hx
-    · convert this (left_mem_Ico.mpr zero_lt_one) using 1
+    · convert! this (left_mem_Ico.mpr zero_lt_one) using 1
       · rw [AddCircle.coe_period, QuotientAddGroup.mk_zero]
       · rw [bernoulliFun_endpoints_eq_of_ne_one (by lia : k ≠ 1)]
   intro y hy
@@ -322,7 +322,7 @@ theorem hasSum_one_div_pow_mul_fourier_mul_bernoulliFun {k : ℕ} (hk : 2 ≤ k)
     has_pointwise_sum_fourier_series_of_summable
       ((summable_bernoulli_fourier hk).congr fun n => (step1 n).symm) y
   simp_rw [step1] at step2
-  convert step2.mul_left (-(2 * ↑π * I) ^ k / (k ! : ℂ)) using 2 with n
+  convert! step2.mul_left (-(2 * ↑π * I) ^ k / (k ! : ℂ)) using 2 with n
   · rw [smul_eq_mul, ← mul_assoc, mul_div, mul_neg, div_mul_cancel₀, neg_neg, mul_pow _ (n : ℂ),
       ← div_div, div_self]
     · rw [Ne, pow_eq_zero_iff', not_and_or]
@@ -341,7 +341,7 @@ theorem hasSum_one_div_nat_pow_mul_fourier {k : ℕ} (hk : 2 ≤ k) {x : ℝ} (h
       (fun n : ℕ =>
         (1 : ℂ) / (n : ℂ) ^ k * (fourier n (x : 𝕌) + (-1 : ℂ) ^ k * fourier (-n) (x : 𝕌)))
       (-(2 * π * I) ^ k / k ! * bernoulliFun k x) := by
-  convert (hasSum_one_div_pow_mul_fourier_mul_bernoulliFun hk hx).nat_add_neg using 1
+  convert! (hasSum_one_div_pow_mul_fourier_mul_bernoulliFun hk hx).nat_add_neg using 1
   · ext1 n
     rw [Int.cast_neg, mul_add, ← mul_assoc]
     conv_rhs => rw [neg_eq_neg_one_mul, mul_pow, ← div_div]
@@ -359,9 +359,7 @@ theorem hasSum_one_div_nat_pow_mul_cos {k : ℕ} (hk : k ≠ 0) {x : ℝ} (hx :
   have :
     HasSum (fun n : ℕ => 1 / (n : ℂ) ^ (2 * k) * (fourier n (x : 𝕌) + fourier (-n) (x : 𝕌)))
       ((-1 : ℂ) ^ (k + 1) * (2 * (π : ℂ)) ^ (2 * k) / (2 * k)! * bernoulliFun (2 * k) x) := by
-    convert
-      hasSum_one_div_nat_pow_mul_fourier (by lia : 2 ≤ 2 * k)
-        hx using 3
+    convert! hasSum_one_div_nat_pow_mul_fourier (by lia : 2 ≤ 2 * k) hx using 3
     · rw [pow_mul (-1 : ℂ), neg_one_sq, one_pow, one_mul]
     · rw [pow_add, pow_one]
       conv_rhs =>
@@ -372,8 +370,8 @@ theorem hasSum_one_div_nat_pow_mul_cos {k : ℕ} (hk : k ≠ 0) {x : ℝ} (hx :
         · rw [pow_mul, I_sq]
       ring
   have ofReal_two : ((2 : ℝ) : ℂ) = 2 := by norm_cast
-  convert ((hasSum_iff _ _).mp (this.div_const 2)).1 with n
-  · convert (ofReal_re _).symm
+  convert! ((hasSum_iff _ _).mp (this.div_const 2)).1 with n
+  · convert! (ofReal_re _).symm
     rw [ofReal_mul]; rw [← mul_div]; congr
     · rw [ofReal_div, ofReal_one, ofReal_pow]; rfl
     · rw [ofReal_cos, ofReal_mul, fourier_coe_apply, fourier_coe_apply, cos, ofReal_one, div_one,
@@ -382,7 +380,7 @@ theorem hasSum_one_div_nat_pow_mul_cos {k : ℕ} (hk : k ≠ 0) {x : ℝ} (hx :
       congr 3
       · ring
       · ring
-  · convert (ofReal_re _).symm
+  · convert! (ofReal_re _).symm
     rw [ofReal_mul, ofReal_div, ofReal_div, ofReal_mul, ofReal_pow, ofReal_pow, ofReal_neg,
       ofReal_natCast, ofReal_mul, ofReal_two, ofReal_one]
     rw [bernoulliFun]
@@ -396,9 +394,7 @@ theorem hasSum_one_div_nat_pow_mul_sin {k : ℕ} (hk : k ≠ 0) {x : ℝ} (hx :
     HasSum (fun n : ℕ => 1 / (n : ℂ) ^ (2 * k + 1) * (fourier n (x : 𝕌) - fourier (-n) (x : 𝕌)))
       ((-1 : ℂ) ^ (k + 1) * I * (2 * π : ℂ) ^ (2 * k + 1) / (2 * k + 1)! *
         bernoulliFun (2 * k + 1) x) := by
-    convert
-      hasSum_one_div_nat_pow_mul_fourier
-        (by lia : 2 ≤ 2 * k + 1) hx using 1
+    convert! hasSum_one_div_nat_pow_mul_fourier (by lia : 2 ≤ 2 * k + 1) hx using 1
     · ext1 n
       rw [pow_add (-1 : ℂ), pow_mul (-1 : ℂ), neg_one_sq, one_pow, one_mul, pow_one, ←
         neg_eq_neg_one_mul, ← sub_eq_add_neg]
@@ -412,8 +408,8 @@ theorem hasSum_one_div_nat_pow_mul_sin {k : ℕ} (hk : k ≠ 0) {x : ℝ} (hx :
         · rw [pow_add, pow_one, pow_mul, I_sq]
       ring
   have ofReal_two : ((2 : ℝ) : ℂ) = 2 := by norm_cast
-  convert ((hasSum_iff _ _).mp (this.div_const (2 * I))).1
-  · convert (ofReal_re _).symm
+  convert! ((hasSum_iff _ _).mp (this.div_const (2 * I))).1
+  · convert! (ofReal_re _).symm
     rw [ofReal_mul]; rw [← mul_div]; congr
     · rw [ofReal_div, ofReal_one, ofReal_pow]; rfl
     · rw [ofReal_sin, ofReal_mul, fourier_coe_apply, fourier_coe_apply, sin, ofReal_one, div_one,
@@ -422,7 +418,7 @@ theorem hasSum_one_div_nat_pow_mul_sin {k : ℕ} (hk : k ≠ 0) {x : ℝ} (hx :
       congr 4
       · ring
       · ring
-  · convert (ofReal_re _).symm
+  · convert! (ofReal_re _).symm
     rw [ofReal_mul, ofReal_div, ofReal_div, ofReal_mul, ofReal_pow, ofReal_pow, ofReal_neg,
       ofReal_natCast, ofReal_mul, ofReal_two, ofReal_one, ← div_div, div_I,
       div_mul_eq_mul_div₀]
@@ -435,7 +431,7 @@ theorem hasSum_zeta_nat {k : ℕ} (hk : k ≠ 0) :
     HasSum (fun n : ℕ => 1 / (n : ℝ) ^ (2 * k))
       ((-1 : ℝ) ^ (k + 1) * (2 : ℝ) ^ (2 * k - 1) * π ^ (2 * k) *
         bernoulli (2 * k) / (2 * k)!) := by
-  convert hasSum_one_div_nat_pow_mul_cos hk (left_mem_Icc.mpr zero_le_one) using 1
+  convert! hasSum_one_div_nat_pow_mul_cos hk (left_mem_Icc.mpr zero_le_one) using 1
   · ext1 n; rw [mul_zero, Real.cos_zero, mul_one]
   rw [Polynomial.eval_zero_map, Polynomial.bernoulli_eval_zero, eq_ratCast]
   have : (2 : ℝ) ^ (2 * k - 1) = (2 : ℝ) ^ (2 * k) / 2 := by
@@ -454,12 +450,12 @@ end Cleanup
 section Examples
 
 theorem hasSum_zeta_two : HasSum (fun n : ℕ => (1 : ℝ) / (n : ℝ) ^ 2) (π ^ 2 / 6) := by
-  convert hasSum_zeta_nat one_ne_zero using 1; rw [mul_one]
+  convert! hasSum_zeta_nat one_ne_zero using 1; rw [mul_one]
   rw [bernoulli_eq_bernoulli'_of_ne_one (by decide : 2 ≠ 1), bernoulli'_two]
   simp [Nat.factorial]; ring
 
 theorem hasSum_zeta_four : HasSum (fun n : ℕ => (1 : ℝ) / (n : ℝ) ^ 4) (π ^ 4 / 90) := by
-  convert hasSum_zeta_nat two_ne_zero using 1
+  convert! hasSum_zeta_nat two_ne_zero using 1
   simp only [Nat.reduceAdd, Nat.reduceMul, Nat.add_one_sub_one]
   rw [bernoulli_eq_bernoulli'_of_ne_one, bernoulli'_four]
   · simp [Nat.factorial]; ring
diff --git a/Mathlib/NumberTheory/Zsqrtd/Basic.lean b/Mathlib/NumberTheory/Zsqrtd/Basic.lean
index 25a68986289d3b..1250002e986ee9 100644
--- a/Mathlib/NumberTheory/Zsqrtd/Basic.lean
+++ b/Mathlib/NumberTheory/Zsqrtd/Basic.lean
@@ -381,7 +381,7 @@ theorem sqLe_mul {d x y z w : ℕ} :
         Int.mul_nonneg (sub_nonneg_of_le (Int.ofNat_le_ofNat_of_le xy))
           (sub_nonneg_of_le (Int.ofNat_le_ofNat_of_le zw))
       refine Int.le_of_ofNat_le_ofNat (le_of_sub_nonneg ?_)
-      convert this using 1
+      convert! this using 1
       simp only [one_mul, Int.natCast_add, Int.natCast_mul]
       ring
 
diff --git a/Mathlib/Order/Antisymmetrization.lean b/Mathlib/Order/Antisymmetrization.lean
index 5dec6e53ca0e48..b978a8279572cb 100644
--- a/Mathlib/Order/Antisymmetrization.lean
+++ b/Mathlib/Order/Antisymmetrization.lean
@@ -294,7 +294,7 @@ set_option backward.isDefEq.respectTransparency false in
 theorem wellFoundedGT_antisymmetrization_iff :
     WellFoundedGT (Antisymmetrization α (· ≤ ·)) ↔ WellFoundedGT α := by
   simp_rw [isWellFounded_iff]
-  convert wellFounded_liftOn₂'_iff with ⟨_⟩ ⟨_⟩
+  convert! wellFounded_liftOn₂'_iff with ⟨_⟩ ⟨_⟩
   exact fun _ _ _ _ h₁ h₂ ↦ propext
     ⟨fun h ↦ (h₂.2.trans_lt h).trans_le h₁.1, fun h ↦ (h₂.1.trans_lt h).trans_le h₁.2⟩
 
diff --git a/Mathlib/Order/Atoms.lean b/Mathlib/Order/Atoms.lean
index 7ec8aa336b79cb..aec6767d9b4053 100644
--- a/Mathlib/Order/Atoms.lean
+++ b/Mathlib/Order/Atoms.lean
@@ -1179,7 +1179,7 @@ theorem ComplementedLattice.isStronglyAtomic [IsAtomic α] : IsStronglyAtomic α
     · obtain rfl : a = b := by simpa [codisjoint_bot, ← Subtype.coe_inj] using ha'.codisjoint
       exact False.elim <| hab.ne rfl
     refine ⟨d ⊔ a, IsUpperModularLattice.covBy_sup_of_inf_covBy ?_, sup_le (hd.2.trans ha'b) hab.le⟩
-    convert hd.1.bot_covBy
+    convert! hd.1.bot_covBy
     rw [← le_bot_iff, ← show a ⊓ a' = ⊥ by simpa using Subtype.coe_inj.2 ha'.inf_eq_bot, inf_comm]
     exact inf_le_inf_left _ hd.2
 
diff --git a/Mathlib/Order/Basic.lean b/Mathlib/Order/Basic.lean
index 3c46756ef31e9f..10104887c9910d 100644
--- a/Mathlib/Order/Basic.lean
+++ b/Mathlib/Order/Basic.lean
@@ -527,7 +527,7 @@ theorem compl_gt [LinearOrder α] : (· > · : α → α → _)ᶜ = (· ≤ ·)
 theorem compl_ge [LinearOrder α] : (· ≥ · : α → α → _)ᶜ = (· < ·) := by simp [compl]
 
 instance Ne.instIsEquiv_compl : IsEquiv α (· ≠ ·)ᶜ := by
-  convert eq_isEquiv α
+  convert! eq_isEquiv α
   simp [compl]
 
 /-! ### Order instances on the function space -/
diff --git a/Mathlib/Order/Bounded.lean b/Mathlib/Order/Bounded.lean
index dddc3d771498da..6e767eb5a7a504 100644
--- a/Mathlib/Order/Bounded.lean
+++ b/Mathlib/Order/Bounded.lean
@@ -285,7 +285,7 @@ theorem bounded_le_inter_lt [LinearOrder α] (a : α) :
 
 theorem unbounded_le_inter_lt [LinearOrder α] (a : α) :
     Unbounded (· ≤ ·) (s ∩ { b | a < b }) ↔ Unbounded (· ≤ ·) s := by
-  convert @unbounded_le_inter_not_le _ s _ a
+  convert! @unbounded_le_inter_not_le _ s _ a
   exact lt_iff_not_ge
 
 theorem bounded_le_inter_le [LinearOrder α] (a : α) :
@@ -313,12 +313,12 @@ theorem unbounded_lt_inter_not_lt [SemilatticeSup α] (a : α) :
 
 theorem bounded_lt_inter_le [LinearOrder α] (a : α) :
     Bounded (· < ·) (s ∩ { b | a ≤ b }) ↔ Bounded (· < ·) s := by
-  convert @bounded_lt_inter_not_lt _ s _ a
+  convert! @bounded_lt_inter_not_lt _ s _ a
   exact not_lt.symm
 
 theorem unbounded_lt_inter_le [LinearOrder α] (a : α) :
     Unbounded (· < ·) (s ∩ { b | a ≤ b }) ↔ Unbounded (· < ·) s := by
-  convert @unbounded_lt_inter_not_lt _ s _ a
+  convert! @unbounded_lt_inter_not_lt _ s _ a
   exact not_lt.symm
 
 theorem bounded_lt_inter_lt [LinearOrder α] [NoMaxOrder α] (a : α) :
diff --git a/Mathlib/Order/CompleteLattice/Basic.lean b/Mathlib/Order/CompleteLattice/Basic.lean
index 3d52bcf1010ffc..b517fcbc73ac36 100644
--- a/Mathlib/Order/CompleteLattice/Basic.lean
+++ b/Mathlib/Order/CompleteLattice/Basic.lean
@@ -186,7 +186,7 @@ theorem Equiv.iSup_comp {g : ι' → α} (e : ι ≃ ι') : ⨆ x, g (e x) = ⨆
 @[to_dual]
 protected theorem Function.Surjective.iSup_congr {g : ι' → α} (h : ι → ι') (h1 : Surjective h)
     (h2 : ∀ x, g (h x) = f x) : ⨆ x, f x = ⨆ y, g y := by
-  convert h1.iSup_comp g
+  convert! h1.iSup_comp g
   exact (h2 _).symm
 
 @[to_dual]
@@ -661,7 +661,7 @@ theorem iSup_split (f : β → α) (p : β → Prop) :
 
 @[to_dual]
 theorem iSup_split_single (f : β → α) (i₀ : β) : ⨆ i, f i = f i₀ ⊔ ⨆ (i) (_ : i ≠ i₀), f i := by
-  convert iSup_split f (fun i => i = i₀)
+  convert! iSup_split f (fun i => i = i₀)
   simp
 
 @[to_dual]
diff --git a/Mathlib/Order/ConditionallyCompleteLattice/Indexed.lean b/Mathlib/Order/ConditionallyCompleteLattice/Indexed.lean
index 8842e00b5713c9..a6924bdcf33a1c 100644
--- a/Mathlib/Order/ConditionallyCompleteLattice/Indexed.lean
+++ b/Mathlib/Order/ConditionallyCompleteLattice/Indexed.lean
@@ -347,12 +347,12 @@ theorem csInf_image {s : Set β} {f : β → α}
 
 theorem cbiSup_id {s : Set α} (hs : BddAbove s) (h : sSup ∅ ≤ sSup s) : ⨆ i ∈ s, i = sSup s := by
   rw [← csSup_image (Subtype.range_coe ▸ hs), Set.image_id']
-  · convert h
+  · convert! h
     rw [← sSup_range, Subtype.range_coe]
 
 theorem cbiInf_id {s : Set α} (hs : BddBelow s) (h : sInf s ≤ sInf ∅) : ⨅ i ∈ s, i = sInf s := by
   rw [← csInf_image (Subtype.range_coe ▸ hs), Set.image_id']
-  · convert h
+  · convert! h
     rw [← sInf_range, Subtype.range_coe]
 
 lemma ciSup_image {ι ι' : Type*} {s : Set ι} {f : ι → ι'} {g : ι' → α}
diff --git a/Mathlib/Order/Cover.lean b/Mathlib/Order/Cover.lean
index b028c0d19d901e..181fc3bf111482 100644
--- a/Mathlib/Order/Cover.lean
+++ b/Mathlib/Order/Cover.lean
@@ -466,7 +466,7 @@ variable {s t : Set α} {a : α}
 
 @[simp] lemma sdiff_singleton_wcovBy (s : Set α) (a : α) : s \ {a} ⩿ s := by
   by_cases ha : a ∈ s
-  · convert wcovBy_insert a _
+  · convert! wcovBy_insert a _
     ext
     simp [ha]
   · simp [ha]
diff --git a/Mathlib/Order/Filter/AtTopBot/Defs.lean b/Mathlib/Order/Filter/AtTopBot/Defs.lean
index e3c5c9422c1d28..bd4d65103d96bd 100644
--- a/Mathlib/Order/Filter/AtTopBot/Defs.lean
+++ b/Mathlib/Order/Filter/AtTopBot/Defs.lean
@@ -122,6 +122,6 @@ theorem Antitone.piecewise_eventually_eq_iInter {β : α → Type*} [Preorder ι
     (hs : Antitone s) (f g : (a : α) → β a) (a : α) :
     ∀ᶠ i in atTop, (s i).piecewise f g a = (⋂ i, s i).piecewise f g a := by
   classical
-  convert ← (compl_anti.comp hs).piecewise_eventually_eq_iUnion g f a using 3
-  · convert congr_fun (Set.piecewise_compl (s _) g f) a
+  convert! ← (compl_anti.comp hs).piecewise_eventually_eq_iUnion g f a using 3
+  · convert! congr_fun (Set.piecewise_compl (s _) g f) a
   · simp only [(· ∘ ·), ← compl_iInter, Set.piecewise_compl]
diff --git a/Mathlib/Order/Filter/Bases/Basic.lean b/Mathlib/Order/Filter/Bases/Basic.lean
index 1e4c67fe5ea543..e1eebb40d3032b 100644
--- a/Mathlib/Order/Filter/Bases/Basic.lean
+++ b/Mathlib/Order/Filter/Bases/Basic.lean
@@ -768,7 +768,7 @@ theorem map_sigma_mk_comap {π : α → Type*} {π' : β → Type*} {f : α →
     (hf : Function.Injective f) (g : ∀ a, π a → π' (f a)) (a : α) (l : Filter (π' (f a))) :
     map (Sigma.mk a) (comap (g a) l) = comap (Sigma.map f g) (map (Sigma.mk (f a)) l) := by
   refine (((basis_sets _).comap _).map _).eq_of_same_basis ?_
-  convert ((basis_sets l).map (Sigma.mk (f a))).comap (Sigma.map f g)
+  convert! ((basis_sets l).map (Sigma.mk (f a))).comap (Sigma.map f g)
   apply image_sigmaMk_preimage_sigmaMap hf
 
 end Filter
diff --git a/Mathlib/Order/Filter/CountablyGenerated.lean b/Mathlib/Order/Filter/CountablyGenerated.lean
index 5edae09f216ec0..acc28986485df4 100644
--- a/Mathlib/Order/Filter/CountablyGenerated.lean
+++ b/Mathlib/Order/Filter/CountablyGenerated.lean
@@ -128,7 +128,7 @@ theorem HasBasis.exists_antitone_subbasis {f : Filter α} [h : f.IsCountablyGene
     exacts [hs.set_index_subset _, (hs.set_index_subset _).trans inter_subset_left]
   refine ⟨fun i => (x i).1, fun i => (x i).2, ?_⟩
   have : (⨅ i, 𝓟 (s (x i).1)).HasAntitoneBasis fun i => s (x i).1 := .iInf_principal x_anti
-  convert this
+  convert! this
   exact
     le_antisymm (le_iInf fun i => le_principal_iff.2 <| by cases i <;> apply hs.set_index_mem)
       (hx'.symm ▸
diff --git a/Mathlib/Order/Filter/ENNReal.lean b/Mathlib/Order/Filter/ENNReal.lean
index ef750e24b29954..63cb8665190c29 100644
--- a/Mathlib/Order/Filter/ENNReal.lean
+++ b/Mathlib/Order/Filter/ENNReal.lean
@@ -30,7 +30,7 @@ lemma limsSup_of_not_isCobounded {f : Filter ℝ} (hf : ¬ f.IsCobounded (· ≤
 @[simp]
 lemma limsSup_of_not_isBounded {f : Filter ℝ} (hf : ¬ f.IsBounded (· ≤ ·)) : limsSup f = 0 := by
   rw [limsSup]
-  convert sInf_empty
+  convert! sInf_empty
   simpa [Set.eq_empty_iff_forall_notMem, IsBounded] using hf
 
 @[simp]
@@ -40,7 +40,7 @@ lemma limsInf_of_not_isCobounded {f : Filter ℝ} (hf : ¬ f.IsCobounded (· ≥
 @[simp]
 lemma limsInf_of_not_isBounded {f : Filter ℝ} (hf : ¬ f.IsBounded (· ≥ ·)) : limsInf f = 0 := by
   rw [limsInf]
-  convert sSup_empty
+  convert! sSup_empty
   simpa [Set.eq_empty_iff_forall_notMem, IsBounded] using hf
 
 @[simp]
@@ -108,7 +108,7 @@ variable {ι : Type*} {f : Filter ι} {u : ι → ℝ≥0}
 @[simp]
 lemma limsSup_of_not_isBounded {f : Filter ℝ≥0} (hf : ¬ f.IsBounded (· ≤ ·)) : limsSup f = 0 := by
   rw [limsSup, ← bot_eq_zero]
-  convert sInf_empty
+  convert! sInf_empty
   simpa [Set.eq_empty_iff_forall_notMem, IsBounded] using hf
 
 @[simp]
diff --git a/Mathlib/Order/Filter/Partial.lean b/Mathlib/Order/Filter/Partial.lean
index a6fa69affb6448..1b50ff84afc531 100644
--- a/Mathlib/Order/Filter/Partial.lean
+++ b/Mathlib/Order/Filter/Partial.lean
@@ -64,7 +64,7 @@ def rmap (r : SetRel α β) (l : Filter α) : Filter β where
   sets_of_superset hs st := mem_of_superset hs (SetRel.core_mono st)
   inter_sets hs ht := by
     simp only [Set.mem_setOf_eq]
-    convert inter_mem hs ht
+    convert! inter_mem hs ht
     rw [← SetRel.core_inter]
 
 theorem rmap_sets (r : SetRel α β) (l : Filter α) : (l.rmap r).sets = r.core ⁻¹' l.sets :=
diff --git a/Mathlib/Order/Filter/Pointwise.lean b/Mathlib/Order/Filter/Pointwise.lean
index 8d16d89bd46af0..bfe4f7a6c88cfa 100644
--- a/Mathlib/Order/Filter/Pointwise.lean
+++ b/Mathlib/Order/Filter/Pointwise.lean
@@ -1134,7 +1134,7 @@ theorem NeBot.zero_smul_nonneg (hg : g.NeBot) : 0 ≤ (0 : Filter α) • g :=
 
 theorem zero_smul_filter_nonpos : (0 : α) • g ≤ 0 := by
   refine fun s hs => mem_smul_filter.2 ?_
-  convert @univ_mem _ g
+  convert! @univ_mem _ g
   refine eq_univ_iff_forall.2 fun a => ?_
   rwa [mem_preimage, zero_smul]
 
diff --git a/Mathlib/Order/Filter/Prod.lean b/Mathlib/Order/Filter/Prod.lean
index 36251aa68c6603..e068ba7e67dc21 100644
--- a/Mathlib/Order/Filter/Prod.lean
+++ b/Mathlib/Order/Filter/Prod.lean
@@ -501,7 +501,8 @@ theorem map_prodMap_coprod_le.{u, v, w, x} {α₁ : Type u} {α₂ : Type v} {β
   intro s
   simp only [mem_map, mem_coprod_iff]
   rintro ⟨⟨u₁, hu₁, h₁⟩, u₂, hu₂, h₂⟩
-  refine ⟨⟨m₁ ⁻¹' u₁, hu₁, fun _ hx => h₁ ?_⟩, ⟨m₂ ⁻¹' u₂, hu₂, fun _ hx => h₂ ?_⟩⟩ <;> convert hx
+  refine ⟨⟨m₁ ⁻¹' u₁, hu₁, fun _ hx => h₁ ?_⟩, ⟨m₂ ⁻¹' u₂, hu₂, fun _ hx => h₂ ?_⟩⟩ <;> convert!
+    hx
 
 /-- Characterization of the coproduct of the `Filter.map`s of two principal filters `𝓟 {a}` and
 `𝓟 {i}`, the first under the constant function `fun a => b` and the second under the identity
diff --git a/Mathlib/Order/Filter/SmallSets.lean b/Mathlib/Order/Filter/SmallSets.lean
index 1af9ebe8b506cb..41b1ae5bc04991 100644
--- a/Mathlib/Order/Filter/SmallSets.lean
+++ b/Mathlib/Order/Filter/SmallSets.lean
@@ -104,7 +104,7 @@ theorem frequently_smallSets_mem (l : Filter α) : ∃ᶠ s in l.smallSets, s 
 theorem frequently_smallSets' {α : Type*} {l : Filter α} {p : Set α → Prop}
     (hp : ∀ ⦃s t : Set α⦄, s ⊆ t → p s → p t) :
     (∃ᶠ s in l.smallSets, p s) ↔ ∀ t ∈ l, p t := by
-  convert not_iff_not.mpr <| l.eventually_smallSets' (p := (¬ p ·)) (by tauto)
+  convert! not_iff_not.mpr <| l.eventually_smallSets' (p := (¬p ·)) (by tauto)
   simp
 
 theorem HasBasis.frequently_smallSets {α : Type*} {ι : Sort*} {p : ι → Prop} {l : Filter α}
diff --git a/Mathlib/Order/Filter/Ultrafilter/Basic.lean b/Mathlib/Order/Filter/Ultrafilter/Basic.lean
index 14a988bb639b12..43971b62f5fbe5 100644
--- a/Mathlib/Order/Filter/Ultrafilter/Basic.lean
+++ b/Mathlib/Order/Filter/Ultrafilter/Basic.lean
@@ -42,7 +42,7 @@ theorem finite_biUnion_mem_iff {is : Set β} {s : β → Set α} (his : is.Finit
 lemma eventually_exists_mem_iff {is : Set β} {P : β → α → Prop} (his : is.Finite) :
     (∀ᶠ i in f, ∃ a ∈ is, P a i) ↔ ∃ a ∈ is, ∀ᶠ i in f, P a i := by
   simp only [Filter.Eventually, Ultrafilter.mem_coe]
-  convert f.finite_biUnion_mem_iff his (s := P) with i
+  convert! f.finite_biUnion_mem_iff his (s := P) with i
   aesop
 
 lemma eventually_exists_iff [Finite β] {P : β → α → Prop} :
diff --git a/Mathlib/Order/Filter/ZeroAndBoundedAtFilter.lean b/Mathlib/Order/Filter/ZeroAndBoundedAtFilter.lean
index bd4c16d95c3ae6..1ead326c8e6afe 100644
--- a/Mathlib/Order/Filter/ZeroAndBoundedAtFilter.lean
+++ b/Mathlib/Order/Filter/ZeroAndBoundedAtFilter.lean
@@ -101,7 +101,7 @@ theorem BoundedAtFilter.smul
 nonrec theorem BoundedAtFilter.mul [SeminormedRing β] {l : Filter α} {f g : α → β}
     (hf : BoundedAtFilter l f) (hg : BoundedAtFilter l g) : BoundedAtFilter l (f * g) := by
   refine (hf.mul hg).trans ?_
-  convert Asymptotics.isBigO_refl (E := ℝ) _ l
+  convert! Asymptotics.isBigO_refl (E := ℝ) _ l
   simp
 
 theorem ZeroAtFilter.mul_boundedAtFilter [SeminormedRing β] {l : Filter α}
diff --git a/Mathlib/Order/Hom/Basic.lean b/Mathlib/Order/Hom/Basic.lean
index ee9ea3256f292b..e2b2ed52abb9a1 100644
--- a/Mathlib/Order/Hom/Basic.lean
+++ b/Mathlib/Order/Hom/Basic.lean
@@ -189,7 +189,7 @@ variable [LE α] [LE β] [EquivLike F α β] [OrderIsoClass F α β]
 
 @[to_dual (attr := simp) le_map_inv_iff]
 theorem map_inv_le_iff (f : F) {a : α} {b : β} : EquivLike.inv f b ≤ a ↔ b ≤ f a := by
-  convert (map_le_map_iff f).symm
+  convert! (map_le_map_iff f).symm
   exact (EquivLike.right_inv f _).symm
 
 @[to_dual self]
@@ -1068,7 +1068,7 @@ def ofCmpEqCmp {α β} [LinearOrder α] [LinearOrder β] (f : α → β) (g : β
     map_rel_iff' := by
       intro a b
       apply le_iff_le_of_cmp_eq_cmp
-      convert (h a (f b)).symm
+      convert! (h a (f b)).symm
       apply gf }
 
 /-- To show that `f : α →o β` and `g : β →o α` make up an order isomorphism it is enough to show
diff --git a/Mathlib/Order/Interval/Finset/Gaps.lean b/Mathlib/Order/Interval/Finset/Gaps.lean
index 822123c9bad279..921d06491ca0b7 100644
--- a/Mathlib/Order/Interval/Finset/Gaps.lean
+++ b/Mathlib/Order/Interval/Finset/Gaps.lean
@@ -78,7 +78,7 @@ theorem intervalGapsWithin_succ_fst_of_lt (hj : j < k) :
 
 theorem intervalGapsWithin_fst_of_lt_lt (hj₁ : 0 < j) (hj₂ : j - 1 < k) :
     (F.intervalGapsWithin h a b j).1 = (F.orderEmbOfFin (α := α ×ₗ α) h ⟨j - 1, hj₂⟩).2 := by
-  convert F.intervalGapsWithin_succ_fst_of_lt h a b (j - 1) hj₂
+  convert! F.intervalGapsWithin_succ_fst_of_lt h a b (j - 1) hj₂
   omega
 
 @[simp]
@@ -101,7 +101,7 @@ theorem intervalGapsWithin_mapsTo : (Set.Iio k).MapsTo
   rw [mem_Iio] at hj
   simp only [intervalGapsWithin_snd_of_lt, intervalGapsWithin_succ_fst_of_lt,
     Prod.mk.eta, SetLike.mem_coe, hj]
-  convert F.orderEmbOfFin_mem h ⟨j, hj⟩ using 1
+  convert! F.orderEmbOfFin_mem h ⟨j, hj⟩ using 1
 
 theorem intervalGapsWithin_injOn : (Set.Iio k).InjOn
     (fun (j : ℕ) ↦ ((F.intervalGapsWithin h a b j).2, (F.intervalGapsWithin h a b j.succ).1)) := by
@@ -147,7 +147,7 @@ theorem intervalGapsWithin_fst_le_snd {a b : α} (hab : a ≤ b)
     (hF : (SetLike.coe F).PairwiseDisjoint (fun z ↦ Set.Icc z.1 z.2)) :
     (F.intervalGapsWithin h a b j).1 ≤ (F.intervalGapsWithin h a b j).2 := by
   wlog hj : j < k + 1 generalizing j
-  · convert this (j : Fin (k + 1)) (by grind) using 3 <;> grind [cast_val_eq_self]
+  · convert! this (j : Fin (k + 1)) (by grind) using 3 <;> grind [cast_val_eq_self]
   by_cases hj₁ : j = 0
   · simp only [hj₁]
     by_cases hk : 0 = k
@@ -157,8 +157,7 @@ theorem intervalGapsWithin_fst_le_snd {a b : α} (hab : a ≤ b)
   have hk : k - 1 + 1 = k := by omega
   by_cases hj₂ : j = k
   · simp only [hj₂, natCast_eq_last, intervalGapsWithin_last_snd, ge_iff_le]
-    convert hFab (F.intervalGapsWithin_mapsTo h a b (x := j - 1) (by grind)) |>.right.right
-      using 1
+    convert! hFab (F.intervalGapsWithin_mapsTo h a b (x := j - 1) (by grind)) |>.right.right using 1
     simp [hj₂, hk]
   rw [intervalGapsWithin_fst_of_lt_lt (hj₁ := by omega) (hj₂ := by omega),
       intervalGapsWithin_snd_of_lt (hj := by omega)]
diff --git a/Mathlib/Order/Interval/Finset/Nat.lean b/Mathlib/Order/Interval/Finset/Nat.lean
index ae335b6fc60d68..1430402996192c 100644
--- a/Mathlib/Order/Interval/Finset/Nat.lean
+++ b/Mathlib/Order/Interval/Finset/Nat.lean
@@ -197,7 +197,7 @@ open Multiset
 
 theorem multiset_Ico_map_mod (n a : ℕ) :
     (Multiset.Ico n (n + a)).map (· % a) = Multiset.range a := by
-  convert congr_arg Finset.val (image_Ico_mod n a)
+  convert! congr_arg Finset.val (image_Ico_mod n a)
   refine ((nodup_map_iff_inj_on (Finset.Ico _ _).nodup).2 <| ?_).dedup.symm
   exact mod_injOn_Ico _ _
 
@@ -232,7 +232,7 @@ theorem range_image_pred_top_sub (n : ℕ) :
 
 theorem range_add_eq_union : range (a + b) = range a ∪ (range b).map (addLeftEmbedding a) := by
   simp_rw [Finset.range_eq_Ico, map_eq_image]
-  convert (Ico_union_Ico_eq_Ico a.zero_le (a.le_add_right b)).symm
+  convert! (Ico_union_Ico_eq_Ico a.zero_le (a.le_add_right b)).symm
   ext x
   simp only [Ico_zero_eq_range, mem_image, mem_range, addLeftEmbedding_apply, mem_Ico]
   constructor
@@ -284,7 +284,7 @@ theorem Nat.cauchy_induction_mul (h : ∀ (n : ℕ), P (n + 1) → P n) (k seed
     (hs : P seed.succ) (hm : ∀ x, seed < x → P x → P (k * x)) (n : ℕ) : P n := by
   apply Nat.cauchy_induction h _ hs (k * ·) fun x hl hP => ⟨_, hm x hl hP⟩
   intro _ hl _
-  convert (Nat.mul_lt_mul_right <| seed.succ_pos.trans_le hl).2 hk
+  convert! (Nat.mul_lt_mul_right <| seed.succ_pos.trans_le hl).2 hk
   rw [one_mul]
 
 theorem Nat.cauchy_induction_two_mul (h : ∀ n, P (n + 1) → P n) (seed : ℕ) (hs : P seed.succ)
diff --git a/Mathlib/Order/Interval/Set/LinearOrder.lean b/Mathlib/Order/Interval/Set/LinearOrder.lean
index fb80627759f72c..8f3a7deda88e1f 100644
--- a/Mathlib/Order/Interval/Set/LinearOrder.lean
+++ b/Mathlib/Order/Interval/Set/LinearOrder.lean
@@ -67,7 +67,7 @@ theorem Ico_subset_Ico_iff (h₁ : a₁ < b₁) : Ico a₁ b₁ ⊆ Ico a₂ b
     fun ⟨h₁, h₂⟩ => Ico_subset_Ico h₁ h₂⟩
 
 theorem Ioc_subset_Ioc_iff (h₁ : a₁ < b₁) : Ioc a₁ b₁ ⊆ Ioc a₂ b₂ ↔ b₁ ≤ b₂ ∧ a₂ ≤ a₁ := by
-  convert @Ico_subset_Ico_iff αᵒᵈ _ b₁ b₂ a₁ a₂ h₁ using 2 <;> exact (@Ico_toDual α _ _ _).symm
+  convert! @Ico_subset_Ico_iff αᵒᵈ _ b₁ b₂ a₁ a₂ h₁ using 2 <;> exact (@Ico_toDual α _ _ _).symm
 
 theorem Ico_eq_Ico_iff (h : a < b ∨ c < d) : Ico a b = Ico c d ↔ a = c ∧ b = d := by
   refine ⟨fun h ↦ ?_, by grind⟩
diff --git a/Mathlib/Order/IsNormal.lean b/Mathlib/Order/IsNormal.lean
index df523f0f92b52c..c690cd0d653863 100644
--- a/Mathlib/Order/IsNormal.lean
+++ b/Mathlib/Order/IsNormal.lean
@@ -128,7 +128,7 @@ theorem map_sSup (hf : IsNormal f) {s : Set α} (hs : s.Nonempty) (hs' : BddAbov
 theorem map_iSup {ι} [Nonempty ι] {g : ι → α} (hf : IsNormal f) (hg : BddAbove (range g)) :
     f (⨆ i, g i) = ⨆ i, f (g i) := by
   unfold iSup
-  convert map_sSup hf (range_nonempty g) hg
+  convert! map_sSup hf (range_nonempty g) hg
   ext
   simp
 
@@ -174,7 +174,7 @@ variable [ConditionallyCompleteLinearOrderBot α] [ConditionallyCompleteLinearOr
 
 theorem apply_of_isSuccLimit (hf : IsNormal f) (ha : IsSuccLimit a) :
     f a = ⨆ b : Iio a, f b := by
-  convert map_iSup hf _
+  convert! map_iSup hf _
   · exact ha.iSup_Iio.symm
   · exact ⟨⊥, ha.bot_lt⟩
   · use a
@@ -214,7 +214,7 @@ theorem ext_iff [OrderBot α] {g : α → β} (hf : IsNormal f) (hg : IsNormal g
   | succ a ha IH => exact H₂ a IH
   | isSuccLimit a ha IH =>
     apply (hf.isLUB_image_Iio_of_isSuccLimit ha).unique
-    convert hg.isLUB_image_Iio_of_isSuccLimit ha using 1
+    convert! hg.isLUB_image_Iio_of_isSuccLimit ha using 1
     aesop
 
 @[deprecated (since := "2026-03-22")] protected alias ext := IsNormal.ext_iff
diff --git a/Mathlib/Order/JordanHolder.lean b/Mathlib/Order/JordanHolder.lean
index 386ead23f835e6..68e4129d5e103f 100644
--- a/Mathlib/Order/JordanHolder.lean
+++ b/Mathlib/Order/JordanHolder.lean
@@ -225,7 +225,7 @@ theorem isMaximal_eraseLast_last {s : CompositionSeries X} (h : 0 < s.length) :
   rw [last_eraseLast, last]
   have := s.step ⟨s.length - 1, by lia⟩
   simp only [Fin.castSucc_mk, Fin.succ_mk, mem_setOf_eq] at this
-  convert this using 3
+  convert! this using 3
   exact (tsub_add_cancel_of_le h).symm
 
 theorem eq_snoc_eraseLast {s : CompositionSeries X} (h : 0 < s.length) :
diff --git a/Mathlib/Order/KonigLemma.lean b/Mathlib/Order/KonigLemma.lean
index 92715e3acab857..a3817edf8f0d0b 100644
--- a/Mathlib/Order/KonigLemma.lean
+++ b/Mathlib/Order/KonigLemma.lean
@@ -149,7 +149,7 @@ theorem exists_seq_forall_proj_of_forall_finite {α : ℕ → Type*} [Finite (α
   have hr : ∀ i, (f i).1 = i :=
     Nat.rec (by rw [hf0, ha₀]) (fun i ih ↦ by rw [← (hcovby.1 (hf i)).2, ih])
   refine ⟨fun i ↦ by rw [← hr i]; exact (f i).2, fun i j hij ↦ ?_⟩
-  convert (f.monotone hij).2 <;>
+  convert! (f.monotone hij).2 <;>
   simp [hr]
 
 end Graded
diff --git a/Mathlib/Order/KrullDimension.lean b/Mathlib/Order/KrullDimension.lean
index 18591ad64e251a..f30bd8ba15a6d6 100644
--- a/Mathlib/Order/KrullDimension.lean
+++ b/Mathlib/Order/KrullDimension.lean
@@ -198,13 +198,13 @@ lemma length_le_height {p : LTSeries α} {x : α} (hlast : p.last ≤ x) :
   · let p' := p.eraseLast.snoc x (by
       apply lt_of_lt_of_le
       · apply p.step ⟨p.length - 1, by lia⟩
-      · convert hlast
+      · convert! hlast
         simp only [Fin.succ_mk, RelSeries.last, Fin.last]
         congr; lia)
     suffices p'.length ≤ height x by
       simp only [RelSeries.snoc_length, RelSeries.eraseLast_length, Nat.cast_add, ENat.coe_sub,
         Nat.cast_one, p'] at this
-      convert this
+      convert! this
       norm_cast
       lia
     refine le_iSup₂_of_le p' ?_ le_rfl
@@ -456,7 +456,7 @@ element.
 -/
 lemma coheight_eq_top_iff {x : α} :
     coheight x = ⊤ ↔ ∀ n, ∃ p : LTSeries α, p.head = x ∧ p.length = n := by
-  convert height_eq_top_iff (α := αᵒᵈ) (x := x) using 2 with n
+  convert! height_eq_top_iff (α := αᵒᵈ) (x := x) using 2 with n
   constructor <;> (intro ⟨p, hp, hl⟩; use p.reverse; constructor <;> simpa)
 
 /-- The elements of height zero are the minimal elements. -/
diff --git a/Mathlib/Order/Minimal.lean b/Mathlib/Order/Minimal.lean
index 29808e0fb325f4..7257dc28c52193 100644
--- a/Mathlib/Order/Minimal.lean
+++ b/Mathlib/Order/Minimal.lean
@@ -514,7 +514,7 @@ namespace OrderIso
 @[to_dual]
 theorem image_setOf_minimal (f : α ≃o β) (P : α → Prop) :
     f '' {x | Minimal P x} = {x | Minimal (fun x ↦ P (f.symm x)) x} := by
-  convert _root_.image_monotone_setOf_minimal (f := f) (by simp [f.le_iff_le])
+  convert! _root_.image_monotone_setOf_minimal (f := f) (by simp [f.le_iff_le])
   aesop
 
 @[to_dual]
diff --git a/Mathlib/Order/Monotone/MonovaryOrder.lean b/Mathlib/Order/Monotone/MonovaryOrder.lean
index 415231ef56917d..9f5841320901e2 100644
--- a/Mathlib/Order/Monotone/MonovaryOrder.lean
+++ b/Mathlib/Order/Monotone/MonovaryOrder.lean
@@ -32,7 +32,7 @@ def MonovaryOrder (i j : ι) : Prop :=
 
 instance : IsStrictTotalOrder ι (MonovaryOrder f g) where
   toTrichotomous := Std.trichotomous_of_rel_or_eq_or_rel_swap fun {a b} ↦ by
-    convert trichotomous_of (Prod.Lex (· < ·) <| Prod.Lex (· < ·) WellOrderingRel) _ _
+    convert! trichotomous_of (Prod.Lex (· < ·) <| Prod.Lex (· < ·) WellOrderingRel) _ _
     · simp only [Prod.ext_iff, ← and_assoc, imp_and, iff_and_self]
       exact ⟨congr_arg _, congr_arg _⟩
     · infer_instance
diff --git a/Mathlib/Order/OmegaCompletePartialOrder.lean b/Mathlib/Order/OmegaCompletePartialOrder.lean
index 223e7b02ac66c9..6ce92605a5d426 100644
--- a/Mathlib/Order/OmegaCompletePartialOrder.lean
+++ b/Mathlib/Order/OmegaCompletePartialOrder.lean
@@ -286,7 +286,7 @@ lemma ωScottContinuous_iff_monotone_map_ωSup :
     ωScottContinuous f ↔ ∃ hf : Monotone f, ∀ c : Chain α, f (ωSup c) = ωSup (c.map ⟨f, hf⟩) := by
   refine ⟨fun hf ↦ ⟨hf.monotone, hf.map_ωSup⟩, ?_⟩
   intro hf _ ⟨c, hc⟩ _ _ _ hda
-  convert isLUB_range_ωSup (c.map { toFun := f, monotone' := hf.1 })
+  convert! isLUB_range_ωSup (c.map { toFun := f, monotone' := hf.1 })
   · simp [← hc, ← (Set.range_comp f ⇑c)]
   · rw [← hc] at hda
     rw [← hf.2 c, ωSup_eq_of_isLUB hda]
diff --git a/Mathlib/Order/OrderDual.lean b/Mathlib/Order/OrderDual.lean
index 6262bd76540bff..5526530a62c3c4 100644
--- a/Mathlib/Order/OrderDual.lean
+++ b/Mathlib/Order/OrderDual.lean
@@ -187,7 +187,7 @@ instance OrderDual.denselyOrdered (α : Type*) [LT α] [h : DenselyOrdered α] :
 
 @[simp]
 theorem denselyOrdered_orderDual [LT α] : DenselyOrdered αᵒᵈ ↔ DenselyOrdered α :=
-  ⟨by convert @OrderDual.denselyOrdered αᵒᵈ _, @OrderDual.denselyOrdered α _⟩
+  ⟨by convert! @OrderDual.denselyOrdered αᵒᵈ _, @OrderDual.denselyOrdered α _⟩
 
 /-! ### Pushing order definitions through `Equiv` -/
 
diff --git a/Mathlib/Order/OrderIsoNat.lean b/Mathlib/Order/OrderIsoNat.lean
index a8112739cb289f..aeb157c2b355e4 100644
--- a/Mathlib/Order/OrderIsoNat.lean
+++ b/Mathlib/Order/OrderIsoNat.lean
@@ -166,7 +166,7 @@ theorem exists_increasing_or_nonincreasing_subseq' (r : α → α → Prop) (f :
         simp only [bad, exists_prop, not_not, Set.mem_setOf_eq, not_forall] at h
         obtain ⟨n', hn1, hn2⟩ := h
         refine ⟨n + n' - n - m, by lia, ?_⟩
-        convert hn2
+        convert! hn2
         lia
       let g' : ℕ → ℕ := @Nat.rec (fun _ => ℕ) m fun n gn => Nat.find (h gn)
       exact
diff --git a/Mathlib/Order/PartialSups.lean b/Mathlib/Order/PartialSups.lean
index bc7425cb3c2e2d..a004355c112736 100644
--- a/Mathlib/Order/PartialSups.lean
+++ b/Mathlib/Order/PartialSups.lean
@@ -119,10 +119,10 @@ lemma partialSups_monotone (f : ι → α) :
 def partialSups.gi :
     GaloisInsertion (partialSups : (ι → α) → ι →o α) (↑) where
   choice f h :=
-    ⟨f, by convert (partialSups f).monotone using 1; exact (le_partialSups f).antisymm h⟩
+    ⟨f, by convert! (partialSups f).monotone using 1; exact (le_partialSups f).antisymm h⟩
   gc f g := by
     refine ⟨(le_partialSups f).trans, fun h ↦ ?_⟩
-    convert partialSups_mono h
+    convert! partialSups_mono h
     exact OrderHom.ext _ _ g.monotone.partialSups_eq.symm
   le_l_u f := le_partialSups f
   choice_eq f h := OrderHom.ext _ _ ((le_partialSups f).antisymm h)
diff --git a/Mathlib/Order/Partition/Finpartition.lean b/Mathlib/Order/Partition/Finpartition.lean
index 467bb5a44a75b6..0fc8a2a365f444 100644
--- a/Mathlib/Order/Partition/Finpartition.lean
+++ b/Mathlib/Order/Partition/Finpartition.lean
@@ -141,13 +141,13 @@ def map {β : Type*} [Lattice β] [OrderBot β] {a : α} (e : α ≃o β) (P : F
     have := P.supIndep hu hb (by simp [hbu]) (map_rel e.symm hx) ?_
     · rw [← e.symm.map_bot] at this
       exact e.symm.map_rel_iff.mp this
-    · convert e.symm.map_rel_iff.mpr hxu
+    · convert! e.symm.map_rel_iff.mpr hxu
       rw [map_finset_sup, sup_map]
       rfl
   sup_parts := by simp [← P.sup_parts]
   bot_notMem := by
     rw [mem_map_equiv]
-    convert P.bot_notMem
+    convert! P.bot_notMem
     exact e.symm.map_bot
 
 @[simp]
@@ -739,7 +739,7 @@ lemma exists_enumeration : ∃ f : s ≃ Σ t : P.parts, Fin #t.1,
   simp [equivSigmaParts, Equiv.sigmaCongr, Equiv.sigmaCongrLeft]
 
 theorem sum_card_parts : ∑ i ∈ P.parts, #i = #s := by
-  convert congr_arg Finset.card P.biUnion_parts
+  convert! congr_arg Finset.card P.biUnion_parts
   rw [card_biUnion P.supIndep.pairwiseDisjoint]
   rfl
 
diff --git a/Mathlib/Order/RelSeries.lean b/Mathlib/Order/RelSeries.lean
index 14132caa579bd6..9bb0aaf8eac96b 100644
--- a/Mathlib/Order/RelSeries.lean
+++ b/Mathlib/Order/RelSeries.lean
@@ -108,7 +108,7 @@ lemma toList_singleton (x : α) : (singleton r x).toList = [x] := by simp [toLis
 lemma isChain_toList (x : RelSeries r) : x.toList.IsChain (· ~[r] ·) := by
   simp_rw [List.isChain_iff_getElem, length_toList, add_lt_add_iff_right]
   intro i h
-  convert x.step ⟨i, by simpa [toList] using h⟩ <;> apply List.get_ofFn
+  convert! x.step ⟨i, by simpa [toList] using h⟩ <;> apply List.get_ofFn
 
 lemma toList_ne_nil (x : RelSeries r) : x.toList ≠ [] := fun m =>
   List.eq_nil_iff_forall_not_mem.mp m (x 0) <| List.mem_ofFn.mpr ⟨_, rfl⟩
@@ -210,7 +210,7 @@ theorem length_ne_zero [r.IsIrrefl] : s.length ≠ 0 ↔ {x | x ∈ s}.Nontrivia
   refine ⟨fun h ↦ ⟨s 0, by simp [mem_def], s 1, by simp [mem_def],
     fun rid ↦ r.irrefl (s 0) ?_⟩, length_ne_zero_of_nontrivial⟩
   nth_rw 2 [rid]
-  convert s.step ⟨0, by lia⟩
+  convert! s.step ⟨0, by lia⟩
   ext
   simpa [Nat.pos_iff_ne_zero]
 
@@ -296,10 +296,10 @@ def append (p q : RelSeries r) (connect : p.last ~[r] q.head) : RelSeries r wher
   step i := by
     obtain hi | rfl | hi :=
       lt_trichotomy i (Fin.castLE (by lia) (Fin.last _ : Fin (p.length + 1)))
-    · convert p.step ⟨i.1, hi⟩ <;> convert Fin.append_left p q _ <;> rfl
-    · convert connect
-      · convert Fin.append_left p q _
-      · convert Fin.append_right p q _; rfl
+    · convert! p.step ⟨i.1, hi⟩ <;> convert! Fin.append_left p q _ <;> rfl
+    · convert! connect
+      · convert! Fin.append_left p q _
+      · convert! Fin.append_right p q _; rfl
     · set x := _; set y := _
       change Fin.append p q x ~[r] Fin.append p q y
       have hx : x = Fin.natAdd _ ⟨i - (p.length + 1), Nat.sub_lt_left_of_lt_add hi <|
@@ -313,7 +313,7 @@ def append (p q : RelSeries r) (connect : p.last ~[r] q.head) : RelSeries r wher
           Nat.add_sub_cancel' <| le_of_lt (show p.length < i.1 from hi), add_comm]
         rfl
       rw [hx, Fin.append_right, hy, Fin.append_right]
-      convert q.step ⟨i - (p.length + 1), Nat.sub_lt_left_of_lt_add hi <| by lia⟩
+      convert! q.step ⟨i - (p.length + 1), Nat.sub_lt_left_of_lt_add hi <| by lia⟩
       rw [Fin.succ_mk, Nat.sub_eq_iff_eq_add (le_of_lt hi : p.length ≤ i),
         Nat.add_assoc _ 1, add_comm 1, Nat.sub_add_cancel]
       exact hi
@@ -325,7 +325,7 @@ lemma append_apply_left (p q : RelSeries r) (connect : p.last ~[r] q.head)
         = p i := by
   delta append
   simp only [Function.comp_apply]
-  convert Fin.append_left _ _ _
+  convert! Fin.append_left _ _ _
 
 lemma append_apply_right (p q : RelSeries r) (connect : p.last ~[r] q.head)
     (i : Fin (q.length + 1)) :
@@ -341,7 +341,7 @@ lemma append_apply_right (p q : RelSeries r) (connect : p.last ~[r] q.head)
 @[simp] lemma last_append (p q : RelSeries r) (connect : p.last ~[r] q.head) :
     (p.append q connect).last = q.last := by
   delta last
-  convert append_apply_right p q connect (Fin.last _)
+  convert! append_apply_right p q connect (Fin.last _)
   ext1
   dsimp
   lia
@@ -391,7 +391,7 @@ def insertNth (p : RelSeries r) (i : Fin p.length) (a : α)
   step m := by
     set x := _; set y := _; change x ~[r] y
     obtain hm | hm | hm := lt_trichotomy m.1 i.1
-    · convert p.step ⟨m, hm.trans i.2⟩
+    · convert! p.step ⟨m, hm.trans i.2⟩
       · change Fin.insertNth _ _ _ _ = _
         rw [Fin.insertNth_apply_below]
         pick_goal 2
@@ -407,14 +407,14 @@ def insertNth (p : RelSeries r) (i : Fin p.length) (a : α)
         pick_goal 2
         · change m.1 < i.1 + 1; exact hm ▸ lt_add_one _
         simp]
-      convert prev_connect
+      convert! prev_connect
       · ext; exact hm
       · change Fin.insertNth _ _ _ _ = _
         rw [show m.succ = i.succ.castSucc by ext; change _ + 1 = _ + 1; rw [hm],
           Fin.insertNth_apply_same]
     · rw [Nat.lt_iff_add_one_le, le_iff_lt_or_eq] at hm
       obtain hm | hm := hm
-      · convert p.step ⟨m.1 - 1, Nat.sub_lt_right_of_lt_add (by lia) m.2⟩
+      · convert! p.step ⟨m.1 - 1, Nat.sub_lt_right_of_lt_add (by lia) m.2⟩
         · change Fin.insertNth _ _ _ _ = _
           rw [Fin.insertNth_apply_above (h := hm)]
           aesop
@@ -425,7 +425,7 @@ def insertNth (p : RelSeries r) (i : Fin p.length) (a : α)
           simp only [Fin.pred_succ, eq_rec_constant, Fin.succ_mk]
           congr
           exact Fin.ext <| Eq.symm <| Nat.succ_pred_eq_of_pos (lt_trans (Nat.zero_lt_succ _) hm)
-      · convert connect_next
+      · convert! connect_next
         · change Fin.insertNth _ _ _ _ = _
           rw [show m.castSucc = i.succ.castSucc from Fin.ext hm.symm, Fin.insertNth_apply_same]
         · change Fin.insertNth _ _ _ _ = _
@@ -446,7 +446,7 @@ def reverse (p : RelSeries r) : RelSeries r.inv where
   step i := by
     rw [Function.comp_apply, Function.comp_apply, SetRel.mem_inv]
     have hi : i.1 + 1 ≤ p.length := by lia
-    convert p.step ⟨p.length - (i.1 + 1), Nat.sub_lt_self (by lia) hi⟩
+    convert! p.step ⟨p.length - (i.1 + 1), Nat.sub_lt_self (by lia) hi⟩
     · ext; simp
     · ext
       simp only [Fin.val_rev, Fin.val_castSucc, Fin.val_succ]
@@ -610,15 +610,16 @@ def inductionOn (motive : RelSeries r → Sort*)
   let this {n : ℕ} (heq : p.length = n) : motive p := by
     induction n generalizing p with
     | zero =>
-      convert singleton p.head
+      convert! singleton p.head
       ext n
       · exact heq
       simp [show n = 0 by lia, apply_zero]
     | succ d hd =>
       have lq := p.tail_length (heq ▸ d.zero_ne_add_one.symm)
       nth_rw 3 [heq] at lq
-      convert cons (p.tail (heq ▸ d.zero_ne_add_one.symm)) p.head
-        (p.3 ⟨0, heq ▸ d.zero_lt_succ⟩) (hd _ lq)
+      convert!
+        cons (p.tail (heq ▸ d.zero_ne_add_one.symm)) p.head (p.3 ⟨0, heq ▸ d.zero_lt_succ⟩)
+          (hd _ lq)
       exact (p.cons_self_tail (heq ▸ d.zero_ne_add_one.symm)).symm
   exact this rfl
 
@@ -645,7 +646,7 @@ def eraseLast (p : RelSeries r) : RelSeries r where
 lemma eraseLast_last_rel_last (p : RelSeries r) (h : p.length ≠ 0) :
     p.eraseLast.last ~[r] p.last := by
   simp only [last, Fin.last, eraseLast_length, eraseLast_toFun]
-  convert p.step ⟨p.length - 1, by lia⟩
+  convert! p.step ⟨p.length - 1, by lia⟩
   simp only [Fin.succ_mk]; lia
 
 @[simp]
@@ -674,15 +675,14 @@ def inductionOn' (motive : RelSeries r → Sort*)
   let this {n : ℕ} (heq : p.length = n) : motive p := by
     induction n generalizing p with
     | zero =>
-      convert singleton p.head
+      convert! singleton p.head
       ext n
       · exact heq
       · simp [show n = 0 by lia, apply_zero]
     | succ d hd =>
       have ne0 : p.length ≠ 0 := by simp [heq]
       have len : p.eraseLast.length = d := by simp [heq]
-      convert snoc p.eraseLast p.last (p.eraseLast_last_rel_last ne0)
-        (hd _ len)
+      convert! snoc p.eraseLast p.last (p.eraseLast_last_rel_last ne0) (hd _ len)
       exact (p.snoc_self_eraseLast ne0).symm
   exact this rfl
 
@@ -697,7 +697,7 @@ def smash (p q : RelSeries r) (connect : p.last = q.head) : RelSeries r where
   step := by
     apply Fin.addCases <;> intro i
     · simp_rw [Fin.castSucc_castAdd, Fin.addCases_left, Fin.succ_castAdd]
-      convert p.step i
+      convert! p.step i
       split_ifs with h
       · rw [Fin.addCases_right, h, ← last, connect, head]
       · apply Fin.addCases_left
@@ -760,7 +760,7 @@ def drop (p : RelSeries r) (i : Fin (p.length + 1)) : RelSeries r where
   length := p.length - i
   toFun := fun ⟨j, h⟩ => p.toFun ⟨j+i, by lia⟩
   step := fun ⟨j, h⟩ => by
-    convert p.step ⟨j+i.1, by lia⟩
+    convert! p.step ⟨j + i.1, by lia⟩
     simp only [Fin.succ_mk]; lia
 
 @[simp]
@@ -987,8 +987,8 @@ theorem exists_relSeries_covBy
         obtain rfl : m = 0 := by simpa [t₃] using (congr_arg Fin.val eq).trans_lt (i j).2
         cases (h (.last _)).ne' (h₂.symm.trans h₁)
     · refine funext (Fin.lastCases ?_ fun j ↦ ?_)
-      · convert h₂; simpa using RelSeries.last_smash ..
-      convert congr_fun ht j using 1
+      · convert! h₂; simpa using RelSeries.last_smash ..
+      convert! congr_fun ht j using 1
       simp [RelSeries.smash_castLE]
     all_goals simp [Fin.snoc, Fin.castPred_zero, hi₁]
 
diff --git a/Mathlib/Order/ScottContinuity/Prod.lean b/Mathlib/Order/ScottContinuity/Prod.lean
index bcafe902695ff0..9cf6a2830551bc 100644
--- a/Mathlib/Order/ScottContinuity/Prod.lean
+++ b/Mathlib/Order/ScottContinuity/Prod.lean
@@ -39,9 +39,9 @@ lemma ScottContinuousOn.fromProd [Preorder α] [Preorder β] [Preorder γ]
       rw [singleton_prod, image_image f (fun b ↦ (a, b))]
       exact h₁ _ (mem_image_of_mem (fun d ↦ Prod.snd '' d) hX) (Nonempty.image Prod.snd hd₁)
         (DirectedOn.snd hd₂) (isLUB_prod.mp hdp).2) _, Set.range]
-  convert (h₂ _
-    (mem_image_of_mem (fun d ↦ Prod.fst '' d) hX) (Nonempty.image Prod.fst hd₁) (DirectedOn.fst hd₂)
-    (isLUB_prod.mp hdp).1)
+  convert!
+    (h₂ _ (mem_image_of_mem (fun d ↦ Prod.fst '' d) hX) (Nonempty.image Prod.fst hd₁)
+      (DirectedOn.fst hd₂) (isLUB_prod.mp hdp).1)
   ext : 1
   simp_all only [Subtype.exists, mem_image, Prod.exists,
     exists_and_right, exists_eq_right, exists_prop, mem_setOf_eq]
diff --git a/Mathlib/Order/SuccPred/Archimedean.lean b/Mathlib/Order/SuccPred/Archimedean.lean
index d02c7abb73e983..c7d5e1091979b0 100644
--- a/Mathlib/Order/SuccPred/Archimedean.lean
+++ b/Mathlib/Order/SuccPred/Archimedean.lean
@@ -46,11 +46,11 @@ variable [Preorder α]
 
 -- `to_dual` cannot yet reorder arguments of arguments
 instance [SuccOrder α] [IsSuccArchimedean α] : IsPredArchimedean αᵒᵈ :=
-  ⟨fun {a b} h => by convert exists_succ_iterate_of_le h.ofDual⟩
+  ⟨fun {a b} h => by convert! exists_succ_iterate_of_le h.ofDual⟩
 
 @[to_dual existing]
 instance [PredOrder α] [IsPredArchimedean α] : IsSuccArchimedean αᵒᵈ :=
-  ⟨fun {a b} h => by convert exists_pred_iterate_of_le h.ofDual⟩
+  ⟨fun {a b} h => by convert! exists_pred_iterate_of_le h.ofDual⟩
 
 section SuccOrder
 
diff --git a/Mathlib/Order/SupIndep.lean b/Mathlib/Order/SupIndep.lean
index babe5b8e4aac5d..df95ae3e376f92 100644
--- a/Mathlib/Order/SupIndep.lean
+++ b/Mathlib/Order/SupIndep.lean
@@ -303,9 +303,9 @@ theorem sSupIndep_pair {a b : α} (hab : a ≠ b) :
   · intro h
     exact h.pairwiseDisjoint (mem_insert _ _) (mem_insert_of_mem _ (mem_singleton _)) hab
   · rintro h c ((rfl : c = a) | (rfl : c = b))
-    · convert h using 1
+    · convert! h using 1
       simp [hab, sSup_singleton]
-    · convert h.symm using 1
+    · convert! h.symm using 1
       simp [hab, sSup_singleton]
 
 include hs in
@@ -390,7 +390,7 @@ theorem iSupIndep_ne_bot :
   cases eq_or_ne (t i) ⊥ with
   | inl hi => simp [hi]
   | inr hi => ?_
-  convert h ⟨i, hi⟩
+  convert! h ⟨i, hi⟩
   have : ∀ j, ⨆ (_ : t j = ⊥), t j = ⊥ := fun j ↦ by simp only [iSup_eq_bot, imp_self]
   rw [iSup_split _ (fun j ↦ t j = ⊥), iSup_subtype]
   simp only [iSup_comm (ι' := _ ≠ i), this, ne_eq, sup_of_le_right, Subtype.mk.injEq, iSup_bot,
diff --git a/Mathlib/Order/SymmDiff.lean b/Mathlib/Order/SymmDiff.lean
index ab24456c535fd1..63d6ff5603f02b 100644
--- a/Mathlib/Order/SymmDiff.lean
+++ b/Mathlib/Order/SymmDiff.lean
@@ -190,7 +190,7 @@ theorem symmDiff_triangle : a ∆ c ≤ a ∆ b ⊔ b ∆ c := by
   rw [sup_comm (c \ b), sup_sup_sup_comm, symmDiff, symmDiff]
 
 theorem le_symmDiff_sup_right (a b : α) : a ≤ (a ∆ b) ⊔ b := by
-  convert symmDiff_triangle a b ⊥ <;> rw [symmDiff_bot]
+  convert! symmDiff_triangle a b ⊥ <;> rw [symmDiff_bot]
 
 theorem le_symmDiff_sup_left (a b : α) : b ≤ (a ∆ b) ⊔ a :=
   symmDiff_comm a b ▸ le_symmDiff_sup_right ..
diff --git a/Mathlib/Order/UpperLower/Basic.lean b/Mathlib/Order/UpperLower/Basic.lean
index 40edd3362a2d80..48c4788f45302f 100644
--- a/Mathlib/Order/UpperLower/Basic.lean
+++ b/Mathlib/Order/UpperLower/Basic.lean
@@ -47,7 +47,7 @@ theorem IsUpperSet.compl (hs : IsUpperSet s) : IsLowerSet sᶜ := fun _a _b h hb
 @[to_dual (attr := simp)]
 theorem isUpperSet_compl : IsUpperSet sᶜ ↔ IsLowerSet s :=
   ⟨fun h => by
-    convert h.compl
+    convert! h.compl
     rw [compl_compl], IsLowerSet.compl⟩
 
 @[to_dual]
diff --git a/Mathlib/Order/WellFoundedSet.lean b/Mathlib/Order/WellFoundedSet.lean
index a6494a349adfe4..e454a686884a8d 100644
--- a/Mathlib/Order/WellFoundedSet.lean
+++ b/Mathlib/Order/WellFoundedSet.lean
@@ -788,7 +788,7 @@ noncomputable def minBadSeqOfBadSeq (r : α → α → Prop) (rk : α → ℕ) (
     have h : ∃ (k : ℕ) (g : ℕ → α), (∀ m, m < n → f m = g m) ∧ IsBadSeq r s g ∧ rk (g n) = k :=
       ⟨_, f, fun _ _ => rfl, hf, rfl⟩
     obtain ⟨h1, h2, h3⟩ := Classical.choose_spec (Nat.find_spec h)
-    refine ⟨Classical.choose (Nat.find_spec h), h1, by convert h2, fun g hg1 hg2 con => ?_⟩
+    refine ⟨Classical.choose (Nat.find_spec h), h1, by convert! h2, fun g hg1 hg2 con => ?_⟩
     refine Nat.find_min h ?_ ⟨g, fun m mn => (h1 m mn).trans (hg1 m mn), con, rfl⟩
     rwa [← h3]
 
@@ -932,7 +932,7 @@ theorem WellFounded.prod_lex_of_wellFoundedOn_fiber (hα : WellFounded (rα on f
   obtain h' | h' := Prod.lex_iff.1 h
   · exact PSigma.Lex.left _ _ h'
   · dsimp only [InvImage, (· on ·)] at h' ⊢
-    convert PSigma.Lex.right (⟨_, c', rfl⟩ : range f) _ using 1; swap
+    convert! PSigma.Lex.right (⟨_, c', rfl⟩ : range f) _ using 1; swap
     exacts [⟨c, h'.1⟩, PSigma.subtype_ext (Subtype.ext h'.1) rfl, h'.2]
 
 theorem Set.WellFoundedOn.prod_lex_of_wellFoundedOn_fiber (hα : s.WellFoundedOn (rα on f))
@@ -957,7 +957,7 @@ theorem WellFounded.sigma_lex_of_wellFoundedOn_fiber (hι : WellFounded (rι on
   obtain h' | ⟨h', h''⟩ := Sigma.lex_iff.1 h
   · exact PSigma.Lex.left _ _ h'
   · dsimp only [InvImage, (· on ·)] at h' ⊢
-    convert PSigma.Lex.right (⟨_, c', rfl⟩ : range f) _ using 1; swap
+    convert! PSigma.Lex.right (⟨_, c', rfl⟩ : range f) _ using 1; swap
     · exact ⟨c, h'⟩
     · exact PSigma.subtype_ext (Subtype.ext h') rfl
     · dsimp only [Subtype.coe_mk, Subrel, Order.Preimage] at *
diff --git a/Mathlib/Probability/CentralLimitTheorem.lean b/Mathlib/Probability/CentralLimitTheorem.lean
index d191006467b698..312e75db6e0570 100644
--- a/Mathlib/Probability/CentralLimitTheorem.lean
+++ b/Mathlib/Probability/CentralLimitTheorem.lean
@@ -61,12 +61,12 @@ lemma tendsto_charFun_inv_sqrt_mul_pow {X : Ω → ℝ}
     have aux : (fun (n : ℕ) ↦ ‖(1 / n : ℂ)‖) = fun (n : ℕ) ↦ ‖(1 / n : ℝ)‖ := by simp
     rw [← Asymptotics.isLittleO_norm_right, aux, Asymptotics.isLittleO_norm_right]
     refine .of_const_mul_right (c := t ^ 2) ?_
-    convert this using 4 with n <;> norm_cast <;> simp [field]
+    convert! this using 4 with n <;> norm_cast <;> simp [field]
   have : Tendsto (fun (n : ℕ) ↦ (√n)⁻¹ * t) atTop (𝓝 0) := by
     rw [← zero_mul t]
     exact .mul_const t (tendsto_inv_atTop_zero.comp <| Real.tendsto_sqrt_atTop.comp <|
       tendsto_natCast_atTop_atTop)
-  convert (taylor_charFun_two hX h0 h1).comp_tendsto this using 2
+  convert! (taylor_charFun_two hX h0 h1).comp_tendsto this using 2
   simp
   ring
 
@@ -108,13 +108,13 @@ private theorem tendstoInDistribution_inv_sqrt_mul_var_mul_sum_sub
     rw [← Finset.sum_div, Finset.sum_sub_distrib]
     simp [field]
   simp_rw [this]
-  convert tendstoInDistribution_inv_sqrt_mul_sum hY ?_ ?_ ?_ ?_
+  convert! tendstoInDistribution_inv_sqrt_mul_sum hY ?_ ?_ ?_ ?_
   · rw [integral_div, integral_sub intX0 (by simp)]
     simp
   · simp only [Pi.pow_apply, div_pow]
     rw [integral_div, ← variance_eq_integral mX0, Real.sq_sqrt (variance_nonneg _ _), div_self hX]
   · exact hindep.comp (fun _ x ↦ (x - P[X 0]) / √Var[X 0; P]) (by fun_prop)
-  · convert fun n ↦ (hident n).comp (u := fun x ↦ (x - P[X 0]) / √Var[X 0; P]) (by fun_prop)
+  · convert! fun n ↦ (hident n).comp (u := fun x ↦ (x - P[X 0]) / √Var[X 0; P]) (by fun_prop)
 
 /-- **Central Limit Theorem:** Given a sequence of random variables `X : ℕ → Ω → ℝ` that are
 independent, identically distributed with mean `μ` and variance `v`, and a random variable
@@ -130,7 +130,7 @@ theorem tendstoInDistribution_inv_sqrt_mul_sum_sub
   obtain h | h := eq_or_ne Var[X 0; P] 0
   · have : ∀ᵐ ω ∂P, ∀ n, X n ω = P[X 0] := by
       refine ae_all_iff.2 fun n ↦ ?_
-      convert (ae_eq_integral_of_variance_eq_zero ((hident n).memLp_iff.2 hX)) ?_ using 3
+      convert! (ae_eq_integral_of_variance_eq_zero ((hident n).memLp_iff.2 hX)) ?_ using 3
       · rw [(hident n).integral_eq]
       · rwa [(hident n).variance_eq]
     have mX (n : ℕ) := (hident n).aemeasurable_fst
@@ -140,11 +140,12 @@ theorem tendstoInDistribution_inv_sqrt_mul_sum_sub
       simp [hω]
     · exact ⟨by fun_prop, by fun_prop, by simp [hY.map_eq, h]⟩
   have : HasLaw (fun ω ↦ Y ω / √Var[X 0; P]) (gaussianReal 0 1) P' := by
-    convert gaussianReal_div_const hY _
+    convert! gaussianReal_div_const hY _
     · simp
     · ext; simp [h]
-  convert (tendstoInDistribution_inv_sqrt_mul_var_mul_sum_sub this h hindep hident).continuous_comp
-    (g := (√Var[X 0; P] * ·)) (by fun_prop)
+  convert!
+    (tendstoInDistribution_inv_sqrt_mul_var_mul_sum_sub this h hindep hident).continuous_comp (g :=
+      (√Var[X 0; P] * ·)) (by fun_prop)
   · simp [field] -- simp [field, hX] triggers the unused simp arguments linter
     field_simp [h]
   · ext
diff --git a/Mathlib/Probability/ConditionalProbability.lean b/Mathlib/Probability/ConditionalProbability.lean
index a61d9e565115e8..434db885ddda22 100644
--- a/Mathlib/Probability/ConditionalProbability.lean
+++ b/Mathlib/Probability/ConditionalProbability.lean
@@ -228,7 +228,7 @@ theorem cond_inter_self (hms : MeasurableSet s) (t : Set Ω) (μ : Measure Ω) :
 theorem inter_pos_of_cond_ne_zero (hms : MeasurableSet s) (hcst : μ[t | s] ≠ 0) :
     0 < μ (s ∩ t) := by
   refine pos_iff_ne_zero.mpr (right_ne_zero_of_mul (a := (μ s)⁻¹) ?_)
-  convert hcst
+  convert! hcst
   simp [hms, Set.inter_comm, cond]
 
 lemma cond_pos_of_inter_ne_zero [IsFiniteMeasure μ] (hms : MeasurableSet s) (hci : μ (s ∩ t) ≠ 0) :
diff --git a/Mathlib/Probability/Distributions/Beta.lean b/Mathlib/Probability/Distributions/Beta.lean
index 6af08ef5c80c9a..04cc8de4a49590 100644
--- a/Mathlib/Probability/Distributions/Beta.lean
+++ b/Mathlib/Probability/Distributions/Beta.lean
@@ -118,10 +118,10 @@ lemma lintegral_betaPDF_eq_one {α β : ℝ} (hα : 0 < α) (hβ : 0 < β) :
       rw [← Complex.ofReal_cpow, ← Complex.ofReal_cpow, RCLike.re_to_complex,
         Complex.re_mul_ofReal, Complex.ofReal_re]
       all_goals linarith
-    convert betaIntegral_convergent (u := α) (v := β) (by simpa) (by simpa)
+    convert! betaIntegral_convergent (u := α) (v := β) (by simpa) (by simpa)
     rw [intervalIntegrable_iff_integrableOn_Ioc_of_le (by simp), IntegrableOn]
   · refine ae_restrict_of_forall_mem measurableSet_Ioo (fun x hx ↦ ?_)
-    convert betaPDFReal_pos hx.1 hx.2 hα hβ |>.le using 1
+    convert! betaPDFReal_pos hx.1 hx.2 hα hβ |>.le using 1
     rw [betaPDFReal, if_pos ⟨hx.1, hx.2⟩]
   · exact Measurable.aestronglyMeasurable (by fun_prop)
 
diff --git a/Mathlib/Probability/Distributions/Exponential.lean b/Mathlib/Probability/Distributions/Exponential.lean
index 904ca9b965e767..5f03844c8318b2 100644
--- a/Mathlib/Probability/Distributions/Exponential.lean
+++ b/Mathlib/Probability/Distributions/Exponential.lean
@@ -110,7 +110,7 @@ open Topology
 
 lemma hasDerivAt_neg_exp_mul_exp {r x : ℝ} :
     HasDerivAt (fun a ↦ -exp (-(r * a))) (r * exp (-(r * x))) x := by
-  convert (((hasDerivAt_id x).const_mul (-r)).exp.const_mul (-1)) using 1
+  convert! (((hasDerivAt_id x).const_mul (-r)).exp.const_mul (-1)) using 1
   · simp only [one_mul, id_eq, neg_mul]
   simp only [id_eq, neg_mul, mul_one, mul_neg, one_mul, neg_neg, mul_comm]
 
diff --git a/Mathlib/Probability/Distributions/Fernique.lean b/Mathlib/Probability/Distributions/Fernique.lean
index d27dc8a53cbf22..c8a13fc19931b0 100644
--- a/Mathlib/Probability/Distributions/Fernique.lean
+++ b/Mathlib/Probability/Distributions/Fernique.lean
@@ -180,7 +180,7 @@ lemma measure_le_mul_measure_gt_normThreshold_le_of_map_rotation_eq_self [SFinit
     (h_rot : (μ.prod μ).map (ContinuousLinearMap.rotation (-(π / 4))) = μ.prod μ) (a : ℝ) (n : ℕ) :
     μ {x | ‖x‖ ≤ a} * μ {x | normThreshold a (n + 1) < ‖x‖}
       ≤ μ {x | normThreshold a n < ‖x‖} ^ 2 := by
-  convert measure_le_mul_measure_gt_le_of_map_rotation_eq_self h_rot _ _
+  convert! measure_le_mul_measure_gt_le_of_map_rotation_eq_self h_rot _ _
   simp [normThreshold_add_one]
 
 lemma lt_normThreshold_zero (ha_pos : 0 < a) : a / (1 - √2) < normThreshold a 0 := by
@@ -364,7 +364,7 @@ lemma lintegral_closedBall_diff_exp_logRatio_mul_sq_le [IsProbabilityMeasure μ]
   _ ≤ .ofReal (rexp (2⁻¹ * Real.log (c.toReal / (1 - c).toReal) * 2 ^ n))
       * c * .ofReal (rexp (-Real.log (c / (1 - c)).toReal * 2 ^ n)) := by
     gcongr ENNReal.ofReal (rexp ?_) * _ * _
-    convert logRatio_mul_normThreshold_add_one_le ha_gt ha_lt n (a := a) using 1
+    convert! logRatio_mul_normThreshold_add_one_le ha_gt ha_lt n (a := a) using 1
     ring
   _ = c * .ofReal (rexp (-2⁻¹ * Real.log (c / (1 - c)).toReal * 2 ^ n)) := by
     rw [mul_comm _ c, mul_assoc, ← ENNReal.ofReal_mul (by positivity), ← Real.exp_add]
diff --git a/Mathlib/Probability/Distributions/Gaussian/Basic.lean b/Mathlib/Probability/Distributions/Gaussian/Basic.lean
index f810a25cb0141b..19eef22c3763a6 100644
--- a/Mathlib/Probability/Distributions/Gaussian/Basic.lean
+++ b/Mathlib/Probability/Distributions/Gaussian/Basic.lean
@@ -113,7 +113,7 @@ instance {x : E} : IsGaussian (Measure.dirac x) where
 omit [IsGaussian μ] in
 lemma IsGaussian.of_subsingleton [Subsingleton E] [IsProbabilityMeasure μ] :
     IsGaussian μ := by
-  convert instIsGaussianDirac (x := (0 : E))
+  convert! instIsGaussianDirac (x := (0 : E))
   ext s -
   apply Subsingleton.set_cases (p := fun s ↦ μ s = _)
   all_goals simp
@@ -123,7 +123,7 @@ lemma IsGaussian.memLp_dual (μ : Measure E) [IsGaussian μ] (L : StrongDual ℝ
     MemLp L p μ := by
   suffices MemLp (id ∘ L) p μ from this
   rw [← memLp_map_measure_iff (by fun_prop) (by fun_prop), IsGaussian.map_eq_gaussianReal L]
-  convert memLp_id_gaussianReal p.toNNReal
+  convert! memLp_id_gaussianReal p.toNNReal
   simp [hp]
 
 @[fun_prop]
diff --git a/Mathlib/Probability/Distributions/Gaussian/Fernique.lean b/Mathlib/Probability/Distributions/Gaussian/Fernique.lean
index f387a7b9ef5330..f14bad7f0a10d5 100644
--- a/Mathlib/Probability/Distributions/Gaussian/Fernique.lean
+++ b/Mathlib/Probability/Distributions/Gaussian/Fernique.lean
@@ -127,7 +127,7 @@ lemma integrable_exp_sq_of_conv_neg (μ : Measure E) [IsGaussian μ] {C C' : ℝ
     simp only [ContinuousLinearEquiv.coe_neg] at hC
     filter_upwards [hC] with y hy
     rw [integrable_map_measure (by fun_prop) (by fun_prop)] at hy
-    convert hy with x
+    convert! hy with x
     simp only [Function.comp_apply, Pi.neg_apply, id_eq, Real.exp_eq_exp, mul_eq_mul_left_iff,
       norm_nonneg, ne_eq, OfNat.ofNat_ne_zero, not_false_eq_true, pow_left_inj₀]
     left
@@ -188,7 +188,7 @@ lemma memLp_id (μ : Measure E) [IsGaussian μ] (p : ℝ≥0∞) (hp : p ≠ ∞
     rw [← memLp_norm_rpow_iff (q := 2) (by fun_prop) (by simp) (by simp)]
     simpa using this
   lift p to ℝ≥0 using hp
-  convert memLp_of_mem_interior_integrableExpSet ?_ (p / 2)
+  convert! memLp_of_mem_interior_integrableExpSet ?_ (p / 2)
   · simp
   obtain ⟨C, hC_pos, hC⟩ := exists_integrable_exp_sq μ
   have hC_neg : Integrable (fun x ↦ rexp (-C * ‖x‖ ^ 2)) μ := by -- `-C` could be any negative
diff --git a/Mathlib/Probability/Distributions/Gaussian/HasGaussianLaw/Basic.lean b/Mathlib/Probability/Distributions/Gaussian/HasGaussianLaw/Basic.lean
index 3902cefe9c2f61..8558e8e9a5ee16 100644
--- a/Mathlib/Probability/Distributions/Gaussian/HasGaussianLaw/Basic.lean
+++ b/Mathlib/Probability/Distributions/Gaussian/HasGaussianLaw/Basic.lean
@@ -229,14 +229,14 @@ lemma sum {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] [MeasurableSpac
     [BorelSpace E] [SecondCountableTopology E]
     {X : ι → Ω → E} (hX : HasGaussianLaw (fun ω ↦ (X · ω)) P) :
     HasGaussianLaw (∑ i, X i) P := by
-  convert hX.map (∑ i, .proj i)
+  convert! hX.map (∑ i, .proj i)
   ext; simp
 
 lemma fun_sum {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] [MeasurableSpace E]
     [BorelSpace E] [SecondCountableTopology E]
     {X : ι → Ω → E} (hX : HasGaussianLaw (fun ω ↦ (X · ω)) P) :
     HasGaussianLaw (fun ω ↦ ∑ i, X i ω) P := by
-  convert hX.sum
+  convert! hX.sum
   simp
 
 end Pi
diff --git a/Mathlib/Probability/Distributions/Gaussian/IsGaussianProcess/Basic.lean b/Mathlib/Probability/Distributions/Gaussian/IsGaussianProcess/Basic.lean
index 45cf789c90ac0a..55cfc2bf51df6b 100644
--- a/Mathlib/Probability/Distributions/Gaussian/IsGaussianProcess/Basic.lean
+++ b/Mathlib/Probability/Distributions/Gaussian/IsGaussianProcess/Basic.lean
@@ -96,12 +96,12 @@ lemma hasGaussianLaw_fun_sub (hX : IsGaussianProcess X P) {s t : T} :
 
 lemma hasGaussianLaw_sum (hX : IsGaussianProcess X P) {I : Finset T} :
     HasGaussianLaw (∑ i ∈ I, X i) P := by
-  convert (hX.hasGaussianLaw I).sum
+  convert! (hX.hasGaussianLaw I).sum
   simp [I.sum_attach X]
 
 lemma hasGaussianLaw_fun_sum (hX : IsGaussianProcess X P) {I : Finset T} :
     HasGaussianLaw (fun ω ↦ ∑ i ∈ I, X i ω) P := by
-  convert hX.hasGaussianLaw_sum (I := I)
+  convert! hX.hasGaussianLaw_sum (I := I)
   simp
 
 /-- The increments of a Gaussian process are Gaussian. -/
diff --git a/Mathlib/Probability/Distributions/Gaussian/Real.lean b/Mathlib/Probability/Distributions/Gaussian/Real.lean
index 820ced3733d57d..7852741f031426 100644
--- a/Mathlib/Probability/Distributions/Gaussian/Real.lean
+++ b/Mathlib/Probability/Distributions/Gaussian/Real.lean
@@ -334,7 +334,7 @@ lemma gaussianReal_map_neg : (gaussianReal μ v).map (fun x ↦ -x) = gaussianRe
 lemma gaussianReal_map_div_const (c : ℝ) :
     (gaussianReal μ v).map (· / c) = gaussianReal (μ / c) (v / .mk (c ^ 2) (sq_nonneg _)) := by
   simp_rw [div_eq_mul_inv]
-  convert gaussianReal_map_mul_const c⁻¹ using 2 <;> rw [mul_comm]
+  convert! gaussianReal_map_mul_const c⁻¹ using 2 <;> rw [mul_comm]
   ext; simp
 
 lemma gaussianReal_map_sub_const (y : ℝ) :
diff --git a/Mathlib/Probability/Distributions/Geometric.lean b/Mathlib/Probability/Distributions/Geometric.lean
index 822c5b5a228caa..8d1e609040c6cc 100644
--- a/Mathlib/Probability/Distributions/Geometric.lean
+++ b/Mathlib/Probability/Distributions/Geometric.lean
@@ -84,7 +84,7 @@ lemma geometricMeasure_real_singleton_pos (h1 : p ≠ 0) (h2 : p ≠ 1) n :
 
 lemma hasSum_one_geometricMeasure (hp : p ≠ 0) :
     HasSum (fun n ↦ (1 - p : ℝ) ^ n * p) 1 := by
-  convert (hasSum_geometric_of_lt_one (r := 1 - p) (by grind) (by grind)).mul_right (p : ℝ)
+  convert! (hasSum_geometric_of_lt_one (r := 1 - p) (by grind) (by grind)).mul_right (p : ℝ)
   grind
 
 instance isProbabilityMeasure_geometricMeasure :
@@ -115,7 +115,7 @@ lemma hasSum_integral_geometricMeasure [CompleteSpace E]
     ext n; rw [ENNReal.toReal_ofReal (geometricMeasure_nonneg p n)]
   rw [this, geometricMeasure_eq hp]
   apply hasSum_integral_sum_dirac (by simp)
-  convert (integrable_geometricMeasure_iff hp).1 hf with n
+  convert! (integrable_geometricMeasure_iff hp).1 hf with n
   rw [ENNReal.toReal_ofReal (geometricMeasure_nonneg p n)]
 
 /-- If a function is integrable with respect to `geometricMeasure p`, then its integral
diff --git a/Mathlib/Probability/Distributions/Poisson/Basic.lean b/Mathlib/Probability/Distributions/Poisson/Basic.lean
index 3bb71bb7b127cc..9454842d7ffa4c 100644
--- a/Mathlib/Probability/Distributions/Poisson/Basic.lean
+++ b/Mathlib/Probability/Distributions/Poisson/Basic.lean
@@ -47,7 +47,7 @@ lemma poissonMeasure_real_singleton_pos {r : ℝ≥0} (n : ℕ) (hr : 0 < r) :
   positivity
 
 lemma hasSum_one_poissonMeasure (r : ℝ≥0) : HasSum (fun n ↦ exp (-r) * r ^ n / (n)!) 1 := by
-  convert (NormedSpace.expSeries_div_hasSum_exp (r : ℝ)).mul_left (exp (-r)) using 1
+  convert! (NormedSpace.expSeries_div_hasSum_exp (r : ℝ)).mul_left (exp (-r)) using 1
   · simp_rw [mul_div_assoc]
   · simp [← exp_eq_exp_ℝ, ← exp_add]
 
@@ -75,7 +75,7 @@ lemma hasSum_integral_poissonMeasure [CompleteSpace E] {r : ℝ≥0} {f : ℕ 
     ext; rw [ENNReal.toReal_ofReal (by positivity)]
   rw [this]
   apply hasSum_integral_sum_dirac (by simp)
-  convert integrable_poissonMeasure_iff.1 hf
+  convert! integrable_poissonMeasure_iff.1 hf
   rw [ENNReal.toReal_ofReal (by positivity)]
 /-- If a function is integrable with respect to `poissonMeasure r`, then its integral
 against this measure is given by its sum weighted by `exp (-r) * r ^ n / n!`.
diff --git a/Mathlib/Probability/IdentDistrib.lean b/Mathlib/Probability/IdentDistrib.lean
index b054385fd16aab..eb1ae121461be6 100644
--- a/Mathlib/Probability/IdentDistrib.lean
+++ b/Mathlib/Probability/IdentDistrib.lean
@@ -281,7 +281,7 @@ lemma inv [Inv γ] [MeasurableInv γ] (h : IdentDistrib f g μ ν) :
 
 theorem evariance_eq {f : α → ℝ} {g : β → ℝ} (h : IdentDistrib f g μ ν) :
     evariance f μ = evariance g ν := by
-  convert (h.sub_const (∫ x, f x ∂μ)).nnnorm.coe_nnreal_ennreal.sq.lintegral_eq
+  convert! (h.sub_const (∫ x, f x ∂μ)).nnnorm.coe_nnreal_ennreal.sq.lintegral_eq
   rw [h.integral_eq]
   rfl
 
diff --git a/Mathlib/Probability/Independence/Basic.lean b/Mathlib/Probability/Independence/Basic.lean
index c4e3c2827fa78c..2123ec8693a88c 100644
--- a/Mathlib/Probability/Independence/Basic.lean
+++ b/Mathlib/Probability/Independence/Basic.lean
@@ -749,7 +749,7 @@ variables defined on the product space `Ω × Ω'`. -/
 lemma indepFun_prod (mX : Measurable X) (mY : Measurable Y) :
     (fun ω ↦ X ω.1) ⟂ᵢ[μ.prod ν] (fun ω ↦ Y ω.2) := by
   refine indepFun_iff_map_prod_eq_prod_map_map (by fun_prop) (by fun_prop) |>.2 ?_
-  convert Measure.map_prod_map μ ν mX mY |>.symm
+  convert! Measure.map_prod_map μ ν mX mY |>.symm
   · rw [← Function.comp_def, ← Measure.map_map mX measurable_fst, Measure.map_fst_prod,
       measure_univ, one_smul]
   · rw [← Function.comp_def, ← Measure.map_map mY measurable_snd, Measure.map_snd_prod,
@@ -1065,7 +1065,7 @@ lemma iIndepFun.cond [Finite ι] (hY : ∀ i, Measurable (Y i))
     iIndepFun X μ[|⋂ i, Y i ⁻¹' t i] := by
   rw [iIndepFun_iff]
   intro s f hf
-  convert cond_iInter hY hindep hf (fun i _ ↦ hy _) ht using 2 with i hi
+  convert! cond_iInter hY hindep hf (fun i _ ↦ hy _) ht using 2 with i hi
   simpa using cond_iInter hY hindep (fun j hj ↦ hf _ <| Finset.mem_singleton.1 hj ▸ hi)
     (fun i _ ↦ hy _) ht
 
diff --git a/Mathlib/Probability/Independence/BoundedContinuousFunction.lean b/Mathlib/Probability/Independence/BoundedContinuousFunction.lean
index ee5a8244a1c172..31b91fcdda347a 100644
--- a/Mathlib/Probability/Independence/BoundedContinuousFunction.lean
+++ b/Mathlib/Probability/Independence/BoundedContinuousFunction.lean
@@ -107,7 +107,7 @@ lemma pi_indepFun_pi_of_prod_bcf (mX : ∀ s, AEMeasurable (X s) P)
     (aemeasurable_pi_lambda _ mY)]
   refine eq_prod_of_integral_prod_mul_prod_boundedContinuousFunction fun f g ↦ ?_
   rw [integral_map, integral_map, integral_map]
-  · convert h f g <;> simp
+  · convert! h f g <;> simp
   any_goals fun_prop
   all_goals exact Measurable.aestronglyMeasurable (by fun_prop)
 
@@ -122,8 +122,9 @@ lemma pi_indepFun_pi_of_bcf (mX : ∀ s, AEMeasurable (X s) P)
     IndepFun (fun ω s ↦ X s ω) (fun ω t ↦ Y t ω) P := by
   have := Fintype.ofFinite S; have := Fintype.ofFinite T
   refine pi_indepFun_pi_of_prod_bcf mX mY fun f g ↦ ?_
-  convert h (∏ s, (f s).compContinuous ⟨Function.eval s, by fun_prop⟩)
-    (∏ t, (g t).compContinuous ⟨Function.eval t, by fun_prop⟩) <;> simp
+  convert!
+    h (∏ s, (f s).compContinuous ⟨Function.eval s, by fun_prop⟩)
+      (∏ t, (g t).compContinuous ⟨Function.eval t, by fun_prop⟩) <;> simp
 
 lemma indepFun_pi_of_prod_bcf (mZ : AEMeasurable Z P)
     (mY : ∀ t, AEMeasurable (Y t) P)
@@ -133,7 +134,7 @@ lemma indepFun_pi_of_prod_bcf (mZ : AEMeasurable Z P)
   rw [indepFun_iff_map_prod_eq_prod_map_map mZ (aemeasurable_pi_lambda _ mY)]
   refine eq_prod_of_integral_mul_prod_boundedContinuousFunction fun f g ↦ ?_
   rw [integral_map, integral_map, integral_map]
-  · convert h f g <;> simp
+  · convert! h f g <;> simp
   any_goals fun_prop
   all_goals exact Measurable.aestronglyMeasurable (by fun_prop)
 
@@ -145,7 +146,7 @@ lemma indepFun_pi_of_bcf (mZ : AEMeasurable Z P)
     IndepFun Z (fun ω t ↦ Y t ω) P := by
   have := Fintype.ofFinite T
   refine indepFun_pi_of_prod_bcf mZ mY fun f g ↦ ?_
-  convert h f (∏ t, (g t).compContinuous ⟨Function.eval t, by fun_prop⟩) <;> simp
+  convert! h f (∏ t, (g t).compContinuous ⟨Function.eval t, by fun_prop⟩) <;> simp
 
 lemma pi_indepFun_of_prod_bcf (mX : ∀ s, AEMeasurable (X s) P)
     (mU : AEMeasurable U P)
@@ -155,7 +156,7 @@ lemma pi_indepFun_of_prod_bcf (mX : ∀ s, AEMeasurable (X s) P)
   rw [indepFun_iff_map_prod_eq_prod_map_map (aemeasurable_pi_lambda _ mX) mU]
   refine eq_prod_of_integral_prod_mul_boundedContinuousFunction fun f g ↦ ?_
   rw [integral_map, integral_map, integral_map]
-  · convert h f g <;> simp
+  · convert! h f g <;> simp
   any_goals fun_prop
   all_goals exact Measurable.aestronglyMeasurable (by fun_prop)
 
@@ -167,7 +168,7 @@ lemma pi_indepFun_of_bcf (mX : ∀ s, AEMeasurable (X s) P)
     IndepFun (fun ω s ↦ X s ω) U P := by
   have := Fintype.ofFinite S
   refine pi_indepFun_of_prod_bcf mX mU fun f g ↦ ?_
-  convert h (∏ s, (f s).compContinuous ⟨Function.eval s, by fun_prop⟩) g <;> simp
+  convert! h (∏ s, (f s).compContinuous ⟨Function.eval s, by fun_prop⟩) g <;> simp
 
 /-- Two random variables $X$ and $Y$ are independent if
 for all real bounded continuous functions $f$ and $g$,
@@ -236,7 +237,7 @@ lemma indicator_indepFun_pi_of_bcf
     (A.indicator (1 : Ω → ℝ)) ⟂ᵢ[P] (fun ω s ↦ X s ω) := by
   have := Fintype.ofFinite S
   refine indicator_indepFun_pi_of_prod_bcf mA mX fun f ↦ ?_
-  convert h (∏ s, (f s).compContinuous ⟨Function.eval s, by fun_prop⟩) <;> simp
+  convert! h (∏ s, (f s).compContinuous ⟨Function.eval s, by fun_prop⟩) <;> simp
 
 /-- The indicator of a set $A$ and a random variable $X$ are independent
 if for all real bounded continuous function $f$,
@@ -248,7 +249,7 @@ lemma indicator_indepFun_of_bcf
   suffices (A.indicator (1 : Ω → ℝ)) ⟂ᵢ[P] (fun ω (_ : Unit) ↦ Z ω) from
     this.comp (measurable_id) (measurable_pi_apply ())
   refine indicator_indepFun_pi_of_prod_bcf mA (fun _ ↦ mZ) fun f ↦ ?_
-  convert h (f ()) <;> simp
+  convert! h (f ()) <;> simp
 
 end Indicator
 
diff --git a/Mathlib/Probability/Independence/CharacteristicFunction.lean b/Mathlib/Probability/Independence/CharacteristicFunction.lean
index c4a4ccd7d5f623..0bc434ae17109c 100644
--- a/Mathlib/Probability/Independence/CharacteristicFunction.lean
+++ b/Mathlib/Probability/Independence/CharacteristicFunction.lean
@@ -145,11 +145,12 @@ lemma iIndepFun.charFunDual_map_finsetSum_eq_prod [NormedSpace ℝ E]
     · exact mX i (mem_insert_self i s)
     · exact Finset.aemeasurable_sum s (fun i hi ↦ (mX i (mem_insert_of_mem hi)))
     symm
-    convert iIndepFun.indepFun_finsetSum_of_notMem₀ (i := ⟨i, mem_insert_self i s⟩)
-      (f := fun (x : (insert i s : Finset ι)) ↦ X x.1) (s := {x | x.1 ∈ s}) hX
-      (fun i ↦ (mX i.1 i.2)) (by simpa)
+    convert!
+      iIndepFun.indepFun_finsetSum_of_notMem₀ (i := ⟨i, mem_insert_self i s⟩) (f :=
+        fun (x : (insert i s : Finset ι)) ↦ X x.1) (s := {x | x.1 ∈ s}) hX (fun i ↦ (mX i.1 i.2))
+        (by simpa)
     let e : ((insert i s) : Finset ι) → ι := Subtype.val
-    convert (Finset.sum_of_injOn Subtype.val ?_ ?_ ?_ ?_).symm
+    convert! (Finset.sum_of_injOn Subtype.val ?_ ?_ ?_ ?_).symm
     · simp
     · intro _ _; grind
     · simp; grind
@@ -166,7 +167,7 @@ lemma iIndepFun.charFunDual_map_sum_eq_prod [Fintype ι] [NormedSpace ℝ E]
 lemma iIndepFun.charFunDual_map_fun_finsetSum_eq_prod [NormedSpace ℝ E]
     (mX : ∀ i ∈ s, AEMeasurable (X i) P) (hX : iIndepFun (s.restrict X) P) :
     charFunDual (P.map (fun ω ↦ ∑ i ∈ s, X i ω)) = ∏ i ∈ s, charFunDual (P.map (X i)) := by
-  convert hX.charFunDual_map_finsetSum_eq_prod mX
+  convert! hX.charFunDual_map_finsetSum_eq_prod mX
   simp
 
 @[deprecated (since := "2026-04-08")]
@@ -204,7 +205,7 @@ lemma iIndepFun.charFun_map_sum_eq_prod [Fintype ι] [InnerProductSpace ℝ E]
 lemma iIndepFun.charFun_map_fun_finsetSum_eq_prod [InnerProductSpace ℝ E]
     (mX : ∀ i ∈ s, AEMeasurable (X i) P) (hX : iIndepFun (s.restrict X) P) :
     charFun (P.map (fun ω ↦ ∑ i ∈ s, X i ω)) = ∏ i ∈ s, charFun (P.map (X i)) := by
-  convert hX.charFun_map_finsetSum_eq_prod mX
+  convert! hX.charFun_map_finsetSum_eq_prod mX
   simp
 
 @[deprecated (since := "2026-04-08")]
diff --git a/Mathlib/Probability/Independence/Conditional.lean b/Mathlib/Probability/Independence/Conditional.lean
index d908d4bfb01301..5200e504eb8cb3 100644
--- a/Mathlib/Probability/Independence/Conditional.lean
+++ b/Mathlib/Probability/Independence/Conditional.lean
@@ -688,7 +688,7 @@ theorem iCondIndepFun_iff_condExp_inter_preimage_eq_mul {β : ι → Type*}
         intro i hi
         rw [(h_sets i hi).choose_spec.2.symm]
         simp only [g, dif_pos hi]
-      convert h with i hi i hi <;> exact hg i hi
+      convert! h with i hi i hi <;> exact hg i hi
 
 theorem condIndepFun_iff_condIndepSet_preimage {mβ : MeasurableSpace β} {mβ' : MeasurableSpace β'}
     (hf : Measurable f) (hg : Measurable g) :
@@ -851,11 +851,11 @@ theorem condIndepFun_iff_map_prod_eq_prod_condDistrib_prod_condDistrib
     rw [@Measure.dirac_apply' _ (mγ.comap k) _ _ (hk_meas hs)]
     congr
   refine ⟨fun h s t u hs ht hu ↦ ?_, fun h ↦ ?_⟩
-  · convert h (hk_meas hs) ht hu
+  · convert! h (hk_meas hs) ht hu
     · exact h_left hs ht hu
     · exact h_right hs ht hu
   · rintro - t u ⟨s, hs, rfl⟩ ht hu
-    convert h hs ht hu
+    convert! h hs ht hu
     · exact (h_left hs ht hu).symm
     · exact (h_right hs ht hu).symm
 
diff --git a/Mathlib/Probability/Independence/Integration.lean b/Mathlib/Probability/Independence/Integration.lean
index d493832fe3cd9d..856eeaa0a51520 100644
--- a/Mathlib/Probability/Independence/Integration.lean
+++ b/Mathlib/Probability/Independence/Integration.lean
@@ -296,7 +296,7 @@ lemma iIndepFun.integral_fun_prod_comp (hX : iIndepFun X μ)
 lemma iIndepFun.integral_prod_comp (hX : iIndepFun X μ)
     (mX : ∀ i, AEMeasurable (X i) μ) (hf : ∀ i, AEStronglyMeasurable (f i) (μ.map (X i))) :
     μ[∏ i, (f i) ∘ (X i)] = ∏ i, μ[(f i) ∘ (X i)] := by
-  convert hX.integral_fun_prod_comp mX hf
+  convert! hX.integral_fun_prod_comp mX hf
   simp
 
 variable {X : (i : ι) → Ω → 𝕜}
diff --git a/Mathlib/Probability/Independence/Kernel/Indep.lean b/Mathlib/Probability/Independence/Kernel/Indep.lean
index 1ba152009dbc17..fa33607bd3e1f6 100644
--- a/Mathlib/Probability/Independence/Kernel/Indep.lean
+++ b/Mathlib/Probability/Independence/Kernel/Indep.lean
@@ -224,7 +224,7 @@ lemma iIndepSets.precomp (hg : Function.Injective g) (h : iIndepSets π κ μ) :
 lemma iIndepSets.of_precomp (hg : Function.Surjective g) (h : iIndepSets (π ∘ g) κ μ) :
     iIndepSets π κ μ := by
   obtain ⟨g', hg'⟩ := hg.hasRightInverse
-  convert h.precomp hg'.injective
+  convert! h.precomp hg'.injective
   rw [Function.comp_assoc, hg'.comp_eq_id, Function.comp_id]
 
 lemma iIndepSets_precomp_of_bijective (hg : Function.Bijective g) :
@@ -640,14 +640,16 @@ theorem indep_iSup_of_directed_le {Ω} {m : ι → MeasurableSpace Ω} {m' m0 :
 theorem iIndepSet.indep_generateFrom_lt [Preorder ι] {s : ι → Set Ω}
     (hsm : ∀ n, MeasurableSet (s n)) (hs : iIndepSet s κ μ) (i : ι) :
     Indep (generateFrom {s i}) (generateFrom { t | ∃ j < i, s j = t }) κ μ := by
-  convert iIndepSet.indep_generateFrom_of_disjoint hsm hs {i} { j | j < i }
-    (Set.disjoint_singleton_left.mpr (lt_irrefl _)) using 1
+  convert!
+    iIndepSet.indep_generateFrom_of_disjoint hsm hs { i } {j | j < i}
+      (Set.disjoint_singleton_left.mpr (lt_irrefl _)) using 1
   simp only [Set.mem_singleton_iff, exists_eq_left, Set.setOf_eq_eq_singleton']
 
 theorem iIndepSet.indep_generateFrom_le [Preorder ι] {s : ι → Set Ω}
     (hsm : ∀ n, MeasurableSet (s n)) (hs : iIndepSet s κ μ) (i : ι) {k : ι} (hk : i < k) :
     Indep (generateFrom {s k}) (generateFrom { t | ∃ j ≤ i, s j = t }) κ μ := by
-  convert iIndepSet.indep_generateFrom_of_disjoint hsm hs {k} { j | j ≤ i }
+  convert!
+    iIndepSet.indep_generateFrom_of_disjoint hsm hs { k } {j | j ≤ i}
       (Set.disjoint_singleton_left.mpr hk.not_ge) using 1
   simp only [Set.mem_singleton_iff, exists_eq_left, Set.setOf_eq_eq_singleton']
 
diff --git a/Mathlib/Probability/Independence/Kernel/IndepFun.lean b/Mathlib/Probability/Independence/Kernel/IndepFun.lean
index f856c5c9599c00..8b0aa910023026 100644
--- a/Mathlib/Probability/Independence/Kernel/IndepFun.lean
+++ b/Mathlib/Probability/Independence/Kernel/IndepFun.lean
@@ -183,7 +183,7 @@ theorem iIndepFun.congr' {β : ι → Type*} {mβ : ∀ i, MeasurableSpace (β i
     filter_upwards [(ae_ball_iff (Finset.countable_toSet S)).2 ha] with ω hω
     change (ω ∈ ⋂ i ∈ S, g i ⁻¹' sets i) = (ω ∈ ⋂ i ∈ S, f i ⁻¹' sets i)
     simp +contextual [hω]
-  convert h'a using 2 with i hi
+  convert! h'a using 2 with i hi
   exact A i hi
 
 theorem iIndepFun_congr' {β : ι → Type*} {mβ : ∀ i, MeasurableSpace (β i)}
@@ -317,7 +317,7 @@ theorem indepFun_iff_compProd_map_prod_eq_compProd_prod_map_map
     specialize h hu hs ht
     rw [Measure.compProd_apply_prod hu (hs.prod ht),
       Measure.compProd_apply_prod hu (hs.prod ht)] at h
-    convert h with ω ω
+    convert! h with ω ω
     · rw [map_apply' _ (by fun_prop) _ (hs.prod ht), mk_preimage_prod]
     · rw [prod_apply_prod, map_apply' _ (by fun_prop) _ hs, map_apply' _ (by fun_prop) _ ht]
 
diff --git a/Mathlib/Probability/Independence/Process/HasIndepIncrements/Basic.lean b/Mathlib/Probability/Independence/Process/HasIndepIncrements/Basic.lean
index b62be7fb5b6801..5f84de13731fdf 100644
--- a/Mathlib/Probability/Independence/Process/HasIndepIncrements/Basic.lean
+++ b/Mathlib/Probability/Independence/Process/HasIndepIncrements/Basic.lean
@@ -76,7 +76,7 @@ protected lemma HasIndepIncrements.of_nat
     HasIndepIncrements X P := by
   intro n t ht
   let t' k := t ⟨min n k, by grind⟩
-  convert (h t' ?_ ?_).precomp Fin.val_injective with i ω
+  convert! (h t' ?_ ?_).precomp Fin.val_injective with i ω
   · grind
   · grind
   · exact fun a b hab ↦ ht (by grind)
diff --git a/Mathlib/Probability/Kernel/Composition/CompProd.lean b/Mathlib/Probability/Kernel/Composition/CompProd.lean
index 8e71864be34c07..f26a30e6b6084e 100644
--- a/Mathlib/Probability/Kernel/Composition/CompProd.lean
+++ b/Mathlib/Probability/Kernel/Composition/CompProd.lean
@@ -203,7 +203,7 @@ lemma compProd_deterministic_apply [MeasurableSingletonClass γ] {f : α × β 
   let t := {b | (b, f (x, b)) ∈ s}
   have ht : MeasurableSet t := (measurable_id.prodMk (hf.comp measurable_prodMk_left)) hs
   rw [← lintegral_add_compl _ ht]
-  convert add_zero _
+  convert! add_zero _
   · suffices ∀ b ∈ tᶜ, (if f (x, b) ∈ Prod.mk b ⁻¹' s then (1 : ℝ≥0∞) else 0) = 0 by
       rw [setLIntegral_congr_fun ht.compl this, lintegral_zero]
     intro b hb
diff --git a/Mathlib/Probability/Kernel/Composition/IntegralCompProd.lean b/Mathlib/Probability/Kernel/Composition/IntegralCompProd.lean
index 6395d12eaccb7b..e956681da19854 100644
--- a/Mathlib/Probability/Kernel/Composition/IntegralCompProd.lean
+++ b/Mathlib/Probability/Kernel/Composition/IntegralCompProd.lean
@@ -254,7 +254,7 @@ theorem integral_compProd :
     simp_rw [integral_add' i_f i_g, Kernel.integral_integral_add' i_f i_g, hf, hg]
   · exact isClosed_eq continuous_integral Kernel.continuous_integral_integral
   · intro f g hfg _ hf
-    convert hf using 1
+    convert! hf using 1
     · exact integral_congr_ae hfg.symm
     · apply integral_congr_ae
       filter_upwards [ae_ae_of_ae_compProd hfg] with x hfgx using
@@ -429,7 +429,7 @@ theorem integral_comp : ∀ {f : γ → E} (_ : Integrable f ((η ∘ₖ κ) a))
     simp_rw [integral_add' i_f i_g, integral_integral_add'_comp i_f i_g, hf, hg]
   · exact isClosed_eq continuous_integral Kernel.continuous_integral_integral_comp
   · rintro f g hfg - hf
-    convert hf using 1
+    convert! hf using 1
     · exact integral_congr_ae hfg.symm
     · apply integral_congr_ae
       filter_upwards [ae_ae_of_ae_comp hfg] with x hfgx using integral_congr_ae (ae_eq_symm hfgx)
diff --git a/Mathlib/Probability/Kernel/Composition/MeasureCompProd.lean b/Mathlib/Probability/Kernel/Composition/MeasureCompProd.lean
index cd7d039fbe6cc8..cccee8bacd55fe 100644
--- a/Mathlib/Probability/Kernel/Composition/MeasureCompProd.lean
+++ b/Mathlib/Probability/Kernel/Composition/MeasureCompProd.lean
@@ -118,7 +118,7 @@ lemma ae_compProd_of_ae_ae {p : α × β → Prop}
 lemma ae_ae_of_ae_compProd [SFinite μ] [IsSFiniteKernel κ] {p : α × β → Prop}
     (h : ∀ᵐ x ∂(μ ⊗ₘ κ), p x) :
     ∀ᵐ a ∂μ, ∀ᵐ b ∂κ a, p (a, b) := by
-  convert Kernel.ae_ae_of_ae_compProd h -- Much faster with `convert`
+  convert! Kernel.ae_ae_of_ae_compProd h -- Much faster with `convert`
 
 lemma ae_compProd_iff [SFinite μ] [IsSFiniteKernel κ] {p : α × β → Prop}
     (hp : MeasurableSet {x | p x}) :
diff --git a/Mathlib/Probability/Kernel/CondDistrib.lean b/Mathlib/Probability/Kernel/CondDistrib.lean
index 4f72713b65caa0..d6d06dde390bee 100644
--- a/Mathlib/Probability/Kernel/CondDistrib.lean
+++ b/Mathlib/Probability/Kernel/CondDistrib.lean
@@ -155,7 +155,7 @@ theorem condDistrib_ae_eq_of_measure_eq_compProd_of_measurable
   rw [heq, condDistrib]
   symm
   refine eq_condKernel_of_measure_eq_compProd _ ?_
-  convert hκ
+  convert! hκ
   exact heq.symm
 
 /-- `condDistrib` is a.e. uniquely defined as the kernel satisfying the defining property of
diff --git a/Mathlib/Probability/Kernel/Condexp.lean b/Mathlib/Probability/Kernel/Condexp.lean
index f33d0180280056..092f097a758ffa 100644
--- a/Mathlib/Probability/Kernel/Condexp.lean
+++ b/Mathlib/Probability/Kernel/Condexp.lean
@@ -168,35 +168,35 @@ theorem _root_.MeasureTheory.Integrable.condExpKernel_ae (hf_int : Integrable f
     ∀ᵐ ω ∂μ, Integrable f (condExpKernel μ m ω) := by
   nontriviality Ω
   rw [condExpKernel_eq]
-  convert Integrable.condDistrib_ae
-    (aemeasurable_id'' μ (inf_le_right : m ⊓ mΩ ≤ mΩ)) aemeasurable_id
-    hf_int.comp_snd_map_prod_id using 1
+  convert!
+    Integrable.condDistrib_ae (aemeasurable_id'' μ (inf_le_right : m ⊓ mΩ ≤ mΩ)) aemeasurable_id
+      hf_int.comp_snd_map_prod_id using 1
 
 theorem _root_.MeasureTheory.Integrable.integral_norm_condExpKernel (hf_int : Integrable f μ) :
     Integrable (fun ω => ∫ y, ‖f y‖ ∂condExpKernel μ m ω) μ := by
   nontriviality Ω
   rw [condExpKernel_eq]
-  convert Integrable.integral_norm_condDistrib
-    (aemeasurable_id'' μ (inf_le_right : m ⊓ mΩ ≤ mΩ)) aemeasurable_id
-    hf_int.comp_snd_map_prod_id using 1
+  convert!
+    Integrable.integral_norm_condDistrib (aemeasurable_id'' μ (inf_le_right : m ⊓ mΩ ≤ mΩ))
+      aemeasurable_id hf_int.comp_snd_map_prod_id using 1
 
 theorem _root_.MeasureTheory.Integrable.norm_integral_condExpKernel [NormedSpace ℝ F]
     (hf_int : Integrable f μ) :
     Integrable (fun ω => ‖∫ y, f y ∂condExpKernel μ m ω‖) μ := by
   nontriviality Ω
   rw [condExpKernel_eq]
-  convert Integrable.norm_integral_condDistrib
-    (aemeasurable_id'' μ (inf_le_right : m ⊓ mΩ ≤ mΩ)) aemeasurable_id
-    hf_int.comp_snd_map_prod_id using 1
+  convert!
+    Integrable.norm_integral_condDistrib (aemeasurable_id'' μ (inf_le_right : m ⊓ mΩ ≤ mΩ))
+      aemeasurable_id hf_int.comp_snd_map_prod_id using 1
 
 theorem _root_.MeasureTheory.Integrable.integral_condExpKernel [NormedSpace ℝ F]
     (hf_int : Integrable f μ) :
     Integrable (fun ω => ∫ y, f y ∂condExpKernel μ m ω) μ := by
   nontriviality Ω
   rw [condExpKernel_eq]
-  convert Integrable.integral_condDistrib
-    (aemeasurable_id'' μ (inf_le_right : m ⊓ mΩ ≤ mΩ)) aemeasurable_id
-    hf_int.comp_snd_map_prod_id using 1
+  convert!
+    Integrable.integral_condDistrib (aemeasurable_id'' μ (inf_le_right : m ⊓ mΩ ≤ mΩ))
+      aemeasurable_id hf_int.comp_snd_map_prod_id using 1
 
 theorem integrable_toReal_condExpKernel {s : Set Ω} (hs : MeasurableSet s) :
     Integrable (fun ω => (condExpKernel μ m ω).real s) μ := by
diff --git a/Mathlib/Probability/Kernel/Disintegration/Basic.lean b/Mathlib/Probability/Kernel/Disintegration/Basic.lean
index d6f44c2f014e5c..b8342df3429a1a 100644
--- a/Mathlib/Probability/Kernel/Disintegration/Basic.lean
+++ b/Mathlib/Probability/Kernel/Disintegration/Basic.lean
@@ -140,7 +140,7 @@ lemma IsCondKernel.isProbabilityMeasure_ae [IsFiniteKernel κ.fst] [κ.IsCondKer
   by_cases h_sfin : IsSFiniteKernel κCond
   swap; · rw [Kernel.compProd_of_not_isSFiniteKernel_right _ _ h_sfin] at h; simp [h.symm]
   suffices ∀ᵐ b ∂(κ.fst a), κCond (a, b) Set.univ = 1 by
-    convert this with b
+    convert! this with b
     exact ⟨fun _ ↦ measure_univ, fun h ↦ ⟨h⟩⟩
   suffices (∀ᵐ b ∂(κ.fst a), κCond (a, b) Set.univ ≤ 1)
       ∧ (∀ᵐ b ∂(κ.fst a), 1 ≤ κCond (a, b) Set.univ) by
diff --git a/Mathlib/Probability/Kernel/Disintegration/Density.lean b/Mathlib/Probability/Kernel/Disintegration/Density.lean
index 2f18ebc7c8f1a6..86c33dfaccb9e3 100644
--- a/Mathlib/Probability/Kernel/Disintegration/Density.lean
+++ b/Mathlib/Probability/Kernel/Disintegration/Density.lean
@@ -600,7 +600,7 @@ lemma tendsto_integral_density_of_monotone (hκν : fst κ ≤ ν) [IsFiniteKern
     · simp only [mem_Iio]
       exact ENNReal.lt_add_right (measure_ne_top _ _) one_ne_zero
   refine h_cont.tendsto.comp ?_
-  convert tendsto_measure_iUnion_atTop (monotone_const.set_prod hseq)
+  convert! tendsto_measure_iUnion_atTop (monotone_const.set_prod hseq)
   rw [← prod_iUnion, hseq_iUnion, univ_prod_univ]
 
 lemma tendsto_integral_density_of_antitone (hκν : fst κ ≤ ν) [IsFiniteKernel ν] (a : α)
@@ -703,14 +703,14 @@ lemma tendsto_densityProcess_fst_atTop_univ_of_monotone (κ : Kernel α (γ × 
       simp only [this, h0, ENNReal.zero_div, tendsto_const_nhds_iff]
       suffices κ a (countablePartitionSet n x ×ˢ univ) = 0 by
         simp only [this, ENNReal.zero_div]
-      convert h0
+      convert! h0
       ext x
       simp only [mem_prod, mem_univ, and_true, mem_setOf_eq]
     refine fun m ↦ measure_mono_null (fun x ↦ ?_) h0
     simp only [mem_prod, mem_setOf_eq, and_imp]
     exact fun h _ ↦ h
   refine ENNReal.Tendsto.div_const ?_ ?_
-  · convert tendsto_measure_iUnion_atTop (monotone_const.set_prod hseq)
+  · convert! tendsto_measure_iUnion_atTop (monotone_const.set_prod hseq)
     rw [← prod_iUnion, hseq_iUnion]
   · exact Or.inr h0
 
@@ -735,7 +735,7 @@ lemma tendsto_density_fst_atTop_ae_of_monotone [IsFiniteKernel κ]
   refine tendsto_of_integral_tendsto_of_monotone ?_ (integrable_const _) ?_ ?_ ?_
   · exact fun m ↦ integrable_density le_rfl _ (hseq_meas m)
   · rw [MeasureTheory.integral_const, smul_eq_mul, mul_one]
-    convert tendsto_integral_density_of_monotone (κ := κ) le_rfl a seq hseq hseq_iUnion hseq_meas
+    convert! tendsto_integral_density_of_monotone (κ := κ) le_rfl a seq hseq hseq_iUnion hseq_meas
     simp only [measureReal_def]
     rw [fst_apply' _ _ MeasurableSet.univ]
     simp only [mem_univ, setOf_true]
diff --git a/Mathlib/Probability/Kernel/Disintegration/MeasurableStieltjes.lean b/Mathlib/Probability/Kernel/Disintegration/MeasurableStieltjes.lean
index 59fbab81c264ca..9f51f0ecb5e416 100644
--- a/Mathlib/Probability/Kernel/Disintegration/MeasurableStieltjes.lean
+++ b/Mathlib/Probability/Kernel/Disintegration/MeasurableStieltjes.lean
@@ -325,7 +325,7 @@ lemma IsMeasurableRatCDF.monotone_stieltjesFunctionAux (a : α) :
 lemma IsMeasurableRatCDF.continuousWithinAt_stieltjesFunctionAux_Ici (a : α) (x : ℝ) :
     ContinuousWithinAt (IsMeasurableRatCDF.stieltjesFunctionAux f a) (Ici x) x := by
   rw [← continuousWithinAt_Ioi_iff_Ici]
-  convert Monotone.tendsto_nhdsGT (monotone_stieltjesFunctionAux hf a) x
+  convert! Monotone.tendsto_nhdsGT (monotone_stieltjesFunctionAux hf a) x
   rw [sInf_image']
   have h' : ⨅ r : Ioi x, stieltjesFunctionAux f a r
       = ⨅ r : { r' : ℚ // x < r' }, stieltjesFunctionAux f a r := by
diff --git a/Mathlib/Probability/Kernel/IonescuTulcea/Maps.lean b/Mathlib/Probability/Kernel/IonescuTulcea/Maps.lean
index 1c308f46a8283f..83efa31050eeba 100644
--- a/Mathlib/Probability/Kernel/IonescuTulcea/Maps.lean
+++ b/Mathlib/Probability/Kernel/IonescuTulcea/Maps.lean
@@ -180,9 +180,9 @@ lemma _root_.IicProdIoc_preimage {a b : ι} (hab : a ≤ b) (s : (i : Iic b) →
   simp only [Set.mem_preimage, Set.mem_pi, Set.mem_univ, IicProdIoc_def, forall_const,
     Subtype.forall, mem_Iic, Set.mem_prod, frestrictLe₂_apply, restrict₂, mem_Ioc]
   refine ⟨fun h ↦ ⟨fun i hi ↦ ?_, fun i ⟨hi1, hi2⟩ ↦ ?_⟩, fun ⟨h1, h2⟩ i hi ↦ ?_⟩
-  · convert h i (hi.trans hab)
+  · convert! h i (hi.trans hab)
     rw [dif_pos hi]
-  · convert h i hi2
+  · convert! h i hi2
     rw [dif_neg (not_le.2 hi1)]
   · split_ifs with hi3
     · exact h1 i hi3
diff --git a/Mathlib/Probability/Kernel/IonescuTulcea/Traj.lean b/Mathlib/Probability/Kernel/IonescuTulcea/Traj.lean
index e0a5e01c262f80..e5c7bf015a6e5e 100644
--- a/Mathlib/Probability/Kernel/IonescuTulcea/Traj.lean
+++ b/Mathlib/Probability/Kernel/IonescuTulcea/Traj.lean
@@ -329,7 +329,7 @@ theorem le_lmarginalPartialTraj_succ {f : ℕ → (Π n, X n) → ℝ≥0∞} {a
   have := le_trans hx ((anti _).le_of_tendsto (tendstoF _) n)
   -- This part below is just to say that this is true for any `x : (i : ι) → X i`,
   -- as `Fₙ` technically depends on all the variables, but really depends only on the first `k + 1`.
-  convert this using 1
+  convert! this using 1
   refine (hcte n).dependsOn_lmarginalPartialTraj _ (mf n) fun i hi ↦ ?_
   simp only [update, updateFinset, mem_Iic]
   split_ifs with h1 h2 <;> try rfl
@@ -426,7 +426,7 @@ theorem trajContent_tendsto_zero {A : ℕ → Set (Π n, X n)}
     | base => exact fun x n ↦ by simpa [z, frestrictLe_iterateInduction] using hpos x n
     | succ k hn h =>
       intro x n
-      convert hind k (fun i ↦ z i.1) h x n
+      convert! hind k (fun i ↦ z i.1) h x n
       ext i
       simp only [updateFinset, mem_Iic, frestrictLe_apply, dite_eq_ite, update, z]
       split_ifs with h1 h2 h3 h4 h5
@@ -441,7 +441,7 @@ theorem trajContent_tendsto_zero {A : ℕ → Set (Π n, X n)}
     nth_rw 1 [← frestrictLe_updateFinset x x₀]
     exact trajContent_eq_lmarginalPartialTraj (mS n) ..
   simp_rw [aux z]
-  convert hl p _
+  convert! hl p _
   rw [hε]
   -- Which means that we want to prove that `ε = 0`. But if `ε > 0`, then for any `n`,
   -- choosing `k > aₙ` we get `ε ≤ χₙ(z₀, ..., z_{aₙ})` and therefore `z ∈ Aₙ`.
@@ -613,7 +613,7 @@ theorem lintegral_traj₀ {a : ℕ} (x₀ : Π i : Iic a, X i) {f : (Π n, X n)
     (mf : AEMeasurable f (traj κ a x₀)) :
     ∫⁻ x, f x ∂traj κ a x₀ = ∫⁻ x, f (updateFinset x (Iic a) x₀) ∂traj κ a x₀ := by
   nth_rw 1 [← traj_map_updateFinset, MeasureTheory.lintegral_map']
-  · convert mf
+  · convert! mf
     exact traj_map_updateFinset x₀
   · exact measurable_updateFinset_left.aemeasurable
 
@@ -630,7 +630,7 @@ theorem integrable_traj {a b : ℕ} (hab : a ≤ b) {f : (Π n, X n) → E}
   rw [← traj_comp_partialTraj hab, integrable_comp_iff] at i_f
   · apply ae_of_ae_map (p := fun x ↦ Integrable f (traj κ b x))
     · fun_prop
-    · convert i_f.1
+    · convert! i_f.1
       rw [← traj_map_frestrictLe, Kernel.map_apply _ (measurable_frestrictLe _)]
   · exact i_f.aestronglyMeasurable
 
@@ -649,7 +649,7 @@ theorem integral_traj {a : ℕ} (x₀ : Π i : Iic a, X i) {f : (Π n, X n) →
     ∫ x, f x ∂traj κ a x₀ = ∫ x, f (updateFinset x (Iic a) x₀) ∂traj κ a x₀ := by
   nth_rw 1 [← traj_map_updateFinset, integral_map]
   · exact measurable_updateFinset_left.aemeasurable
-  · convert mf
+  · convert! mf
     rw [traj_map_updateFinset]
 
 lemma partialTraj_compProd_traj {a b : ℕ} (hab : a ≤ b) (u : Π i : Iic a, X i) :
@@ -699,7 +699,7 @@ theorem setIntegral_traj_partialTraj' {a b : ℕ} (hab : a ≤ b) {u : (Π i : I
   rw [← integral_integral_indicator _ _ _ hA, integral_traj_partialTraj' hab]
   · simp_rw [← Set.indicator_comp_right, ← integral_indicator (measurable_frestrictLe b hA)]
     rfl
-  convert hf.indicator (hA.prod .univ)
+  convert! hf.indicator (hA.prod .univ)
   ext ⟨x, y⟩
   by_cases hx : x ∈ A <;> simp [uncurry_def, hx]
 
diff --git a/Mathlib/Probability/Kernel/Posterior.lean b/Mathlib/Probability/Kernel/Posterior.lean
index a3ea8f8586d04f..693ef7d21089ae 100644
--- a/Mathlib/Probability/Kernel/Posterior.lean
+++ b/Mathlib/Probability/Kernel/Posterior.lean
@@ -268,7 +268,10 @@ lemma rnDeriv_posterior_ae_prod (h_ac : ∀ᵐ ω ∂μ, κ ω ≪ κ ∘ₘ μ)
 lemma rnDeriv_posterior (h_ac : ∀ᵐ ω ∂μ, κ ω ≪ κ ∘ₘ μ) :
     ∀ᵐ ω ∂μ, ∀ᵐ x ∂(κ ∘ₘ μ),
       (κ†μ).rnDeriv (Kernel.const _ μ) x ω = κ.rnDeriv (Kernel.const _ (κ ∘ₘ μ)) ω x := by
-  convert Measure.ae_ae_of_ae_prod (rnDeriv_posterior_ae_prod h_ac) -- much faster than `exact`
+  convert!
+    Measure.ae_ae_of_ae_prod
+      (rnDeriv_posterior_ae_prod h_ac) -- much faster than `exact`
+         -- much faster than `exact`
 
 lemma rnDeriv_posterior_symm (h_ac : ∀ᵐ ω ∂μ, κ ω ≪ κ ∘ₘ μ) :
     ∀ᵐ x ∂(κ ∘ₘ μ), ∀ᵐ ω ∂μ,
diff --git a/Mathlib/Probability/Martingale/BorelCantelli.lean b/Mathlib/Probability/Martingale/BorelCantelli.lean
index e0fe69747c9bc9..ef5a464411616d 100644
--- a/Mathlib/Probability/Martingale/BorelCantelli.lean
+++ b/Mathlib/Probability/Martingale/BorelCantelli.lean
@@ -155,7 +155,7 @@ theorem Submartingale.bddAbove_iff_exists_tendsto [IsFiniteMeasure μ] (hf : Sub
   have hgbdd : ∀ᵐ ω ∂μ, ∀ i : ℕ, |g (i + 1) ω - g i ω| ≤ ↑R := by
     simpa only [g, sub_sub_sub_cancel_right]
   filter_upwards [hg.bddAbove_iff_exists_tendsto_aux hg0 hgbdd] with ω hω
-  convert hω using 1
+  convert! hω using 1
   · refine ⟨fun h => ?_, fun h => ?_⟩ <;> obtain ⟨b, hb⟩ := h <;>
     refine ⟨b + |f 0 ω|, fun y hy => ?_⟩ <;> obtain ⟨n, rfl⟩ := hy
     · simp_rw [g, sub_eq_add_neg]
@@ -205,7 +205,7 @@ theorem Martingale.bddAbove_range_iff_bddBelow_range [IsFiniteMeasure μ] (hf :
     constructor <;> rintro ⟨c, hc⟩
     · exact ⟨-c, hc.neg⟩
     · refine ⟨-c, ?_⟩
-      convert hc.neg
+      convert! hc.neg
       simp only [neg_neg, Pi.neg_apply]
   rw [hω₁, this, ← hω₂]
   constructor <;> rintro ⟨c, hc⟩ <;> refine ⟨-c, fun ω hω => ?_⟩
diff --git a/Mathlib/Probability/Martingale/OptionalStopping.lean b/Mathlib/Probability/Martingale/OptionalStopping.lean
index bf516f6ea7ef55..ffd7a0c4fa5013 100644
--- a/Mathlib/Probability/Martingale/OptionalStopping.lean
+++ b/Mathlib/Probability/Martingale/OptionalStopping.lean
@@ -50,7 +50,7 @@ theorem Submartingale.expected_stoppedValue_mono {E : Type*} [NormedAddCommGroup
     have : ∀ i, MeasurableSet[𝒢 i] {ω : Ω | τ ω ≤ i ∧ i < π ω} := by
       intro i
       refine (hτ i).inter ?_
-      convert (hπ i).compl using 1
+      convert! (hπ i).compl using 1
       ext x
       simp; rfl
     rw [integral_finsetSum]
@@ -169,7 +169,7 @@ theorem maximal_ineq [IsFiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnon
           f n ω ∂μ) := by
       rw [← ENNReal.ofReal_add, ← setIntegral_union]
       · rw [← setIntegral_univ]
-        convert rfl
+        convert! rfl
         ext ω
         change (ε : ℝ) ≤ _ ∨ _ < (ε : ℝ) ↔ _
         simp only [le_or_gt, Set.mem_univ]
@@ -207,7 +207,7 @@ theorem maximal_ineq [IsFiniteMeasure μ] (hsub : Submartingale f 𝒢 μ) (hnon
         (∫ ω, stoppedValue f (fun ω ↦ (hittingBtwn f {y : ℝ | ε ≤ y} 0 n ω : ℕ)) ω ∂μ) := by
       rw [← ENNReal.ofReal_add, ← setIntegral_union]
       · rw [← setIntegral_univ (μ := μ)]
-        convert rfl
+        convert! rfl
         ext ω
         change _ ↔ (ε : ℝ) ≤ _ ∨ _ < (ε : ℝ)
         simp only [le_or_gt, Set.mem_univ]
diff --git a/Mathlib/Probability/Martingale/Upcrossing.lean b/Mathlib/Probability/Martingale/Upcrossing.lean
index 44c3143edc0e77..7e02bbb1a86c04 100644
--- a/Mathlib/Probability/Martingale/Upcrossing.lean
+++ b/Mathlib/Probability/Martingale/Upcrossing.lean
@@ -302,8 +302,8 @@ theorem upperCrossingTime_bound_eq (f : ℕ → Ω → ℝ) (N : ℕ) (ω : Ω)
         (Set.Iic (Nat.find (exists_upperCrossingTime_eq f N ω hab)).pred) := by
       refine strictMonoOn_Iic_of_lt_succ fun m hm => upperCrossingTime_lt_succ hab ?_
       rw [Nat.lt_pred_iff] at hm
-      convert Nat.find_min _ hm
-    convert StrictMonoOn.Iic_id_le hmono N (Nat.le_sub_one_of_lt hN')
+      convert! Nat.find_min _ hm
+    convert! StrictMonoOn.Iic_id_le hmono N (Nat.le_sub_one_of_lt hN')
   · rw [not_lt] at hN'
     exact upperCrossingTime_stabilize hN' (Nat.find_spec (exists_upperCrossingTime_eq f N ω hab))
 
@@ -414,7 +414,7 @@ theorem Submartingale.sum_mul_upcrossingStrat_le [IsFiniteMeasure μ] (hf : Subm
       Pi.mul_apply]
     refine integral_sub (Integrable.sub (integrable_finsetSum _ fun i _ => hf.integrable _)
       (integrable_finsetSum _ fun i _ => hf.integrable _)) ?_
-    convert (hf.sum_upcrossingStrat_mul a b N).integrable n using 1
+    convert! (hf.sum_upcrossingStrat_mul a b N).integrable n using 1
     ext; simp
   rw [h₂, sub_nonneg] at h₁
   refine le_trans h₁ ?_
@@ -445,7 +445,7 @@ theorem upperCrossingTime_lt_of_le_upcrossingsBefore (hN : 0 < N) (hab : a < b)
 theorem upperCrossingTime_eq_of_upcrossingsBefore_lt (hab : a < b)
     (hn : upcrossingsBefore a b f N ω < n) : upperCrossingTime a b f N n ω = N := by
   refine le_antisymm upperCrossingTime_le (not_lt.1 ?_)
-  convert notMem_of_csSup_lt hn (upperCrossingTime_lt_bddAbove hab) using 1
+  convert! notMem_of_csSup_lt hn (upperCrossingTime_lt_bddAbove hab) using 1
 
 theorem upcrossingsBefore_le (f : ℕ → Ω → ℝ) (ω : Ω) (hab : a < b) :
     upcrossingsBefore a b f N ω ≤ N := by
diff --git a/Mathlib/Probability/Moments/ComplexMGF.lean b/Mathlib/Probability/Moments/ComplexMGF.lean
index 4f643782527476..90eaf77896a72e 100644
--- a/Mathlib/Probability/Moments/ComplexMGF.lean
+++ b/Mathlib/Probability/Moments/ComplexMGF.lean
@@ -162,14 +162,14 @@ lemma hasDerivAt_integral_pow_mul_exp (hz : z.re ∈ interior (integrableExpSet
     simp_rw [pow_succ, mul_assoc]
     refine HasDerivAt.const_mul _ ?_
     simp_rw [← smul_eq_mul, Complex.exp_eq_exp_ℂ]
-    convert hasDerivAt_exp_smul_const (X ω : ℂ) ε using 1
+    convert! hasDerivAt_exp_smul_const (X ω : ℂ) ε using 1
     rw [smul_eq_mul, mul_comm]
 
 /-- For all `z : ℂ` with `z.re ∈ interior (integrableExpSet X μ)`,
 `complexMGF X μ` is differentiable at `z` with derivative `μ[X * exp (z * X)]`. -/
 theorem hasDerivAt_complexMGF (hz : z.re ∈ interior (integrableExpSet X μ)) :
     HasDerivAt (complexMGF X μ) μ[fun ω ↦ X ω * cexp (z * X ω)] z := by
-  convert hasDerivAt_integral_pow_mul_exp hz 0
+  convert! hasDerivAt_integral_pow_mul_exp hz 0
   · simp [complexMGF]
   · simp
 
diff --git a/Mathlib/Probability/Moments/Covariance.lean b/Mathlib/Probability/Moments/Covariance.lean
index 81f31c1cdb7704..03971b7964bb57 100644
--- a/Mathlib/Probability/Moments/Covariance.lean
+++ b/Mathlib/Probability/Moments/Covariance.lean
@@ -236,12 +236,12 @@ lemma covariance_sum_left [Fintype ι] (hX : ∀ i, MemLp (X i) 2 μ) (hY : MemL
 
 lemma covariance_fun_sum_left' (hX : ∀ i ∈ s, MemLp (X i) 2 μ) (hY : MemLp Y 2 μ) :
     cov[fun ω ↦ ∑ i ∈ s, X i ω, Y; μ] = ∑ i ∈ s, cov[X i, Y; μ] := by
-  convert covariance_sum_left' hX hY
+  convert! covariance_sum_left' hX hY
   simp
 
 lemma covariance_fun_sum_left [Fintype ι] (hX : ∀ i, MemLp (X i) 2 μ) (hY : MemLp Y 2 μ) :
     cov[fun ω ↦ ∑ i, X i ω, Y; μ] = ∑ i, cov[X i, Y; μ] := by
-  convert covariance_sum_left hX hY
+  convert! covariance_sum_left hX hY
   simp
 
 lemma covariance_sum_right' (hX : ∀ i ∈ s, MemLp (X i) 2 μ) (hY : MemLp Y 2 μ) :
@@ -255,7 +255,7 @@ lemma covariance_sum_right [Fintype ι] (hX : ∀ i, MemLp (X i) 2 μ) (hY : Mem
 
 lemma covariance_fun_sum_right' (hX : ∀ i ∈ s, MemLp (X i) 2 μ) (hY : MemLp Y 2 μ) :
     cov[Y, fun ω ↦ ∑ i ∈ s, X i ω; μ] = ∑ i ∈ s, cov[Y, X i; μ] := by
-  convert covariance_sum_right' hX hY
+  convert! covariance_sum_right' hX hY
   simp
 
 lemma covariance_fun_sum_right [Fintype ι] (hX : ∀ i, MemLp (X i) 2 μ) (hY : MemLp Y 2 μ) :
@@ -278,7 +278,7 @@ lemma covariance_fun_sum_fun_sum' {ι' : Type*} {Y : ι' → Ω → ℝ} {t : Fi
     (hX : ∀ i ∈ s, MemLp (X i) 2 μ) (hY : ∀ i ∈ t, MemLp (Y i) 2 μ) :
     cov[fun ω ↦ ∑ i ∈ s, X i ω, fun ω ↦ ∑ j ∈ t, Y j ω; μ]
       = ∑ i ∈ s, ∑ j ∈ t, cov[X i, Y j; μ] := by
-  convert covariance_sum_sum' hX hY
+  convert! covariance_sum_sum' hX hY
   all_goals simp
 
 lemma covariance_fun_sum_fun_sum [Fintype ι] {ι' : Type*} [Fintype ι'] {Y : ι' → Ω → ℝ}
diff --git a/Mathlib/Probability/Moments/CovarianceBilin.lean b/Mathlib/Probability/Moments/CovarianceBilin.lean
index 6147c411d926fc..96ba36fdb87bff 100644
--- a/Mathlib/Probability/Moments/CovarianceBilin.lean
+++ b/Mathlib/Probability/Moments/CovarianceBilin.lean
@@ -136,7 +136,7 @@ lemma covarianceBilin_map_const_add [CompleteSpace E] [IsProbabilityMeasure μ]
     rw [covarianceBilin_of_not_memLp, covarianceBilin_of_not_memLp h]
     rw [(measurableEmbedding_addLeft _).memLp_map_measure_iff.not]
     contrapose h
-    convert (memLp_const (-c)).add h
+    convert! (memLp_const (-c)).add h
     ext; simp
 
 lemma covarianceBilin_apply_basisFun {ι Ω : Type*} [Fintype ι] {mΩ : MeasurableSpace Ω}
diff --git a/Mathlib/Probability/Moments/IntegrableExpMul.lean b/Mathlib/Probability/Moments/IntegrableExpMul.lean
index 9c6245b16ba8da..922dc2bf731375 100644
--- a/Mathlib/Probability/Moments/IntegrableExpMul.lean
+++ b/Mathlib/Probability/Moments/IntegrableExpMul.lean
@@ -223,7 +223,7 @@ lemma rpow_abs_le_mul_max_exp_of_pos (x : ℝ) {t p : ℝ} (hp : 0 ≤ p) (ht :
   calc |x| ^ p
   _ ≤ ((t / p)⁻¹ * max (exp (t / p * x)) (exp (-t / p * x))) ^ p := by
     gcongr
-    convert h_abs_le (t / p) (div_pos ht (hp.lt_of_ne' hp_zero)) using 5
+    convert! h_abs_le (t / p) (div_pos ht (hp.lt_of_ne' hp_zero)) using 5
     rw [neg_div]
   _ = (p / t) ^ p * max (exp (t * x)) (exp (-t * x)) := by
     rw [mul_rpow (by positivity) (by positivity)]
@@ -237,7 +237,7 @@ lemma rpow_abs_le_mul_max_exp (x : ℝ) {t p : ℝ} (hp : 0 ≤ p) (ht : t ≠ 0
     |x| ^ p ≤ (p / |t|) ^ p * max (exp (t * x)) (exp (-t * x)) := by
   rcases lt_or_gt_of_ne ht with ht_neg | ht_pos
   · rw [abs_of_nonpos ht_neg.le, sup_comm]
-    convert rpow_abs_le_mul_max_exp_of_pos x hp (t := -t) (by simp [ht_neg])
+    convert! rpow_abs_le_mul_max_exp_of_pos x hp (t := -t) (by simp [ht_neg])
     simp
   · rw [abs_of_nonneg ht_pos.le]
     exact rpow_abs_le_mul_max_exp_of_pos x hp ht_pos
@@ -279,7 +279,7 @@ lemma integrable_rpow_abs_mul_exp_add_of_integrable_exp_mul {x : ℝ}
     nth_rw 2 [this]
     rw [add_mul, exp_add, ← mul_assoc]
     gcongr ?_ * _
-    convert rpow_abs_le_mul_exp_abs (X a) hp (t := |t| - x) _ using 4
+    convert! rpow_abs_le_mul_exp_abs (X a) hp (t := |t| - x) _ using 4
     · nth_rw 2 [abs_of_nonneg]
       simp [hx.le]
     · nth_rw 2 [abs_of_nonneg]
@@ -308,8 +308,9 @@ lemma integrable_pow_abs_mul_exp_add_of_integrable_exp_mul {x : ℝ}
     (h_int_neg : Integrable (fun ω ↦ exp ((v - t) * X ω)) μ) (h_nonneg : 0 ≤ x) (hx : x < |t|)
     (n : ℕ) :
     Integrable (fun a ↦ |X a| ^ n * exp (v * X a + x * |X a|)) μ := by
-  convert integrable_rpow_abs_mul_exp_add_of_integrable_exp_mul h_int_pos h_int_neg h_nonneg hx
-    n.cast_nonneg
+  convert!
+    integrable_rpow_abs_mul_exp_add_of_integrable_exp_mul h_int_pos h_int_neg h_nonneg hx
+      n.cast_nonneg
   simp
 
 /-- If `exp ((v + t) * X)` and `exp ((v - t) * X)` are integrable
@@ -318,8 +319,8 @@ lemma integrable_rpow_abs_mul_exp_of_integrable_exp_mul (ht : t ≠ 0)
     (ht_int_pos : Integrable (fun ω ↦ exp ((v + t) * X ω)) μ)
     (ht_int_neg : Integrable (fun ω ↦ exp ((v - t) * X ω)) μ) {p : ℝ} (hp : 0 ≤ p) :
     Integrable (fun ω ↦ |X ω| ^ p * exp (v * X ω)) μ := by
-  convert integrable_rpow_abs_mul_exp_add_of_integrable_exp_mul ht_int_pos ht_int_neg le_rfl _ hp
-    using 4
+  convert!
+    integrable_rpow_abs_mul_exp_add_of_integrable_exp_mul ht_int_pos ht_int_neg le_rfl _ hp using 4
   · simp
   · simp [ht]
 
@@ -329,8 +330,10 @@ lemma integrable_pow_abs_mul_exp_of_integrable_exp_mul (ht : t ≠ 0)
     (ht_int_pos : Integrable (fun ω ↦ exp ((v + t) * X ω)) μ)
     (ht_int_neg : Integrable (fun ω ↦ exp ((v - t) * X ω)) μ) (n : ℕ) :
     Integrable (fun ω ↦ |X ω| ^ n * exp (v * X ω)) μ := by
-  convert integrable_rpow_abs_mul_exp_of_integrable_exp_mul ht ht_int_pos ht_int_neg
-    (by positivity : 0 ≤ (n : ℝ)) with ω
+  convert!
+    integrable_rpow_abs_mul_exp_of_integrable_exp_mul ht ht_int_pos ht_int_neg
+      (by positivity : 0 ≤ (n : ℝ)) with
+    ω
   simp
 
 /-- If `exp ((v + t) * X)` and `exp ((v - t) * X)` are integrable, then for all nonnegative `p : ℝ`,
@@ -358,8 +361,10 @@ lemma integrable_pow_mul_exp_of_integrable_exp_mul (ht : t ≠ 0)
     (ht_int_pos : Integrable (fun ω ↦ exp ((v + t) * X ω)) μ)
     (ht_int_neg : Integrable (fun ω ↦ exp ((v - t) * X ω)) μ) (n : ℕ) :
     Integrable (fun ω ↦ X ω ^ n * exp (v * X ω)) μ := by
-  convert integrable_rpow_mul_exp_of_integrable_exp_mul ht ht_int_pos ht_int_neg
-    (by positivity : 0 ≤ (n : ℝ)) with ω
+  convert!
+    integrable_rpow_mul_exp_of_integrable_exp_mul ht ht_int_pos ht_int_neg
+      (by positivity : 0 ≤ (n : ℝ)) with
+    ω
   simp
 
 /-- If `ω ↦ exp (t * X ω)` is integrable at `t` and `-t` for `t ≠ 0`, then `ω ↦ |X ω| ^ p` is
@@ -379,8 +384,10 @@ lemma integrable_pow_abs_of_integrable_exp_mul (ht : t ≠ 0)
     (ht_int_pos : Integrable (fun ω ↦ exp (t * X ω)) μ)
     (ht_int_neg : Integrable (fun ω ↦ exp (-t * X ω)) μ) (n : ℕ) :
     Integrable (fun ω ↦ |X ω| ^ n) μ := by
-  convert integrable_rpow_abs_of_integrable_exp_mul ht ht_int_pos ht_int_neg
-    (by positivity : 0 ≤ (n : ℝ)) with ω
+  convert!
+    integrable_rpow_abs_of_integrable_exp_mul ht ht_int_pos ht_int_neg
+      (by positivity : 0 ≤ (n : ℝ)) with
+    ω
   simp
 
 /-- If `ω ↦ exp (t * X ω)` is integrable at `t` and `-t` for `t ≠ 0`, then `ω ↦ X ω ^ p` is
@@ -400,8 +407,10 @@ lemma integrable_pow_of_integrable_exp_mul (ht : t ≠ 0)
     (ht_int_pos : Integrable (fun ω ↦ exp (t * X ω)) μ)
     (ht_int_neg : Integrable (fun ω ↦ exp (-t * X ω)) μ) (n : ℕ) :
     Integrable (fun ω ↦ X ω ^ n) μ := by
-  convert integrable_rpow_of_integrable_exp_mul ht ht_int_pos ht_int_neg
-    (by positivity : 0 ≤ (n : ℝ)) with ω
+  convert!
+    integrable_rpow_of_integrable_exp_mul ht ht_int_pos ht_int_neg
+      (by positivity : 0 ≤ (n : ℝ)) with
+    ω
   simp
 
 section IntegrableExpSet
@@ -468,8 +477,10 @@ then `|X| ^ n * exp (v * X)` is integrable for all `n : ℕ`. -/
 lemma integrable_pow_abs_mul_exp_of_mem_interior_integrableExpSet
     (hv : v ∈ interior (integrableExpSet X μ)) (n : ℕ) :
     Integrable (fun ω ↦ |X ω| ^ n * exp (v * X ω)) μ := by
-  convert integrable_rpow_abs_mul_exp_of_mem_interior_integrableExpSet hv
-    (by positivity : 0 ≤ (n : ℝ)) with ω
+  convert!
+    integrable_rpow_abs_mul_exp_of_mem_interior_integrableExpSet hv
+      (by positivity : 0 ≤ (n : ℝ)) with
+    ω
   simp
 
 /-- If `v` belongs to the interior of the interval `integrableExpSet X μ`,
@@ -491,8 +502,8 @@ then `X ^ n * exp (v * X)` is integrable for all `n : ℕ`. -/
 lemma integrable_pow_mul_exp_of_mem_interior_integrableExpSet
     (hv : v ∈ interior (integrableExpSet X μ)) (n : ℕ) :
     Integrable (fun ω ↦ X ω ^ n * exp (v * X ω)) μ := by
-  convert integrable_rpow_mul_exp_of_mem_interior_integrableExpSet hv
-    (by positivity : 0 ≤ (n : ℝ)) with ω
+  convert!
+    integrable_rpow_mul_exp_of_mem_interior_integrableExpSet hv (by positivity : 0 ≤ (n : ℝ)) with ω
   simp
 
 /-- If 0 belongs to the interior of the interval `integrableExpSet X μ`,
@@ -500,7 +511,7 @@ then `|X| ^ n` is integrable for all nonnegative `p : ℝ`. -/
 lemma integrable_rpow_abs_of_mem_interior_integrableExpSet
     (h : 0 ∈ interior (integrableExpSet X μ)) {p : ℝ} (hp : 0 ≤ p) :
     Integrable (fun ω ↦ |X ω| ^ p) μ := by
-  convert integrable_rpow_abs_mul_exp_of_mem_interior_integrableExpSet h hp using 1
+  convert! integrable_rpow_abs_mul_exp_of_mem_interior_integrableExpSet h hp using 1
   simp
 
 /-- If 0 belongs to the interior of the interval `integrableExpSet X μ`,
@@ -508,7 +519,7 @@ then `|X| ^ n` is integrable for all `n : ℕ`. -/
 lemma integrable_pow_abs_of_mem_interior_integrableExpSet
     (h : 0 ∈ interior (integrableExpSet X μ)) (n : ℕ) :
     Integrable (fun ω ↦ |X ω| ^ n) μ := by
-  convert integrable_pow_abs_mul_exp_of_mem_interior_integrableExpSet h n
+  convert! integrable_pow_abs_mul_exp_of_mem_interior_integrableExpSet h n
   simp
 
 /-- If 0 belongs to the interior of the interval `integrableExpSet X μ`,
@@ -516,7 +527,7 @@ then `X ^ n` is integrable for all nonnegative `p : ℝ`. -/
 lemma integrable_rpow_of_mem_interior_integrableExpSet
     (h : 0 ∈ interior (integrableExpSet X μ)) {p : ℝ} (hp : 0 ≤ p) :
     Integrable (fun ω ↦ X ω ^ p) μ := by
-  convert integrable_rpow_mul_exp_of_mem_interior_integrableExpSet h hp using 1
+  convert! integrable_rpow_mul_exp_of_mem_interior_integrableExpSet h hp using 1
   simp
 
 /-- If 0 belongs to the interior of the interval `integrableExpSet X μ`,
@@ -524,7 +535,7 @@ then `X ^ n` is integrable for all `n : ℕ`. -/
 lemma integrable_pow_of_mem_interior_integrableExpSet
     (h : 0 ∈ interior (integrableExpSet X μ)) (n : ℕ) :
     Integrable (fun ω ↦ X ω ^ n) μ := by
-  convert integrable_pow_mul_exp_of_mem_interior_integrableExpSet h n
+  convert! integrable_pow_mul_exp_of_mem_interior_integrableExpSet h n
   simp
 
 /-- If 0 belongs to the interior of `integrableExpSet X μ`, then `X` is in `ℒp` for all
@@ -575,7 +586,7 @@ lemma integrable_rpow_abs_mul_cexp_of_re_mem_interior_integrableExpSet
 lemma integrable_pow_abs_mul_cexp_of_re_mem_interior_integrableExpSet
     (hz : z.re ∈ interior (integrableExpSet X μ)) (n : ℕ) :
     Integrable (fun ω ↦ |X ω| ^ n * cexp (z * X ω)) μ := by
-  convert integrable_rpow_abs_mul_cexp_of_re_mem_interior_integrableExpSet hz (Nat.cast_nonneg n)
+  convert! integrable_rpow_abs_mul_cexp_of_re_mem_interior_integrableExpSet hz (Nat.cast_nonneg n)
   simp
 
 lemma integrable_rpow_mul_cexp_of_re_mem_interior_integrableExpSet
@@ -596,7 +607,7 @@ lemma integrable_rpow_mul_cexp_of_re_mem_interior_integrableExpSet
 lemma integrable_pow_mul_cexp_of_re_mem_interior_integrableExpSet
     (hz : z.re ∈ interior (integrableExpSet X μ)) (n : ℕ) :
     Integrable (fun ω ↦ X ω ^ n * cexp (z * X ω)) μ := by
-  convert integrable_rpow_mul_cexp_of_re_mem_interior_integrableExpSet hz (Nat.cast_nonneg n)
+  convert! integrable_rpow_mul_cexp_of_re_mem_interior_integrableExpSet hz (Nat.cast_nonneg n)
   simp
 
 end Complex
diff --git a/Mathlib/Probability/Moments/MGFAnalytic.lean b/Mathlib/Probability/Moments/MGFAnalytic.lean
index b3972043489349..ad059254382fdf 100644
--- a/Mathlib/Probability/Moments/MGFAnalytic.lean
+++ b/Mathlib/Probability/Moments/MGFAnalytic.lean
@@ -60,7 +60,7 @@ section DerivMGF
 `μ[X * exp (t * X)]`. -/
 lemma hasDerivAt_mgf (h : t ∈ interior (integrableExpSet X μ)) :
     HasDerivAt (mgf X μ) (μ[fun ω ↦ X ω * exp (t * X ω)]) t := by
-  convert hasDerivAt_integral_pow_mul_exp_real h 0
+  convert! hasDerivAt_integral_pow_mul_exp_real h 0
   · simp [mgf]
   · simp
 
@@ -124,7 +124,7 @@ lemma hasFPowerSeriesAt_mgf (hv : v ∈ interior (integrableExpSet X μ)) :
     HasFPowerSeriesAt (mgf X μ)
       (FormalMultilinearSeries.ofScalars ℝ
         (fun n ↦ (μ[fun ω ↦ X ω ^ n * exp (v * X ω)] : ℝ) / n !)) v := by
-  convert (analyticAt_mgf hv).hasFPowerSeriesAt
+  convert! (analyticAt_mgf hv).hasFPowerSeriesAt
   rw [iteratedDeriv_mgf hv]
 
 lemma differentiableAt_mgf (ht : t ∈ interior (integrableExpSet X μ)) :
@@ -140,7 +140,7 @@ lemma continuousOn_mgf : ContinuousOn (mgf X μ) (interior (integrableExpSet X 
 lemma continuous_mgf (h : ∀ t, Integrable (fun ω ↦ exp (t * X ω)) μ) :
     Continuous (mgf X μ) := by
   rw [← continuousOn_univ]
-  convert continuousOn_mgf
+  convert! continuousOn_mgf
   symm
   rw [interior_eq_univ]
   ext t
@@ -233,7 +233,7 @@ lemma iteratedDeriv_two_cgf (h : v ∈ interior (integrableExpSet X μ)) :
       ring
   _ = (∫ ω, (X ω) ^ 2 * exp (v * X ω) ∂μ) / mgf X μ v - deriv (cgf X μ) v ^ 2 := by
     congr
-    convert (hasDerivAt_integral_pow_mul_exp_real h 1).deriv using 1
+    convert! (hasDerivAt_integral_pow_mul_exp_real h 1).deriv using 1
     simp
 
 lemma iteratedDeriv_two_cgf_eq_integral (h : v ∈ interior (integrableExpSet X μ)) :
@@ -259,7 +259,7 @@ lemma iteratedDeriv_two_cgf_eq_integral (h : v ∈ interior (integrableExpSet X
       refine Integrable.const_mul ?_ _
       simp_rw [← mul_assoc]
       refine Integrable.mul_const ?_ _
-      convert integrable_pow_mul_exp_of_mem_interior_integrableExpSet h 1
+      convert! integrable_pow_mul_exp_of_mem_interior_integrableExpSet h 1
       simp
     rw [integral_add]
     rotate_left
@@ -282,9 +282,9 @@ lemma exists_cgf_eq_iteratedDeriv_two_cgf_mul [IsZeroOrProbabilityMeasure μ] (h
   rw [← sub_zero (cgf X μ t)]
   nth_rw 3 [← sub_zero t]
   rw [← Set.uIoo_of_lt ht]
-  convert taylor_mean_remainder_lagrange_iteratedDeriv ht.ne ?_
+  convert! taylor_mean_remainder_lagrange_iteratedDeriv ht.ne ?_
   · have hd : derivWithin (cgf X μ) (Set.Icc 0 t) 0 = 0 := by
-      convert (analyticAt_cgf (hs ⟨le_refl 0, le_of_lt ht⟩)).differentiableAt.derivWithin _
+      convert! (analyticAt_cgf (hs ⟨le_refl 0, le_of_lt ht⟩)).differentiableAt.derivWithin _
       · simpa [hc] using (deriv_cgf_zero (hs ⟨le_refl 0, le_of_lt ht⟩)).symm
       · exact hu 0 ⟨le_refl 0, le_of_lt ht⟩
     simp [hd, Set.uIcc_of_lt ht]
diff --git a/Mathlib/Probability/Moments/SubGaussian.lean b/Mathlib/Probability/Moments/SubGaussian.lean
index 92f50261b235b4..f7ed8fd38929a4 100644
--- a/Mathlib/Probability/Moments/SubGaussian.lean
+++ b/Mathlib/Probability/Moments/SubGaussian.lean
@@ -181,7 +181,7 @@ lemma ae_forall_memLp_exp_mul (h : HasSubgaussianMGF X c κ ν) (p : ℝ≥0) :
     rw [eLpNorm_lt_top_iff_lintegral_rpow_enorm_lt_top (mod_cast hp) (by simp),
       ENNReal.coe_toReal]
     have hf := (hi (p * t)).lintegral_lt_top
-    convert hf using 3 with ω
+    convert! hf using 3 with ω
     rw [enorm_eq_ofReal (by positivity), ENNReal.ofReal_rpow_of_nonneg (by positivity),
       ← exp_mul, mul_comm, ← mul_assoc]
     positivity
@@ -196,7 +196,7 @@ lemma memLp_exp_mul (h : HasSubgaussianMGF X c κ ν) (t : ℝ) (p : ℝ≥0) :
     simp only [ENNReal.coe_toReal]
     have h' := (h.integrable_exp_mul (p * t)).2
     rw [hasFiniteIntegral_def] at h'
-    convert h' using 3 with ω
+    convert! h' using 3 with ω
     rw [enorm_eq_ofReal (by positivity), enorm_eq_ofReal (by positivity),
       ENNReal.ofReal_rpow_of_nonneg (by positivity), ← exp_mul, mul_comm, ← mul_assoc]
     positivity
@@ -289,10 +289,10 @@ lemma of_map {Ω'' : Type*} {mΩ'' : MeasurableSpace Ω''} {κ : Kernel Ω' Ω''
       at h1
   mgf_le := by
     filter_upwards [h.ae_forall_integrable_exp_mul, h.mgf_le] with ω' h_int h_mgf t
-    convert h_mgf t
+    convert! h_mgf t
     ext t
     rw [map_apply _ hY, mgf_map hY.aemeasurable]
-    convert (h_int t).1
+    convert! (h_int t).1
     rw [map_apply _ hY]
 
 lemma id_map_iff (hX : Measurable X) :
@@ -418,7 +418,7 @@ lemma add {Y : Ω → ℝ} {cX cY : ℝ≥0} (hX : HasSubgaussianMGF X cX κ ν)
   exact
   { integrable_exp_mul t := by
       simp_rw [mul_add, exp_add]
-      convert MemLp.integrable_mul (hX.memLp_exp_mul t 2) (hY.memLp_exp_mul t 2)
+      convert! MemLp.integrable_mul (hX.memLp_exp_mul t 2) (hY.memLp_exp_mul t 2)
       norm_cast
       infer_instance
     mgf_le := by
@@ -653,7 +653,7 @@ lemma of_map {Ω' : Type*} {mΩ' : MeasurableSpace Ω'} {μ : Measure Ω'}
     have h1 := h.integrable_exp_mul t
     rwa [integrable_map_measure h1.aestronglyMeasurable (by fun_prop)] at h1
   mgf_le t := by
-    convert h.mgf_le t using 1
+    convert! h.mgf_le t using 1
     rw [mgf_map hY (h.integrable_exp_mul t).1]
 
 lemma id_map_iff (hX : AEMeasurable X μ) :
@@ -728,7 +728,7 @@ lemma add_of_indepFun {Y : Ω → ℝ} {cX cY : ℝ≥0} (hX : HasSubgaussianMGF
     HasSubgaussianMGF (fun ω ↦ X ω + Y ω) (cX + cY) μ where
   integrable_exp_mul t := by
     simp_rw [mul_add, exp_add]
-    convert MemLp.integrable_mul (hX.memLp_exp_mul t 2) (hY.memLp_exp_mul t 2)
+    convert! MemLp.integrable_mul (hX.memLp_exp_mul t 2) (hY.memLp_exp_mul t 2)
     norm_cast
     infer_instance
   mgf_le t := by
@@ -762,7 +762,7 @@ private lemma sum_of_iIndepFun_of_forall_aemeasurable
     have h_indep' := (h_indep.indepFun_finsetSum_of_notMem₀ h_meas his).symm
     refine add_of_indepFun (h_subG _ (Finset.mem_insert_self _ _)) (h ?_) ?_
     · exact fun i hi ↦ h_subG _ (Finset.mem_insert_of_mem hi)
-    · convert h_indep'
+    · convert! h_indep'
       rw [Finset.sum_apply]
 
 lemma sum_of_iIndepFun {ι : Type*} {X : ι → Ω → ℝ} (h_indep : iIndepFun X μ) {c : ι → ℝ≥0}
@@ -831,7 +831,7 @@ protected lemma mgf_le_of_mem_Icc_of_integral_eq_zero [IsProbabilityMeasure μ]
   _ = Var[X; μ.tilted (u * X ·)] := by
     rw [← variance_tilted_mul (hs (Set.mem_Icc_of_Ioo h1))]
   _ ≤ ((b - a) / 2) ^ 2 := by
-    convert variance_le_sq_of_bounded ((tilted_absolutelyContinuous μ (u * X ·)) hb) _
+    convert! variance_le_sq_of_bounded ((tilted_absolutelyContinuous μ (u * X ·)) hb) _
     · exact isProbabilityMeasure_tilted (hi u)
     · exact hm.mono_ac (tilted_absolutelyContinuous μ (u * X ·))
   _ = (‖b - a‖₊ / 2) ^ 2 := by simp [field]
@@ -891,7 +891,7 @@ lemma HasSubgaussianMGF.add_of_hasCondSubgaussianMGF [IsFiniteMeasure μ]
   rw [HasSubgaussianMGF_iff_kernel] at hX ⊢
   have hY' : Kernel.HasSubgaussianMGF Y cY (condExpKernel μ m)
       (Kernel.const Unit (μ.trim hm) ∘ₘ Measure.dirac ()) := by simpa
-  convert hX.add_comp hY'
+  convert! hX.add_comp hY'
   ext
   rw [Kernel.const_apply, ← Measure.compProd, compProd_trim_condExpKernel]
 
diff --git a/Mathlib/Probability/Moments/Variance.lean b/Mathlib/Probability/Moments/Variance.lean
index 490b1a67102d56..fe52ac300a94a8 100644
--- a/Mathlib/Probability/Moments/Variance.lean
+++ b/Mathlib/Probability/Moments/Variance.lean
@@ -116,7 +116,7 @@ theorem evariance_eq_top [IsFiniteMeasure μ] (hXm : AEStronglyMeasurable X μ)
     simp only [ENNReal.toReal_ofNat, ENNReal.rpow_two]
     exact ENNReal.rpow_lt_top_of_nonneg (by linarith) h.ne
   refine hX ?_
-  convert this.add (memLp_const μ[X])
+  convert! this.add (memLp_const μ[X])
   ext ω
   rw [Pi.add_apply, sub_add_cancel]
 
@@ -218,7 +218,7 @@ theorem variance_smul (c : ℝ) (X : Ω → ℝ) (μ : Measure Ω) :
 
 theorem variance_smul' {A : Type*} [CommSemiring A] [Algebra A ℝ] (c : A) (X : Ω → ℝ)
     (μ : Measure Ω) : variance (c • X) μ = c ^ 2 • variance X μ := by
-  convert variance_smul (algebraMap A ℝ c) X μ using 1
+  convert! variance_smul (algebraMap A ℝ c) X μ using 1
   · simp only [algebraMap_smul]
   · simp only [Algebra.smul_def, map_pow]
 
@@ -244,7 +244,7 @@ lemma variance_const_add [IsProbabilityMeasure μ] (hX : AEStronglyMeasurable X
   simp_rw [add_comm c, variance_add_const hX c]
 
 lemma variance_fun_neg : Var[fun ω ↦ -X ω; μ] = Var[X; μ] := by
-  convert variance_const_mul (-1) X μ
+  convert! variance_const_mul (-1) X μ
   · ext; ring
   · simp
 
@@ -297,12 +297,12 @@ lemma variance_sum [IsFiniteMeasure μ] [Fintype ι] (hX : ∀ i, MemLp (X i) 2
 
 lemma variance_fun_sum' [IsFiniteMeasure μ] (hX : ∀ i ∈ s, MemLp (X i) 2 μ) :
     Var[fun ω ↦ ∑ i ∈ s, X i ω; μ] = ∑ i ∈ s, ∑ j ∈ s, cov[X i, X j; μ] := by
-  convert variance_sum' hX
+  convert! variance_sum' hX
   simp
 
 lemma variance_fun_sum [IsFiniteMeasure μ] [Fintype ι] (hX : ∀ i, MemLp (X i) 2 μ) :
     Var[fun ω ↦ ∑ i, X i ω; μ] = ∑ i, ∑ j, cov[X i, X j; μ] := by
-  convert variance_sum hX
+  convert! variance_sum hX
   simp
 
 variable {X : Ω → ℝ}
@@ -353,7 +353,7 @@ theorem variance_le_expectation_sq [IsProbabilityMeasure μ] {X : Ω → ℝ}
         (memLp_two_iff_integrable_sq (by fun_prop)).2 h
       have B : MemLp (fun _ : Ω => μ[X]) 2 μ := memLp_const _
       apply hX
-      convert A.add B
+      convert! A.add B
       simp
   · exact Eventually.of_forall fun x => sq_nonneg _
   · exact (AEMeasurable.pow_const (hm.aemeasurable.sub_const _) _).aestronglyMeasurable
@@ -382,8 +382,9 @@ theorem meas_ge_le_evariance_div_sq {X : Ω → ℝ} (hX : AEStronglyMeasurable
     (hc : c ≠ 0) : μ {ω | ↑c ≤ |X ω - μ[X]|} ≤ evariance X μ / c ^ 2 := by
   have A : (c : ℝ≥0∞) ≠ 0 := by rwa [Ne, ENNReal.coe_eq_zero]
   have B : AEStronglyMeasurable (fun _ : Ω => μ[X]) μ := aestronglyMeasurable_const
-  convert meas_ge_le_mul_pow_eLpNorm_enorm μ two_ne_zero ENNReal.ofNat_ne_top
-      (hX.sub B) A (by simp) using 1
+  convert!
+      meas_ge_le_mul_pow_eLpNorm_enorm μ two_ne_zero ENNReal.ofNat_ne_top (hX.sub B) A (by simp)
+    using 1
   · norm_cast
   rw [eLpNorm_eq_lintegral_rpow_enorm_toReal two_ne_zero ENNReal.ofNat_ne_top]
   simp only [ENNReal.toReal_ofNat, one_div, Pi.sub_apply]
@@ -397,7 +398,7 @@ from its expectation in terms of the variance. -/
 theorem meas_ge_le_variance_div_sq [IsFiniteMeasure μ] {X : Ω → ℝ} (hX : MemLp X 2 μ) {c : ℝ}
     (hc : 0 < c) : μ {ω | c ≤ |X ω - μ[X]|} ≤ ENNReal.ofReal (variance X μ / c ^ 2) := by
   rw [ENNReal.ofReal_div_of_pos (sq_pos_of_ne_zero hc.ne.symm), hX.ofReal_variance_eq]
-  convert @meas_ge_le_evariance_div_sq _ _ _ _ hX.1 c.toNNReal (by simp [hc]) using 1
+  convert! @meas_ge_le_evariance_div_sq _ _ _ _ hX.1 c.toNNReal (by simp [hc]) using 1
   · simp
   · rw [ENNReal.ofReal_pow hc.le]
     rfl
diff --git a/Mathlib/Probability/ProbabilityMassFunction/Binomial.lean b/Mathlib/Probability/ProbabilityMassFunction/Binomial.lean
index a8b9b9d3bd1805..e1563766b878ff 100644
--- a/Mathlib/Probability/ProbabilityMassFunction/Binomial.lean
+++ b/Mathlib/Probability/ProbabilityMassFunction/Binomial.lean
@@ -31,7 +31,7 @@ def binomial (p : ℝ≥0) (h : p ≤ 1) (n : ℕ) : PMF (Fin (n + 1)) :=
       ↑(p ^ (i : ℕ) * (1 - p) ^ ((Fin.last n - i) : ℕ) * (n.choose i : ℕ))) (by
     dsimp only
     norm_cast
-    convert (add_pow p (1 - p) n).symm
+    convert! (add_pow p (1 - p) n).symm
     · rw [Finset.sum_fin_eq_sum_range]
       apply Finset.sum_congr rfl
       intro i hi
diff --git a/Mathlib/Probability/Process/Adapted.lean b/Mathlib/Probability/Process/Adapted.lean
index 698a269f58a097..4b0473c6c2ada0 100644
--- a/Mathlib/Probability/Process/Adapted.lean
+++ b/Mathlib/Probability/Process/Adapted.lean
@@ -311,7 +311,7 @@ protected alias finset_prod' := MeasureTheory.IsStronglyProgressive.finsetProd'
 protected theorem finsetProd {γ} [CommMonoid β] [ContinuousMul β] {U : γ → ι → Ω → β}
     {s : Finset γ} (h : ∀ c ∈ s, IsStronglyProgressive f (U c)) :
     IsStronglyProgressive f fun i a => ∏ c ∈ s, U c i a := by
-  convert IsStronglyProgressive.finsetProd' h using 1; ext (i a); simp only [Finset.prod_apply]
+  convert! IsStronglyProgressive.finsetProd' h using 1; ext (i a); simp only [Finset.prod_apply]
 
 @[deprecated (since := "2026-04-08")]
 protected alias finset_sum := MeasureTheory.IsStronglyProgressive.finsetSum
diff --git a/Mathlib/Probability/Process/Kolmogorov.lean b/Mathlib/Probability/Process/Kolmogorov.lean
index 74d32fb5c4d8e3..33a3de483a7edc 100644
--- a/Mathlib/Probability/Process/Kolmogorov.lean
+++ b/Mathlib/Probability/Process/Kolmogorov.lean
@@ -82,7 +82,7 @@ lemma ae_eq_mk (h : IsAEKolmogorovProcess X P p q M) : ∀ t, X t =ᵐ[P] h.mk X
 
 lemma kolmogorovCondition (hX : IsAEKolmogorovProcess X P p q M) (s t : T) :
     ∫⁻ ω, edist (X s ω) (X t ω) ^ p ∂P ≤ M * edist s t ^ q := by
-  convert hX.IsKolmogorovProcess_mk.kolmogorovCondition s t using 1
+  convert! hX.IsKolmogorovProcess_mk.kolmogorovCondition s t using 1
   refine lintegral_congr_ae ?_
   filter_upwards [hX.ae_eq_mk s, hX.ae_eq_mk t] with ω hω₁ hω₂
   simp_rw [hω₁, hω₂]
diff --git a/Mathlib/Probability/Process/LocalProperty.lean b/Mathlib/Probability/Process/LocalProperty.lean
index 375633b3c1065e..4078759db74a29 100644
--- a/Mathlib/Probability/Process/LocalProperty.lean
+++ b/Mathlib/Probability/Process/LocalProperty.lean
@@ -170,8 +170,9 @@ lemma IsStable.locally_and_iff (hp : IsStable 𝓕 p) (hq : IsStable 𝓕 q) :
     simp_rw [inf_comm hpX.localSeq]
     exact this q p hq hp hqX hpX
   intro p q hp hq hpX hqX
-  convert hp _ (hpX.stoppedProcess_localSeq n) _ <|
-    hqX.isLocalizingSequence_localSeq.isStoppingTime n using 1
+  convert!
+    hp _ (hpX.stoppedProcess_localSeq n) _ <|
+      hqX.isLocalizingSequence_localSeq.isStoppingTime n using 1
   ext i ω
   simp_rw [stoppedProcess_indicator_comm, Pi.inf_apply, lt_inf_iff, inf_comm (hpX.localSeq n)]
   rw [← stoppedProcess_stoppedProcess, ← stoppedProcess_indicator_comm, Set.setOf_and,
@@ -214,8 +215,8 @@ lemma IsStable.locally_of_isPreLocalizingSequence
   rw [stoppedProcess_indicator_comm', ← stoppedProcess_stoppedProcess_of_le_right
     (τ := fun ω ↦ τ n ω) (fun _ ↦ (iInf_le _ n).trans <| iInf_le _ le_rfl),
     ← stoppedProcess_indicator_comm']
-  convert hp _ (hpτ n) (fun ω ↦ ⨅ j ≥ n, τ j ω) <|
-    hτ.isLocalizingSequence_biInf.isStoppingTime n using 2
+  convert!
+    hp _ (hpτ n) (fun ω ↦ ⨅ j ≥ n, τ j ω) <| hτ.isLocalizingSequence_biInf.isStoppingTime n using 2
   ext i ω
   rw [stoppedProcess_indicator_comm', Set.indicator_indicator]
   congr with ω
@@ -310,7 +311,7 @@ lemma IsStable.locally_locally_iff [IsRightContinuous 𝓕] (hp : IsStable 𝓕
   obtain ⟨nk, hnk, hpre⟩ :=
     hL.isLocalizingSequence_localSeq.isPrelocalizingSequence_inf_extraction hτ₁
   refine locally_of_isPreLocalizingSequence hp hpre <| fun n ↦ ?_
-  convert hτ₂ n (nk n) using 1 with
+  convert! hτ₂ n (nk n) using 1 with
   ext i ω
   rw [stoppedProcess_indicator_comm', stoppedProcess_indicator_comm',
     stoppedProcess_stoppedProcess, stoppedProcess_indicator_comm']
diff --git a/Mathlib/Probability/Process/PartitionFiltration.lean b/Mathlib/Probability/Process/PartitionFiltration.lean
index 9edb2ab461038e..1f100fc7eda116 100644
--- a/Mathlib/Probability/Process/PartitionFiltration.lean
+++ b/Mathlib/Probability/Process/PartitionFiltration.lean
@@ -73,7 +73,7 @@ lemma measurable_memPartitionSet_subtype (ht : ∀ n, MeasurableSet (t n)) (n :
     (partitionFiltration ht n) _ (fun s ↦ ?_)
   rcases s with ⟨s, hs⟩
   suffices MeasurableSet[partitionFiltration ht n] {x | memPartitionSet t n x = s} by
-    convert this
+    convert! this
     ext x
     simp
   simp_rw [memPartitionSet_eq_iff _ hs]
diff --git a/Mathlib/Probability/Process/Stopping.lean b/Mathlib/Probability/Process/Stopping.lean
index 749ed011ec5f4a..672b3a57cd6f9c 100644
--- a/Mathlib/Probability/Process/Stopping.lean
+++ b/Mathlib/Probability/Process/Stopping.lean
@@ -387,7 +387,7 @@ protected lemma iInf [ConditionallyCompleteLinearOrderBot ι] [TopologicalSpace
     {κ : Type*} [Countable κ] {f : Filtration ι m} {τ : κ → Ω → WithTop ι}
     [f.IsRightContinuous] (hτ : ∀ n, IsStoppingTime f (τ n)) :
     IsStoppingTime f (fun ω ↦ ⨅ n, τ n ω) := by
-  convert IsStoppingTime.biInf (κ := κ) Set.countable_univ (fun n _ => hτ n) using 2
+  convert! IsStoppingTime.biInf (κ := κ) Set.countable_univ (fun n _ => hτ n) using 2
   simp
 
 theorem add_const [AddGroup ι] [Preorder ι] [AddRightMono ι]
@@ -762,7 +762,7 @@ theorem measurableSet_eq_stopping_time_min [TopologicalSpace ι]
     ext; simp only [Set.mem_setOf_eq, le_antisymm_iff, Set.mem_inter_iff]
   rw [this]
   refine MeasurableSet.inter (measurableSet_stopping_time_le_min hτ hπ) ?_
-  convert (measurableSet_stopping_time_le_min hπ hτ) using 3
+  convert! (measurableSet_stopping_time_le_min hπ hτ) using 3
   rw [min_comm]
 
 theorem measurableSet_eq_stopping_time [TopologicalSpace ι] [OrderTopology ι]
@@ -917,7 +917,7 @@ theorem isStronglyProgressive_min_stopping_time [PseudoMetrizableSpace ι]
     · lift τ (ω : Set.Iic i × Ω).2 to ι using h with t ht
       norm_cast
       refine hx_fst_le.trans (le_of_lt ?_)
-      convert ω.prop
+      convert! ω.prop
       simp only [sc, s, not_le, Set.mem_compl_iff, Set.mem_setOf_eq, ← ht]
       norm_cast
 
@@ -1157,7 +1157,7 @@ theorem memLp_stoppedProcess_of_mem_finset (hτ : IsStoppingTime ℱ τ) (hu : 
   refine MemLp.add ?_ ?_
   · exact MemLp.indicator (ℱ.le n {a : Ω | n ≤ τ a} (hτ.measurableSet_ge n)) (hu n)
   · suffices MemLp (fun ω => ∑ i ∈ s with i < n, {a : Ω | τ a = i}.indicator (u i) ω) p μ by
-      convert this using 1; ext1 ω; simp only [Finset.sum_apply]
+      convert! this using 1; ext1 ω; simp only [Finset.sum_apply]
     refine memLp_finsetSum _ fun i _ => MemLp.indicator ?_ (hu i)
     exact ℱ.le i {a : Ω | τ a = i} (hτ.measurableSet_eq i)
 
diff --git a/Mathlib/Probability/ProductMeasure.lean b/Mathlib/Probability/ProductMeasure.lean
index 49333de91686c9..58ab7130e5ee7d 100644
--- a/Mathlib/Probability/ProductMeasure.lean
+++ b/Mathlib/Probability/ProductMeasure.lean
@@ -321,16 +321,16 @@ theorem piContent_tendsto_zero {A : ℕ → Set (Π i, X i)} (A_mem : ∀ n, A n
   obtain u_fin | u_inf := finite_or_infinite u
   · let _ := Fintype.ofFinite u
     simp_rw [fun n ↦ piContent_eq_measure_pi (fun i : u ↦ μ i) (mB n)]
-    convert tendsto_measure_iInter_atTop (fun n ↦ (mB n).nullMeasurableSet) B_anti
-      ⟨0, measure_ne_top _ _⟩
+    convert!
+      tendsto_measure_iInter_atTop (fun n ↦ (mB n).nullMeasurableSet) B_anti ⟨0, measure_ne_top _ _⟩
     · rw [B_inter, measure_empty]
     · infer_instance
   · -- If `u` is infinite, then we have an equivalence with `ℕ` so we can apply `secondLemma`.
     have count_u : Countable u := Set.countable_iUnion (fun n ↦ (s n).countable_toSet)
     obtain ⟨φ, -⟩ := Classical.exists_true_of_nonempty (α := ℕ ≃ u) nonempty_equiv_of_countable
     conv => enter [1]; ext n; rw [← infinitePiNat_map_piCongrLeft _ φ (B_mem n)]
-    convert tendsto_measure_iInter_atTop (fun n ↦ (mB n).nullMeasurableSet) B_anti
-      ⟨0, measure_ne_top _ _⟩
+    convert!
+      tendsto_measure_iInter_atTop (fun n ↦ (mB n).nullMeasurableSet) B_anti ⟨0, measure_ne_top _ _⟩
     · rw [B_inter, measure_empty]
     · infer_instance
 
@@ -551,7 +551,7 @@ lemma infinitePi_map_curry_symm :
         (MeasurableEquiv.curry ι κ X).symm = ⇑(MeasurableEquiv.piCurry (fun _ _ ↦ X)).symm := by
       ext; simp [piCongrLeft, Equiv.piCongrLeft, Sigma.uncurry]
     rw [this, infinitePi_map_piCurry_symm]
-    convert infinitePi_map_piCongrLeft (fun p ↦ μ p.1 p.2) (Equiv.sigmaEquivProd ι κ).symm |>.symm
+    convert! infinitePi_map_piCongrLeft (fun p ↦ μ p.1 p.2) (Equiv.sigmaEquivProd ι κ).symm |>.symm
   all_goals fun_prop
 
 lemma infinitePi_map_curry :
diff --git a/Mathlib/Probability/StrongLaw.lean b/Mathlib/Probability/StrongLaw.lean
index 6253ae7727ce17..53c6b47a496a70 100644
--- a/Mathlib/Probability/StrongLaw.lean
+++ b/Mathlib/Probability/StrongLaw.lean
@@ -431,7 +431,7 @@ theorem strong_law_aux1 {c : ℝ} (c_one : 1 < c) {ε : ℝ} (εpos : 0 < ε) :
         · simp only [Nat.cast_zero]
           simp only [Y, Nat.cast_zero, truncation_zero, variance_zero, mul_zero, le_rfl]
         apply mul_le_mul_of_nonneg_right _ (variance_nonneg _ _)
-        convert sum_div_nat_floor_pow_sq_le_div_sq N (Nat.cast_pos.2 hj) c_one using 2
+        convert! sum_div_nat_floor_pow_sq_le_div_sq N (Nat.cast_pos.2 hj) c_one using 2
         · simp only [u, Nat.cast_lt]
         · simp only [u, one_div]
       _ = c ^ 5 * (c - 1)⁻¹ ^ 3 * ∑ j ∈ range (u (N - 1)), ((j : ℝ) ^ 2)⁻¹ * Var[Y j] := by
@@ -468,7 +468,7 @@ theorem strong_law_aux1 {c : ℝ} (c_one : 1 < c) {ε : ℝ} (εpos : 0 < ε) :
       ENNReal.ofReal_lt_top
   filter_upwards [ae_eventually_notMem I4.ne] with ω hω
   simp_rw [S, not_le, mul_comm, sum_apply] at hω
-  convert hω; simp only [Y, u, sum_apply]
+  convert! hω; simp only [Y, u, sum_apply]
 
 include hint hindep hident hnonneg in
 /-- The truncation of `Xᵢ` up to `i` satisfies the strong law of large numbers
@@ -494,10 +494,10 @@ expectation. This follows from convergence and Cesàro averaging. -/
 theorem strong_law_aux3 :
     (fun n => 𝔼[∑ i ∈ range n, truncation (X i) i] - n * 𝔼[X 0]) =o[atTop] ((↑) : ℕ → ℝ) := by
   have A : Tendsto (fun i => 𝔼[truncation (X i) i]) atTop (𝓝 𝔼[X 0]) := by
-    convert (tendsto_integral_truncation hint).comp tendsto_natCast_atTop_atTop using 1
+    convert! (tendsto_integral_truncation hint).comp tendsto_natCast_atTop_atTop using 1
     ext i
     exact (hident i).truncation.integral_eq
-  convert Asymptotics.isLittleO_sum_range_of_tendsto_zero (tendsto_sub_nhds_zero_iff.2 A) using 1
+  convert! Asymptotics.isLittleO_sum_range_of_tendsto_zero (tendsto_sub_nhds_zero_iff.2 A) using 1
   ext1 n
   simp only [sum_sub_distrib, sum_const, card_range, nsmul_eq_mul, sum_apply, sub_left_inj]
   rw [integral_finsetSum _ fun i _ => ?_]
@@ -514,7 +514,7 @@ theorem strong_law_aux4 {c : ℝ} (c_one : 1 < c) :
   filter_upwards [strong_law_aux2 X hint hindep hident hnonneg c_one] with ω hω
   have A : Tendsto (fun n : ℕ => ⌊c ^ n⌋₊) atTop atTop :=
     tendsto_nat_floor_atTop.comp (tendsto_pow_atTop_atTop_of_one_lt c_one)
-  convert hω.add ((strong_law_aux3 X hint hident).comp_tendsto A) using 1
+  convert! hω.add ((strong_law_aux3 X hint hident).comp_tendsto A) using 1
   ext1 n
   simp
 
@@ -526,7 +526,7 @@ theorem strong_law_aux5 :
     ∀ᵐ ω, (fun n : ℕ => ∑ i ∈ range n, truncation (X i) i ω - ∑ i ∈ range n, X i ω) =o[atTop]
     fun n : ℕ => (n : ℝ) := by
   have A : (∑' j : ℕ, ℙ {ω | X j ω ∈ Set.Ioi (j : ℝ)}) < ∞ := by
-    convert tsum_prob_mem_Ioi_lt_top hint (hnonneg 0) using 2
+    convert! tsum_prob_mem_Ioi_lt_top hint (hnonneg 0) using 2
     ext1 j
     exact (hident j).measure_mem_eq measurableSet_Ioi
   have B : ∀ᵐ ω, Tendsto (fun n : ℕ => truncation (X n) n ω - X n ω) atTop (𝓝 0) := by
@@ -542,7 +542,7 @@ theorem strong_law_aux5 :
       simp only [this, true_and, not_le] at h
       exact (hn h).elim
   filter_upwards [B] with ω hω
-  convert isLittleO_sum_range_of_tendsto_zero hω using 1
+  convert! isLittleO_sum_range_of_tendsto_zero hω using 1
   ext n
   rw [sum_sub_distrib]
 
@@ -563,10 +563,10 @@ theorem strong_law_aux6 {c : ℝ} (c_one : 1 < c) :
       (⌊c ^ n⌋₊ : ℝ) := by
     have A : Tendsto (fun n : ℕ => ⌊c ^ n⌋₊) atTop atTop :=
       tendsto_nat_floor_atTop.comp (tendsto_pow_atTop_atTop_of_one_lt c_one)
-    convert hω.sub (h'ω.comp_tendsto A) using 1
+    convert! hω.sub (h'ω.comp_tendsto A) using 1
     ext1 n
     simp only [Function.comp_apply, sub_sub_sub_cancel_left]
-  convert L.mul_isBigO (isBigO_refl (fun n : ℕ => (⌊c ^ n⌋₊ : ℝ)⁻¹) atTop) using 1 <;>
+  convert! L.mul_isBigO (isBigO_refl (fun n : ℕ => (⌊c ^ n⌋₊ : ℝ)⁻¹) atTop) using 1 <;>
   (ext1 n; field [(H n).ne'])
 
 include hint hindep hident hnonneg in
@@ -624,7 +624,7 @@ theorem strong_law_ae_real {Ω : Type*} {m : MeasurableSpace Ω} {μ : Measure 
     strong_law_aux7 _ hint.neg_part (fun i j hij => (hindep hij).comp negm negm)
       (fun i => (hident i).comp negm) fun i ω => le_max_right _ _
   filter_upwards [A, B] with ω hωpos hωneg
-  convert hωpos.sub hωneg using 2
+  convert! hωpos.sub hωneg using 2
   · simp only [pos, neg, ← sub_div, ← sum_sub_distrib, max_zero_sub_max_neg_zero_eq_self,
       Function.comp_apply]
   · simp +instances only [pos, neg, ← integral_sub hint.pos_part hint.neg_part,
@@ -676,11 +676,11 @@ lemma strong_law_ae_simpleFunc_comp (X : ℕ → Ω → E) (h' : Measurable (X 0
       ext
       simp
     simp only [I, integral_smul_const]
-    convert Tendsto.smul_const hω c using 1
+    convert! Tendsto.smul_const hω c using 1
     simp [F, Y, ← sum_smul, smul_smul]
   · rintro φ ψ - hφ hψ
     filter_upwards [hφ, hψ] with ω hωφ hωψ
-    convert hωφ.add hωψ using 1
+    convert! hωφ.add hωψ using 1
     · simp [sum_add_distrib]
     · congr 1
       rw [← integral_add]
diff --git a/Mathlib/RepresentationTheory/Action.lean b/Mathlib/RepresentationTheory/Action.lean
index 9bdb1eb56558d9..23a83f8787f1c5 100644
--- a/Mathlib/RepresentationTheory/Action.lean
+++ b/Mathlib/RepresentationTheory/Action.lean
@@ -154,7 +154,7 @@ lemma μ_comp_assoc : ((linearizeMap (α_ X Y Z).hom).comp
     TensorProduct.assoc_tmul, LinearMap.lTensor_tmul, toLinearMap_apply]
   -- after fixing the defeq problems in `Action` and in the monoidal category structure of `types`
   -- this line should close the goal so this is left as an indicator.
-  with_reducible convert dsimp% linearizeMap_single (α_ X Y Z).hom ((x, y), z) (1 : k)
+  with_reducible convert! dsimp% linearizeMap_single (α_ X Y Z).hom ((x, y), z) (1 : k)
   all_goals with_reducible simp
 
 variable (X) in
diff --git a/Mathlib/RepresentationTheory/Character.lean b/Mathlib/RepresentationTheory/Character.lean
index d9173aa051e474..5b1acb384378ab 100644
--- a/Mathlib/RepresentationTheory/Character.lean
+++ b/Mathlib/RepresentationTheory/Character.lean
@@ -64,7 +64,7 @@ theorem char_one (V : FDRep k G) : V.character 1 = Module.finrank k V := by
 /-- The character is multiplicative under the tensor product. -/
 @[simp]
 theorem char_tensor (V W : FDRep k G) : (V ⊗ W).character = V.character * W.character := by
-  ext g; convert trace_tensorProduct' (V.ρ g) (W.ρ g)
+  ext g; convert! trace_tensorProduct' (V.ρ g) (W.ρ g)
 
 /-- The character of isomorphic representations is the same. -/
 theorem char_iso {V W : FDRep k G} (i : V ≅ W) : V.character = W.character := by
@@ -163,7 +163,7 @@ theorem char_one (ρ : Representation k G V) : ρ.character 1 = Module.finrank k
 /-- The character is multiplicative under the tensor product. -/
 @[simp]
 theorem char_tensor : (tprod ρ σ).character = ρ.character * σ.character := by
-  ext g; convert trace_tensorProduct' (ρ g) (σ g)
+  ext g; convert! trace_tensorProduct' (ρ g) (σ g)
 
 omit [FiniteDimensional k V] [FiniteDimensional k W] in
 variable {ρ σ} in
diff --git a/Mathlib/RepresentationTheory/Homological/GroupHomology/Functoriality.lean b/Mathlib/RepresentationTheory/Homological/GroupHomology/Functoriality.lean
index 9e0abfbb54948a..130e3cd83743ac 100644
--- a/Mathlib/RepresentationTheory/Homological/GroupHomology/Functoriality.lean
+++ b/Mathlib/RepresentationTheory/Homological/GroupHomology/Functoriality.lean
@@ -424,7 +424,7 @@ noncomputable def H1CoresCoinfOfTrivial :
 
 instance map₁_quotientGroupMk'_epi :
     Epi (map (QuotientGroup.mk' S) (resOfQuotientIso A S).inv 1) := by
-  convert epi_of_epi (H1π A) _
+  convert! epi_of_epi (H1π A) _
   rw [H1π_comp_map]
   exact @epi_comp _ _ _ _ _ _ (mapCycles₁_quotientGroupMk'_epi A S) (H1π _) inferInstance
 
diff --git a/Mathlib/RepresentationTheory/Submodule.lean b/Mathlib/RepresentationTheory/Submodule.lean
index 709eeb26d00866..dae58013ec3545 100644
--- a/Mathlib/RepresentationTheory/Submodule.lean
+++ b/Mathlib/RepresentationTheory/Submodule.lean
@@ -79,7 +79,7 @@ noncomputable def mapSubmodule : ρ.invtSubmodule ≃o Submodule k[G] ρ.asModul
     rw [invtSubmodule, Sublattice.mem_iInf]
     intro g v hv
     simp only [Submodule.orderIsoMapComap_symm_apply, Submodule.mem_comap] at hv ⊢
-    convert q.smul_mem (MonoidAlgebra.of k G g) hv using 1
+    convert! q.smul_mem (MonoidAlgebra.of k G g) hv using 1
     rw [LinearEquiv.coe_coe, ← asModuleEquiv_symm_map_rho]⟩
   left_inv p := by ext; simp
   right_inv q := by ext; aesop
diff --git a/Mathlib/RingTheory/AdicCompletion/Basic.lean b/Mathlib/RingTheory/AdicCompletion/Basic.lean
index b328fb7d5d1e15..031a570bed7988 100644
--- a/Mathlib/RingTheory/AdicCompletion/Basic.lean
+++ b/Mathlib/RingTheory/AdicCompletion/Basic.lean
@@ -888,7 +888,7 @@ theorem le_jacobson_bot [IsAdicComplete I R] : I ≤ (⊥ : Ideal R).jacobson :=
   rw [SModEq.sub_mem, smul_eq_mul, Ideal.mul_top] at hL ⊢
   rw [sub_zero]
   suffices (1 - x * y) * f n - 1 ∈ I ^ n by
-    convert Ideal.sub_mem _ this (Ideal.mul_mem_left _ (1 + -(x * y)) hL) using 1
+    convert! Ideal.sub_mem _ this (Ideal.mul_mem_left _ (1 + -(x * y)) hL) using 1
     ring
   cases n
   · simp only [Ideal.one_eq_top, pow_zero, mem_top]
diff --git a/Mathlib/RingTheory/Adjoin/PowerBasis.lean b/Mathlib/RingTheory/Adjoin/PowerBasis.lean
index d75794aca16099..22eea1d4c8c47c 100644
--- a/Mathlib/RingTheory/Adjoin/PowerBasis.lean
+++ b/Mathlib/RingTheory/Adjoin/PowerBasis.lean
@@ -32,7 +32,7 @@ noncomputable def adjoin.powerBasisAux {x : S} (hx : IsIntegral K x) :
   have hx' :
     IsIntegral K (⟨x, subset_adjoin (Set.mem_singleton x)⟩ : K[(x : S)]) := by
     apply (isIntegral_algebraMap_iff hST).mp
-    convert hx
+    convert! hx
   apply Basis.mk (v := fun i : Fin _ ↦ ⟨x, subset_adjoin (Set.mem_singleton x)⟩ ^ (i : ℕ))
   · have : LinearIndependent K _ := linearIndependent_pow
       (⟨x, self_mem_adjoin_singleton _ _⟩ : K[x])
diff --git a/Mathlib/RingTheory/Adjoin/Tower.lean b/Mathlib/RingTheory/Adjoin/Tower.lean
index 7a1082197337f9..585ddd6c46ce98 100644
--- a/Mathlib/RingTheory/Adjoin/Tower.lean
+++ b/Mathlib/RingTheory/Adjoin/Tower.lean
@@ -122,7 +122,7 @@ theorem exists_subalgebra_of_fg (hAC : (⊤ : Subalgebra A C).FG) (hBC : (⊤ :
                   mem_image₂_of_mem (mem_union_right _ <| mul_mem_mul hyi hyj) hyk⟩
               (subset_span <| Set.mem_insert_of_mem _ hyk : yk ∈ _))
   refine ⟨Algebra.adjoin A (↑s : Set B), Subalgebra.fg_adjoin_finset _, insert 1 y, ?_⟩
-  convert restrictScalars_injective A (Algebra.adjoin A (s : Set B)) C _
+  convert! restrictScalars_injective A (Algebra.adjoin A (s : Set B)) C _
   rw [restrictScalars_top, eq_top_iff, ← Algebra.top_toSubmodule, ← hx, Algebra.adjoin_eq_span,
     span_le]
   refine fun r hr =>
diff --git a/Mathlib/RingTheory/AdjoinRoot.lean b/Mathlib/RingTheory/AdjoinRoot.lean
index 307287e3d544fa..c8423bc7357438 100644
--- a/Mathlib/RingTheory/AdjoinRoot.lean
+++ b/Mathlib/RingTheory/AdjoinRoot.lean
@@ -344,7 +344,7 @@ section AdjoinInv
 
 @[simp]
 theorem root_isInv (r : R) : of _ r * root (C r * X - 1) = 1 := by
-  convert sub_eq_zero.1 ((eval₂_sub _).symm.trans <| eval₂_root <| C r * X - 1) <;>
+  convert! sub_eq_zero.1 ((eval₂_sub _).symm.trans <| eval₂_root <| C r * X - 1) <;>
     simp only [eval₂_mul, eval₂_C, eval₂_X, eval₂_one]
 
 theorem algHom_subsingleton {S : Type*} [CommRing S] [Algebra R S] {r : R} :
diff --git a/Mathlib/RingTheory/Algebraic/Basic.lean b/Mathlib/RingTheory/Algebraic/Basic.lean
index d8786723e0bf6c..d1fefdb9b42f5a 100644
--- a/Mathlib/RingTheory/Algebraic/Basic.lean
+++ b/Mathlib/RingTheory/Algebraic/Basic.lean
@@ -115,7 +115,7 @@ theorem transcendental_iff_ker_eq_bot {x : A} :
 theorem Algebra.isAlgebraic_of_not_injective (h : ¬ Function.Injective (algebraMap R A)) :
     Algebra.IsAlgebraic R A where
   isAlgebraic a := isAlgebraic_iff_not_injective.mpr
-    fun inj ↦ h <| by convert inj.comp C_injective; ext; simp
+    fun inj ↦ h <| by convert! inj.comp C_injective; ext; simp
 
 theorem Algebra.injective_of_transcendental [h : Algebra.Transcendental R A] :
     Function.Injective (algebraMap R A) := by
@@ -659,11 +659,12 @@ theorem inv_eq_of_aeval_divX_ne_zero {x : L} {p : K[X]} (aeval_ne : aeval x (div
 
 theorem inv_eq_of_root_of_coeff_zero_ne_zero {x : L} {p : K[X]} (aeval_eq : aeval x p = 0)
     (coeff_zero_ne : p.coeff 0 ≠ 0) : x⁻¹ = -(aeval x (divX p) / algebraMap _ _ (p.coeff 0)) := by
-  convert inv_eq_of_aeval_divX_ne_zero (p := p) (L := L)
-    (mt (fun h => (algebraMap K L).injective ?_) coeff_zero_ne) using 1
+  convert!
+    inv_eq_of_aeval_divX_ne_zero (p := p) (L := L)
+      (mt (fun h => (algebraMap K L).injective ?_) coeff_zero_ne) using 1
   · rw [aeval_eq, zero_sub, div_neg]
   rw [RingHom.map_zero]
-  convert aeval_eq
+  convert! aeval_eq
   conv_rhs => rw [← divX_mul_X_add p]
   rw [map_add, map_mul, h, zero_mul, zero_add, aeval_C]
 
diff --git a/Mathlib/RingTheory/AlgebraicIndependent/Basic.lean b/Mathlib/RingTheory/AlgebraicIndependent/Basic.lean
index a916bfe1192369..94856a80f5a219 100644
--- a/Mathlib/RingTheory/AlgebraicIndependent/Basic.lean
+++ b/Mathlib/RingTheory/AlgebraicIndependent/Basic.lean
@@ -241,7 +241,7 @@ theorem algebraicIndependent_finset_map_embedding_subtype (s : Set A)
       rw [Finset.mem_map] at h
       obtain ⟨a, _, rfl⟩ := h
       simp only [Subtype.coe_prop, Embedding.coe_subtype]⟩
-  convert AlgebraicIndependent.comp li f _
+  convert! AlgebraicIndependent.comp li f _
   rintro ⟨x, hx⟩ ⟨y, hy⟩
   rw [Finset.mem_map] at hx hy
   obtain ⟨a, _, rfl⟩ := hx
@@ -311,11 +311,11 @@ lemma IsTranscendenceBasis.of_comp_algebraMap [Algebra A A'] [IsScalarTower R A
 for the composition with an algebraic extension. -/
 theorem AlgEquiv.isTranscendenceBasis (e : A ≃ₐ[R] A') (hx : IsTranscendenceBasis R x) :
     IsTranscendenceBasis R (e ∘ x) :=
-  .of_comp e.symm.toAlgHom e.symm.injective (by convert hx; ext; simp)
+  .of_comp e.symm.toAlgHom e.symm.injective (by convert! hx; ext; simp)
 
 theorem AlgEquiv.isTranscendenceBasis_iff (e : A ≃ₐ[R] A') :
     IsTranscendenceBasis R (e ∘ x) ↔ IsTranscendenceBasis R x :=
-  ⟨fun hx ↦ by convert e.symm.isTranscendenceBasis hx; ext; simp, e.isTranscendenceBasis⟩
+  ⟨fun hx ↦ by convert! e.symm.isTranscendenceBasis hx; ext; simp, e.isTranscendenceBasis⟩
 
 section trdeg
 
@@ -346,7 +346,7 @@ theorem lift_trdeg_le_of_surjective (f : A →ₐ[R] A') (hf : Surjective f) :
   rw [trdeg, lift_iSup bddAbove_of_small]
   refine ciSup_le' fun i ↦ (lift_cardinalMk_le_trdeg (x := fun a : i.1 ↦ (⇑f).invFun a) <|
     of_comp f ?_)
-  convert i.2; simp [invFun_eq (hf _)]
+  convert! i.2; simp [invFun_eq (hf _)]
 
 theorem trdeg_le_of_surjective {A' : Type v} [CommRing A'] [Algebra R A'] (f : A →ₐ[R] A')
     (hf : Surjective f) : trdeg R A' ≤ trdeg R A := by
@@ -399,7 +399,7 @@ theorem AlgebraicIndependent.image_of_comp {ι ι'} (s : Set ι) (f : ι → ι'
 theorem AlgebraicIndependent.image {ι} {s : Set ι} {f : ι → A}
     (hs : AlgebraicIndependent R fun x : s => f x) :
     AlgebraicIndependent R fun x : f '' s => (x : A) := by
-  convert AlgebraicIndependent.image_of_comp s f id hs
+  convert! AlgebraicIndependent.image_of_comp s f id hs
 
 theorem algebraicIndependent_iUnion_of_directed {η : Type*} [Nonempty η] {s : η → Set A}
     (hs : Directed (· ⊆ ·) s) (h : ∀ i, AlgebraicIndependent R ((↑) : s i → A)) :
diff --git a/Mathlib/RingTheory/AlgebraicIndependent/TranscendenceBasis.lean b/Mathlib/RingTheory/AlgebraicIndependent/TranscendenceBasis.lean
index 1b261c9e579b6f..95ed4ca9810e96 100644
--- a/Mathlib/RingTheory/AlgebraicIndependent/TranscendenceBasis.lean
+++ b/Mathlib/RingTheory/AlgebraicIndependent/TranscendenceBasis.lean
@@ -185,7 +185,7 @@ theorem IsTranscendenceBasis.polynomial [Nonempty ι] [Subsingleton ι] :
   have := (nonempty_unique ι).some
   refine (isTranscendenceBasis_equiv (Equiv.equivPUnit.{_, 1} _).symm).mp <|
     (MvPolynomial.uniqueAlgEquiv R PUnit).symm.isTranscendenceBasis_iff.mp ?_
-  convert IsTranscendenceBasis.mvPolynomial PUnit R
+  convert! IsTranscendenceBasis.mvPolynomial PUnit R
   ext; simp
 
 variable {ι R}
@@ -575,8 +575,12 @@ lemma of_isAlgebraic_adjoin_insert_diff (hj : j ∈ insert i s)
     rwa [insert_eq_of_mem hi] at H₂
   obtain eq | ne := eq_or_ne (v i) (v j)
   · classical
-    convert H₁.comp_equiv <| .symm <| ((Equiv.swap j i).image s).trans <|
-      .setCongr <| Equiv.image_swap_of_mem_of_notMem hj hi with ⟨x, rfl | hxi, hxj⟩
+    convert!
+      H₁.comp_equiv <|
+        .symm <|
+          ((Equiv.swap j i).image s).trans <|
+            .setCongr <| Equiv.image_swap_of_mem_of_notMem hj hi with
+      ⟨x, rfl | hxi, hxj⟩
     · simp [eq]
     · simp [Equiv.swap_apply_of_ne_of_ne hxj (ne_of_mem_of_not_mem hxi hi)]
   have hi' : v i ∉ v '' s := fun his ↦ Hj <| by
diff --git a/Mathlib/RingTheory/AlgebraicIndependent/Transcendental.lean b/Mathlib/RingTheory/AlgebraicIndependent/Transcendental.lean
index b0136e12d0851f..9266cdcd630040 100644
--- a/Mathlib/RingTheory/AlgebraicIndependent/Transcendental.lean
+++ b/Mathlib/RingTheory/AlgebraicIndependent/Transcendental.lean
@@ -118,7 +118,7 @@ theorem AlgebraicIndepOn.insert_iff {s : Set ι} {i : ι} (h : i ∉ s) :
       AlgebraicIndepOn R x s ∧ Transcendental (adjoin R (x '' s)) (x i) := by
   classical simp_rw [← algebraicIndependent_equiv (subtypeInsertEquivOption h).symm,
     AlgebraicIndepOn]
-  convert option_iff (x := fun i : s ↦ x i) (a := x i) using 2
+  convert! option_iff (x := fun i : s ↦ x i) (a := x i) using 2
   · ext (_ | _) <;> rfl
   · rw [Set.image_eq_range]
 
@@ -141,10 +141,13 @@ theorem algebraicIndependent_of_set_of_finite (s : Set ι)
   refine hfin.diff.induction_on_subset _ (ind.comp (inclusion <| by simp) (inclusion_injective _))
     fun {a u} ha hu ha' h ↦ ?_
   have : a ∉ t ∩ s ∪ u := (·.elim (ha.2 ·.2) ha')
-  convert (((image_eq_range .. ▸ h.option_iff_transcendental <| x a).2 <| H _ (hfin.subset
-      (union_subset inter_subset_left <| hu.trans diff_subset)) h a ha.2 this).comp _
-      (subtypeInsertEquivOption this).injective).comp
-    (Equiv.setCongr union_insert) (Equiv.injective _) with x
+  convert!
+    (((image_eq_range .. ▸ h.option_iff_transcendental <| x a).2 <|
+              H _ (hfin.subset (union_subset inter_subset_left <| hu.trans diff_subset)) h a ha.2
+                this).comp
+          _ (subtypeInsertEquivOption this).injective).comp
+      (Equiv.setCongr union_insert) (Equiv.injective _) with
+    x
   by_cases h : ↑x = a <;> simp [h, Set.subtypeInsertEquivOption]
 
 /-- Variant of `algebraicIndependent_of_finite_type` using `Transcendental`. -/
@@ -181,14 +184,14 @@ theorem iff_adjoin_image (s : Set ι) :
     AlgebraicIndependent R x ↔ AlgebraicIndependent R (fun i : s ↦ x i) ∧
       AlgebraicIndepOn (adjoin R (x '' s)) x sᶜ := by
   rw [show x '' s = range fun i : s ↦ x i by ext; simp]
-  convert ← sumElim_iff
+  convert! ← sumElim_iff
   classical apply algebraicIndependent_equiv' ((Equiv.sumComm ..).trans (Equiv.Set.sumCompl ..))
   ext (_ | _) <;> rfl
 
 theorem iff_adjoin_image_compl (s : Set ι) :
     AlgebraicIndependent R x ↔ AlgebraicIndependent R (fun i : ↥sᶜ ↦ x i) ∧
       AlgebraicIndepOn (adjoin R (x '' sᶜ)) x s := by
-  convert ← iff_adjoin_image _; apply compl_compl
+  convert! ← iff_adjoin_image _; apply compl_compl
 
 theorem iff_transcendental_adjoin_image (i : ι) :
     AlgebraicIndependent R x ↔ AlgebraicIndependent R (fun j : {j // j ≠ i} ↦ x j) ∧
@@ -232,13 +235,13 @@ theorem adjoin_iff_disjoint [Nontrivial A] {s t : Set ι} :
 
 theorem transcendental_adjoin {s : Set ι} {i : ι} (hi : i ∉ s) :
     Transcendental (adjoin R (x '' s)) (x i) := by
-  convert ← hx.adjoin_of_disjoint (Set.disjoint_singleton_right.mpr hi)
+  convert! ← hx.adjoin_of_disjoint (Set.disjoint_singleton_right.mpr hi)
   rw [algebraicIndependent_singleton_iff ⟨i, rfl⟩]
 
 theorem transcendental_adjoin_iff [Nontrivial A] {s : Set ι} {i : ι} :
     Transcendental (adjoin R (x '' s)) (x i) ↔ i ∉ s := by
   rw [← Set.disjoint_singleton_right]
-  convert ← hx.adjoin_iff_disjoint (t := {i})
+  convert! ← hx.adjoin_iff_disjoint (t := { i })
   rw [algebraicIndependent_singleton_iff ⟨i, rfl⟩]
 
 end AlgebraicIndependent
@@ -282,6 +285,6 @@ theorem AlgebraicIndependent.polynomial_aeval_of_transcendental
     (hx : AlgebraicIndependent R x)
     {f : ι → Polynomial R} (hf : ∀ i, Transcendental R (f i)) :
     AlgebraicIndependent R fun i ↦ Polynomial.aeval (x i) (f i) := by
-  convert aeval_of_algebraicIndependent hx (algebraicIndependent_polynomial_aeval_X _ hf)
+  convert! aeval_of_algebraicIndependent hx (algebraicIndependent_polynomial_aeval_X _ hf)
   rw [← AlgHom.comp_apply]
   congr 1; ext1; simp
diff --git a/Mathlib/RingTheory/Artinian/Module.lean b/Mathlib/RingTheory/Artinian/Module.lean
index 5d6fecae1db8e7..47f74093b6d109 100644
--- a/Mathlib/RingTheory/Artinian/Module.lean
+++ b/Mathlib/RingTheory/Artinian/Module.lean
@@ -536,7 +536,7 @@ lemma isField_of_isDomain [IsDomain R] : IsField R := by
   obtain ⟨n, y, hy⟩ := IsArtinian.exists_pow_succ_smul_dvd x (1 : R)
   replace hy : x ^ n * (x * y - 1) = 0 := by
     rw [mul_sub, sub_eq_zero]
-    convert hy using 1
+    convert! hy using 1
     simp [Nat.succ_eq_add_one, pow_add, mul_assoc]
   rw [mul_eq_zero, sub_eq_zero] at hy
   exact ⟨_, hy.resolve_left <| pow_ne_zero _ hx⟩
diff --git a/Mathlib/RingTheory/ChainOfDivisors.lean b/Mathlib/RingTheory/ChainOfDivisors.lean
index 5030ac217e7549..20568210dadabd 100644
--- a/Mathlib/RingTheory/ChainOfDivisors.lean
+++ b/Mathlib/RingTheory/ChainOfDivisors.lean
@@ -186,7 +186,7 @@ theorem eq_pow_second_of_chain_of_has_chain {q : Associates M} {n : ℕ} (hn : n
     (h₂ : ∀ {r : Associates M}, r ≤ q ↔ ∃ i, r = c i) (hq : q ≠ 0) : q = c 1 ^ n := by
   classical
     obtain ⟨i, hi'⟩ := element_of_chain_eq_pow_second_of_chain hn h₁ (@fun r => h₂) (dvd_refl q) hq
-    convert hi'
+    convert! hi'
     refine (Nat.lt_succ_iff.1 i.prop).antisymm' (Nat.le_of_succ_le_succ ?_)
     calc
       n + 1 = (Finset.univ : Finset (Fin (n + 1))).card := (Finset.card_fin _).symm
@@ -387,7 +387,7 @@ theorem mem_normalizedFactors_factor_dvd_iso_of_mem_normalizedFactors {m p : M}
       associatesEquivOfUniqueUnits_symm_apply] at this
     obtain ⟨q, hq, hq'⟩ :=
       exists_mem_normalizedFactors_of_dvd hn this.irreducible
-        (d ⟨p, by apply dvd_of_mem_normalizedFactors; convert hp⟩).prop
+        (d ⟨p, by apply dvd_of_mem_normalizedFactors; convert! hp⟩).prop
     rwa [associated_iff_eq.mp hq']
   have :
     Associates.mk
@@ -404,7 +404,7 @@ theorem mem_normalizedFactors_factor_dvd_iso_of_mem_normalizedFactors {m p : M}
   refine map_prime_of_factor_orderIso (mk_ne_zero.mpr hn) ?_ _
   obtain ⟨q, hq, hq'⟩ :=
     exists_mem_normalizedFactors_of_dvd (mk_ne_zero.mpr hm)
-      (prime_mk.mpr (prime_of_normalized_factor p (by convert hp))).irreducible
+      (prime_mk.mpr (prime_of_normalized_factor p (by convert! hp))).irreducible
       (mk_le_mk_of_dvd (dvd_of_mem_normalizedFactors hp))
   simpa only [associated_iff_eq.mp hq', associatesEquivOfUniqueUnits_symm_apply] using hq
 
diff --git a/Mathlib/RingTheory/ClassGroup.lean b/Mathlib/RingTheory/ClassGroup.lean
index 9e8cfdfac63933..ecf2702d81d56c 100644
--- a/Mathlib/RingTheory/ClassGroup.lean
+++ b/Mathlib/RingTheory/ClassGroup.lean
@@ -140,7 +140,7 @@ theorem ClassGroup.mk_eq_mk_of_coe_ideal {I J : (FractionalIdeal R⁰ <| Fractio
       simpa only [isUnit_iff_ne_zero, ne_eq, mk'_eq_zero_iff_eq_zero] using hx
     refine ⟨this.unit, ?_⟩
     rw [mul_comm, ← Units.val_inj, Units.val_mul, coe_toPrincipalIdeal]
-    convert
+    convert!
       (mk'_mul_coeIdeal_eq_coeIdeal (FractionRing R) <| mem_nonZeroDivisors_of_ne_zero hy).2 h
 
 theorem ClassGroup.mk_eq_one_of_coe_ideal {I : (FractionalIdeal R⁰ <| FractionRing R)ˣ}
@@ -408,7 +408,7 @@ theorem card_classGroup_eq_one [IsPrincipalIdealRing R] : Fintype.card (ClassGro
 /-- The class number is `1` iff the ring of integers is a principal ideal domain. -/
 theorem card_classGroup_eq_one_iff [IsDedekindDomain R] [Fintype (ClassGroup R)] :
     Fintype.card (ClassGroup R) = 1 ↔ IsPrincipalIdealRing R := by
-  constructor; swap; · intros; convert card_classGroup_eq_one (R := R)
+  constructor; swap; · intros; convert! card_classGroup_eq_one (R := R)
   rw [Fintype.card_eq_one_iff]
   rintro ⟨I, hI⟩
   have eq_one : ∀ J : ClassGroup R, J = 1 := fun J => (hI J).trans (hI 1).symm
diff --git a/Mathlib/RingTheory/Coalgebra/TensorProduct.lean b/Mathlib/RingTheory/Coalgebra/TensorProduct.lean
index 177af1a91e0a1e..e5847a6f5d5664 100644
--- a/Mathlib/RingTheory/Coalgebra/TensorProduct.lean
+++ b/Mathlib/RingTheory/Coalgebra/TensorProduct.lean
@@ -107,7 +107,7 @@ private lemma coassoc :
       A ⊗[R] B ⊗[S] (A ⊗[R] B ⊗[S] (A ⊗[R] B)) :=
     TensorProduct.mapOfCompatibleSMul .. ∘ₗ
         TensorProduct.map .id (TensorProduct.mapOfCompatibleSMul ..) ∘ₗ F.toLinearMap
-  convert congr(F ($(Coalgebra.coassoc_apply x) ⊗ₜ[R] $(Coalgebra.coassoc_apply y))) using 1
+  convert! congr(F ($(Coalgebra.coassoc_apply x) ⊗ₜ[R] $(Coalgebra.coassoc_apply y))) using 1
   · dsimp
     hopf_tensor_induction comul (R := S) x with x₁ x₂
     hopf_tensor_induction comul (R := R) y with y₁ y₂
@@ -130,9 +130,10 @@ instance instCoalgebra : Coalgebra S (A ⊗[R] B) where
   coassoc := coassoc (R := R)
   rTensor_counit_comp_comul := by
     ext x y
-    convert congr((TensorProduct.lid S _).symm
-      (TensorProduct.lid _ _ $(rTensor_counit_comul (R := S) x) ⊗ₜ[R]
-        TensorProduct.lid _ _ $(rTensor_counit_comul (R := R) y)))
+    convert!
+      congr((TensorProduct.lid S _).symm
+        (TensorProduct.lid _ _ $(rTensor_counit_comul (R := S) x) ⊗ₜ[R]
+          TensorProduct.lid _ _ $(rTensor_counit_comul (R := R) y)))
     · dsimp
       hopf_tensor_induction comul (R := S) x with x₁ x₂
       hopf_tensor_induction comul (R := R) y with y₁ y₂
@@ -143,9 +144,10 @@ instance instCoalgebra : Coalgebra S (A ⊗[R] B) where
       simp only [one_smul]
   lTensor_counit_comp_comul := by
     ext x y
-    convert congr((TensorProduct.rid S _).symm
-      (TensorProduct.rid _ _ $(lTensor_counit_comul (R := S) x) ⊗ₜ[R]
-        TensorProduct.rid _ _ $(lTensor_counit_comul (R := R) y)))
+    convert!
+      congr((TensorProduct.rid S _).symm
+        (TensorProduct.rid _ _ $(lTensor_counit_comul (R := S) x) ⊗ₜ[R]
+          TensorProduct.rid _ _ $(lTensor_counit_comul (R := R) y)))
     · dsimp
       hopf_tensor_induction comul (R := S) x with x₁ x₂
       hopf_tensor_induction comul (R := R) y with y₁ y₂
diff --git a/Mathlib/RingTheory/Congruence/Hom.lean b/Mathlib/RingTheory/Congruence/Hom.lean
index c57e8351325866..24730a89106c74 100644
--- a/Mathlib/RingTheory/Congruence/Hom.lean
+++ b/Mathlib/RingTheory/Congruence/Hom.lean
@@ -340,7 +340,7 @@ noncomputable def comapQuotientEquivOfSurj
 @[simp] lemma comapQuotientEquivOfSurj_symm_mk' (c : RingCon M) (f : N ≃+* M)
     {d : RingCon N} (hcd : d = c.comap f) (x : N) :
     (comapQuotientEquivOfSurj c (f : N →+* M) f.surjective hcd).symm ⟦f x⟧ = ↑x := by
-  convert RingEquiv.symm_apply_apply _ _
+  convert! RingEquiv.symm_apply_apply _ _
   rw [comapQuotientEquivOfSurj_mk, RingEquiv.coe_toRingHom]
   rfl
 
diff --git a/Mathlib/RingTheory/Coprime/Ideal.lean b/Mathlib/RingTheory/Coprime/Ideal.lean
index b82965f124b6b9..a33ce013e1590b 100644
--- a/Mathlib/RingTheory/Coprime/Ideal.lean
+++ b/Mathlib/RingTheory/Coprime/Ideal.lean
@@ -67,7 +67,7 @@ theorem iSup_iInf_eq_top_iff_pairwise {t : Finset ι} (h : t.Nonempty) (I : ι 
     case a3 =>
       rw [← @if_pos _ _ h.choose_spec R (μ a) 0, ← Finset.sum_pi_single', ← Finset.sum_add_distrib]
         at hμ
-      convert hμ
+      convert! hμ
       rename_i i _
       rw [Pi.add_apply, Submodule.coe_add, Submodule.coe_mk]
       by_cases hi : i = h.choose
diff --git a/Mathlib/RingTheory/Coprime/Lemmas.lean b/Mathlib/RingTheory/Coprime/Lemmas.lean
index 9c65eddd26194f..d5c4654c6cf11b 100644
--- a/Mathlib/RingTheory/Coprime/Lemmas.lean
+++ b/Mathlib/RingTheory/Coprime/Lemmas.lean
@@ -141,11 +141,11 @@ theorem exists_sum_eq_one_iff_pairwise_coprime [DecidableEq I] (h : t.Nonempty)
           @if_pos _ _ h.choose_spec R (_ * _) 0, ← sum_pi_single', ← sum_add_distrib] at hμ
         rw [← hμ, sum_congr rfl]
         intro x hx
-        convert add_mul (R := R) _ _ _ using 2
+        convert! add_mul (R := R) _ _ _ using 2
         · by_cases hx : x = h.choose
           · rw [hx, Pi.single_eq_same, Pi.single_eq_same]
           · rw [Pi.single_eq_of_ne hx, Pi.single_eq_of_ne hx, zero_mul]
-        · convert (mul_assoc _ _ _).symm
+        · convert! (mul_assoc _ _ _).symm
           rw [prod_eq_prod_diff_singleton_mul (mem x hx), mul_comm, sdiff_sdiff_comm,
             sdiff_singleton_eq_erase a, erase_insert hat]
       · have : IsCoprime (s b) (s a) :=
@@ -177,7 +177,7 @@ theorem exists_sum_eq_one_iff_pairwise_coprime [DecidableEq I] (h : t.Nonempty)
 
 theorem exists_sum_eq_one_iff_pairwise_coprime' [Fintype I] [Nonempty I] [DecidableEq I] :
     (∃ μ : I → R, (∑ i : I, μ i * ∏ j ∈ {i}ᶜ, s j) = 1) ↔ Pairwise (IsCoprime on s) := by
-  convert exists_sum_eq_one_iff_pairwise_coprime Finset.univ_nonempty (s := s) using 1
+  convert! exists_sum_eq_one_iff_pairwise_coprime Finset.univ_nonempty (s := s) using 1
   simp only [pairwise_subtype_iff_pairwise_finset', coe_univ, Set.pairwise_univ]
 
 theorem pairwise_coprime_iff_coprime_prod [DecidableEq I] :
diff --git a/Mathlib/RingTheory/DedekindDomain/AdicValuation.lean b/Mathlib/RingTheory/DedekindDomain/AdicValuation.lean
index acedc29b14dc74..d55c1661cb1077 100644
--- a/Mathlib/RingTheory/DedekindDomain/AdicValuation.lean
+++ b/Mathlib/RingTheory/DedekindDomain/AdicValuation.lean
@@ -732,7 +732,7 @@ theorem adicCompletionIntegers.mem_units_iff_valued_eq_one {a : (v.adicCompletio
     a ∈ (v.adicCompletionIntegers K).units ↔ Valued.v a.1 = 1 := by
   refine ⟨fun h ↦ ?_, fun h ↦
      ⟨h.le, by simp [mem_adicCompletionIntegers, inv_le_one_iff₀, h.symm.le]⟩⟩
-  convert isUnit_iff_valued_eq_one.1 (Submonoid.unitsEquivIsUnitSubmonoid _ ⟨_, h⟩).2
+  convert! isUnit_iff_valued_eq_one.1 (Submonoid.unitsEquivIsUnitSubmonoid _ ⟨_, h⟩).2
 
 section AbsoluteValue
 
diff --git a/Mathlib/RingTheory/DedekindDomain/Different.lean b/Mathlib/RingTheory/DedekindDomain/Different.lean
index 1e25be883fcef2..f8423b5d363d6e 100644
--- a/Mathlib/RingTheory/DedekindDomain/Different.lean
+++ b/Mathlib/RingTheory/DedekindDomain/Different.lean
@@ -129,7 +129,7 @@ variable [IsDomain A] [IsFractionRing A K] [FiniteDimensional K L] [Algebra.IsSe
 
 lemma traceDual_top [Decidable (IsField A)] :
     (⊤ : Submodule B L)ᵛ = if IsField A then ⊤ else ⊥ := by
-  convert traceDual_top'
+  convert! traceDual_top'
   rw [← IsFractionRing.surjective_iff_isField (R := A) (K := K),
     LinearMap.range_eq_top.mpr (Algebra.trace_surjective K L),
     ← RingHom.range_eq_top, _root_.eq_top_iff]
@@ -240,7 +240,7 @@ def dual (I : FractionalIdeal B⁰ L) :
     · rw [← (IsIntegralClosure.algebraMap_injective B A L).ne_iff, hy, map_zero,
         ← (algebraMap K L).map_zero, (algebraMap K L).injective.ne_iff]
       exact discr_not_zero_of_basis K b
-    · convert isIntegral_discr_mul_of_mem_traceDual I hb hx' hz using 1
+    · convert! isIntegral_discr_mul_of_mem_traceDual I hb hx' hz using 1
       · ext w; exact (IsIntegralClosure.isIntegral_iff (A := B)).symm
       · rw [Algebra.smul_def, map_mul, hy, ← Algebra.smul_def]⟩
 
@@ -297,7 +297,7 @@ lemma dual_ne_zero (hI : I ≠ 0) :
   apply IsIntegrallyClosed.isIntegral_iff.mp
   apply isIntegral_trace
   dsimp
-  convert hb' a ha using 1
+  convert! hb' a ha using 1
   · ext w
     exact IsIntegralClosure.isIntegral_iff (A := B)
   · exact (Algebra.smul_def _ _).symm
@@ -913,8 +913,9 @@ theorem not_dvd_differentIdeal_iff
     let K := FractionRing A
     let L := FractionRing B
     have : IsLocalization B⁰ (Localization.AtPrime (⊥ : Ideal B)) := by
-      convert (inferInstance :
-        IsLocalization (⊥ : Ideal B).primeCompl (Localization.AtPrime (⊥ : Ideal B)))
+      convert!
+        (inferInstance :
+          IsLocalization (⊥ : Ideal B).primeCompl (Localization.AtPrime (⊥ : Ideal B)))
       ext; simp [Ideal.primeCompl]
     refine (Algebra.FormallyUnramified.iff_of_equiv (A := L)
       ((IsLocalization.algEquiv B⁰ _ _).restrictScalars A)).mp ?_
diff --git a/Mathlib/RingTheory/DedekindDomain/Factorization.lean b/Mathlib/RingTheory/DedekindDomain/Factorization.lean
index ab246fc4d92ba2..bcbafee9cef0a0 100644
--- a/Mathlib/RingTheory/DedekindDomain/Factorization.lean
+++ b/Mathlib/RingTheory/DedekindDomain/Factorization.lean
@@ -533,7 +533,7 @@ theorem count_finprod (exps : HeightOneSpectrum R → ℤ)
     (h_exps : ∀ᶠ v : HeightOneSpectrum R in Filter.cofinite, exps v = 0) :
     count K v (∏ᶠ v : HeightOneSpectrum R,
       (v.asIdeal : FractionalIdeal R⁰ K) ^ exps v) = exps v := by
-  convert count_finsuppProd K v (Finsupp.mk h_exps.toFinset exps (fun _ ↦ h_exps.mem_toFinset))
+  convert! count_finsuppProd K v (Finsupp.mk h_exps.toFinset exps (fun _ ↦ h_exps.mem_toFinset))
   rw [finprod_eq_finsetProd_of_mulSupport_subset (s := h_exps.toFinset), Finsupp.prod]
   · rfl
   · rw [Finite.coe_toFinset]
@@ -610,7 +610,7 @@ theorem finite_factors (I : FractionalIdeal R⁰ K) :
   by_cases hI : I = 0
   · simp only [hI, count_zero, Filter.eventually_cofinite, not_true_eq_false, setOf_false,
       finite_empty]
-  · convert finite_factors' hI (choose_spec (choose_spec (exists_eq_spanSingleton_mul I))).2
+  · convert! finite_factors' hI (choose_spec (choose_spec (exists_eq_spanSingleton_mul I))).2
     rw [count_ne_zero K _ hI]
 
 end FractionalIdeal
@@ -665,7 +665,7 @@ lemma IsDedekindDomain.exists_sup_span_eq {I J : Ideal R} (hIJ : I ≤ J) (hI :
   rintro ⟨q, hq⟩
   by_cases hqp : q = p'
   · subst hqp
-    convert sub_mem H₁ H₂
+    convert! sub_mem H₁ H₂
     rw [Finset.sum_eq_add_sum_diff_singleton_of_mem hp's, add_sub_cancel_right]
   · refine Ideal.mul_mono_right ?_ (ha p' hp's)
     exact Ideal.prod_le_inf.trans (Finset.inf_le (b := q) (by simpa [hq] using hqp))
@@ -786,7 +786,7 @@ def quotientEquiv (I J I' J' : FractionalIdeal R⁰ K)
     refine inf_le_inf ?_ le_rfl
     intro x hx
     rw [spanSingleton_inv]
-    convert mul_mem_mul (mem_spanSingleton_self _ _) hx
+    convert! mul_mem_mul (mem_spanSingleton_self _ _) hx
     simp [H']
   · have H : Submodule.map (Algebra.lsmul R R K (I'.divMod I J')) ↑I =
         (spanSingleton R⁰ (I'.divMod I J') * I) := by
diff --git a/Mathlib/RingTheory/DedekindDomain/Ideal/Basic.lean b/Mathlib/RingTheory/DedekindDomain/Ideal/Basic.lean
index 78cf95c4ea7e67..497e84753a0c09 100644
--- a/Mathlib/RingTheory/DedekindDomain/Ideal/Basic.lean
+++ b/Mathlib/RingTheory/DedekindDomain/Ideal/Basic.lean
@@ -89,7 +89,7 @@ theorem FractionalIdeal.adjoinIntegral_eq_one_of_isUnit [Algebra A K] [IsFractio
     apply coeToSubmodule_injective
     simp only [coe_mul, adjoinIntegral_coe, I]
     rw [(Algebra.adjoin A {x}).isIdempotentElem_toSubmodule]
-  convert congr_arg (· * I⁻¹) mul_self <;>
+  convert! congr_arg (· * I⁻¹) mul_self <;>
     simp only [(mul_inv_cancel_iff_isUnit K).mpr hI, mul_assoc, mul_one]
 
 namespace IsDedekindDomainInv
@@ -218,7 +218,7 @@ theorem PrimeSpectrum.exists_multiset_prod_cons_le_and_prod_not_le [IsDedekindDo
     subst hPM'
     -- By minimality of `Z`, erasing `P` from `Z` is exactly what we need.
     refine ⟨Z.erase P, ?_, ?_⟩
-    · convert hZI
+    · convert! hZI
       rw [this, Multiset.cons_erase hPZ']
     · refine fun h => h_eraseZ (Z.erase P) ⟨h, ?_⟩ (Multiset.erase_lt.mpr hPZ)
       exact hZP0
@@ -425,7 +425,7 @@ theorem Ideal.dvdNotUnit_iff_lt {I J : Ideal A} : DvdNotUnit I J ↔ J < I :=
 instance : WfDvdMonoid (Ideal A) where
   wf := by
     have : WellFoundedGT (Ideal A) := inferInstance
-    convert this.wf using 3
+    convert! this.wf using 3
     exact Ideal.dvdNotUnit_iff_lt
 
 instance Ideal.uniqueFactorizationMonoid : UniqueFactorizationMonoid (Ideal A) :=
diff --git a/Mathlib/RingTheory/DedekindDomain/Ideal/Lemmas.lean b/Mathlib/RingTheory/DedekindDomain/Ideal/Lemmas.lean
index 261fc6880813c5..0db61abbd4130b 100644
--- a/Mathlib/RingTheory/DedekindDomain/Ideal/Lemmas.lean
+++ b/Mathlib/RingTheory/DedekindDomain/Ideal/Lemmas.lean
@@ -168,7 +168,7 @@ theorem pow_right_strictAnti (I : Ideal A) (hI0 : I ≠ ⊥) (hI1 : I ≠ ⊤) :
 
 theorem pow_lt_self (I : Ideal A) (hI0 : I ≠ ⊥) (hI1 : I ≠ ⊤) (e : ℕ) (he : 2 ≤ e) :
     I ^ e < I := by
-  convert I.pow_right_strictAnti hI0 hI1 he
+  convert! I.pow_right_strictAnti hI0 hI1 he
   dsimp only
   rw [pow_one]
 
@@ -370,7 +370,7 @@ lemma FractionalIdeal.sup_mul_inf (I J : FractionalIdeal A⁰ K) :
   rw [mul_left_comm, ← mul_add, ← mul_add, ← mul_inf₀ (FractionalIdeal.zero_le _),
     ← mul_inf₀ (FractionalIdeal.zero_le _)] at this
   simp only [FractionalIdeal.sup_eq_add, _root_.map_mul, ← spanSingleton_mul_spanSingleton]
-  convert this using 1 <;> ring
+  convert! this using 1 <;> ring
 
 end Gcd
 
diff --git a/Mathlib/RingTheory/DedekindDomain/LinearDisjoint.lean b/Mathlib/RingTheory/DedekindDomain/LinearDisjoint.lean
index 16a70a0fded7bb..b6d0791e01c094 100644
--- a/Mathlib/RingTheory/DedekindDomain/LinearDisjoint.lean
+++ b/Mathlib/RingTheory/DedekindDomain/LinearDisjoint.lean
@@ -228,8 +228,9 @@ noncomputable def ofIsCoprimeDifferentIdeal (h₁ : F₁.LinearDisjoint F₂)
     apply map_injective_of_injective (f := (IsScalarTower.toAlgHom R₁ B L).toLinearMap)
       (FaithfulSMul.algebraMap_injective B L)
     rw [map_span, ← Set.range_comp]
-    convert Module.Basis.ofIsCoprimeDifferentIdeal_aux A B R₁ R₂ h₁ h₂ h₃ b₂
-      (b.localizationLocalization_span K A⁰ F₂)
+    convert!
+      Module.Basis.ofIsCoprimeDifferentIdeal_aux A B R₁ R₂ h₁ h₂ h₃ b₂
+        (b.localizationLocalization_span K A⁰ F₂)
     · ext
       simp [b₂, v, ← IsScalarTower.algebraMap_apply]
     · ext; simp
diff --git a/Mathlib/RingTheory/Derivation/MapCoeffs.lean b/Mathlib/RingTheory/Derivation/MapCoeffs.lean
index ec0737106fd727..b237b66fdd3274 100644
--- a/Mathlib/RingTheory/Derivation/MapCoeffs.lean
+++ b/Mathlib/RingTheory/Derivation/MapCoeffs.lean
@@ -99,7 +99,7 @@ theorem apply_aeval_eq [IsScalarTower R A B] [IsScalarTower A B M'] (d : Derivat
     (x : B) (p : A[X]) :
     d (aeval x p) = PolynomialModule.eval x ((d.compAlgebraMap A).mapCoeffs p) +
       aeval x (derivative p) • d x := by
-  convert apply_aeval_eq' (d.compAlgebraMap A) d LinearMap.id _ x p
+  convert! apply_aeval_eq' (d.compAlgebraMap A) d LinearMap.id _ x p
   · apply Finsupp.ext
     intro x
     rfl
@@ -144,7 +144,7 @@ variable {R : Type*} [CommRing R] [Differential R] [Algebra A R] [DifferentialAl
 
 theorem deriv_aeval_eq (x : R) (p : A[X]) :
     (aeval x p)′ = aeval x (mapCoeffs p) + aeval x (derivative p) * x′ := by
-  convert Derivation.apply_aeval_eq' Differential.deriv _ (Algebra.linearMap A R) ..
+  convert! Derivation.apply_aeval_eq' Differential.deriv _ (Algebra.linearMap A R) ..
   · simp [mapCoeffs]
   · simp [deriv_algebraMap]
 
diff --git a/Mathlib/RingTheory/Derivation/ToSquareZero.lean b/Mathlib/RingTheory/Derivation/ToSquareZero.lean
index 3710e74867ed53..a49ac0ff2b1f1f 100644
--- a/Mathlib/RingTheory/Derivation/ToSquareZero.lean
+++ b/Mathlib/RingTheory/Derivation/ToSquareZero.lean
@@ -58,7 +58,7 @@ def derivationToSquareZeroOfLift [IsScalarTower R A B] (hI : I ^ 2 = ⊥) (f : A
     let F := diffToIdealOfQuotientCompEq I f (IsScalarTower.toAlgHom R A B) (by rw [e]; ext; rfl)
     have : (f x - algebraMap A B x) * (f y - algebraMap A B y) = 0 := by
       rw [← Ideal.mem_bot, ← hI, pow_two]
-      convert Ideal.mul_mem_mul (F x).2 (F y).2 using 1
+      convert! Ideal.mul_mem_mul (F x).2 (F y).2 using 1
     ext
     dsimp only [Submodule.coe_add, Submodule.coe_mk, LinearMap.coe_mk,
       diffToIdealOfQuotientCompEq_apply, Submodule.coe_smul_of_tower, IsScalarTower.coe_toAlgHom',
@@ -88,7 +88,7 @@ def liftOfDerivationToSquareZero [IsScalarTower R A B] (hI : I ^ 2 = ⊥) (f : D
     map_mul' := fun x y => by
       have : (f x : B) * f y = 0 := by
         rw [← Ideal.mem_bot, ← hI, pow_two]
-        convert Ideal.mul_mem_mul (f x).2 (f y).2 using 1
+        convert! Ideal.mul_mem_mul (f x).2 (f y).2 using 1
       simp only [map_mul, f.leibniz, add_mul, mul_add, Submodule.coe_add,
         Submodule.coe_smul_of_tower, Algebra.smul_def, this]
       ring
diff --git a/Mathlib/RingTheory/DiscreteValuationRing/TFAE.lean b/Mathlib/RingTheory/DiscreteValuationRing/TFAE.lean
index 78364d2f2209ef..ccf0649bb93f6f 100644
--- a/Mathlib/RingTheory/DiscreteValuationRing/TFAE.lean
+++ b/Mathlib/RingTheory/DiscreteValuationRing/TFAE.lean
@@ -219,7 +219,7 @@ theorem IsDiscreteValuationRing.TFAE [IsNoetherianRing R] [IsLocalRing R] [IsDom
     simp [Nat.le_one_iff_eq_zero_or_eq_one, finrank_cotangentSpace_eq_zero_iff, h]
   rw [this]
   have : maximalIdeal R ≠ ⊥ := isField_iff_maximalIdeal_eq.not.mp h
-  convert tfae_of_isNoetherianRing_of_isLocalRing_of_isDomain R
+  convert! tfae_of_isNoetherianRing_of_isLocalRing_of_isDomain R
   · exact ⟨fun _ ↦ inferInstance, fun h ↦ { h with not_a_field' := this }⟩
   · exact ⟨fun h P h₁ h₂ ↦ h.unique ⟨h₁, h₂⟩ ⟨this, inferInstance⟩,
       fun H ↦ ⟨_, ⟨this, inferInstance⟩, fun P hP ↦ H P hP.1 hP.2⟩⟩
diff --git a/Mathlib/RingTheory/Discriminant.lean b/Mathlib/RingTheory/Discriminant.lean
index cb304cbad648b4..d1a54cd687e0ef 100644
--- a/Mathlib/RingTheory/Discriminant.lean
+++ b/Mathlib/RingTheory/Discriminant.lean
@@ -299,7 +299,7 @@ section Int
 /-- Two (finite) ℤ-bases have the same discriminant. -/
 theorem discr_eq_discr (b : Basis ι ℤ A) (b' : Basis ι ℤ A) :
     Algebra.discr ℤ b = Algebra.discr ℤ b' := by
-  convert Algebra.discr_of_matrix_vecMul b' (b'.toMatrix b)
+  convert! Algebra.discr_of_matrix_vecMul b' (b'.toMatrix b)
   · rw [Basis.toMatrix_map_vecMul]
   · suffices IsUnit (b'.toMatrix b).det by
       rw [Int.isUnit_iff, ← sq_eq_one_iff] at this
diff --git a/Mathlib/RingTheory/DividedPowerAlgebra/Init.lean b/Mathlib/RingTheory/DividedPowerAlgebra/Init.lean
index 4332663e273c86..1fb73707b3541a 100644
--- a/Mathlib/RingTheory/DividedPowerAlgebra/Init.lean
+++ b/Mathlib/RingTheory/DividedPowerAlgebra/Init.lean
@@ -125,7 +125,7 @@ protected theorem induction_on' {P : DividedPowerAlgebra R M → Prop} (f : Divi
   rw [← hf]
   induction F using MvPolynomial.induction_on generalizing f with
   | C a =>
-      convert h_C a using 1
+      convert! h_C a using 1
       rw [mkAlgHom, AlgHom.coe_mk]
   | add g1 g2 hg1 hg2 =>
       rw [map_add]
diff --git a/Mathlib/RingTheory/DividedPowers/Basic.lean b/Mathlib/RingTheory/DividedPowers/Basic.lean
index 33f9b232d19512..2bf5f7e6a79e5a 100644
--- a/Mathlib/RingTheory/DividedPowers/Basic.lean
+++ b/Mathlib/RingTheory/DividedPowers/Basic.lean
@@ -320,7 +320,7 @@ theorem dpow_sum' {M : Type*} [AddCommMonoid M] {I : AddSubmonoid M} (dpow : ℕ
       conv_lhs => rw [← m.fill_filterNe a]
       exact Sym.count_coe_fill_of_ne (ne_of_mem_of_not_mem hi ha)
     · intro m hm
-      convert sym_filterNe_mem a hm
+      convert! sym_filterNe_mem a hm
       rw [erase_insert ha]
 
 variable {ι : Type*} [DecidableEq ι]
diff --git a/Mathlib/RingTheory/Etale/Kaehler.lean b/Mathlib/RingTheory/Etale/Kaehler.lean
index f548898ec50c78..5aabf14d3d3bbf 100644
--- a/Mathlib/RingTheory/Etale/Kaehler.lean
+++ b/Mathlib/RingTheory/Etale/Kaehler.lean
@@ -53,7 +53,7 @@ lemma KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_symm_D_algebraMap
 lemma KaehlerDifferential.isBaseChange_of_formallyEtale [Algebra.FormallyEtale S T] :
     IsBaseChange T (map R R S T) := by
   change Function.Bijective _
-  convert (tensorKaehlerEquivOfFormallyEtale R S T).bijective using 1
+  convert! (tensorKaehlerEquivOfFormallyEtale R S T).bijective using 1
   change _ = ((tensorKaehlerEquivOfFormallyEtale
     R S T).toLinearMap.restrictScalars S : T ⊗[S] Ω[S⁄R] → _)
   congr!
@@ -68,8 +68,9 @@ instance KaehlerDifferential.isLocalizedModule_map (M : Submonoid S) [IsLocaliza
 lemma KaehlerDifferential.span_range_map_derivation_of_isLocalization
     (M : Submonoid S) [IsLocalization M T] :
     Submodule.span T (Set.range <| map R R S T ∘ D R S) = ⊤ := by
-  convert span_eq_top_of_isLocalizedModule T M (map R R S T) (v := Set.range <| D R S)
-    (span_range_derivation R S)
+  convert!
+    span_eq_top_of_isLocalizedModule T M (map R R S T) (v := Set.range <| D R S)
+      (span_range_derivation R S)
   rw [← Set.range_comp, Function.comp_def]
 
 namespace Algebra.Extension
@@ -306,7 +307,7 @@ def tensorH1CotangentOfIsLocalization (M : Submonoid S) [IsLocalization M T] :
     .of_algebraMap_eq fun r ↦ (f.algebraMap_toRingHom r).symm
   haveI : IsLocalizedModule M' (IsScalarTower.toAlgHom P.Ring S T).toLinearMap := by
     rw [isLocalizedModule_iff_isLocalization]
-    convert ‹IsLocalization M T› using 1
+    convert! ‹IsLocalization M T› using 1
     exact Submonoid.map_comap_eq_of_surjective P.algebraMap_surjective _
   refine Extension.tensorH1CotangentOfFormallyEtale f rfl ?_ ?_ ≪≫ₗ
       Extension.equivH1CotangentOfFormallySmooth _
diff --git a/Mathlib/RingTheory/Etale/QuasiFinite.lean b/Mathlib/RingTheory/Etale/QuasiFinite.lean
index c2b5ef8531246b..f2b347843c95ab 100644
--- a/Mathlib/RingTheory/Etale/QuasiFinite.lean
+++ b/Mathlib/RingTheory/Etale/QuasiFinite.lean
@@ -129,7 +129,7 @@ lemma Localization.exists_finite_awayMapₐ_of_surjective_awayMapₐ
       simp_rw [← hs, map_pow, AlgHom.commutes, ← pow_mul] at this
       refine ⟨s ^ m * b, (n + m' * m), 0, this ▸ ?_⟩
       simp [pow_add, mul_assoc]
-    convert h₁.trans _ _ (RingHom.IsIntegral.of_finite (.of_surjective _ h₂)) using 1
+    convert! h₁.trans _ _ (RingHom.IsIntegral.of_finite (.of_surjective _ h₂)) using 1
     refine IsLocalization.ringHom_ext (.powers r) (RingHom.ext fun x ↦ ?_)
     simp [Localization.awayMap, IsLocalization.Away.map, ← IsScalarTower.algebraMap_apply R T]
   · algebraize [(Localization.awayMapₐ (Algebra.ofId R T) r).toRingHom]
@@ -359,7 +359,7 @@ lemma Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_aux₂
       (Localization.Away (φ e))
       (Localization.Away (Algebra.ofId R' (Localization.Away e) f))
   refine RingHom.finite_algebraMap.mp ?_
-  convert equiv.symm.toRingEquiv.finite.comp hf
+  convert! equiv.symm.toRingEquiv.finite.comp hf
   apply IsLocalization.ringHom_ext (.powers f)
   dsimp [-AlgEquiv.symm_toRingEquiv,
     ← AlgEquiv.toAlgHom_toRingHom, -AlgHomClass.toRingHom_toAlgHom]
@@ -426,7 +426,7 @@ lemma Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq
     rwa [← P'f.over_def P']
   · suffices Function.Bijective ⇑(Ideal.ResidueField.mapₐ P Pf
         (IsScalarTower.toAlgHom R R' (Localization.Away f)) (Pf.over_def P)) by
-      convert this.comp hpP; rw [← AlgHom.coe_comp]; congr; ext
+      convert! this.comp hpP; rw [← AlgHom.coe_comp]; congr; ext
     exact (RingHom.surjectiveOnStalks_of_isLocalization (.powers f)
       _).residueFieldMap_bijective _ _ _
   · intro P'' _ _ hP''
diff --git a/Mathlib/RingTheory/Extension/Basic.lean b/Mathlib/RingTheory/Extension/Basic.lean
index b71de23caf2efe..eefde687aba817 100644
--- a/Mathlib/RingTheory/Extension/Basic.lean
+++ b/Mathlib/RingTheory/Extension/Basic.lean
@@ -517,7 +517,7 @@ noncomputable def cotangentEquiv : S ⊗[P.Ring] P.ker ≃ₗ[S] P.Cotangent :=
       · rw [smul_tmul]; rfl
       · simp_all [Algebra.smul_def]
     · intro a ha b hb ha' hb'
-      convert congr($ha' + $hb')
+      convert! congr($ha' + $hb')
       rw [← tmul_add]
       rfl
   · intro x
diff --git a/Mathlib/RingTheory/Extension/Cotangent/BaseChange.lean b/Mathlib/RingTheory/Extension/Cotangent/BaseChange.lean
index 04fd2e26e6b62c..18941666d8d90e 100644
--- a/Mathlib/RingTheory/Extension/Cotangent/BaseChange.lean
+++ b/Mathlib/RingTheory/Extension/Cotangent/BaseChange.lean
@@ -57,7 +57,7 @@ def tensorCotangentSpace (P : Extension.{u} R S) (T : Type*) [CommRing T] [Algeb
       rfl
   letI PT : Extension T (T ⊗[R] S) := P.baseChange
   haveI : IsPushout R T P.Ring PT.Ring := by
-    convert TensorProduct.isPushout (R := R) (T := P.Ring) (S := T)
+    convert! TensorProduct.isPushout (R := R) (T := P.Ring) (S := T)
     exact Algebra.algebra_ext _ _ fun _ ↦ rfl
   haveI : IsScalarTower P.Ring PT.Ring (T ⊗[R] S) := .of_algebraMap_eq' rfl
   (IsTensorProduct.assocOfMapSMul (TensorProduct.mk R T S) (isTensorProduct _ _ _)
diff --git a/Mathlib/RingTheory/Extension/Cotangent/Basic.lean b/Mathlib/RingTheory/Extension/Cotangent/Basic.lean
index 9b1e8c7ecf9d6c..48280df50545d6 100644
--- a/Mathlib/RingTheory/Extension/Cotangent/Basic.lean
+++ b/Mathlib/RingTheory/Extension/Cotangent/Basic.lean
@@ -223,7 +223,7 @@ lemma Hom.sub_aux (f g : Hom P P') (x y) :
         Function.comp_apply,
         ker, RingHom.mem_ker, map_sub, algebraMap_toRingHom,
         algebraMap_σ, sub_self, toAlgHom_apply]
-  convert this using 1
+  convert! this using 1
   simp only [map_mul]
   ring
 
diff --git a/Mathlib/RingTheory/Extension/Cotangent/Basis.lean b/Mathlib/RingTheory/Extension/Cotangent/Basis.lean
index 57be2b7a9908e7..1e7ce2133a4172 100644
--- a/Mathlib/RingTheory/Extension/Cotangent/Basis.lean
+++ b/Mathlib/RingTheory/Extension/Cotangent/Basis.lean
@@ -90,7 +90,7 @@ set_option backward.isDefEq.respectTransparency false in
 instance : IsLocalization.Away D.gbar S := by
   refine .of_surjective_of_isScalarTower (n := 1) ?_ ?_ _ ?_ (by simpa using D.hg)
   · refine .of_comp (g := algebraMap P.Ring D.T) ?_
-    convert P.algebraMap_surjective
+    convert! P.algebraMap_surjective
     ext x
     exact (IsScalarTower.algebraMap_apply _ D.T S x).symm
   · simp [T, Ideal.Quotient.mk_surjective]
@@ -297,7 +297,7 @@ public lemma exists_presentation_of_basis_cotangent [Algebra.FinitePresentation
   have hJfg : P.ker.FG := by
     rw [P.ker_eq_ker_aeval_val]
     apply FinitePresentation.ker_fG_of_surjective
-    convert P.algebraMap_surjective
+    convert! P.algebraMap_surjective
     simp [P.algebraMap_eq]
   have hJ : J ≤ P.ker := by simp [J, Ideal.span_le, Set.range_subset_iff]
   suffices hJ : P.ker ≤ J ⊔ P.ker • P.ker by
@@ -318,7 +318,7 @@ public lemma exists_presentation_of_basis_cotangent [Algebra.FinitePresentation
     Function.comp_def, ← Submodule.restrictScalars_span P.Ring S P.algebraMap_surjective]
   refine le_trans le_top (top_le_iff.mpr ?_)
   rw [Submodule.restrictScalars_eq_top_iff]
-  convert b₀.span_eq
+  convert! b₀.span_eq
   exact hf _
 
 open PresentationOfFreeCotangent in
diff --git a/Mathlib/RingTheory/Extension/Generators.lean b/Mathlib/RingTheory/Extension/Generators.lean
index 5ea6b2b1bdedfd..25e43405b706bc 100644
--- a/Mathlib/RingTheory/Extension/Generators.lean
+++ b/Mathlib/RingTheory/Extension/Generators.lean
@@ -531,7 +531,7 @@ lemma ofComp_toAlgHom_monomial_sumElim (Q : Generators S T ι') (P : Generators
 lemma toComp_toAlgHom_monomial (Q : Generators S T ι') (P : Generators R S ι) (j a) :
     (Q.toComp P).toAlgHom (monomial j a) =
       monomial (Finsupp.sumElim 0 j) a := by
-  convert rename_monomial _ _ _
+  convert! rename_monomial _ _ _
   ext f (i₁ | i₂) <;>
     simp [Finsupp.mapDomain_notin_range, Finsupp.mapDomain_apply Sum.inr_injective]
 
@@ -700,9 +700,9 @@ lemma map_toComp_ker (Q : Generators S T ι') (P : Generators R S ι) :
         simp only [coeff_add, map_add, ite_add_zero]
         rw [finsum_add_distrib, hp, hq]
         · refine (((support p).map e).finite_toSet.subset ?_)
-          convert this p
+          convert! this p
         · refine (((support q).map e).finite_toSet.subset ?_)
-          convert this q
+          convert! this q
 
 /--
 Given `R[X] → S` and `S[Y] → T`, this is the lift of an element in `ker(S[Y] → T)`
diff --git a/Mathlib/RingTheory/Extension/Presentation/Basic.lean b/Mathlib/RingTheory/Extension/Presentation/Basic.lean
index 6aba6035755878..20b88f8700f9c0 100644
--- a/Mathlib/RingTheory/Extension/Presentation/Basic.lean
+++ b/Mathlib/RingTheory/Extension/Presentation/Basic.lean
@@ -133,7 +133,7 @@ lemma exists_presentation_fin [FinitePresentation R S] :
   let v : Fin m → MvPolynomial (Fin n) R := H'.choose_spec.choose
   have hv : Ideal.span (Set.range v) = RingHom.ker f := H'.choose_spec.choose_spec
   ⟨n, m,
-    ⟨{__ := Generators.ofSurjective (fun x ↦ f (.X x)) (by convert hf; ext; simp)
+    ⟨{__ := Generators.ofSurjective (fun x ↦ f (.X x)) (by convert! hf; ext; simp)
       relation := v
       span_range_relation_eq_ker := hv.trans (by congr; ext; simp) }⟩⟩
 
@@ -285,7 +285,7 @@ lemma span_range_relation_eq_ker_baseChange :
       Ideal.comap_symm, ← Ideal.map_coe, ← Ideal.map_coe _ (Ideal.span _), Ideal.map_map,
       Ideal.map_span, ← Set.range_comp, AlgEquiv.toRingEquiv_toRingHom, RingHom.coe_comp,
       RingHom.coe_coe] at H'
-    convert H'
+    convert! H'
     simp [e]
 
 /-- If `P` is a presentation of `S` over `R` and `T` is an `R`-algebra, we
diff --git a/Mathlib/RingTheory/Extension/Presentation/Core.lean b/Mathlib/RingTheory/Extension/Presentation/Core.lean
index 3f588b2ad6ca8c..0e3a5b9dd35491 100644
--- a/Mathlib/RingTheory/Extension/Presentation/Core.lean
+++ b/Mathlib/RingTheory/Extension/Presentation/Core.lean
@@ -246,7 +246,7 @@ lemma jacobianRelations_spec [DecidableEq σ] [Fintype σ] :
     ∑ i, P.jacobianRelations i * P.relation i =
       P.jacobiMatrix.det * P.σ ↑(P.jacobian_isUnit.unit⁻¹) - 1 := by
   delta jacobianRelations
-  convert P.exists_sum_eq_σ_jacobian_mul_σ_jacobian_inv_sub_one.choose_spec
+  convert! P.exists_sum_eq_σ_jacobian_mul_σ_jacobian_inv_sub_one.choose_spec
 
 /-- The set of coefficients that is enough to descend a submersive presentation `P`. -/
 def coeffs : Set R :=
@@ -352,7 +352,7 @@ def ofHasCoeffs [FaithfulSMul R₀ R] :
       $(P.sum_jacobianRelationsOfHasCoeffs_mul_relationOfHasCoeffs R₀))
     simp only [map_sum, map_mul, Ideal.Quotient.mk_span_range, mul_zero, Finset.sum_const_zero,
       map_sub, map_one, @eq_comm (P.ModelOfHasCoeffs R₀) 0, sub_eq_zero] at this
-    convert IsUnit.of_mul_eq_one _ this
+    convert! IsUnit.of_mul_eq_one _ this
     rw [PreSubmersivePresentation.jacobian_eq_jacobiMatrix_det]
     simp [jacobianOfHasCoeffs]
 
diff --git a/Mathlib/RingTheory/Extension/Presentation/Submersive.lean b/Mathlib/RingTheory/Extension/Presentation/Submersive.lean
index 715b28ed3779e1..98b855e0765b18 100644
--- a/Mathlib/RingTheory/Extension/Presentation/Submersive.lean
+++ b/Mathlib/RingTheory/Extension/Presentation/Submersive.lean
@@ -171,7 +171,7 @@ lemma isUnit_jacobian_of_linearIndependent_of_span_eq_top
   classical
   rw [isUnit_jacobian_iff_aevalDifferential_bijective]
   exact LinearMap.bijective_of_linearIndependent_of_span_eq_top (Pi.basisFun _ _).span_eq
-    (by convert hli; simp) (by convert hsp; simp)
+    (by convert! hli; simp) (by convert! hsp; simp)
 
 end
 
@@ -380,8 +380,9 @@ lemma comp_jacobian_eq_jacobian_smul_jacobian [Finite σ] [Finite σ'] :
     (aeval (Q.comp P).val) (Q.comp P).jacobiMatrix.toBlocks₂₂.det = P.jacobian • Q.jacobian
   · simp only [Generators.algebraMap_apply, ← map_mul]
     congr
-    convert Matrix.det_fromBlocks_zero₁₂ (Q.comp P).jacobiMatrix.toBlocks₁₁
-      (Q.comp P).jacobiMatrix.toBlocks₂₁ (Q.comp P).jacobiMatrix.toBlocks₂₂
+    convert!
+      Matrix.det_fromBlocks_zero₁₂ (Q.comp P).jacobiMatrix.toBlocks₁₁
+        (Q.comp P).jacobiMatrix.toBlocks₂₁ (Q.comp P).jacobiMatrix.toBlocks₂₂
   · rw [jacobiMatrix_comp_₁₁_det, jacobiMatrix_comp_₂₂_det, mul_comm, Algebra.smul_def]
 
 end Composition
@@ -607,7 +608,7 @@ noncomputable def aevalDifferentialEquiv (P : SubmersivePresentation R S ι σ)
   haveI : Fintype σ := Fintype.ofFinite σ
   have :
       IsUnit (LinearMap.toMatrix (Pi.basisFun S σ) (Pi.basisFun S σ) P.aevalDifferential).det := by
-    convert P.jacobian_isUnit
+    convert! P.jacobian_isUnit
     rw [LinearMap.toMatrix_eq_toMatrix', jacobian_eq_jacobiMatrix_det,
       aevalDifferential_toMatrix'_eq_mapMatrix_jacobiMatrix, P.algebraMap_eq]
     simp [RingHom.map_det]
diff --git a/Mathlib/RingTheory/Filtration.lean b/Mathlib/RingTheory/Filtration.lean
index a1c518f401a09e..37b4837f7daaca 100644
--- a/Mathlib/RingTheory/Filtration.lean
+++ b/Mathlib/RingTheory/Filtration.lean
@@ -202,7 +202,7 @@ theorem Stable.exists_pow_smul_eq_of_ge (h : F.Stable) :
   obtain ⟨n₀, hn₀⟩ := h.exists_pow_smul_eq
   use n₀
   intro n hn
-  convert hn₀ (n - n₀)
+  convert! hn₀ (n - n₀)
   rw [add_comm, tsub_add_cancel_of_le hn]
 
 theorem stable_iff_exists_pow_smul_eq_of_ge :
@@ -430,7 +430,7 @@ theorem Ideal.iInf_pow_smul_eq_bot_of_isLocalRing [IsNoetherianRing R] [IsLocalR
 /-- **Krull's intersection theorem** for Noetherian local rings. -/
 theorem Ideal.iInf_pow_eq_bot_of_isLocalRing [IsNoetherianRing R] [IsLocalRing R] (h : I ≠ ⊤) :
     ⨅ i : ℕ, I ^ i = ⊥ := by
-  convert I.iInf_pow_smul_eq_bot_of_isLocalRing (M := R) h
+  convert! I.iInf_pow_smul_eq_bot_of_isLocalRing (M := R) h
   ext i
   rw [smul_eq_mul, ← Ideal.one_eq_top, mul_one]
 
@@ -466,5 +466,5 @@ alias Ideal.iInf_pow_smul_eq_bot_of_noZeroSMulDivisors :=
 /-- **Krull's intersection theorem** for Noetherian domains. -/
 theorem Ideal.iInf_pow_eq_bot_of_isDomain [IsNoetherianRing R] [IsDomain R] (h : I ≠ ⊤) :
     ⨅ i : ℕ, I ^ i = ⊥ := by
-  convert I.iInf_pow_smul_eq_bot_of_isTorsionFree (M := R) h
+  convert! I.iInf_pow_smul_eq_bot_of_isTorsionFree (M := R) h
   simp
diff --git a/Mathlib/RingTheory/FinitePresentation.lean b/Mathlib/RingTheory/FinitePresentation.lean
index 9c26929a9b247e..d80c56569c5154 100644
--- a/Mathlib/RingTheory/FinitePresentation.lean
+++ b/Mathlib/RingTheory/FinitePresentation.lean
@@ -373,7 +373,7 @@ theorem ker_fg_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A
 theorem ker_fG_of_surjective (f : A →ₐ[R] B) (hf : Function.Surjective f)
     [FinitePresentation R A] [FinitePresentation R B] : (RingHom.ker f.toRingHom).FG := by
   obtain ⟨n, g, hg, _⟩ := FinitePresentation.out (R := R) (A := A)
-  convert (ker_fg_of_mvPolynomial (f.comp g) (hf.comp hg)).map g.toRingHom
+  convert! (ker_fg_of_mvPolynomial (f.comp g) (hf.comp hg)).map g.toRingHom
   simp_rw [RingHom.ker_eq_comap_bot, AlgHom.toRingHom_eq_coe, AlgHom.comp_toRingHom]
   rw [← Ideal.comap_comap, Ideal.map_comap_of_surjective (g : MvPolynomial (Fin n) R →+* A) hg]
 
@@ -488,7 +488,7 @@ lemma polynomial_induction
   | zero =>
     refine fg_ker _ _ _ (hg.comp (MvPolynomial.C_surjective (Fin 0))) ?_
     rw [← comap_ker]
-    convert hg'.map (MvPolynomial.isEmptyRingEquiv R (Fin 0)).toRingHom using 1
+    convert! hg'.map (MvPolynomial.isEmptyRingEquiv R (Fin 0)).toRingHom using 1
     simp only [RingEquiv.toRingHom_eq_coe]
     exact Ideal.comap_symm (MvPolynomial.isEmptyRingEquiv R (Fin 0))
   | succ n IH =>
@@ -496,10 +496,10 @@ lemma polynomial_induction
       (MvPolynomial.renameEquiv R (finSuccEquiv n)).trans (MvPolynomial.optionEquivRight R (Fin n))
     have he : (ker (g'.comp <| RingHomClass.toRingHom e.symm)).FG := by
       rw [← RingHom.comap_ker]
-      convert hg'.map e.toAlgHom.toRingHom using 1
+      convert! hg'.map e.toAlgHom.toRingHom using 1
       exact Ideal.comap_symm e.toRingEquiv
     have := IH (R := R[X]) (S := S) (g'.comp e.symm) (hg.comp e.symm.surjective) he
-    convert comp _ _ _ _ _ (polynomial _) this using 1
+    convert! comp _ _ _ _ _ (polynomial _) this using 1
     rw [comp_assoc, comp_assoc]
     congr 1 with r
     simp [e]
@@ -544,7 +544,7 @@ theorem comp_surjective {f : A →ₐ[R] B} {g : B →ₐ[R] C} (hf : f.FinitePr
 theorem of_surjective (f : A →ₐ[R] B) (hf : Surjective f) (hker : (RingHom.ker f.toRingHom).FG) :
     f.FinitePresentation := by
   -- Porting note: added `convert`
-  convert RingHom.FinitePresentation.of_surjective f hf hker
+  convert! RingHom.FinitePresentation.of_surjective f hf hker
 
 theorem of_finiteType [IsNoetherianRing A] {f : A →ₐ[R] B} : f.FiniteType ↔ f.FinitePresentation :=
   RingHom.FinitePresentation.of_finiteType
diff --git a/Mathlib/RingTheory/FiniteType.lean b/Mathlib/RingTheory/FiniteType.lean
index 6b3368b754c46e..58734998b2a1fb 100644
--- a/Mathlib/RingTheory/FiniteType.lean
+++ b/Mathlib/RingTheory/FiniteType.lean
@@ -85,7 +85,7 @@ variable {R S A B}
 
 theorem of_surjective [FiniteType R A] (f : A →ₐ[R] B) (hf : Surjective f) : FiniteType R B :=
   ⟨by
-    convert ‹FiniteType R A›.1.map f
+    convert! ‹FiniteType R A›.1.map f
     simpa only [map_top f, @eq_comm _ ⊤, eq_top_iff, AlgHom.mem_range] using hf⟩
 
 theorem equiv (hRA : FiniteType R A) (e : A ≃ₐ[R] B) : FiniteType R B :=
diff --git a/Mathlib/RingTheory/Finiteness/Defs.lean b/Mathlib/RingTheory/Finiteness/Defs.lean
index 8a0762d17ac8a0..0ef614fce85e26 100644
--- a/Mathlib/RingTheory/Finiteness/Defs.lean
+++ b/Mathlib/RingTheory/Finiteness/Defs.lean
@@ -75,7 +75,7 @@ lemma fg_iff_exists_finite_generating_family {A : Type u} [Semiring A] {M : Type
   · intro hN
     obtain ⟨n, f, h⟩ := fg_iff_exists_fin_generating_family.mp hN
     refine ⟨ULift (Fin n), inferInstance, f ∘ ULift.down, ?_⟩
-    convert h
+    convert! h
     ext
     simp
   · rintro ⟨G, _, g, hg⟩
diff --git a/Mathlib/RingTheory/Finiteness/FinitePresentationLocal.lean b/Mathlib/RingTheory/Finiteness/FinitePresentationLocal.lean
index 3c286be52d0f2f..0b759d65bcc3dc 100644
--- a/Mathlib/RingTheory/Finiteness/FinitePresentationLocal.lean
+++ b/Mathlib/RingTheory/Finiteness/FinitePresentationLocal.lean
@@ -112,7 +112,7 @@ lemma of_span_eq_top_target (s : Set S) (hs : Ideal.span (s : Set S) = ⊤)
   have Ht (g : t) : Algebra.FinitePresentation R (Localization.Away (f' g)) := by
     have : ∃ (a : S) (hb : a ∈ s), (Ideal.Quotient.mk I) (g' ⟨a, hb⟩) = g.val := by
       obtain ⟨g, hg⟩ := g
-      convert hg
+      convert! hg
       simp [A, t]
     obtain ⟨r, hr, hrr⟩ := this
     simp only [f']
diff --git a/Mathlib/RingTheory/Finiteness/FiniteTypeLocal.lean b/Mathlib/RingTheory/Finiteness/FiniteTypeLocal.lean
index adebc0a54bd6e3..f41af9b621f778 100644
--- a/Mathlib/RingTheory/Finiteness/FiniteTypeLocal.lean
+++ b/Mathlib/RingTheory/Finiteness/FiniteTypeLocal.lean
@@ -55,7 +55,7 @@ theorem IsLocalization.exists_smul_mem_of_mem_adjoin [Algebra R S']
   rw [Algebra.smul_def, ← map_mul] at hx''
   obtain ⟨a, ha₂⟩ := (IsLocalization.eq_iff_exists M S').mp hx''
   use a * y ^ n
-  convert A.mul_mem hx' (hA₂ a.prop) using 1
+  convert! A.mul_mem hx' (hA₂ a.prop) using 1
   rw [Submonoid.smul_def, smul_eq_mul, Submonoid.coe_mul, SubmonoidClass.coe_pow, mul_assoc, ← ha₂,
     mul_comm]
 
@@ -145,7 +145,7 @@ lemma Algebra.FiniteType.of_span_eq_top_source (s : Set R) (hs : Ideal.span (s :
   choose s₁ s₂ using H
   let sf := fun x : s => IsLocalization.finsetIntegerMultiple (Submonoid.powers (f x)) (s₁ x)
   use s.attach.biUnion sf
-  convert (Algebra.adjoin_attach_biUnion (R := R) sf).trans _
+  convert! (Algebra.adjoin_attach_biUnion (R := R) sf).trans _
   rw [eq_top_iff]
   rintro x -
   apply (⨆ x : s, Algebra.adjoin R (sf x : Set S)).toSubmodule.mem_of_span_eq_top_of_smul_pow_mem
diff --git a/Mathlib/RingTheory/Finiteness/NilpotentKer.lean b/Mathlib/RingTheory/Finiteness/NilpotentKer.lean
index 07d454680f56ca..e33b8a92bd02e4 100644
--- a/Mathlib/RingTheory/Finiteness/NilpotentKer.lean
+++ b/Mathlib/RingTheory/Finiteness/NilpotentKer.lean
@@ -55,7 +55,7 @@ lemma Module.finite_of_surjective_of_ker_le_nilradical
         rw [LinearMap.ker_comp, ← Submodule.map_le_map_iff_of_injective (I ^ n).subtype_injective,
           Submodule.map_smul'', Submodule.map_comap_eq]
         simpa [pow_succ'] using Ideal.mul_le_left (I := I) (J := I ^ n)
-      convert Module.Finite.fg_top.map (ψ.restrictScalars R) using 1
+      convert! Module.Finite.fg_top.map (ψ.restrictScalars R) using 1
       suffices LinearMap.ker φ.toLinearMap = Submodule.map (I ^ (n + 1)).mkQ (I ^ n) by
         simpa [LinearMap.range_restrictScalars, ψ, LinearMap.range_comp, Submodule.range_liftQ]
       apply Submodule.comap_injective_of_surjective (I ^ (n + 1)).mkQ_surjective
diff --git a/Mathlib/RingTheory/Fintype.lean b/Mathlib/RingTheory/Fintype.lean
index 2c5ef98aab5853..b33e82d29cdd25 100644
--- a/Mathlib/RingTheory/Fintype.lean
+++ b/Mathlib/RingTheory/Fintype.lean
@@ -26,7 +26,7 @@ lemma Finset.univ_of_card_le_two (h : Fintype.card R ≤ 2) :
   rcases subsingleton_or_nontrivial R
   · exact le_antisymm (fun a _ ↦ by simp [Subsingleton.elim a 0]) (Finset.subset_univ _)
   · refine (eq_of_subset_of_card_le (subset_univ _) ?_).symm
-    convert h
+    convert! h
     simp
 
 lemma Finset.univ_of_card_le_three (h : Fintype.card R ≤ 3) :
diff --git a/Mathlib/RingTheory/Flat/Basic.lean b/Mathlib/RingTheory/Flat/Basic.lean
index 7fe3ea31c77c8e..14a10a5b7b5e5a 100644
--- a/Mathlib/RingTheory/Flat/Basic.lean
+++ b/Mathlib/RingTheory/Flat/Basic.lean
@@ -165,7 +165,7 @@ instance instSubalgebraToSubmodule {S : Type v} [Semiring S] [Algebra R S]
 instance self : Flat R R where
   out _ _ _ _ I _ := by
     rw [← (TensorProduct.rid R I).symm.injective_comp, ← (TensorProduct.rid R _).comp_injective]
-    convert Subtype.coe_injective using 1
+    convert! Subtype.coe_injective using 1
     ext; simp
 
 /-- A retract of a flat `R`-module is flat. -/
@@ -409,14 +409,16 @@ namespace Algebra.TensorProduct
 
 theorem includeLeft_injective [Module.Flat R A] (hb : Function.Injective (algebraMap R B)) :
     Function.Injective (includeLeft : A →ₐ[S] A ⊗[R] B) := by
-  convert Module.Flat.lTensor_preserves_injective_linearMap (M := A) (Algebra.linearMap R B) hb
-    |>.comp (_root_.TensorProduct.rid R A).symm.injective
+  convert!
+    Module.Flat.lTensor_preserves_injective_linearMap (M := A) (Algebra.linearMap R B) hb |>.comp
+      (_root_.TensorProduct.rid R A).symm.injective
   ext; simp
 
 theorem includeRight_injective [Module.Flat R B] (ha : Function.Injective (algebraMap R A)) :
     Function.Injective (includeRight : B →ₐ[R] A ⊗[R] B) := by
-  convert Module.Flat.rTensor_preserves_injective_linearMap (M := B) (Algebra.linearMap R A) ha
-    |>.comp (_root_.TensorProduct.lid R B).symm.injective
+  convert!
+    Module.Flat.rTensor_preserves_injective_linearMap (M := B) (Algebra.linearMap R A) ha |>.comp
+      (_root_.TensorProduct.lid R B).symm.injective
   ext; simp
 
 end Algebra.TensorProduct
@@ -501,8 +503,9 @@ See `LinearIndependent.tmul_of_isDomain`. -/
 lemma _root_.LinearIndependent.tmul_of_flat_left [Module.Flat R M] (hv : LinearIndependent R v)
     (hw : LinearIndependent R w) : LinearIndependent R fun i : ι × κ ↦ v i.1 ⊗ₜ[R] w i.2 := by
   rw [LinearIndependent]
-  convert (TensorProduct.map_injective_of_flat_flat _ _ hv hw).comp
-    (finsuppTensorFinsupp' _ _ _).symm.injective
+  convert!
+    (TensorProduct.map_injective_of_flat_flat _ _ hv hw).comp
+      (finsuppTensorFinsupp' _ _ _).symm.injective
   rw [← LinearEquiv.coe_toLinearMap, ← LinearMap.coe_comp]
   congr!
   ext i
diff --git a/Mathlib/RingTheory/Flat/Domain.lean b/Mathlib/RingTheory/Flat/Domain.lean
index 2e299f80c8e651..102ee114547d10 100644
--- a/Mathlib/RingTheory/Flat/Domain.lean
+++ b/Mathlib/RingTheory/Flat/Domain.lean
@@ -44,7 +44,7 @@ lemma TensorProduct.map_injective_of_flat_flat_of_isDomain
   have H₆ := Module.Flat.rTensor_preserves_injective_linearMap (M := P ⊗[R] Q)
     (Algebra.linearMap R K) (FaithfulSMul.algebraMap_injective R K)
   have H₇ := (TensorProduct.lid R (P ⊗[R] Q)).symm.injective
-  convert H₅.comp <| H₃.comp <| H₁.comp <| H₂.comp <| H₄.comp <| H₆.comp <| H₇
+  convert! H₅.comp <| H₃.comp <| H₁.comp <| H₂.comp <| H₄.comp <| H₆.comp <| H₇
   dsimp only [← LinearMap.coe_comp, ← LinearEquiv.coe_toLinearMap,
     ← @LinearMap.coe_restrictScalars R K]
   congr! 1
@@ -62,8 +62,9 @@ See `LinearIndependent.tmul_of_flat_left`. -/
 lemma LinearIndependent.tmul_of_isDomain (hv : LinearIndependent R v) (hw : LinearIndependent R w) :
     LinearIndependent R fun i : ι × κ ↦ v i.1 ⊗ₜ[R] w i.2 := by
   rw [LinearIndependent]
-  convert (TensorProduct.map_injective_of_flat_flat_of_isDomain _ _ hv hw).comp
-    (finsuppTensorFinsupp' _ _ _).symm.injective
+  convert!
+    (TensorProduct.map_injective_of_flat_flat_of_isDomain _ _ hv hw).comp
+      (finsuppTensorFinsupp' _ _ _).symm.injective
   rw [← LinearEquiv.coe_toLinearMap, ← LinearMap.coe_comp]
   congr!
   ext i
diff --git a/Mathlib/RingTheory/Flat/EquationalCriterion.lean b/Mathlib/RingTheory/Flat/EquationalCriterion.lean
index ef55e75c7709ac..d0ac675194ac4f 100644
--- a/Mathlib/RingTheory/Flat/EquationalCriterion.lean
+++ b/Mathlib/RingTheory/Flat/EquationalCriterion.lean
@@ -245,7 +245,7 @@ private theorem exists_factorization_of_comp_eq_zero_of_free_aux [Flat R M] {K :
       use k₂, a₂ ∘ₗ a₁, y₂
       simp_rw [comp_assoc]
       exact ⟨trivial, sup_le (ha₁.trans (ker_le_ker_comp _ _)) ha₂⟩
-  convert this ⊤ Finite.fg_top
+  convert! this ⊤ Finite.fg_top
   simp only [top_le_iff, ker_eq_top]
 
 /-- Let $M$ be a flat module. Let $K$ and $N$ be finite $R$-modules with $N$
diff --git a/Mathlib/RingTheory/Flat/TorsionFree.lean b/Mathlib/RingTheory/Flat/TorsionFree.lean
index 4ee77069223be0..9cb449c7699f52 100644
--- a/Mathlib/RingTheory/Flat/TorsionFree.lean
+++ b/Mathlib/RingTheory/Flat/TorsionFree.lean
@@ -116,7 +116,7 @@ theorem flat_iff_torsion_eq_bot_of_isBezout [IsBezout R] [IsDomain R] :
     rw [← Submodule.isTorsionFree_iff_torsion_eq_bot] at htors
     refine Function.Injective.comp (LinearMap.lsmul_injective this) ?_
     rw [← Equiv.injective_comp (TensorProduct.lid R M).symm.toEquiv]
-    convert Function.injective_id
+    convert! Function.injective_id
     ext
     simp
 
diff --git a/Mathlib/RingTheory/FractionalIdeal/Basic.lean b/Mathlib/RingTheory/FractionalIdeal/Basic.lean
index 0ccda531d73680..7da7550e129b2f 100644
--- a/Mathlib/RingTheory/FractionalIdeal/Basic.lean
+++ b/Mathlib/RingTheory/FractionalIdeal/Basic.lean
@@ -195,7 +195,7 @@ theorem ext {I J : FractionalIdeal S P} : (∀ x, x ∈ I ↔ x ∈ J) → I = J
 Useful to fix definitional equalities. -/
 protected def copy (p : FractionalIdeal S P) (s : Set P) (hs : s = ↑p) : FractionalIdeal S P :=
   ⟨Submodule.copy p s hs, by
-    convert p.isFractional
+    convert! p.isFractional
     ext
     simp only [hs]
     rfl⟩
@@ -419,7 +419,7 @@ theorem coe_le_coe {I J : FractionalIdeal S P} :
 
 theorem zero_le (I : FractionalIdeal S P) : 0 ≤ I := by
   intro x hx
-  convert zero_mem I
+  convert! zero_mem I
   rw [(mem_zero_iff _).mp hx]
 
 instance orderBot : OrderBot (FractionalIdeal S P) where
@@ -506,7 +506,7 @@ theorem _root_.IsFractional.nsmul {I : Submodule R P} :
     ∀ n : ℕ, IsFractional S I → IsFractional S (n • I : Submodule R P)
   | 0, _ => by
     rw [zero_smul]
-    convert ((0 : Ideal R) : FractionalIdeal S P).isFractional
+    convert! ((0 : Ideal R) : FractionalIdeal S P).isFractional
     simp
   | n + 1, h => by
     rw [succ_nsmul]
diff --git a/Mathlib/RingTheory/FractionalIdeal/Norm.lean b/Mathlib/RingTheory/FractionalIdeal/Norm.lean
index 306957c34f719b..7ad462af5eec8b 100644
--- a/Mathlib/RingTheory/FractionalIdeal/Norm.lean
+++ b/Mathlib/RingTheory/FractionalIdeal/Norm.lean
@@ -88,7 +88,7 @@ theorem absNorm_nonneg (I : FractionalIdeal R⁰ K) : 0 ≤ absNorm I := by dsim
 
 theorem absNorm_bot : absNorm (⊥ : FractionalIdeal R⁰ K) = 0 := absNorm.map_zero'
 
-theorem absNorm_one : absNorm (1 : FractionalIdeal R⁰ K) = 1 := by convert absNorm.map_one'
+theorem absNorm_one : absNorm (1 : FractionalIdeal R⁰ K) = 1 := by convert! absNorm.map_one'
 
 theorem absNorm_eq_zero_iff [IsDomain K] {I : FractionalIdeal R⁰ K} :
     absNorm I = 0 ↔ I = 0 := by
diff --git a/Mathlib/RingTheory/FractionalIdeal/Operations.lean b/Mathlib/RingTheory/FractionalIdeal/Operations.lean
index 74119c26b13972..e40d786a0f1ebd 100644
--- a/Mathlib/RingTheory/FractionalIdeal/Operations.lean
+++ b/Mathlib/RingTheory/FractionalIdeal/Operations.lean
@@ -263,7 +263,7 @@ theorem canonicalEquiv_coeIdeal (I : Ideal R) : canonicalEquiv S P P' I = I := b
 @[simp]
 theorem canonicalEquiv_self : canonicalEquiv S P P = RingEquiv.refl _ := by
   rw [← canonicalEquiv_trans_canonicalEquiv S P P]
-  convert (canonicalEquiv S P P).symm_trans_self
+  convert! (canonicalEquiv S P P).symm_trans_self
   exact (canonicalEquiv_symm S P P).symm
 
 end
@@ -358,7 +358,7 @@ instance : Nontrivial (FractionalIdeal R₁⁰ K) :=
 theorem ne_zero_of_mul_eq_one (I J : FractionalIdeal R₁⁰ K) (h : I * J = 1) : I ≠ 0 := fun hI =>
   zero_ne_one' (FractionalIdeal R₁⁰ K)
     (by
-      convert h
+      convert! h
       simp [hI])
 
 variable [IsFractionRing R₁ K] [IsDomain R₁]
@@ -382,7 +382,7 @@ theorem _root_.IsFractional.div_of_nonzero {I J : Submodule R₁ K} :
       apply notMem_zero
       simpa
     intro b hb
-    convert hI _ (hb _ (Submodule.smul_mem _ aJ mem_J)) using 1
+    convert! hI _ (hb _ (Submodule.smul_mem _ aJ mem_J)) using 1
     rw [← hy', mul_comm b, ← Algebra.smul_def, mul_smul]
 
 theorem isFractional_div_of_ne_zero {I J : FractionalIdeal R₁⁰ K} (h : J ≠ 0) :
@@ -447,7 +447,7 @@ theorem div_one {I : FractionalIdeal R₁⁰ K} : I / 1 = I := by
   · simpa using mem_div_iff_forall_mul_mem.mp h 1 ((algebraMap R₁ K).map_one ▸ coe_mem_one R₁⁰ 1)
   · apply mem_div_iff_forall_mul_mem.mpr
     rintro y ⟨y', _, rfl⟩
-    convert Submodule.smul_mem _ y' h using 1
+    convert! Submodule.smul_mem _ y' h using 1
     rw [mul_comm, Algebra.linearMap_apply, ← Algebra.smul_def]
 
 theorem eq_one_div_of_mul_eq_one_right (I J : FractionalIdeal R₁⁰ K) (h : I * J = 1) :
@@ -587,7 +587,7 @@ theorem den_mul_self_eq_num' (I : FractionalIdeal S P) :
   apply coeToSubmodule_injective
   dsimp only
   rw [coe_mul, ← smul_eq_mul, coe_spanSingleton, smul_eq_mul, Submodule.span_singleton_mul]
-  convert I.den_mul_self_eq_num using 1
+  convert! I.den_mul_self_eq_num using 1
   ext
   rw [mem_smul_pointwise_iff_exists, mem_smul_pointwise_iff_exists]
   simp [smul_eq_mul, Algebra.smul_def, Submonoid.smul_def]
@@ -960,12 +960,12 @@ noncomputable def ringEquivOfRingEquiv :
     left_inv I := by
       simp only [RingEquiv.symm_symm, val_eq_coe, ← Submodule.map_comp, LinearEquiv.comp_coe,
         coe_ext_iff, coe_mk]
-      convert Submodule.map_id _
+      convert! Submodule.map_id _
       ext; simp [semilinearEquivOfRingEquiv, IsLocalization.map_map]
     right_inv I := by
       simp only [RingEquiv.symm_symm, val_eq_coe, ← Submodule.map_comp, LinearEquiv.comp_coe,
         coe_ext_iff, coe_mk]
-      convert Submodule.map_id _
+      convert! Submodule.map_id _
       ext; simp [semilinearEquivOfRingEquiv, IsLocalization.map_map]}
 
 lemma ringEquivOfRingEquiv_apply (f : R ≃+* S) (I : FractionalIdeal (nonZeroDivisors R) K) :
diff --git a/Mathlib/RingTheory/Frobenius.lean b/Mathlib/RingTheory/Frobenius.lean
index 14696d429510d0..e0b10ae2bb310e 100644
--- a/Mathlib/RingTheory/Frobenius.lean
+++ b/Mathlib/RingTheory/Frobenius.lean
@@ -272,8 +272,9 @@ lemma _root_.isConj_arithFrobAt
     (H : Q.under R = Q'.under R) : IsConj (arithFrobAt R G Q) (arithFrobAt R G Q') := by
   obtain ⟨P, hP, h₁, h₂⟩ : ∃ P : Ideal R, P.IsPrime ∧ P = Q.under R ∧ P = Q'.under R :=
     ⟨Q.under R, inferInstance, rfl, H⟩
-  convert (exists_primesOver_isConj S G P
-      ⟨⟨Q, ‹_›, ⟨h₁⟩⟩, ‹Finite (S ⧸ Q)›⟩).choose_spec.2 ⟨Q, ‹_›, ⟨h₁⟩⟩ ⟨Q', ‹_›, ⟨h₂⟩⟩
+  convert!
+    (exists_primesOver_isConj S G P ⟨⟨Q, ‹_›, ⟨h₁⟩⟩, ‹Finite (S ⧸ Q)›⟩).choose_spec.2 ⟨Q, ‹_›, ⟨h₁⟩⟩
+      ⟨Q', ‹_›, ⟨h₂⟩⟩
   · subst h₁; rfl
   · subst h₂; rfl
 
diff --git a/Mathlib/RingTheory/GradedAlgebra/Homogeneous/Ideal.lean b/Mathlib/RingTheory/GradedAlgebra/Homogeneous/Ideal.lean
index e031f8a0496af7..6bb4bfed265a05 100644
--- a/Mathlib/RingTheory/GradedAlgebra/Homogeneous/Ideal.lean
+++ b/Mathlib/RingTheory/GradedAlgebra/Homogeneous/Ideal.lean
@@ -202,7 +202,7 @@ theorem Ideal.IsHomogeneous.toIdeal_homogeneousCore_eq_self (h : I.IsHomogeneous
 theorem HomogeneousIdeal.toIdeal_homogeneousCore_eq_self (I : HomogeneousIdeal 𝒜) :
     I.toIdeal.homogeneousCore 𝒜 = I := by
   ext1
-  convert Ideal.IsHomogeneous.toIdeal_homogeneousCore_eq_self I.isHomogeneous
+  convert! Ideal.IsHomogeneous.toIdeal_homogeneousCore_eq_self I.isHomogeneous
 
 variable (𝒜 I)
 
@@ -454,7 +454,7 @@ theorem Ideal.homogeneousCore'_eq_sSup :
   refine (IsLUB.sSup_eq ?_).symm
   apply IsGreatest.isLUB
   have coe_mono : Monotone (toIdeal : HomogeneousIdeal 𝒜 → Ideal A) := fun x y => id
-  convert coe_mono.map_isGreatest (Ideal.homogeneousCore.gc 𝒜).isGreatest_u using 1
+  convert! coe_mono.map_isGreatest (Ideal.homogeneousCore.gc 𝒜).isGreatest_u using 1
   ext x
   rw [mem_image, mem_setOf_eq]
   refine ⟨fun hI => ⟨⟨x, hI.1⟩, ⟨hI.2, rfl⟩⟩, ?_⟩
diff --git a/Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean b/Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean
index 79c0709e5040d1..3a02d3896d7e81 100644
--- a/Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean
+++ b/Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean
@@ -327,7 +327,7 @@ instance : SMul α (HomogeneousLocalization 𝒜 x) where
   smul m := Quotient.map' (m • ·) fun c1 c2 (h : Localization.mk _ _ = Localization.mk _ _) => by
     change Localization.mk _ _ = Localization.mk _ _
     simp only [num_smul, den_smul]
-    convert congr_arg (fun z : at x => m • z) h <;> rw [Localization.smul_mk]
+    convert! congr_arg (fun z : at x => m • z) h <;> rw [Localization.smul_mk]
 
 @[simp] lemma mk_smul (i : NumDenSameDeg 𝒜 x) (m : α) : mk (m • i) = m • mk i := rfl
 
@@ -386,7 +386,7 @@ instance hasPow : Pow (HomogeneousLocalization 𝒜 x) ℕ where
     (Quotient.map' (· ^ n) fun c1 c2 (h : Localization.mk _ _ = Localization.mk _ _) => by
           change Localization.mk _ _ = Localization.mk _ _
           simp only [num_pow, den_pow]
-          convert congr_arg (fun z : at x => z ^ n) h <;> rw [Localization.mk_pow] <;> rfl :
+          convert! congr_arg (fun z : at x => z ^ n) h <;> rw [Localization.mk_pow] <;> rfl :
         HomogeneousLocalization 𝒜 x → HomogeneousLocalization 𝒜 x)
       z
 
@@ -399,7 +399,7 @@ instance : Add (HomogeneousLocalization 𝒜 x) where
         (h' : Localization.mk _ _ = Localization.mk _ _) => by
       change Localization.mk _ _ = Localization.mk _ _
       simp only [num_add, den_add]
-      convert congr_arg₂ (· + ·) h h' <;> rw [Localization.add_mk] <;> rfl
+      convert! congr_arg₂ (· + ·) h h' <;> rw [Localization.add_mk] <;> rfl
 
 @[simp] lemma mk_add (i j : NumDenSameDeg 𝒜 x) : mk (i + j) = mk i + mk j := rfl
 
@@ -412,7 +412,7 @@ instance : Mul (HomogeneousLocalization 𝒜 x) where
         (h' : Localization.mk _ _ = Localization.mk _ _) => by
       change Localization.mk _ _ = Localization.mk _ _
       simp only [num_mul, den_mul]
-      convert congr_arg₂ (· * ·) h h' <;> rw [Localization.mk_mul] <;> rfl
+      convert! congr_arg₂ (· * ·) h h' <;> rw [Localization.mk_mul] <;> rfl
 
 @[simp] lemma mk_mul (i j : NumDenSameDeg 𝒜 x) : mk (i * j) = mk i * mk j := rfl
 
@@ -844,7 +844,7 @@ lemma awayMap_fromZeroRingHom (a) :
   ext
   simp only [fromZeroRingHom, RingHom.coe_mk, MonoidHom.coe_mk, OneHom.coe_mk,
     val_awayMap, val_mk]
-  convert IsLocalization.lift_eq _ _
+  convert! IsLocalization.lift_eq _ _
 
 lemma val_awayMap_mk (n a i hi) : (awayMap 𝒜 hg hx (mk ⟨n, a, ⟨f ^ i, hi⟩, ⟨i, rfl⟩⟩)).val =
     Localization.mk (a * g ^ i) ⟨x ^ i, (Submonoid.mem_powers_iff _ _).mpr ⟨i, rfl⟩⟩ := by
@@ -875,7 +875,7 @@ variable {e d : ℕ} {f : A} (hf : f ∈ 𝒜 d) {g : A} (hg : g ∈ 𝒜 e)
 
 /-- The element `t := g ^ d / f ^ e` such that `A_{(fg)} = A_{(f)}[1/t]`. -/
 abbrev Away.isLocalizationElem : Away 𝒜 f :=
-  Away.mk 𝒜 hf e (g ^ d) (by convert SetLike.pow_mem_graded d hg using 2; exact mul_comm _ _)
+  Away.mk 𝒜 hf e (g ^ d) (by convert! SetLike.pow_mem_graded d hg using 2; exact mul_comm _ _)
 
 variable {x : A} (hx : x = f * g)
 
@@ -889,8 +889,9 @@ theorem Away.isLocalization_mul (hd : d ≠ 0) :
     rw [map_pow, RingHom.algebraMap_toAlgebra]
     let z : Away 𝒜 x := Away.mk 𝒜 (hx ▸ SetLike.mul_mem_graded hf hg) (d + e)
         (g ^ e * f ^ (2 * e + d)) <| by
-      convert SetLike.mul_mem_graded (SetLike.pow_mem_graded e hg)
-        (SetLike.pow_mem_graded (2 * e + d) hf) using 2
+      convert!
+        SetLike.mul_mem_graded (SetLike.pow_mem_graded e hg)
+          (SetLike.pow_mem_graded (2 * e + d) hf) using 2
       ring
     refine (isUnit_iff_exists_inv.mpr ⟨z, ?_⟩).pow _
     ext
@@ -904,7 +905,7 @@ theorem Away.isLocalization_mul (hd : d ≠ 0) :
     rcases d with - | d
     · contradiction
     let t : Away 𝒜 f := Away.mk 𝒜 hf (n * (e + 1)) (s * g ^ (n * d)) <| by
-      convert SetLike.mul_mem_graded hs (SetLike.pow_mem_graded _ hg) using 2; simp; ring
+      convert! SetLike.mul_mem_graded hs (SetLike.pow_mem_graded _ hg) using 2; simp; ring
     refine ⟨⟨t, ⟨_, ⟨n, rfl⟩⟩⟩, ?_⟩
     ext
     simp only [RingHom.algebraMap_toAlgebra, map_pow, awayMap_mk, val_mul, val_mk, val_pow,
@@ -927,7 +928,7 @@ theorem Away.isLocalization_mul (hd : d ≠ 0) :
     rcases d with - | d
     · contradiction
     subst hx
-    convert congr(f ^ (e * (k + m + n)) * g ^ (d * (k + m + n)) * $hc) using 1 <;> ring
+    convert! congr(f ^ (e * (k + m + n)) * g ^ (d * (k + m + n)) * $hc) using 1 <;> ring
 
 end isLocalization
 
@@ -973,20 +974,20 @@ theorem Away.span_mk_prod_pow_eq_top {f : A} {d : ι} (hf : f ∈ 𝒜 d)
         congr
         refine (DirectSum.decompose_of_mem_same _ ?_).symm
         exact H ▸ SetLike.prod_pow_mem_graded _ _ _ _ fun i _ ↦ hxd i
-    · convert zero_mem (Submodule.span (𝒜 0) _)
+    · convert! zero_mem (Submodule.span (𝒜 0) _)
       ext
       have : (DirectSum.decompose 𝒜 (∏ i : ι', v i ^ ai i) n).1 = 0 := by
         refine DirectSum.decompose_of_mem_ne _ ?_ H
         exact SetLike.prod_pow_mem_graded _ _ _ _ fun i _ ↦ hxd i
       simp [this, Localization.mk_zero]
   | zero =>
-    convert zero_mem (Submodule.span (𝒜 0) _)
+    convert! zero_mem (Submodule.span (𝒜 0) _)
     ext; simp [Localization.mk_zero]
   | add s t hs ht hs' ht' =>
-    convert add_mem hs' ht'
+    convert! add_mem hs' ht'
     ext; simp [← Localization.add_mk_self]
   | smul r x hx hx' =>
-    convert Submodule.smul_mem _ r hx'
+    convert! Submodule.smul_mem _ r hx'
     ext
     simp [Algebra.smul_def, algebraMap_eq, fromZeroRingHom, Localization.mk_mul,
       -decompose_mul, coe_decompose_mul_of_left_mem_zero 𝒜 r.2]
@@ -1102,14 +1103,14 @@ lemma Away.finiteType (f : A) (d : ℕ) (hf : f ∈ 𝒜 d) :
     rintro _ ⟨a, ai, hai, hai', rfl⟩
     obtain rfl : ai = 0 := funext <| by simpa [hd, hdx] using hai
     simp only [Finset.univ_eq_attach, Pi.zero_apply, pow_zero, Finset.prod_const_one, mem_coe]
-    convert pow_mem (Algebra.self_mem_adjoin_singleton (𝒜 0) f') a using 1
+    convert! pow_mem (Algebra.self_mem_adjoin_singleton (𝒜 0) f') a using 1
     ext
     simp [f', Localization.mk_pow]
   refine ⟨_, ?_, le_rfl⟩
   let b := ∑ i, dx i
   let s' : Set ((Fin (b + 1)) × (s → Fin (d + 1))) := { ai | ∑ i, (ai.2 i).1 * dx i = ai.1 * d }
   let F : s' → Away 𝒜 f := fun ai ↦ Away.mk 𝒜 hf ai.1.1.1 (∏ i, i ^ (ai.1.2 i).1)
-    (by convert SetLike.prod_pow_mem_graded _ _ _ _ fun i _ ↦ hxd i; exact ai.2.symm)
+    (by convert! SetLike.prod_pow_mem_graded _ _ _ _ fun i _ ↦ hxd i; exact ai.2.symm)
   apply (Set.finite_range F).subset
   rintro _ ⟨a, ai, hai, hai', rfl⟩
   refine ⟨⟨⟨⟨a, ?_⟩, fun i ↦ ⟨ai i, (hai' i).trans_lt d.lt_succ_self⟩⟩, hai⟩, rfl⟩
diff --git a/Mathlib/RingTheory/GradedAlgebra/Radical.lean b/Mathlib/RingTheory/GradedAlgebra/Radical.lean
index 59f7e908baf1fd..bbdea52c8b271b 100644
--- a/Mathlib/RingTheory/GradedAlgebra/Radical.lean
+++ b/Mathlib/RingTheory/GradedAlgebra/Radical.lean
@@ -104,7 +104,7 @@ theorem Ideal.IsHomogeneous.isPrime_of_homogeneous_mem_or_mem {I : Ideal A} (hI
         simp only [antidiag, mem_erase, Prod.mk_inj, Ne, mem_filter, mem_product] at H
         rcases H with ⟨H₁, ⟨H₂, H₃⟩, H₄⟩
         have max_lt : max₁ < i ∨ max₂ < j := by
-          convert le_or_lt_of_add_le_add H₄.ge using 1
+          convert! le_or_lt_of_add_le_add H₄.ge using 1
           rw [Ne.le_iff_lt]
           rintro rfl
           cases H₁ ⟨rfl, add_left_cancel H₄⟩
diff --git a/Mathlib/RingTheory/HahnSeries/Addition.lean b/Mathlib/RingTheory/HahnSeries/Addition.lean
index 0bc3b8db2b6d1e..3980046d3b6e78 100644
--- a/Mathlib/RingTheory/HahnSeries/Addition.lean
+++ b/Mathlib/RingTheory/HahnSeries/Addition.lean
@@ -135,8 +135,8 @@ and the additive opposite of Hahn series over `Γ` with coefficients `R`.
 -/
 @[simps -isSimp]
 def addOppositeEquiv : Rᵃᵒᵖ⟦Γ⟧ ≃+ R⟦Γ⟧ᵃᵒᵖ where
-  toFun x := .op ⟨fun a ↦ (x.coeff a).unop, by convert x.isPWO_support; ext; simp⟩
-  invFun x := ⟨fun a ↦ .op (x.unop.coeff a), by convert x.unop.isPWO_support; ext; simp⟩
+  toFun x := .op ⟨fun a ↦ (x.coeff a).unop, by convert! x.isPWO_support; ext; simp⟩
+  invFun x := ⟨fun a ↦ .op (x.unop.coeff a), by convert! x.unop.isPWO_support; ext; simp⟩
   left_inv x := by simp
   right_inv x := by
     apply AddOpposite.unop_injective
diff --git a/Mathlib/RingTheory/HahnSeries/Lex.lean b/Mathlib/RingTheory/HahnSeries/Lex.lean
index 24fc842b4477a6..842ad48b5145fd 100644
--- a/Mathlib/RingTheory/HahnSeries/Lex.lean
+++ b/Mathlib/RingTheory/HahnSeries/Lex.lean
@@ -201,7 +201,7 @@ theorem archimedeanClassMk_le_archimedeanClassMk_iff_of_orderTop_ofLex {x y : Le
     · -- impossible case: `x` and `y` differ before their leading coefficients
       have hjlt' : j < (ofLex |y|).orderTop := h'.symm ▸ hjlt
       simp [coeff_eq_zero_of_lt_orderTop hjlt, coeff_eq_zero_of_lt_orderTop hjlt'] at hi
-    · convert hi.le <;> exact (WithTop.untop_eq_iff _).mpr hjeq.symm
+    · convert! hi.le <;> exact (WithTop.untop_eq_iff _).mpr hjeq.symm
     · exact (hj _ ((WithTop.untop_lt_iff _).mpr hjgt)).le
   · -- `mk x.leadingCoeff ≤ mk y.leadingCoeff → mk x ≤ mk y`
     intro ⟨n, hn⟩
@@ -221,7 +221,7 @@ theorem archimedeanClassMk_le_archimedeanClassMk_iff_of_orderTop_ofLex {x y : Le
       simp_rw [← leadingCoeff_abs] at this
       rw [leadingCoeff_of_ne_zero (by simpa using hy), leadingCoeff_of_ne_zero (by simpa using hx)]
         at this
-      convert this using 3 <;> simp [h]
+      convert! this using 3 <;> simp [h]
     refine lt_of_le_of_lt hn <| nsmul_lt_nsmul_left ?_ (by simp)
     rwa [abs_pos, leadingCoeff_ne_zero]
 
diff --git a/Mathlib/RingTheory/HahnSeries/PowerSeries.lean b/Mathlib/RingTheory/HahnSeries/PowerSeries.lean
index 7c20a709677b15..98a1946698c521 100644
--- a/Mathlib/RingTheory/HahnSeries/PowerSeries.lean
+++ b/Mathlib/RingTheory/HahnSeries/PowerSeries.lean
@@ -117,7 +117,7 @@ theorem ofPowerSeries_C (r : R) : ofPowerSeries Γ R (PowerSeries.C r) = HahnSer
     coeff_single]
   split_ifs with hn
   · subst hn
-    convert embDomain_coeff (a := 0) <;> simp
+    convert! embDomain_coeff (a := 0) <;> simp
   · rw [embDomain_notin_image_support]
     simp only [not_exists, Set.mem_image, toPowerSeries_symm_apply_coeff, mem_support,
       PowerSeries.coeff_C]
@@ -130,7 +130,7 @@ theorem ofPowerSeries_X : ofPowerSeries Γ R PowerSeries.X = single 1 1 := by
   simp only [coeff_single, ofPowerSeries_apply]
   split_ifs with hn
   · rw [hn]
-    convert embDomain_coeff (a := 1) <;> simp
+    convert! embDomain_coeff (a := 1) <;> simp
   · rw [embDomain_notin_image_support]
     simp only [not_exists, Set.mem_image, toPowerSeries_symm_apply_coeff, mem_support,
       PowerSeries.coeff_X]
diff --git a/Mathlib/RingTheory/Henselian.lean b/Mathlib/RingTheory/Henselian.lean
index dd077f36e3b45a..bbafc12bf78162 100644
--- a/Mathlib/RingTheory/Henselian.lean
+++ b/Mathlib/RingTheory/Henselian.lean
@@ -200,7 +200,7 @@ instance (priority := 100) IsAdicComplete.henselianRing (R : Type*) [CommRing R]
         intro n
         haveI := isLocalHom_of_le_jacobson_bot I (IsAdicComplete.le_jacobson_bot I)
         apply IsUnit.of_map (Ideal.Quotient.mk I)
-        convert h₂ using 1
+        convert! h₂ using 1
         exact SModEq.def.mp ((hc_mod n).eval _)
       have hfcI : ∀ n, f.eval (c n) ∈ I ^ (n + 1) := by
         intro n
diff --git a/Mathlib/RingTheory/HopfAlgebra/TensorProduct.lean b/Mathlib/RingTheory/HopfAlgebra/TensorProduct.lean
index 62706afae60a13..5f9d1d798b714d 100644
--- a/Mathlib/RingTheory/HopfAlgebra/TensorProduct.lean
+++ b/Mathlib/RingTheory/HopfAlgebra/TensorProduct.lean
@@ -49,7 +49,7 @@ instance : HopfAlgebra S (B ⊗[R] A) where
   antipode := AlgebraTensorModule.map (HopfAlgebra.antipode S) (HopfAlgebra.antipode R)
   mul_antipode_rTensor_comul := by
     ext x y
-    convert congr($(mul_antipode_rTensor_comul_apply (R := S) x) ⊗ₜ[R]
+    convert! congr($(mul_antipode_rTensor_comul_apply (R := S) x) ⊗ₜ[R]
       $(mul_antipode_rTensor_comul_apply (R := R) y)) using 1
     · dsimp
       hopf_tensor_induction comul (R := S) x with x₁ x₂
@@ -59,7 +59,7 @@ instance : HopfAlgebra S (B ⊗[R] A) where
       simp [Algebra.algebraMap_eq_smul_one, smul_tmul']
   mul_antipode_lTensor_comul := by
     ext x y
-    convert congr($(mul_antipode_lTensor_comul_apply (R := S) x) ⊗ₜ[R]
+    convert! congr($(mul_antipode_lTensor_comul_apply (R := S) x) ⊗ₜ[R]
       $(mul_antipode_lTensor_comul_apply (R := R) y)) using 1
     · dsimp [Algebra.TensorProduct.one_def]
       hopf_tensor_induction comul (R := S) x with x₁ x₂
diff --git a/Mathlib/RingTheory/Ideal/AssociatedPrime/Finiteness.lean b/Mathlib/RingTheory/Ideal/AssociatedPrime/Finiteness.lean
index 1aa49162e112ce..6ac47fae8b3425 100644
--- a/Mathlib/RingTheory/Ideal/AssociatedPrime/Finiteness.lean
+++ b/Mathlib/RingTheory/Ideal/AssociatedPrime/Finiteness.lean
@@ -63,7 +63,7 @@ theorem Submodule.isQuotientEquivQuotientPrime_iff {N₁ N₂ : Submodule A M} :
   · obtain ⟨⟨x, hx⟩, hx'⟩ := Submodule.mkQ_surjective _ (e.symm 1)
     have hx'' : N₁.mkQ x = f (e.symm 1) := by simp [f, ← hx']
     refine ⟨x, ?_, ?_⟩
-    · convert p.2
+    · convert! p.2
       ext r
       simp [hx'', ← map_smul, Algebra.smul_def, show f _ = 0 ↔ _ from congr(_ ∈ $hf₁),
         Ideal.Quotient.eq_zero_iff_mem]
diff --git a/Mathlib/RingTheory/Ideal/Cotangent.lean b/Mathlib/RingTheory/Ideal/Cotangent.lean
index dd460bf7ed8760..6083d133137ba5 100644
--- a/Mathlib/RingTheory/Ideal/Cotangent.lean
+++ b/Mathlib/RingTheory/Ideal/Cotangent.lean
@@ -213,8 +213,9 @@ def mapCotangent (I₁ : Ideal A) (I₂ : Ideal B) (f : A →ₐ[R] B) (h : I₁
     refine Submodule.smul_induction_on hx ?_ (fun _ _ ↦ add_mem)
     rintro a ha ⟨b, hb⟩ -
     simp only [SetLike.mk_smul_mk, smul_eq_mul, Submodule.mem_comap, Submodule.restrictScalars_mem]
-    convert (Submodule.smul_mem_smul (M := I₂) (r := f a)
-      (n := ⟨f b, h hb⟩) (h ha) (Submodule.mem_top)) using 1
+    convert!
+      (Submodule.smul_mem_smul (M := I₂) (r := f a) (n := ⟨f b, h hb⟩) (h ha)
+        (Submodule.mem_top)) using 1
     ext
     exact map_mul f a b
 
@@ -389,5 +390,5 @@ lemma Ideal.mapCotangent_ker_of_surjective (surj : Function.Surjective (algebraM
   · rw [Submodule.map_le_iff_le_comap, ← LinearMap.ker_comp]
     intro x hx
     simp only [LinearMap.mem_ker, LinearMap.comp_apply, Ideal.mapCotangent_toCotangent]
-    convert map_zero I.toCotangent
+    convert! map_zero I.toCotangent
     exact (Ideal.mem_inf.mp hx).1
diff --git a/Mathlib/RingTheory/Ideal/GoingUp.lean b/Mathlib/RingTheory/Ideal/GoingUp.lean
index f4a2a90dffae96..3d31f778aeae30 100644
--- a/Mathlib/RingTheory/Ideal/GoingUp.lean
+++ b/Mathlib/RingTheory/Ideal/GoingUp.lean
@@ -139,7 +139,7 @@ theorem exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff [IsPrime I] (hIJ :
     (p.map (Ideal.Quotient.mk (I.comap f))).eval₂ (Quotient.lift (I.comap f) _ quotient_f)
         (Ideal.Quotient.mk I r) =
       0 := by
-    convert Quotient.eq_zero_iff_mem.mpr hpI
+    convert! Quotient.eq_zero_iff_mem.mpr hpI
     exact _root_.trans (eval₂_map _ _ _) (hom_eval₂ p f (Ideal.Quotient.mk I) r).symm
   obtain ⟨i, ne_zero, mem⟩ :=
     exists_coeff_ne_zero_mem_comap_of_root_mem rbar_ne_zero rbar_mem_J p_ne_zero rbar_root
@@ -162,7 +162,7 @@ theorem comap_lt_comap_of_integral_mem_sdiff [Algebra R S] [hI : I.IsPrime] (hIJ
     I.comap (algebraMap R S) < J.comap (algebraMap R S) := by
   obtain ⟨p, p_monic, hpx⟩ := integral
   refine comap_lt_comap_of_root_mem_sdiff hIJ mem (map_monic_ne_zero p_monic) ?_
-  convert I.zero_mem
+  convert! I.zero_mem
 
 theorem comap_ne_bot_of_root_mem [IsDomain S] {r : S} (r_ne_zero : r ≠ 0) (hr : r ∈ I) {p : R[X]}
     (p_ne_zero : p ≠ 0) (hp : p.eval₂ f r = 0) : I.comap f ≠ ⊥ := fun h =>
@@ -288,7 +288,7 @@ theorem exists_ideal_over_prime_of_isIntegral_of_isDomain [Algebra.IsIntegral R
   have Qₚ_max : IsMaximal (comap _ Qₚ) :=
     isMaximal_comap_of_isIntegral_of_isMaximal (R := Rₚ) (S := Sₚ) Qₚ
   refine ⟨comap (algebraMap S Sₚ) Qₚ, ⟨comap_isPrime _ Qₚ, ?_⟩⟩
-  convert Localization.AtPrime.under_maximalIdeal (I := P)
+  convert! Localization.AtPrime.under_maximalIdeal (I := P)
   rw [comap_comap, ← IsLocalRing.eq_maximalIdeal Qₚ_max,
     ← IsLocalization.map_comp (P := S) (Q := Sₚ) (g := algebraMap R S)
     (M := P.primeCompl) (T := Algebra.algebraMapSubmonoid S P.primeCompl) (S := Rₚ)
diff --git a/Mathlib/RingTheory/Ideal/Height.lean b/Mathlib/RingTheory/Ideal/Height.lean
index 52d06e6ec73e24..d9337df234b282 100644
--- a/Mathlib/RingTheory/Ideal/Height.lean
+++ b/Mathlib/RingTheory/Ideal/Height.lean
@@ -209,7 +209,7 @@ then J is a minimal prime over I -/
 lemma Ideal.mem_minimalPrimes_of_height_eq {I J : Ideal R} (e : I ≤ J) [J.IsPrime]
     [FiniteHeight J] (e' : J.height ≤ I.height) : J ∈ I.minimalPrimes := by
   obtain ⟨p, h₁, h₂⟩ := Ideal.exists_minimalPrimes_le e
-  convert h₁
+  convert! h₁
   refine (eq_of_le_of_not_lt h₂ fun h₃ ↦ ?_).symm
   have := h₁.isPrime
   have := finiteHeight_of_le h₂ IsPrime.ne_top'
diff --git a/Mathlib/RingTheory/Ideal/KrullsHeightTheorem.lean b/Mathlib/RingTheory/Ideal/KrullsHeightTheorem.lean
index 5aa2e8787d83d3..81af20f4775e36 100644
--- a/Mathlib/RingTheory/Ideal/KrullsHeightTheorem.lean
+++ b/Mathlib/RingTheory/Ideal/KrullsHeightTheorem.lean
@@ -50,7 +50,7 @@ lemma IsLocalRing.quotient_artinian_of_mem_minimalPrimes_of_isLocalRing
     IsArtinianRing (R ⧸ I) :=
   have : Ring.KrullDimLE 0 (R ⧸ I) := Ring.krullDimLE_zero_iff.mpr fun J prime ↦
     Ideal.isMaximal_of_isIntegral_of_isMaximal_comap _ <| by
-      convert IsLocalRing.maximalIdeal.isMaximal R
+      convert! IsLocalRing.maximalIdeal.isMaximal R
       rw [Ideal.minimalPrimes, Set.mem_setOf] at hp
       have := prime.comap (Ideal.Quotient.mk I)
       exact hp.eq_of_le ⟨this, .trans (by simp) (Ideal.ker_le_comap _)⟩ (le_maximalIdeal this.1)
@@ -227,7 +227,7 @@ nonrec lemma Ideal.height_le_spanRank_toENat_of_mem_minimalPrimes
           simpa using Finset.card_lt_card (Finset.ssubset_insert hxs')).trans_le hn)
         (H _ (tcard.trans_lt n.lt_succ_self) q t hq rfl).trans (by norm_cast)
       rw [Finset.coe_insert] at hp
-      convert mem_minimalPrimes_span_of_mem_minimalPrimes_span_insert hpq _ _ hp _ ht ?_
+      convert! mem_minimalPrimes_span_of_mem_minimalPrimes_span_insert hpq _ _ hp _ ht ?_
       · simp [t]
       refine hspan.trans <| radical_mono ?_
       rw [← Set.union_singleton, span_union]
@@ -289,7 +289,7 @@ lemma Ideal.exists_spanRank_eq_and_height_eq (I : Ideal R) (hI : I ≠ ⊤) :
   rw [ENat.coe_toNat_eq_self.mpr (Ideal.height_ne_top hI)] at hJ₃
   refine ⟨J, hJ₁, le_antisymm ?_ (le_trans ?_ (J.height_le_spanRank ?_)),
     le_antisymm (Ideal.height_mono hJ₁) hJ₃⟩
-  · convert hJ₂
+  · convert! hJ₂
     exact Cardinal.ofENat_eq_nat.mpr (ENat.coe_toNat (I.height_ne_top hI)).symm
   · exact Cardinal.ofENat_le_ofENat_of_le hJ₃
   · rintro rfl
@@ -352,7 +352,7 @@ lemma Ideal.height_le_height_add_spanFinrank_of_le {I p : Ideal R} [p.IsPrime] (
   rw [Finset.coe_union, Set.Finite.coe_toFinset, span_union, sup_comm, span,
     Submodule.span_generators]
   refine Ideal.mem_minimalPrimes_sup hrp ?_
-  convert hps
+  convert! hps
   simp [Ideal.map_span, ← himgo]
 
 lemma height_le_ringKrullDim_quotient_add_spanFinrank {p I : Ideal R} [p.IsPrime] (h : I ≤ p) :
@@ -390,12 +390,12 @@ lemma Ideal.height_le_ringKrullDim_quotient_add_encard {p : Ideal R} [p.IsPrime]
 
 lemma Ideal.height_le_height_add_one_of_mem {r : R} {p : Ideal R} [p.IsPrime] (hrm : r ∈ p) :
     p.height ≤ (p.map (Quotient.mk (span {r}))).height + 1 := by
-  convert height_le_height_add_encard_of_subset {r} (p := p) (by simpa)
+  convert! height_le_height_add_encard_of_subset { r } (p := p) (by simpa)
   simp
 
 lemma Ideal.height_le_ringKrullDim_quotient_add_one {r : R} {p : Ideal R} [p.IsPrime]
     (hrp : r ∈ p) : p.height ≤ ringKrullDim (R ⧸ span {r}) + 1 := by
-  convert Ideal.height_le_ringKrullDim_quotient_add_encard {r} (by simpa)
+  convert! Ideal.height_le_ringKrullDim_quotient_add_encard { r } (by simpa)
   simp
 
 lemma ringKrullDim_le_ringKrullDim_quotient_add_encard (s : Set R) (hs : s ⊆ Ring.jacobson R) :
@@ -407,7 +407,7 @@ lemma ringKrullDim_le_ringKrullDim_quotient_add_encard (s : Set R) (hs : s ⊆ R
 lemma ringKrullDim_le_ringKrullDim_quotient_add_card (s : Finset R)
     (hs : (s : Set R) ⊆ Ring.jacobson R) :
     ringKrullDim R ≤ ringKrullDim (R ⧸ Ideal.span (s : Set R)) + s.card := by
-  convert ringKrullDim_le_ringKrullDim_quotient_add_encard s hs
+  convert! ringKrullDim_le_ringKrullDim_quotient_add_encard s hs
   norm_cast
 
 section Algebra
@@ -449,7 +449,7 @@ lemma Ideal.height_le_height_add_of_liesOver [IsNoetherianRing S] (p : Ideal R)
   have : Ideal.span t = Ideal.map (algebraMap R S) (.span s) ⊔ .span o := by
     simp [t, Ideal.map_span]
   refine this ▸ map_sup_mem_minimalPrimes_of_map_quotientMk_mem_minimalPrimes hp (span_le.mpr ho) ?_
-  convert hP'
+  convert! hP'
   simp [Ideal.map_span, ← himgo]
 
 /--
diff --git a/Mathlib/RingTheory/Ideal/Maps.lean b/Mathlib/RingTheory/Ideal/Maps.lean
index 96e4372dc96fc2..5294ae60494428 100644
--- a/Mathlib/RingTheory/Ideal/Maps.lean
+++ b/Mathlib/RingTheory/Ideal/Maps.lean
@@ -376,8 +376,9 @@ theorem IsMaximal.comap_piEvalRingHom {ι : Type*} {R : ι → Type*} [∀ i, Se
   refine isMaximal_iff.mpr ⟨I.ne_top_iff_one.mp h.ne_top, fun J x le hxI hxJ ↦ ?_⟩
   have ⟨r, y, hy, eq⟩ := h.exists_inv hxI
   classical
-  convert J.add_mem (J.mul_mem_left (update 0 i r) hxJ)
-    (b := update 1 i y) (le <| by apply update_self i y 1 ▸ hy)
+  convert!
+    J.add_mem (J.mul_mem_left (update 0 i r) hxJ) (b := update 1 i y)
+      (le <| by apply update_self i y 1 ▸ hy)
   ext j
   obtain rfl | ne := eq_or_ne j i
   · simpa [eq_comm] using eq
@@ -1087,7 +1088,7 @@ theorem map_isPrime_of_surjective {f : F} (hf : Function.Surjective f) {I : Idea
     rcases hxy with ⟨c, hc, hc'⟩
     rw [← sub_eq_zero, ← map_sub] at hc'
     have : a * b ∈ I := by
-      convert I.sub_mem hc (hk (hc' : c - a * b ∈ RingHom.ker f)) using 1
+      convert! I.sub_mem hc (hk (hc' : c - a * b ∈ RingHom.ker f)) using 1
       abel
     exact
       (H.mem_or_mem this).imp (fun h => ha ▸ mem_map_of_mem f h) fun h => hb ▸ mem_map_of_mem f h
@@ -1118,7 +1119,7 @@ theorem map_radical_of_surjective {f : R →+* S} (hf : Function.Surjective f) {
     (h : RingHom.ker f ≤ I) : map f I.radical = (map f I).radical := by
   rw [radical_eq_sInf, radical_eq_sInf]
   have : ∀ J ∈ {J : Ideal R | I ≤ J ∧ J.IsPrime}, RingHom.ker f ≤ J := fun J hJ => h.trans hJ.left
-  convert map_sInf hf this
+  convert! map_sInf hf this
   ext j
   constructor
   · rintro ⟨hj, hj'⟩
diff --git a/Mathlib/RingTheory/Ideal/MinimalPrime/Basic.lean b/Mathlib/RingTheory/Ideal/MinimalPrime/Basic.lean
index 1d4dea8b6ad45e..23e037a198388a 100644
--- a/Mathlib/RingTheory/Ideal/MinimalPrime/Basic.lean
+++ b/Mathlib/RingTheory/Ideal/MinimalPrime/Basic.lean
@@ -205,7 +205,7 @@ lemma Ideal.map_sup_mem_minimalPrimes_of_map_quotientMk_mem_minimalPrimes
     have h1 : p.map (algebraMap R S) ≤ q := by
       rw [Ideal.map_le_iff_le_comap]
       refine hI.2 ⟨inferInstance, le_trans Ideal.le_comap_map (Ideal.comap_mono hleq.1)⟩ ?_
-      convert Ideal.comap_mono hqle
+      convert! Ideal.comap_mono hqle
       exact Ideal.LiesOver.over
     have h2 : P.map (Ideal.Quotient.mk (p.map (algebraMap R S))) ≤
         q.map (Ideal.Quotient.mk (p.map (algebraMap R S))) :=
diff --git a/Mathlib/RingTheory/Ideal/Nonunits.lean b/Mathlib/RingTheory/Ideal/Nonunits.lean
index e1608235a69950..0c2acbd0278c37 100644
--- a/Mathlib/RingTheory/Ideal/Nonunits.lean
+++ b/Mathlib/RingTheory/Ideal/Nonunits.lean
@@ -72,7 +72,7 @@ variable {C : Type*} [SetLike C α]
 theorem inv_mem_of_isUnit [DivisionMonoid α] [SubmonoidClass C α] {S : C} {a : S} (ha : IsUnit a) :
     (a : α)⁻¹ ∈ S := by
   obtain ⟨u, rfl⟩ := ha
-  convert u⁻¹.1.2
+  convert! u⁻¹.1.2
   exact (map_inv ((subtype <| ofClass S).comp <| Units.coeHom S) u).symm
 
 section Group
diff --git a/Mathlib/RingTheory/Ideal/Norm/AbsNorm.lean b/Mathlib/RingTheory/Ideal/Norm/AbsNorm.lean
index a091dae00c491b..0b107f99397c57 100644
--- a/Mathlib/RingTheory/Ideal/Norm/AbsNorm.lean
+++ b/Mathlib/RingTheory/Ideal/Norm/AbsNorm.lean
@@ -105,7 +105,7 @@ theorem Ideal.mul_add_mem_pow_succ_inj (P : Ideal S) {i : ℕ} (a d d' e e' : S)
   have : a * d - a * d' ∈ P ^ (i + 1) := by
     simp only [← mul_sub]
     exact Ideal.mul_mem_mul a_mem h
-  convert Ideal.add_mem _ this (Ideal.sub_mem _ e_mem e'_mem) using 1
+  convert! Ideal.add_mem _ this (Ideal.sub_mem _ e_mem e'_mem) using 1
   ring
 
 section PPrime
@@ -144,7 +144,7 @@ theorem Ideal.mul_add_mem_pow_succ_unique [IsDedekindDomain S] (hP : P ≠ ⊥)
     (a_notMem : a ∉ P ^ (i + 1)) (e_mem : e ∈ P ^ (i + 1)) (e'_mem : e' ∈ P ^ (i + 1))
     (h : a * d + e - (a * d' + e') ∈ P ^ (i + 1)) : d - d' ∈ P := by
   have h' : a * (d - d') ∈ P ^ (i + 1) := by
-    convert Ideal.add_mem _ h (Ideal.sub_mem _ e'_mem e_mem) using 1
+    convert! Ideal.add_mem _ h (Ideal.sub_mem _ e'_mem e_mem) using 1
     ring
   exact Ideal.mem_prime_of_mul_mem_pow hP a_notMem h'
 
diff --git a/Mathlib/RingTheory/Ideal/Norm/RelNorm.lean b/Mathlib/RingTheory/Ideal/Norm/RelNorm.lean
index 3244a3ca908c0a..e7004eed7607e4 100644
--- a/Mathlib/RingTheory/Ideal/Norm/RelNorm.lean
+++ b/Mathlib/RingTheory/Ideal/Norm/RelNorm.lean
@@ -320,7 +320,7 @@ theorem relNorm_map_algEquiv {T : Type*} [CommRing T] [IsDedekindDomain T] [IsIn
     [Algebra R T] [Module.Finite R T] [IsTorsionFree R T] (σ : S ≃ₐ[R] T) (I : Ideal S) :
     relNorm R (I.map σ) = relNorm R I := by
   refine le_antisymm (relNorm_map_algEquiv_aux σ I) ?_
-  convert relNorm_map_algEquiv_aux σ.symm (I.map σ)
+  convert! relNorm_map_algEquiv_aux σ.symm (I.map σ)
   change I = map σ.symm.toAlgHom (map σ.toAlgHom I)
   simp [map_mapₐ]
 
diff --git a/Mathlib/RingTheory/Ideal/Quotient/ChineseRemainder.lean b/Mathlib/RingTheory/Ideal/Quotient/ChineseRemainder.lean
index d0647fb45356b0..c7f4f9fd5cc482 100644
--- a/Mathlib/RingTheory/Ideal/Quotient/ChineseRemainder.lean
+++ b/Mathlib/RingTheory/Ideal/Quotient/ChineseRemainder.lean
@@ -50,7 +50,7 @@ theorem ker_tensorProductMk_quotient :
       (⨅ i, I i) • (⊤ : Submodule R M) := by
   have := rTensor_exact M (exact_subtype_ker_map _) (pi_mkQ_surjective hI)
   rw [← (TensorProduct.lid R M).conj_exact_iff_exact, exact_iff] at this
-  convert this
+  convert! this
   · classical simp [pi_mkQ_rTensor, LinearMap.comp_assoc]
   refine le_antisymm (Submodule.smul_le.mpr fun r hr m _ ↦ ⟨⟨r, ?_⟩ ⊗ₜ m, rfl⟩) ?_
   · simpa only [ker_pi, Submodule.ker_mkQ]
diff --git a/Mathlib/RingTheory/Ideal/Quotient/Operations.lean b/Mathlib/RingTheory/Ideal/Quotient/Operations.lean
index 23d93bd29f0403..8a5d73d16743ff 100644
--- a/Mathlib/RingTheory/Ideal/Quotient/Operations.lean
+++ b/Mathlib/RingTheory/Ideal/Quotient/Operations.lean
@@ -577,7 +577,7 @@ lemma _root_.AlgHom.liftOfSurjective_comp (f : A →ₐ[R] B) (hf : Function.Sur
 lemma _root_.AlgHom.liftOfSurjective_surjective (f : A →ₐ[R] B) (hf : Function.Surjective f)
     (g : A →ₐ[R] C) (H : RingHom.ker f.toRingHom ≤ RingHom.ker g.toRingHom)
     (hg : Function.Surjective g) : Function.Surjective (AlgHom.liftOfSurjective f hf g H) :=
-  .of_comp (g := f) (by convert hg; ext; simp)
+  .of_comp (g := f) (by convert! hg; ext; simp)
 
 end liftOfSurjective
 
diff --git a/Mathlib/RingTheory/IntegralClosure/IntegralRestrict.lean b/Mathlib/RingTheory/IntegralClosure/IntegralRestrict.lean
index 2d61bab942f57d..4632e56e931129 100644
--- a/Mathlib/RingTheory/IntegralClosure/IntegralRestrict.lean
+++ b/Mathlib/RingTheory/IntegralClosure/IntegralRestrict.lean
@@ -519,7 +519,7 @@ lemma Algebra.algebraMap_intNorm_of_isGalois [IsGalois (FractionRing A) (Fractio
   haveI : FiniteDimensional (FractionRing A) (FractionRing B) := .of_isLocalization A B A⁰
   rw [← (galRestrict A (FractionRing A) (FractionRing B) B).toEquiv.prod_comp]
   simp only [MulEquiv.toEquiv_eq_coe, EquivLike.coe_coe]
-  convert (prod_galRestrict_eq_norm A (FractionRing A) (FractionRing B) B x).symm
+  convert! (prod_galRestrict_eq_norm A (FractionRing A) (FractionRing B) B x).symm
 
 open Polynomial IsScalarTower in
 theorem Algebra.dvd_algebraMap_intNorm_self (x : B) : x ∣ algebraMap A B (intNorm A B x) := by
diff --git a/Mathlib/RingTheory/IntegralClosure/IntegrallyClosed.lean b/Mathlib/RingTheory/IntegralClosure/IntegrallyClosed.lean
index 3004ea70521c57..1d3a91951ec546 100644
--- a/Mathlib/RingTheory/IntegralClosure/IntegrallyClosed.lean
+++ b/Mathlib/RingTheory/IntegralClosure/IntegrallyClosed.lean
@@ -83,7 +83,7 @@ theorem AlgHom.isIntegrallyClosedIn (f : A →ₐ[R] B) (hf : Function.Injective
     IsIntegrallyClosedIn R B → IsIntegrallyClosedIn R A := by
   rintro ⟨inj, cl⟩
   refine ⟨Function.Injective.of_comp (f := f) ?_, fun hx => ?_, ?_⟩
-  · convert inj
+  · convert! inj
     aesop
   · obtain ⟨y, fx_eq⟩ := cl.mp ((isIntegral_algHom_iff f hf).mpr hx)
     aesop
@@ -282,7 +282,7 @@ lemma of_isIntegrallyClosedIn
     (FaithfulSMul.algebraMap_injective R K)
   rw [isIntegrallyClosed_iff (K := FractionRing R)]
   intro x hx
-  convert (IsIntegralClosure.isIntegral_iff (A := R)).mp (hx.map f)
+  convert! (IsIntegralClosure.isIntegral_iff (A := R)).mp (hx.map f)
   simp [← f.toRingHom.injective.eq_iff]
 
 lemma _root_.IsIntegralClosure.of_isIntegralClosure_of_isIntegrallyClosedIn
diff --git a/Mathlib/RingTheory/IntegralClosure/IsIntegralClosure/Basic.lean b/Mathlib/RingTheory/IntegralClosure/IsIntegralClosure/Basic.lean
index 1d6ef074373620..62098ee34b1a3e 100644
--- a/Mathlib/RingTheory/IntegralClosure/IsIntegralClosure/Basic.lean
+++ b/Mathlib/RingTheory/IntegralClosure/IsIntegralClosure/Basic.lean
@@ -202,7 +202,7 @@ theorem IsIntegral.of_mul_unit {x y : B} {r : R} (hr : algebraMap R B r * y = 1)
     (hx : IsIntegral R (x * y)) : IsIntegral R x := by
   obtain ⟨p, p_monic, hp⟩ := hx
   refine ⟨scaleRoots p r, (monic_scaleRoots_iff r).2 p_monic, ?_⟩
-  convert scaleRoots_aeval_eq_zero hp
+  convert! scaleRoots_aeval_eq_zero hp
   rw [Algebra.commutes] at hr ⊢
   rw [mul_assoc, hr, mul_one]; rfl
 
@@ -485,7 +485,7 @@ theorem isIntegral_trans [Algebra.IsIntegral R A] (x : B) (hx : IsIntegral A x)
   let p' : S[X] := p.toSubring S.toSubring subset_adjoin
   have hSx : IsIntegral S x := ⟨p', (p.monic_toSubring _ _).mpr pmonic, by
     rw [IsScalarTower.algebraMap_eq S A B, ← eval₂_map]
-    convert hp; apply p.map_toSubring S.toSubring⟩
+    convert! hp; apply p.map_toSubring S.toSubring⟩
   let Sx := Subalgebra.toSubmodule (S[x])
   let MSx : Module S Sx := SMulMemClass.toModule _ -- the next line times out without this
   have : Module.Finite S Sx := .of_fg hSx.fg_adjoin_singleton
diff --git a/Mathlib/RingTheory/IsAdjoinRoot.lean b/Mathlib/RingTheory/IsAdjoinRoot.lean
index 855071079c8f79..eb6034e89f1241 100644
--- a/Mathlib/RingTheory/IsAdjoinRoot.lean
+++ b/Mathlib/RingTheory/IsAdjoinRoot.lean
@@ -639,7 +639,7 @@ theorem minpoly_eq [IsDomain R] [IsDomain S] [IsTorsionFree R S] [IsIntegrallyCl
   let ⟨q, hq⟩ := minpoly.isIntegrallyClosed_dvd h.isIntegral_root h.aeval_root_self
   symm <|
     eq_of_monic_of_associated h.monic (minpoly.monic h.isIntegral_root) <| by
-      convert
+      convert!
         Associated.mul_left (minpoly R h.root) <|
           associated_one_iff_isUnit.2 <|
             (hirr.isUnit_or_isUnit hq).resolve_left <| minpoly.not_isUnit R h.root
diff --git a/Mathlib/RingTheory/IsTensorProduct.lean b/Mathlib/RingTheory/IsTensorProduct.lean
index beac6cdd2c57b5..17ca73745966cc 100644
--- a/Mathlib/RingTheory/IsTensorProduct.lean
+++ b/Mathlib/RingTheory/IsTensorProduct.lean
@@ -350,7 +350,7 @@ noncomputable nonrec def IsBaseChange.lift (g : M →ₗ[R] Q) : N →ₗ[S] Q :
 
 nonrec theorem IsBaseChange.lift_eq (g : M →ₗ[R] Q) (x : M) : h.lift g (f x) = g x := by
   have hF : ∀ (s : S) (m : M), h.lift g (s • f m) = s • g m := h.lift_eq _
-  convert hF 1 x <;> rw [one_smul]
+  convert! hF 1 x <;> rw [one_smul]
 
 theorem IsBaseChange.lift_comp (g : M →ₗ[R] Q) : ((h.lift g).restrictScalars R).comp f = g :=
   LinearMap.ext (h.lift_eq g)
@@ -386,7 +386,7 @@ variable (R M N S)
 
 theorem TensorProduct.isBaseChange : IsBaseChange S (TensorProduct.mk R S M 1) := by
   delta IsBaseChange
-  convert TensorProduct.isTensorProduct R S M using 1
+  convert! TensorProduct.isTensorProduct R S M using 1
   ext s x
   change s • (1 : S) ⊗ₜ[R] x = s ⊗ₜ[R] x
   rw [TensorProduct.smul_tmul']
@@ -434,11 +434,11 @@ lemma IsBaseChange.iff_of_equiv_comm (eM : M ≃ₗ[R] P) (eN : N ≃ₗ[S] Q)
   simp only [IsBaseChange]
   have (m : M) : f' (eM m) = eN (f m) := LinearMap.congr_fun comm m
   refine ⟨fun ist ↦ ?_, fun ist ↦ ?_⟩
-  · convert (ist.compl₂_linearEquiv eM.symm).compr₂_linearEquiv (eN.restrictScalars R)
+  · convert! (ist.compl₂_linearEquiv eM.symm).compr₂_linearEquiv (eN.restrictScalars R)
     ext s m'
     obtain ⟨m, rfl⟩ := eM.surjective m'
     simp [this]
-  · convert (ist.compl₂_linearEquiv eM).compr₂_linearEquiv (eN.symm.restrictScalars R)
+  · convert! (ist.compl₂_linearEquiv eM).compr₂_linearEquiv (eN.symm.restrictScalars R)
     ext s m
     simp [this]
 
@@ -687,7 +687,7 @@ lemma Algebra.IsPushout.tensorProduct_tensorProduct
       Algebra.TensorProduct.includeRight.toRingHom) :
     Algebra.IsPushout A B (A ⊗[R] S) (B ⊗[R] S) := by
   constructor
-  convert isBaseChange_tensorProduct_map (R := R) (P := S) _ (IsBaseChange.linearMap A B)
+  convert! isBaseChange_tensorProduct_map (R := R) (P := S) _ (IsBaseChange.linearMap A B)
   ext s
   simpa using congr($H s)
 
diff --git a/Mathlib/RingTheory/Jacobson/Ideal.lean b/Mathlib/RingTheory/Jacobson/Ideal.lean
index d05460530f1dab..0004ab71fe433a 100644
--- a/Mathlib/RingTheory/Jacobson/Ideal.lean
+++ b/Mathlib/RingTheory/Jacobson/Ideal.lean
@@ -127,7 +127,7 @@ theorem exists_mul_add_sub_mem_of_mem_jacobson {I : Ideal R} (r : R) (h : r ∈
 
 theorem exists_mul_sub_mem_of_sub_one_mem_jacobson {I : Ideal R} (r : R) (h : r - 1 ∈ jacobson I) :
     ∃ s, s * r - 1 ∈ I := by
-  convert exists_mul_add_sub_mem_of_mem_jacobson _ h
+  convert! exists_mul_add_sub_mem_of_mem_jacobson _ h
   simp
 
 /-- An ideal equals its Jacobson radical iff it is the intersection of a set of maximal ideals.
diff --git a/Mathlib/RingTheory/Jacobson/Radical.lean b/Mathlib/RingTheory/Jacobson/Radical.lean
index 8bb3956f69910c..cea9cb8d9c956f 100644
--- a/Mathlib/RingTheory/Jacobson/Radical.lean
+++ b/Mathlib/RingTheory/Jacobson/Radical.lean
@@ -196,7 +196,7 @@ theorem FG.jacobson_smul_lt {N : Submodule R M} (ne_bot : N ≠ ⊥) (fg : N.FG)
     Ring.jacobson R • N < N := by
   rw [← Module.Finite.iff_fg] at fg
   rw [← nontrivial_iff_ne_bot] at ne_bot
-  convert map_strictMono_of_injective N.injective_subtype (jacobson_smul_lt_top ⊤)
+  convert! map_strictMono_of_injective N.injective_subtype (jacobson_smul_lt_top ⊤)
   on_goal 1 => rw [map_smul'']
   all_goals rw [Submodule.map_top, range_subtype]
 
diff --git a/Mathlib/RingTheory/Jacobson/Ring.lean b/Mathlib/RingTheory/Jacobson/Ring.lean
index 545f932032e2ff..6ebd25e6b2312f 100644
--- a/Mathlib/RingTheory/Jacobson/Ring.lean
+++ b/Mathlib/RingTheory/Jacobson/Ring.lean
@@ -173,7 +173,7 @@ theorem IsLocalization.isMaximal_iff_isMaximal_disjoint [H : IsJacobsonRing R] (
     rw [← H.out hJ.left.isRadical, jacobson, Submodule.mem_toAddSubmonoid, Ideal.mem_sInf] at this
     push Not at this
     rcases this with ⟨I, ⟨hJI, hIm⟩, hI'⟩
-    convert hIm
+    convert! hIm
     by_cases hJ : J = I.map (algebraMap R S)
     · rw [hJ, under_map_of_isPrime_disjoint (powers y) S hIm.isPrime]
       rwa [disjoint_powers_iff_notMem_of_isPrime]
@@ -657,7 +657,7 @@ theorem comp_C_integral_of_surjective_of_isJacobsonRing {R : Type*} [CommRing R]
     rw [← hfg, coe_comp] at hf'
     exact Function.Surjective.of_comp hf'
   rw [RingHom.comp_assoc] at this
-  convert this
+  convert! this
   refine RingHom.ext fun x => ?_
   exact ((renameEquiv R e).commutes' x).symm
 
diff --git a/Mathlib/RingTheory/Kaehler/Basic.lean b/Mathlib/RingTheory/Kaehler/Basic.lean
index f8825c1c4efed4..d2f1097820f797 100644
--- a/Mathlib/RingTheory/Kaehler/Basic.lean
+++ b/Mathlib/RingTheory/Kaehler/Basic.lean
@@ -206,8 +206,9 @@ def KaehlerDifferential.D : Derivation R S Ω[S⁄R] :=
       rw [← LinearMap.map_smul_of_tower (ideal R S).toCotangent,
         ← LinearMap.map_smul_of_tower (ideal R S).toCotangent,
         ← map_add (ideal R S).toCotangent, Ideal.toCotangent_eq, pow_two]
-      convert Submodule.mul_mem_mul (KaehlerDifferential.one_smul_sub_smul_one_mem_ideal R a :)
-        (KaehlerDifferential.one_smul_sub_smul_one_mem_ideal R b :) using 1
+      convert!
+        Submodule.mul_mem_mul (KaehlerDifferential.one_smul_sub_smul_one_mem_ideal R a :)
+          (KaehlerDifferential.one_smul_sub_smul_one_mem_ideal R b :) using 1
       simp only [Submodule.coe_add,
         TensorProduct.tmul_mul_tmul, mul_sub, sub_mul, mul_comm b, Submodule.coe_smul_of_tower,
         smul_sub, TensorProduct.smul_tmul', smul_eq_mul, mul_one]
@@ -572,7 +573,7 @@ theorem KaehlerDifferential.quotKerTotalEquiv_symm_comp_D :
     (KaehlerDifferential.quotKerTotalEquiv R S).symm.toLinearMap.compDer
         (KaehlerDifferential.D R S) =
       KaehlerDifferential.derivationQuotKerTotal R S := by
-  convert (KaehlerDifferential.derivationQuotKerTotal R S).liftKaehlerDifferential_comp
+  convert! (KaehlerDifferential.derivationQuotKerTotal R S).liftKaehlerDifferential_comp
 
 end Presentation
 
@@ -691,7 +692,7 @@ lemma KaehlerDifferential.ker_map_of_surjective (h : Function.Surjective (algebr
     Submodule.map_sup, ← kerTotal_eq, ← Submodule.comap_bot,
     Submodule.map_comap_eq_of_surjective (linearCombination_surjective _ _),
     bot_sup_eq, Submodule.map_span, ← Set.range_comp]
-  convert bot_sup_eq _
+  convert! bot_sup_eq _
   rw [Submodule.span_eq_bot]; simp
 
 open IsScalarTower (toAlgHom)
@@ -740,7 +741,7 @@ lemma KaehlerDifferential.range_mapBaseChange :
   · convert_to (kerTotal A B).map (Finsupp.linearCombination B (D R B)) ≤ _
     · rw [KaehlerDifferential.ker_map]
       congr 1
-      convert Submodule.comap_id _
+      convert! Submodule.comap_id _
       · ext; simp
     rw [Submodule.map_le_iff_le_comap, kerTotal, Submodule.span_le]
     rintro f ((⟨⟨x, y⟩, rfl⟩ | ⟨⟨x, y⟩, rfl⟩) | ⟨x, rfl⟩)
@@ -829,7 +830,7 @@ theorem KaehlerDifferential.range_kerCotangentToTensor
       rw [← TensorProduct.smul_tmul, ← Algebra.algebraMap_eq_smul_one, RingHom.mem_ker.mp this,
         TensorProduct.zero_tmul]
     · have : x i ≠ 0 ∧ algebraMap A B i = c := by
-        convert i.prop
+        convert! i.prop
         simp_rw [Finset.mem_filter, Finsupp.mem_support_iff]
       simp [RingHom.mem_ker, ha, this.2]
 
diff --git a/Mathlib/RingTheory/Kaehler/JacobiZariski.lean b/Mathlib/RingTheory/Kaehler/JacobiZariski.lean
index 8b1a760ee522bb..05ca6273a6ebc8 100644
--- a/Mathlib/RingTheory/Kaehler/JacobiZariski.lean
+++ b/Mathlib/RingTheory/Kaehler/JacobiZariski.lean
@@ -82,7 +82,7 @@ lemma Cotangent.exact :
     ext x
     obtain ⟨⟨x, hx⟩, rfl⟩ := Extension.Cotangent.mk_surjective x
     simp only [map_mk, val_mk, LinearMap.zero_apply, val_zero]
-    convert Q.ker.toCotangent.map_zero
+    convert! Q.ker.toCotangent.map_zero
     trans ((IsScalarTower.toAlgHom R _ _).comp (IsScalarTower.toAlgHom R P.Ring S)) x
     · congr
       refine MvPolynomial.algHom_ext fun i ↦ ?_
diff --git a/Mathlib/RingTheory/Kaehler/TensorProduct.lean b/Mathlib/RingTheory/Kaehler/TensorProduct.lean
index 5b0145398db1a4..cdd675e28d7d12 100644
--- a/Mathlib/RingTheory/Kaehler/TensorProduct.lean
+++ b/Mathlib/RingTheory/Kaehler/TensorProduct.lean
@@ -224,8 +224,9 @@ then `Ω[B⁄S]` is the base change of `Ω[A⁄R]` along `R → S`.
 -/
 lemma isBaseChange [h : Algebra.IsPushout R S A B] :
     IsBaseChange S ((map R S A B).restrictScalars R) := by
-  convert (TensorProduct.isBaseChange R Ω[A⁄R] S).comp
-    (IsBaseChange.ofEquiv (tensorKaehlerEquivBase R S A B))
+  convert!
+    (TensorProduct.isBaseChange R Ω[A⁄R] S).comp
+      (IsBaseChange.ofEquiv (tensorKaehlerEquivBase R S A B))
   refine LinearMap.ext fun x ↦ ?_
   simp only [LinearMap.coe_restrictScalars, LinearMap.coe_comp, LinearEquiv.coe_coe,
     Function.comp_apply, mk_apply, tensorKaehlerEquivBase_tmul, one_smul]
diff --git a/Mathlib/RingTheory/KrullDimension/NonZeroDivisors.lean b/Mathlib/RingTheory/KrullDimension/NonZeroDivisors.lean
index d9b38899130523..f9485349cf4bc1 100644
--- a/Mathlib/RingTheory/KrullDimension/NonZeroDivisors.lean
+++ b/Mathlib/RingTheory/KrullDimension/NonZeroDivisors.lean
@@ -81,7 +81,7 @@ lemma ringKrullDim_add_natCard_le_ringKrullDim_mvPolynomial (σ : Type*) [Finite
     ringKrullDim R + Nat.card σ ≤ ringKrullDim (MvPolynomial σ R) := by
   induction σ using Finite.induction_empty_option with
   | of_equiv e H =>
-    convert ← H using 1
+    convert! ← H using 1
     · rw [Nat.card_congr e]
     · exact ringKrullDim_eq_of_ringEquiv (renameEquiv _ e).toRingEquiv
   | h_empty => simp
diff --git a/Mathlib/RingTheory/KrullDimension/Polynomial.lean b/Mathlib/RingTheory/KrullDimension/Polynomial.lean
index c51a9d6e6540a5..e7a74a3b40a9b9 100644
--- a/Mathlib/RingTheory/KrullDimension/Polynomial.lean
+++ b/Mathlib/RingTheory/KrullDimension/Polynomial.lean
@@ -120,7 +120,7 @@ lemma MvPolynomial.ringKrullDim_of_isNoetherianRing {ι : Type*} [Finite ι] :
     ringKrullDim (MvPolynomial ι R) = ringKrullDim R + Nat.card ι := by
   induction ι using Finite.induction_empty_option with
   | of_equiv e H =>
-    convert ← H using 1
+    convert! ← H using 1
     · exact ringKrullDim_eq_of_ringEquiv (renameEquiv _ e).toRingEquiv
     · rw [Nat.card_congr e]
   | h_empty => simp
diff --git a/Mathlib/RingTheory/LaurentSeries.lean b/Mathlib/RingTheory/LaurentSeries.lean
index d016489916f2a9..9805e9fddab378 100644
--- a/Mathlib/RingTheory/LaurentSeries.lean
+++ b/Mathlib/RingTheory/LaurentSeries.lean
@@ -441,7 +441,7 @@ theorem intValuation_eq_of_coe (P : K[X]) :
   rw [Ideal.count_associates_factors_eq span_ne_zero.1
     (Ideal.span_singleton_prime Polynomial.X_ne_zero |>.mpr prime_X) span_ne_zero.2,
     Ideal.count_associates_factors_eq]
-  on_goal 1 => convert (normalized_count_X_eq_of_coe hP).symm
+  on_goal 1 => convert! (normalized_count_X_eq_of_coe hP).symm
   exacts [Ideal.count_span_normalizedFactors_eq_of_normUnit hP Polynomial.normUnit_X prime_X,
     Ideal.count_span_normalizedFactors_eq_of_normUnit (by simp [hP]) normUnit_X X_prime,
     span_ne_zero'.1, (idealX K).isPrime, span_ne_zero'.2]
@@ -469,8 +469,9 @@ theorem valuation_eq_LaurentSeries_valuation (P : K⟮X⟯) :
   refine RatFunc.induction_on' P ?_
   intro f g h
   rw [Polynomial.valuation_of_mk K f h, RatFunc.mk_eq_mk' f h, Eq.comm]
-  convert @valuation_of_mk' K⟦X⟧ _ _ K⸨X⸩ _ _ _ (PowerSeries.idealX K) f
-        ⟨g, mem_nonZeroDivisors_iff_ne_zero.2 <| (by simp [h])⟩
+  convert!
+    @valuation_of_mk' K⟦X⟧ _ _ K⸨X⸩ _ _ _ (PowerSeries.idealX K) f
+      ⟨g, mem_nonZeroDivisors_iff_ne_zero.2 <| (by simp [h])⟩
   · simp [← IsScalarTower.algebraMap_apply K[X] K⟮X⟯ K⸨X⸩]
   exacts [intValuation_eq_of_coe _, intValuation_eq_of_coe _]
 
@@ -769,7 +770,7 @@ theorem Cauchy.coeff_eventually_equal {ℱ : Filter K⸨X⸩} (hℱ : Cauchy ℱ
     constructor
     · have := (exists_lb_coeff_ne hℱ).choose_spec
       rw [Filter.eventually_iff] at this
-      convert this
+      convert! this
       ext
       simp only [Set.mem_iInter, Set.mem_setOf_eq]; rfl
     · rw [biInter_mem (Set.finite_Icc ℓ N)]
diff --git a/Mathlib/RingTheory/LinearDisjoint.lean b/Mathlib/RingTheory/LinearDisjoint.lean
index 817a5c486804c3..9eff591bf9b898 100644
--- a/Mathlib/RingTheory/LinearDisjoint.lean
+++ b/Mathlib/RingTheory/LinearDisjoint.lean
@@ -651,7 +651,7 @@ theorem _root_.Algebra.TensorProduct.not_isField_of_transcendental
     refine ⟨⟨a, by simp [fa]⟩, ⟨b, hf ?_⟩⟩
     simp_rw [fb, Algebra.TensorProduct.includeRight_apply, f,
       Algebra.TensorProduct.mapOfCompatibleSMul_tmul]
-    convert ← (TensorProduct.smul_tmul (R := R[X]) (R' := R[X]) (M := A) (N := B) X 1 1).symm <;>
+    convert! ← (TensorProduct.smul_tmul (R := R[X]) (R' := R[X]) (M := A) (N := B) X 1 1).symm <;>
       (simp_rw [Algebra.smul_def, mul_one]; exact aeval_X _)
   have key3 := (Subalgebra.inclusion key2).comp (AlgEquiv.ofInjective gab htab).toAlgHom
     |>.toLinearMap.lift_rank_le_of_injective
diff --git a/Mathlib/RingTheory/LittleWedderburn.lean b/Mathlib/RingTheory/LittleWedderburn.lean
index 588558be698a30..20425e0914f877 100644
--- a/Mathlib/RingTheory/LittleWedderburn.lean
+++ b/Mathlib/RingTheory/LittleWedderburn.lean
@@ -92,7 +92,7 @@ private theorem center_eq_top [Finite D] (hD : InductionHyp D) : Subring.center
     rw [eval_sub, eval_X_pow, eval_one, ← key, Int.dvd_add_left this] at contra
     refine (Nat.le_of_dvd ?_ ?_).not_gt (sub_one_lt_natAbs_cyclotomic_eval (n := n) ?_ hq.ne')
     · exact tsub_pos_of_lt hq
-    · convert Int.natAbs_dvd_natAbs.mpr contra
+    · convert! Int.natAbs_dvd_natAbs.mpr contra
       clear_value q
       simp only [eq_comm, Int.natAbs_eq_iff, Nat.cast_sub hq.le, Nat.cast_one, neg_sub, true_or]
     · by_contra! h
@@ -153,7 +153,7 @@ private theorem center_eq_top [Finite D] : Subring.center D = ⊤ := by
   rw [IH (Fintype.card R) _ R inferInstance rfl]
   · trivial
   rw [← hn, ← Subring.card_top D]
-  convert Set.card_lt_card hR
+  convert! Set.card_lt_card hR
 
 end LittleWedderburn
 
diff --git a/Mathlib/RingTheory/LocalProperties/Basic.lean b/Mathlib/RingTheory/LocalProperties/Basic.lean
index e332b43d3356e7..93684cdd70eae3 100644
--- a/Mathlib/RingTheory/LocalProperties/Basic.lean
+++ b/Mathlib/RingTheory/LocalProperties/Basic.lean
@@ -317,7 +317,7 @@ lemma RingHom.LocalizationAwayPreserves.respectsIso
       IsLocalization.away_of_isUnit_of_bijective _ isUnit_one (Equiv.refl _).bijective
     have : IsLocalization.Away (f 1) T :=
       IsLocalization.away_of_isUnit_of_bijective _ (by simp) e.bijective
-    convert hP f 1 R T hf
+    convert! hP f 1 R T hf
     trans (IsLocalization.Away.map R T f 1).comp (algebraMap R R)
     · rw [IsLocalization.Away.map, IsLocalization.map_comp]; rfl
     · rfl
@@ -327,7 +327,7 @@ lemma RingHom.LocalizationAwayPreserves.respectsIso
       IsLocalization.away_of_isUnit_of_bijective _ isUnit_one e.symm.bijective
     have : IsLocalization.Away (f 1) T :=
       IsLocalization.away_of_isUnit_of_bijective _ (by simp) (Equiv.refl _).bijective
-    convert hP f 1 R T hf
+    convert! hP f 1 R T hf
     have : RingHomInvPair (e : R →+* S) e.symm := RingHomInvPair.of_ringEquiv _
     have : (IsLocalization.Away.map R T f 1).comp e.symm.toRingHom = f :=
       IsLocalization.map_comp ..
@@ -431,8 +431,7 @@ lemma RingHom.OfLocalizationSpanTarget.ofIsLocalization
   apply hP _ s hs
   intro r
   obtain ⟨T, _, _, _, hT⟩ := hT r
-  convert hP'.1 _
-    (Localization.algEquiv (R := S) (Submonoid.powers (r : S)) T).symm.toRingEquiv hT
+  convert! hP'.1 _ (Localization.algEquiv (R := S) (Submonoid.powers (r : S)) T).symm.toRingEquiv hT
   rw [← RingHom.comp_assoc, RingEquiv.toRingHom_eq_coe,
     AlgEquiv.toRingEquiv_toRingHom, Localization.coe_algEquiv_symm, IsLocalization.map_comp,
     RingHom.comp_id]
diff --git a/Mathlib/RingTheory/LocalProperties/IntegrallyClosed.lean b/Mathlib/RingTheory/LocalProperties/IntegrallyClosed.lean
index 3c879444d5d9d8..fa70ddb50a5a32 100644
--- a/Mathlib/RingTheory/LocalProperties/IntegrallyClosed.lean
+++ b/Mathlib/RingTheory/LocalProperties/IntegrallyClosed.lean
@@ -75,7 +75,7 @@ theorem IsIntegrallyClosed.of_localization_maximal [IsDomain R]
   · rintro ⟨p, rfl⟩
     exact h p.asIdeal (Ring.ne_bot_of_isMaximal_of_not_isField p.isMaximal hf)
   · rw [iInf_range]
-    convert MaximalSpectrum.iInf_localization_eq_bot R (FractionRing R)
+    convert! MaximalSpectrum.iInf_localization_eq_bot R (FractionRing R)
     rw [subalgebra.ofField_eq, MaximalSpectrum.toPrimeSpectrum]
 
 theorem isIntegrallyClosed_ofLocalizationMaximal :
diff --git a/Mathlib/RingTheory/LocalProperties/Projective.lean b/Mathlib/RingTheory/LocalProperties/Projective.lean
index 2396844623e0ce..dd21844f8b3c84 100644
--- a/Mathlib/RingTheory/LocalProperties/Projective.lean
+++ b/Mathlib/RingTheory/LocalProperties/Projective.lean
@@ -56,7 +56,7 @@ theorem Module.lift_rank_of_isLocalizedModule_of_free
   have := (IsLocalizedModule.isBaseChange S Rₛ f).equiv.lift_rank_eq.symm
   simp only [rank_tensorProduct, rank_self,
     Cardinal.lift_one, one_mul, Cardinal.lift_lift] at this ⊢
-  convert this
+  convert! this
   exact Cardinal.lift_umax
 
 theorem Module.finrank_of_isLocalizedModule_of_free
@@ -92,7 +92,7 @@ theorem LinearMap.split_surjective_of_localization_maximal
   rw [LocalizedModule.map_id]
   have : LinearMap.id ∈ LinearMap.range (LinearMap.llcomp _
     (LocalizedModule I.primeCompl N) _ _ (LocalizedModule.map I.primeCompl f)) := H I hI
-  convert this
+  convert! this
   · ext f
     constructor
     · intro hf
@@ -137,7 +137,7 @@ theorem Module.projective_of_localization_maximal (H : ∀ (I : Ideal R) (_ : I.
   let f : N →ₗ[R] M := Finsupp.linearCombination R (Subtype.val : s → M)
   have hf : Function.Surjective f := by
     rw [← LinearMap.range_eq_top, Finsupp.range_linearCombination, Subtype.range_val]
-    convert hs
+    convert! hs
   have (I : Ideal R) (hI : I.IsMaximal) :=
     letI := H I hI
     Module.projective_lifting_property (LocalizedModule.map I.primeCompl f) LinearMap.id
diff --git a/Mathlib/RingTheory/LocalRing/Module.lean b/Mathlib/RingTheory/LocalRing/Module.lean
index 14d5b3f5a407fc..a9f3caf4ab23f4 100644
--- a/Mathlib/RingTheory/LocalRing/Module.lean
+++ b/Mathlib/RingTheory/LocalRing/Module.lean
@@ -271,11 +271,11 @@ theorem IsLocalRing.linearIndependent_of_flat [Flat R M] {ι : Type u} (v : ι 
   have a_eq i : a i j = a' i.1 := by simp_rw [a', dif_pos i.2]
   have hfn : f n = -(∑ i ∈ s, f i * a' i) * hj.unit⁻¹ := by
     rw [← hj.mul_left_inj, mul_assoc, hj.val_inv_mul, mul_one, eq_neg_iff_add_eq_zero]
-    convert hfa j
+    convert! hfa j
     simp_rw [a_eq, Finset.sum_coe_sort _ (fun i ↦ f i * a' i), s.sum_insert hn, n_def]
   let c (i : ι) : R := -(if i = n then 0 else a' i) * hj.unit⁻¹
   specialize ih (v + (c · • v n)) ?_ ?_
-  · convert (linearIndependent_add_smul_iff (c := Ideal.Quotient.mk _ ∘ c) (i := n.1) ?_).mpr h
+  · convert! (linearIndependent_add_smul_iff (c := Ideal.Quotient.mk _ ∘ c) (i := n.1) ?_).mpr h
     · ext; simp [tmul_add]; rfl
     simp_rw [Function.comp_def, c, if_pos, neg_zero, zero_mul, map_zero]
   · rw [Finset.sum_coe_sort _ (fun i ↦ f i • v i), s.sum_insert hn, add_comm, hfn] at hfv
@@ -413,7 +413,7 @@ at every maximal ideal, then `M` is free of rank `n`. -/
   apply IsLocalRing.linearCombination_bijective_of_flat
   rw [← (AlgebraTensorModule.cancelBaseChange _ _ P.ResidueField ..).comp_bijective,
     ← (AlgebraTensorModule.cancelBaseChange R (R ⧸ P) P.ResidueField ..).symm.comp_bijective]
-  convert ((b' ⟨P, ‹_›⟩).repr.lTensor _ ≪≫ₗ finsuppScalarRight _ _ P.ResidueField _).symm.bijective
+  convert! ((b' ⟨P, ‹_›⟩).repr.lTensor _ ≪≫ₗ finsuppScalarRight _ _ P.ResidueField _).symm.bijective
   refine funext fun r ↦ Finsupp.induction_linear r (by simp) (by simp +contextual) fun _ _ ↦ ?_
   simp [smul_tmul', ← funext_iff.mp (hb _)]
 
diff --git a/Mathlib/RingTheory/LocalRing/ResidueField/Fiber.lean b/Mathlib/RingTheory/LocalRing/ResidueField/Fiber.lean
index dae55a28f2e1c8..bd12a4d1deff18 100644
--- a/Mathlib/RingTheory/LocalRing/ResidueField/Fiber.lean
+++ b/Mathlib/RingTheory/LocalRing/ResidueField/Fiber.lean
@@ -111,7 +111,7 @@ noncomputable def PrimeSpectrum.preimageEquivFiber (p : PrimeSpectrum R) :
       ← Ideal.IsPrime.mul_mem_left_iff (x := algebraMap _ _ r), ← Algebra.smul_def, e]
     · simp
     · rw [← Ideal.mem_comap, ← PrimeSpectrum.comap_asIdeal]
-      convert hr
+      convert! hr
       exact (residueField_comap _).le ⟨q.comap (algebraMap _ _), rfl⟩
     · simpa [-Algebra.algebraMap_self, -AlgHom.commutes, -AlgHom.map_algebraMap,
         -Ideal.ResidueField.map_algebraMap]
@@ -165,8 +165,8 @@ noncomputable def PrimeSpectrum.preimageHomeomorphFiber (R S : Type*) [CommRing
   exact
   { __ := preimageOrderIsoFiber R S p
     continuous_toFun := by
-      convert (H.toHomeomorphOfSurjective
-        (preimageOrderIsoFiber R S p).symm.surjective).symm.continuous
+      convert!
+        (H.toHomeomorphOfSurjective (preimageOrderIsoFiber R S p).symm.surjective).symm.continuous
       ext1 x
       obtain ⟨x, rfl⟩ := (H.toHomeomorphOfSurjective
         (preimageOrderIsoFiber R S p).symm.surjective).surjective x
diff --git a/Mathlib/RingTheory/Localization/AsSubring.lean b/Mathlib/RingTheory/Localization/AsSubring.lean
index ea364019aa7163..9cb5fec4087df7 100644
--- a/Mathlib/RingTheory/Localization/AsSubring.lean
+++ b/Mathlib/RingTheory/Localization/AsSubring.lean
@@ -112,7 +112,7 @@ theorem mem_range_mapToFractionRing_iff_ofField (B : Type*) [CommRing B] [Algebr
     x ∈ (mapToFractionRing K S B hS).range ↔
       ∃ (a s : A) (_ : s ∈ S), x = algebraMap A K a * (algebraMap A K s)⁻¹ := by
   rw [mem_range_mapToFractionRing_iff]
-  convert Iff.rfl
+  convert! Iff.rfl
   congr
   rw [Units.val_inv_eq_inv_val]
   rfl
diff --git a/Mathlib/RingTheory/Localization/AtPrime/Basic.lean b/Mathlib/RingTheory/Localization/AtPrime/Basic.lean
index bf561bdba02b0e..1aa90ef816f916 100644
--- a/Mathlib/RingTheory/Localization/AtPrime/Basic.lean
+++ b/Mathlib/RingTheory/Localization/AtPrime/Basic.lean
@@ -209,7 +209,7 @@ it is the unique maximal ideal given by the local ring structure `AtPrime.isLoca
 theorem AtPrime.map_eq_maximalIdeal :
     Ideal.map (algebraMap R (Localization.AtPrime I)) I =
       IsLocalRing.maximalIdeal (Localization I.primeCompl) := by
-  convert congr_arg (Ideal.map _) AtPrime.under_maximalIdeal.symm
+  convert! congr_arg (Ideal.map _) AtPrime.under_maximalIdeal.symm
   rw [map_under I.primeCompl]
 
 lemma AtPrime.eq_maximalIdeal_iff_under_eq {J : Ideal (Localization.AtPrime I)} :
@@ -483,7 +483,7 @@ theorem isPrime_map_of_liesOver [P.IsPrime] [P.LiesOver p] : (P.map (algebraMap
   isPrime_of_isPrime_disjoint _ _ _ inferInstance (Ideal.disjoint_primeCompl_of_liesOver P p)
 
 theorem map_eq_maximalIdeal : p.map (algebraMap R Rₚ) = maximalIdeal Rₚ := by
-  convert congr_arg (Ideal.map (algebraMap R Rₚ)) (under_maximalIdeal Rₚ p).symm
+  convert! congr_arg (Ideal.map (algebraMap R Rₚ)) (under_maximalIdeal Rₚ p).symm
   rw [map_under p.primeCompl]
 
 instance isMaximal_map : (p.map (algebraMap R Rₚ)).IsMaximal := by
diff --git a/Mathlib/RingTheory/Localization/Away/Basic.lean b/Mathlib/RingTheory/Localization/Away/Basic.lean
index 6a7eadfbfdecb7..a4ee8db93c0331 100644
--- a/Mathlib/RingTheory/Localization/Away/Basic.lean
+++ b/Mathlib/RingTheory/Localization/Away/Basic.lean
@@ -60,7 +60,7 @@ noncomputable def invSelf : S :=
 
 @[simp]
 theorem mul_invSelf : algebraMap R S x * invSelf x = 1 := by
-  convert IsLocalization.mk'_mul_mk'_eq_one (M := Submonoid.powers x) (S := S) _ 1
+  convert! IsLocalization.mk'_mul_mk'_eq_one (M := Submonoid.powers x) (S := S) _ 1
   symm
   apply IsLocalization.mk'_one
 
@@ -306,7 +306,7 @@ lemma commutes {R : Type*} [CommSemiring R] (S₁ S₂ T : Type*) [CommSemiring
     [IsLocalization.Away x S₁] [IsLocalization.Away y S₂]
     [IsLocalization.Away (algebraMap R S₂ x) T] :
     IsLocalization.Away (algebraMap R S₁ y) T := by
-  convert IsLocalization.commutes S₁ S₂ T (Submonoid.powers x) (Submonoid.powers y)
+  convert! IsLocalization.commutes S₁ S₂ T (Submonoid.powers x) (Submonoid.powers y)
   ext x
   simp
 
diff --git a/Mathlib/RingTheory/Localization/BaseChange.lean b/Mathlib/RingTheory/Localization/BaseChange.lean
index fd34209bf88d48..1ee7a99f5f08af 100644
--- a/Mathlib/RingTheory/Localization/BaseChange.lean
+++ b/Mathlib/RingTheory/Localization/BaseChange.lean
@@ -49,7 +49,7 @@ theorem isLocalizedModule_iff_isBaseChange : IsLocalizedModule S f ↔ IsBaseCha
   letI : Module A (LocalizedModule S M) := LocalizedModule.moduleOfIsLocalization ..
   have : IsBaseChange A (LocalizedModule.mkLinearMap S M) := IsLocalizedModule.isBaseChange S A _
   let e := (this.equiv.symm.trans h.equiv).restrictScalars R
-  convert IsLocalizedModule.of_linearEquiv S (LocalizedModule.mkLinearMap S M) e
+  convert! IsLocalizedModule.of_linearEquiv S (LocalizedModule.mkLinearMap S M) e
   ext
   rw [LinearMap.coe_comp, LinearEquiv.coe_coe, Function.comp_apply,
     LinearEquiv.restrictScalars_apply, LinearEquiv.trans_apply, IsBaseChange.equiv_symm_apply,
@@ -117,9 +117,10 @@ instance (N N') [AddCommMonoid N] [Module R N] [AddCommMonoid N'] [Module R N']
     IsLocalizedModule S (TensorProduct.map f g) := by
   let eM := IsLocalizedModule.linearEquiv S f (TensorProduct.mk R (Localization S) M 1)
   let eN := IsLocalizedModule.linearEquiv S g (TensorProduct.mk R (Localization S) N 1)
-  convert IsLocalizedModule.of_linearEquiv S (TensorProduct.mk R (Localization S) (M ⊗[R] N) 1) <|
-    (AlgebraTensorModule.distribBaseChange R (Localization S) ..).restrictScalars R ≪≫ₗ
-    (congr eM eN ≪≫ₗ TensorProduct.equivOfCompatibleSMul ..).symm
+  convert!
+    IsLocalizedModule.of_linearEquiv S (TensorProduct.mk R (Localization S) (M ⊗[R] N) 1) <|
+      (AlgebraTensorModule.distribBaseChange R (Localization S) ..).restrictScalars R ≪≫ₗ
+        (congr eM eN ≪≫ₗ TensorProduct.equivOfCompatibleSMul ..).symm
   ext; congrm (?_ ⊗ₜ ?_) <;> simp [LinearEquiv.eq_symm_apply, eM, eN]
 
 /-- If `A` is a localization of `R`, tensoring two `A`-modules over `A` is the same as
@@ -206,11 +207,11 @@ instance {α} [IsLocalizedModule S f] :
   let e' : Localization S ⊗[R] (α →₀ M) ≃ₗ[R] (α →₀ M') :=
     finsuppRight R R (Localization S) M α ≪≫ₗ Finsupp.mapRange.linearEquiv e
   suffices IsLocalizedModule S (e'.symm.toLinearMap ∘ₗ Finsupp.mapRange.linearMap f) by
-    convert this.of_linearEquiv (e := e')
+    convert! this.of_linearEquiv (e := e')
     ext
     simp
   rw [isLocalizedModule_iff_isBaseChange S (Localization S)]
-  convert TensorProduct.isBaseChange R (α →₀ M) (Localization S) using 1
+  convert! TensorProduct.isBaseChange R (α →₀ M) (Localization S) using 1
   ext a m
   apply (finsuppRight R R (Localization S) M α).injective
   ext b
diff --git a/Mathlib/RingTheory/Localization/Basic.lean b/Mathlib/RingTheory/Localization/Basic.lean
index cc570c4196e4cb..40fc2f722e7d2b 100644
--- a/Mathlib/RingTheory/Localization/Basic.lean
+++ b/Mathlib/RingTheory/Localization/Basic.lean
@@ -327,7 +327,7 @@ theorem isLocalization_of_algEquiv [Algebra R P] [IsLocalization M S] (h : S ≃
     IsLocalization M P := by
   constructor; constructor
   · intro y
-    convert (IsLocalization.map_units S y).map h.toAlgHom.toRingHom.toMonoidHom
+    convert! (IsLocalization.map_units S y).map h.toAlgHom.toRingHom.toMonoidHom
     exact (h.commutes y).symm
   · intro y
     obtain ⟨⟨x, s⟩, e⟩ := IsLocalization.surj M (h.symm y)
diff --git a/Mathlib/RingTheory/Localization/Defs.lean b/Mathlib/RingTheory/Localization/Defs.lean
index d044fb59df3cc2..592c4ebd1f3d1f 100644
--- a/Mathlib/RingTheory/Localization/Defs.lean
+++ b/Mathlib/RingTheory/Localization/Defs.lean
@@ -739,14 +739,14 @@ theorem isLocalization_of_base_ringEquiv [IsLocalization M S] (h : R ≃+* P) :
   letI : Algebra P S := ((algebraMap R S).comp h.symm.toRingHom).toAlgebra
   constructor; constructor
   · rintro ⟨_, ⟨y, hy, rfl⟩⟩
-    convert IsLocalization.map_units S ⟨y, hy⟩
+    convert! IsLocalization.map_units S ⟨y, hy⟩
     dsimp only [RingHom.algebraMap_toAlgebra, RingHom.comp_apply]
     exact congr_arg _ (h.symm_apply_apply _)
   · intro y
     obtain ⟨⟨x, s⟩, e⟩ := IsLocalization.surj M y
     refine ⟨⟨h x, _, _, s.prop, rfl⟩, ?_⟩
     dsimp only [RingHom.algebraMap_toAlgebra, RingHom.comp_apply] at e ⊢
-    convert e <;> exact h.symm_apply_apply _
+    convert! e <;> exact h.symm_apply_apply _
   · intro x y
     rw [RingHom.algebraMap_toAlgebra, RingHom.comp_apply, RingHom.comp_apply,
       IsLocalization.eq_iff_exists M S]
@@ -759,7 +759,7 @@ theorem isLocalization_iff_of_base_ringEquiv (h : R ≃+* P) :
   letI : Algebra P S := ((algebraMap R S).comp h.symm.toRingHom).toAlgebra
   refine ⟨fun _ => isLocalization_of_base_ringEquiv M S h, ?_⟩
   intro (H : IsLocalization (Submonoid.map (h : R ≃* P) M) S)
-  convert isLocalization_of_base_ringEquiv (Submonoid.map (h : R ≃* P) M) S h.symm
+  convert! isLocalization_of_base_ringEquiv (Submonoid.map (h : R ≃* P) M) S h.symm
   · rw [← Submonoid.map_coe_toMulEquiv, RingEquiv.coe_toMulEquiv_symm, ←
       Submonoid.comap_equiv_eq_map_symm, Submonoid.comap_map_eq_of_injective]
     exact h.toEquiv.injective
@@ -774,7 +774,7 @@ theorem of_ringEquiv_left {S : Type*} [CommSemiring S] {K : Type*} [CommSemiring
     (hM : M₂.map e = M₁) (h : ∀ x, algebraMap R K x = algebraMap S K (e x)) [IsLocalization M₁ K] :
     IsLocalization M₂ K := by
   rw [IsLocalization.isLocalization_iff_of_base_ringEquiv _ _ e, hM]
-  convert (inferInstance : IsLocalization M₁ K)
+  convert! (inferInstance : IsLocalization M₁ K)
   exact Algebra.algebra_ext _ _ (by simp [RingHom.algebraMap_toAlgebra, h])
 
 end
diff --git a/Mathlib/RingTheory/Localization/Finiteness.lean b/Mathlib/RingTheory/Localization/Finiteness.lean
index 84ac4fc6d6822d..5bdc2560b3a220 100644
--- a/Mathlib/RingTheory/Localization/Finiteness.lean
+++ b/Mathlib/RingTheory/Localization/Finiteness.lean
@@ -74,10 +74,12 @@ theorem IsLocalization.smul_mem_finsetIntegerMultiple_span [Algebra R S] [Algebr
   obtain ⟨⟨_, a, ha₁, rfl⟩, ha₂⟩ :=
     (IsLocalization.eq_iff_exists (M.map (algebraMap R S)) S').mp hx''
   use (⟨a, ha₁⟩ : M) * (⟨y', hy'⟩ : M)
-  convert (Submodule.span R
-    (IsLocalization.finsetIntegerMultiple (Submonoid.map (algebraMap R S) M) s : Set S)).smul_mem
+  convert!
+    (Submodule.span R
+          (IsLocalization.finsetIntegerMultiple (Submonoid.map (algebraMap R S) M) s :
+            Set S)).smul_mem
       a hx' using 1
-  convert ha₂.symm using 1
+  convert! ha₂.symm using 1
   · rw [Subtype.coe_mk, Submonoid.smul_def, Submonoid.coe_mul, ← smul_smul]
     exact Algebra.smul_def _ _
   · exact Algebra.smul_def _ _
diff --git a/Mathlib/RingTheory/Localization/FractionRing.lean b/Mathlib/RingTheory/Localization/FractionRing.lean
index de83899e98af91..da773812892e92 100644
--- a/Mathlib/RingTheory/Localization/FractionRing.lean
+++ b/Mathlib/RingTheory/Localization/FractionRing.lean
@@ -600,7 +600,7 @@ theorem isFractionRing_iff_of_base_ringEquiv (h : R ≃+* P) :
     IsFractionRing R S ↔
       @IsFractionRing P _ S _ ((algebraMap R S).comp h.symm.toRingHom).toAlgebra := by
   delta IsFractionRing
-  convert isLocalization_iff_of_base_ringEquiv (nonZeroDivisors R) S h
+  convert! isLocalization_iff_of_base_ringEquiv (nonZeroDivisors R) S h
   exact (MulEquivClass.map_nonZeroDivisors h).symm
 
 variable (R S : Type*) [CommSemiring R] [CommSemiring S] [Algebra R S] [h : IsFractionRing R S]
diff --git a/Mathlib/RingTheory/Localization/Ideal.lean b/Mathlib/RingTheory/Localization/Ideal.lean
index f23b9fe931088b..f2cb0211365cf5 100644
--- a/Mathlib/RingTheory/Localization/Ideal.lean
+++ b/Mathlib/RingTheory/Localization/Ideal.lean
@@ -265,7 +265,7 @@ lemma map_radical (I : Ideal R) :
   obtain ⟨x, s, rfl⟩ := IsLocalization.exists_mk'_eq M x
   simp only [← IsLocalization.mk'_pow, IsLocalization.mk'_mem_map_algebraMap_iff M] at hn ⊢
   obtain ⟨s, hs, h⟩ := hn
-  refine ⟨s, hs, n + 1, by convert I.mul_mem_left (s ^ n * x) h; ring⟩
+  refine ⟨s, hs, n + 1, by convert! I.mul_mem_left (s ^ n * x) h; ring⟩
 
 theorem ideal_eq_iInf_under_map_away {S : Finset R} (hS : Ideal.span (α := R) S = ⊤) (I : Ideal R) :
     I = ⨅ f ∈ S, (I.map (algebraMap R (Localization.Away f))).under R := by
@@ -317,7 +317,7 @@ theorem surjective_quotientMap_of_maximal_of_localization {I : Ideal S} [I.IsPri
   · have : I = ⊤ := by
       rw [Ideal.eq_top_iff_one]
       rw [Ideal.Quotient.eq_zero_iff_mem, Ideal.mem_comap] at hM
-      convert I.mul_mem_right (mk' S (1 : R) ⟨m, hm⟩) hM
+      convert! I.mul_mem_right (mk' S (1 : R) ⟨m, hm⟩) hM
       rw [← mk'_eq_mul_mk'_one, mk'_self]
     exact ⟨0, eq_comm.1 (by simp [Ideal.Quotient.eq_zero_iff_mem, this])⟩
   · rw [Ideal.Quotient.maximal_ideal_iff_isField_quotient] at hI
@@ -346,8 +346,9 @@ theorem bot_lt_under_prime [IsDomain R] (hM : M ≤ R⁰) (p : Ideal S) [hpp : p
     (hp0 : p ≠ ⊥) : ⊥ < p.under R := by
   haveI : IsDomain S := isDomain_of_le_nonZeroDivisors _ hM
   rw [← Ideal.comap_bot_of_injective (algebraMap R S) (IsLocalization.injective _ hM)]
-  convert (orderIsoOfPrime M S).lt_iff_lt.mpr (show (⟨⊥, Ideal.isPrime_bot⟩ :
-    { p : Ideal S // p.IsPrime }) < ⟨p, hpp⟩ from hp0.bot_lt)
+  convert!
+    (orderIsoOfPrime M S).lt_iff_lt.mpr
+      (show (⟨⊥, Ideal.isPrime_bot⟩ : { p : Ideal S // p.IsPrime }) < ⟨p, hpp⟩ from hp0.bot_lt)
 
 @[deprecated (since := "2026-04-09")] alias bot_lt_comap_prime := bot_lt_under_prime
 
diff --git a/Mathlib/RingTheory/Localization/Integral.lean b/Mathlib/RingTheory/Localization/Integral.lean
index 790fa6bfc3a36f..b275d814e3f4c3 100644
--- a/Mathlib/RingTheory/Localization/Integral.lean
+++ b/Mathlib/RingTheory/Localization/Integral.lean
@@ -312,7 +312,7 @@ lemma IsLocalization.Away.exists_isIntegral_mul_of_isIntegral_mk'
     (hx : IsIntegral R (IsLocalization.mk' Sₘ x a)) : ∃ n, IsIntegral R (r ^ n * x) := by
   refine IsLocalization.Away.exists_isIntegral_mul_of_isIntegral_algebraMap (Sₘ := Sₘ) hr ?_
   obtain ⟨_, ⟨n, rfl⟩⟩ := a
-  convert (hr.pow n).algebraMap.mul hx
+  convert! (hr.pow n).algebraMap.mul hx
   exact (mk'_spec'_mk ..).symm
 
 /-- If `t` is integral over `R[1/t]`, then it is integral over `R`. -/
@@ -449,7 +449,8 @@ protected lemma IsLocalization.integralClosure
       (integralClosure Rf Sf) := by
   refine ⟨⟨?_, ?_, ?_⟩⟩
   · rintro ⟨_, f, hf, rfl⟩
-    convert (IsLocalization.map_units (S := Rf) ⟨f, hf⟩).map (algebraMap Rf (integralClosure Rf Sf))
+    convert!
+      (IsLocalization.map_units (S := Rf) ⟨f, hf⟩).map (algebraMap Rf (integralClosure Rf Sf))
     simp [← IsScalarTower.algebraMap_apply]
   · rintro ⟨s, hs⟩
     obtain ⟨⟨x, _, m₁, hm₁, rfl⟩, e⟩ := IsLocalization.surj (Algebra.algebraMapSubmonoid S M) s
@@ -481,7 +482,7 @@ protected lemma IsLocalization.Away.integralClosure
     [IsScalarTower (integralClosure R S) (integralClosure Rf Sf) Sf]
     [IsScalarTower R (integralClosure R S) (integralClosure Rf Sf)] :
     IsLocalization.Away (algebraMap R (integralClosure R S) f) (integralClosure Rf Sf) := by
-  convert IsLocalization.integralClosure (S := S) (Rf := Rf) (Sf := Sf) (.powers f)
+  convert! IsLocalization.integralClosure (S := S) (Rf := Rf) (Sf := Sf) (.powers f)
   simp
 
 end
diff --git a/Mathlib/RingTheory/Localization/InvSubmonoid.lean b/Mathlib/RingTheory/Localization/InvSubmonoid.lean
index 69e4627ebe4c72..d6b42c75f9d9ff 100644
--- a/Mathlib/RingTheory/Localization/InvSubmonoid.lean
+++ b/Mathlib/RingTheory/Localization/InvSubmonoid.lean
@@ -70,7 +70,7 @@ theorem mul_toInvSubmonoid (m : M) : algebraMap R S m * (toInvSubmonoid M S m :
 
 @[simp]
 theorem smul_toInvSubmonoid (m : M) : m • (toInvSubmonoid M S m : S) = 1 := by
-  convert mul_toInvSubmonoid M S m
+  convert! mul_toInvSubmonoid M S m
   ext
   rw [← Algebra.smul_def]
   rfl
diff --git a/Mathlib/RingTheory/Localization/LocalizationLocalization.lean b/Mathlib/RingTheory/Localization/LocalizationLocalization.lean
index bc9e49824819de..cb74f3db46f621 100644
--- a/Mathlib/RingTheory/Localization/LocalizationLocalization.lean
+++ b/Mathlib/RingTheory/Localization/LocalizationLocalization.lean
@@ -120,7 +120,7 @@ localization is a localization.
 -/
 theorem localization_localization_isLocalization_of_has_all_units [IsLocalization N T]
     (H : ∀ x : S, IsUnit x → x ∈ N) : IsLocalization (N.comap (algebraMap R S)) T := by
-  convert localization_localization_isLocalization M N T using 1
+  convert! localization_localization_isLocalization M N T using 1
   dsimp [localizationLocalizationSubmodule]
   congr
   symm
@@ -196,7 +196,7 @@ theorem isLocalization_of_submonoid_le (M N : Submonoid R) (h : M ≤ N) [IsLoca
     IsLocalization (N.map (algebraMap R S)) T where
   map_units := by
     rintro ⟨_, ⟨y, hy, rfl⟩⟩
-    convert IsLocalization.map_units T ⟨y, hy⟩
+    convert! IsLocalization.map_units T ⟨y, hy⟩
     exact (IsScalarTower.algebraMap_apply _ _ _ _).symm
   surj y := by
     obtain ⟨⟨x, s⟩, e⟩ := IsLocalization.surj N y
@@ -223,7 +223,7 @@ theorem isLocalization_of_submonoid_le (M N : Submonoid R) (h : M ≤ N) [IsLoca
       simpa only [mul_comm] using this
     simp_rw [IsLocalization.eq_iff_exists N T, IsLocalization.eq_iff_exists M S]
     intro ⟨a, e⟩
-    exact ⟨a, 1, by convert e using 1 <;> simp⟩
+    exact ⟨a, 1, by convert! e using 1 <;> simp⟩
 
 /-- If `M ≤ N` are submonoids of `R` such that `∀ x : N, ∃ m : R, m * x ∈ M`, then the
 localization at `N` is equal to the localization of `M`. -/
diff --git a/Mathlib/RingTheory/MatrixAlgebra.lean b/Mathlib/RingTheory/MatrixAlgebra.lean
index 53dc48fde3a691..6b41a99a0d7c73 100644
--- a/Mathlib/RingTheory/MatrixAlgebra.lean
+++ b/Mathlib/RingTheory/MatrixAlgebra.lean
@@ -175,11 +175,11 @@ theorem invFun_algebraMap (M : Matrix n n R) : invFun n R A (M.map (algebraMap R
   simp only [Algebra.algebraMap_eq_smul_one, smul_tmul, ← tmul_sum]
   congr
   conv_rhs => rw [matrix_eq_sum_single M]
-  convert Finset.sum_product (β := Matrix n n R) ..; simp
+  convert! Finset.sum_product (β := Matrix n n R) ..; simp
 
 theorem right_inv (M : Matrix n n A) : (toFunAlgHom n R A) (invFun n R A M) = M := by
   simp only [invFun, map_sum, toFunAlgHom_apply]
-  convert Finset.sum_product (β := Matrix n n A) ..
+  convert! Finset.sum_product (β := Matrix n n A) ..
   conv_lhs => rw [matrix_eq_sum_single M]
   simp
 
diff --git a/Mathlib/RingTheory/MvPolynomial/EulerIdentity.lean b/Mathlib/RingTheory/MvPolynomial/EulerIdentity.lean
index 6659601fbf3955..8bc83d1e7b65e8 100644
--- a/Mathlib/RingTheory/MvPolynomial/EulerIdentity.lean
+++ b/Mathlib/RingTheory/MvPolynomial/EulerIdentity.lean
@@ -39,7 +39,7 @@ protected lemma IsWeightedHomogeneous.pderiv [AddCancelCommMonoid M] {w : σ →
     simp_rw [single_eq_monomial, pderiv_monomial, one_mul]
     by_cases hi : m i = 0
     · rw [hi, Nat.cast_zero, monomial_zero]; apply isWeightedHomogeneous_zero
-    convert isWeightedHomogeneous_monomial ..
+    convert! isWeightedHomogeneous_monomial ..
     rw [← add_right_cancel_iff (a := w i), h', ← hm, weight_sub_single_add hi]
   · rw [map_zero]; apply isWeightedHomogeneous_zero
   · rw [map_add]; exact hp.add hq
diff --git a/Mathlib/RingTheory/MvPolynomial/Groebner.lean b/Mathlib/RingTheory/MvPolynomial/Groebner.lean
index d377151ef834f4..ed9074f1d22a98 100644
--- a/Mathlib/RingTheory/MvPolynomial/Groebner.lean
+++ b/Mathlib/RingTheory/MvPolynomial/Groebner.lean
@@ -198,7 +198,7 @@ theorem div {ι : Type*} {b : ι → MvPolynomial σ R}
       · intro c hc i
         by_cases hc' : c ∈ r'.support
         · exact H'.2.2 c hc' i
-        · convert hf i
+        · convert! hf i
           classical
           have := MvPolynomial.support_add hc
           rw [Finset.mem_union, Classical.or_iff_not_imp_left] at this
diff --git a/Mathlib/RingTheory/MvPolynomial/Homogeneous.lean b/Mathlib/RingTheory/MvPolynomial/Homogeneous.lean
index 5d870524ddfc12..a8da1a458de839 100644
--- a/Mathlib/RingTheory/MvPolynomial/Homogeneous.lean
+++ b/Mathlib/RingTheory/MvPolynomial/Homogeneous.lean
@@ -209,7 +209,7 @@ lemma homogeneousSubmodule_one_pow (n : ℕ) :
     | zero => simp
     | add p q _ _ hp hq => exact Submodule.add_mem _ hp hq
     | monomial d r hr =>
-      convert monomial_mem_homogeneousSubmodule_pow_degree _ _
+      convert! monomial_mem_homogeneousSubmodule_pow_degree _ _
       rw [Finsupp.degree_eq_weight_one, ← Pi.one_def, ← hr]
 
 end
@@ -277,7 +277,7 @@ lemma eval₂ (hφ : φ.IsHomogeneous m) (f : R →+* MvPolynomial τ S) (g : σ
   intro i hi
   rw [← zero_add (n * m)]
   apply IsHomogeneous.mul (hf _) _
-  convert IsHomogeneous.prod _ _ (fun k ↦ n * i k) _
+  convert! IsHomogeneous.prod _ _ (fun k ↦ n * i k) _
   · rw [Finsupp.mem_support_iff] at hi
     rw [← Finset.mul_sum, ← hφ hi, weight_apply]
     simp_rw [smul_eq_mul, Finsupp.sum, Pi.one_apply, mul_one]
@@ -339,13 +339,13 @@ theorem rename_isHomogeneous {f : σ → τ} (h : φ.IsHomogeneous n) :
   apply IsHomogeneous.sum _ _ _ fun d hd ↦ isHomogeneous_monomial _ _
   intro d hd
   apply (Finsupp.sum_mapDomain_index_addMonoidHom fun _ ↦ .id ℕ).trans
-  convert h (mem_support_iff.mp hd)
+  convert! h (mem_support_iff.mp hd)
   simp only [weight_apply, AddMonoidHom.id_apply, Pi.one_apply, smul_eq_mul, mul_one]
 
 theorem rename_isHomogeneous_iff {f : σ → τ} (hf : f.Injective) :
     (rename f φ).IsHomogeneous n ↔ φ.IsHomogeneous n := by
   refine ⟨fun h d hd ↦ ?_, rename_isHomogeneous⟩
-  convert ← @h (d.mapDomain f) _
+  convert! ← @h (d.mapDomain f) _
   · simp only [weight_apply, Pi.one_apply, smul_eq_mul, mul_one]
     exact Finsupp.sum_mapDomain_index_inj (h := fun _ ↦ id) hf
   · rwa [coeff_rename_mapDomain f hf]
@@ -375,7 +375,7 @@ lemma coeff_isHomogeneous_of_optionEquivLeft_symm
   have hφ : φ.IsHomogeneous n := hp.rename_isHomogeneous
   suffices IsHomogeneous (F (p.coeff i)) j by
     rwa [← (IsHomogeneous.rename_isHomogeneous_iff e.injective)]
-  convert hφ.finSuccEquiv_coeff_isHomogeneous i j h using 1
+  convert! hφ.finSuccEquiv_coeff_isHomogeneous i j h using 1
   dsimp only [φ, F', F, renameEquiv_apply]
   rw [finSuccEquiv_rename_finSuccEquiv, AlgEquiv.apply_symm_apply]
   simp
@@ -534,12 +534,12 @@ theorem homogeneousComponent_mem :
 theorem coeff_homogeneousComponent (d : σ →₀ ℕ) :
     coeff d (homogeneousComponent n φ) = if d.degree = n then coeff d φ else 0 := by
   rw [degree_eq_weight_one]
-  convert coeff_weightedHomogeneousComponent n φ d
+  convert! coeff_weightedHomogeneousComponent n φ d
 
 theorem homogeneousComponent_apply :
     homogeneousComponent n φ = ∑ d ∈ φ.support with d.degree = n, monomial d (coeff d φ) := by
   simp_rw [degree_eq_weight_one]
-  convert weightedHomogeneousComponent_apply n φ
+  convert! weightedHomogeneousComponent_apply n φ
 
 theorem homogeneousComponent_isHomogeneous : (homogeneousComponent n φ).IsHomogeneous n :=
   weightedHomogeneousComponent_isWeightedHomogeneous n φ
diff --git a/Mathlib/RingTheory/MvPolynomial/Ideal.lean b/Mathlib/RingTheory/MvPolynomial/Ideal.lean
index d799ff1235311a..48aec1bdae1c52 100644
--- a/Mathlib/RingTheory/MvPolynomial/Ideal.lean
+++ b/Mathlib/RingTheory/MvPolynomial/Ideal.lean
@@ -167,8 +167,9 @@ lemma span_leadingTerm_eq_span_monomial {B : Set (MvPolynomial σ R)}
   · rw [Set.mem_preimage, SetLike.mem_coe, ← C_mul_leadingCoeff_monomial_degree]
     exact Ideal.mul_mem_left _ _ (Ideal.subset_span ⟨_, hp, rfl⟩)
   · rw [Set.mem_preimage, SetLike.mem_coe]
-    convert (span <| m.leadingTerm '' B).mul_mem_left
-      (MvPolynomial.C (hB p hp).unit⁻¹.val) <| subset_span ⟨p, hp, rfl⟩
+    convert!
+      (span <| m.leadingTerm '' B).mul_mem_left (MvPolynomial.C (hB p hp).unit⁻¹.val) <|
+        subset_span ⟨p, hp, rfl⟩
     rw [← C_mul_leadingCoeff_monomial_degree, ← mul_assoc, ← map_mul,
       IsUnit.val_inv_mul, MvPolynomial.C_1, one_mul]
 
diff --git a/Mathlib/RingTheory/MvPolynomial/Symmetric/FundamentalTheorem.lean b/Mathlib/RingTheory/MvPolynomial/Symmetric/FundamentalTheorem.lean
index d42b8982aeae50..a20511d3dcb445 100644
--- a/Mathlib/RingTheory/MvPolynomial/Symmetric/FundamentalTheorem.lean
+++ b/Mathlib/RingTheory/MvPolynomial/Symmetric/FundamentalTheorem.lean
@@ -75,7 +75,7 @@ def invAccumulate (n m : ℕ) (s : Fin m → ℕ) (i : Fin n) : ℕ :=
 lemma accumulate_rec {i n m : ℕ} (hin : i < n) (him : i + 1 < m) (t : Fin n → ℕ) :
     accumulate n m t ⟨i, Nat.lt_of_succ_lt him⟩ = t ⟨i, hin⟩ + accumulate n m t ⟨i + 1, him⟩ := by
   simp_rw [accumulate_apply]
-  convert (add_sum_erase _ _ _).symm
+  convert! (add_sum_erase _ _ _).symm
   · ext
     rw [mem_erase]
     simp_rw [mem_filter_univ, i.succ_le_iff, lt_iff_le_and_ne]
@@ -305,11 +305,11 @@ lemma esymmAlgHom_fin_bijective (n : ℕ) :
     · exact accumulate_invAccumulate le_rfl hp.antitone_supDegree
     · rwa [Ne, leadingCoeff_eq_zero toLex.injective]
   obtain he | hne := eq_or_ne p (esymmAlgHomMonomial _ t <| p.leadingCoeff toLex)
-  · convert AlgHom.mem_range_self _ (monomial t <| p.leadingCoeff toLex)
+  · convert! AlgHom.mem_range_self _ (monomial t <| p.leadingCoeff toLex)
   have := (supDegree_sub_lt_of_leadingCoeff_eq toLex.injective hd.symm ?_).resolve_right hne
   · specialize ih _ this _ (Subalgebra.sub_mem _ hp <| isSymmetric_esymmAlgHomMonomial _ _) _ rfl
     · rwa [sub_ne_zero]
-    convert ← Subalgebra.add_mem _ ih ⟨monomial t (p.leadingCoeff toLex), rfl⟩
+    convert! ← Subalgebra.add_mem _ ih ⟨monomial t (p.leadingCoeff toLex), rfl⟩
     apply sub_add_cancel p
   · rw [leadingCoeff_esymmAlgHomMonomial t le_rfl]
 
diff --git a/Mathlib/RingTheory/MvPolynomial/Tower.lean b/Mathlib/RingTheory/MvPolynomial/Tower.lean
index cb4914cb023fac..2e1db24e749498 100644
--- a/Mathlib/RingTheory/MvPolynomial/Tower.lean
+++ b/Mathlib/RingTheory/MvPolynomial/Tower.lean
@@ -80,7 +80,7 @@ variable {R A} [CommSemiring R] [CommSemiring A] [Algebra R A]
 
 @[simp]
 theorem mvPolynomial_aeval_coe (S : Subalgebra R A) (x : σ → S) (p : MvPolynomial σ R) :
-    aeval (fun i => (x i : A)) p = aeval x p := by convert aeval_algebraMap_apply A x p
+    aeval (fun i => (x i : A)) p = aeval x p := by convert! aeval_algebraMap_apply A x p
 
 end CommSemiring
 
diff --git a/Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean b/Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean
index e9b69b061fa3cc..70d87eb2d9c186 100644
--- a/Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean
+++ b/Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean
@@ -350,14 +350,14 @@ theorem coeff_weightedHomogeneousComponent [DecidableEq M] (d : σ →₀ ℕ) :
     coeff d (weightedHomogeneousComponent w n φ) =
       if weight w d = n then coeff d φ else 0 :=
   letI := Classical.decEq M
-  Finsupp.filter_apply (fun d : σ →₀ ℕ => weight w d = n) φ d |>.trans <| by convert rfl
+  Finsupp.filter_apply (fun d : σ →₀ ℕ => weight w d = n) φ d |>.trans <| by convert! rfl
 
 set_option backward.isDefEq.respectTransparency false in
 theorem weightedHomogeneousComponent_apply [DecidableEq M] :
     weightedHomogeneousComponent w n φ =
       ∑ d ∈ φ.support with weight w d = n, monomial d (coeff d φ) :=
   letI := Classical.decEq M
-  Finsupp.filter_eq_sum (fun d : σ →₀ ℕ => weight w d = n) φ |>.trans <| by convert rfl
+  Finsupp.filter_eq_sum (fun d : σ →₀ ℕ => weight w d = n) φ |>.trans <| by convert! rfl
 
 /-- The `n` weighted homogeneous component of a polynomial is weighted homogeneous of
 weighted degree `n`. -/
@@ -507,7 +507,7 @@ theorem weightedHomogeneousComponent_directSum [DecidableEq M]
       ((DirectSum.coeLinearMap fun i : M => weightedHomogeneousSubmodule R w i) x) = x m := by
   classical
   rw [DirectSum.coeLinearMap_eq_dfinsuppSum, DFinsupp.sum, map_sum]
-  convert @Finset.sum_eq_single M (MvPolynomial σ R) _ (DFinsupp.support x) _ m _ _
+  convert! @Finset.sum_eq_single M (MvPolynomial σ R) _ (DFinsupp.support x) _ m _ _
   · rw [IsWeightedHomogeneous.weightedHomogeneousComponent_same (x m).prop]
   · intro n _ hmn
     exact IsWeightedHomogeneous.weightedHomogeneousComponent_ne m (x n).prop hmn.symm
diff --git a/Mathlib/RingTheory/MvPowerSeries/Basic.lean b/Mathlib/RingTheory/MvPowerSeries/Basic.lean
index bf39107c81059c..9b66b8e47090d6 100644
--- a/Mathlib/RingTheory/MvPowerSeries/Basic.lean
+++ b/Mathlib/RingTheory/MvPowerSeries/Basic.lean
@@ -154,7 +154,7 @@ theorem monomial_def [DecidableEq σ] (n : σ →₀ ℕ) :
     monomial n = LinearMap.single R (fun _ ↦ R) n := by
   rw [monomial]
   -- unify the `Decidable` arguments
-  convert rfl
+  convert! rfl
 
 set_option backward.isDefEq.respectTransparency false in
 theorem coeff_monomial [DecidableEq σ] (m n : σ →₀ ℕ) (a : R) :
@@ -747,7 +747,7 @@ theorem coeff_eq_zero_of_constantCoeff_nilpotent {f : MvPowerSeries σ R} {m : 
   simp only [add_comm m, Nat.add_le_add_iff_right, ← hk.1,
     ← sum_sdiff (hs), sum_eq_zero (s := s) hs'', add_zero]
   rw [← hs_def]
-  convert Finset.card_nsmul_le_sum (range n \ s) (fun x ↦ degree (k x)) 1 _
+  convert! Finset.card_nsmul_le_sum (range n \ s) (fun x ↦ degree (k x)) 1 _
   · simp only [smul_eq_mul, mul_one]
   · simp only [degree_eq_weight_one, map_sum]
   · simp only [hs_def, mem_filter, mem_sdiff, mem_range, not_and, and_imp]
diff --git a/Mathlib/RingTheory/MvPowerSeries/Equiv.lean b/Mathlib/RingTheory/MvPowerSeries/Equiv.lean
index 663c688cc3fb81..b5bc70584d0f87 100644
--- a/Mathlib/RingTheory/MvPowerSeries/Equiv.lean
+++ b/Mathlib/RingTheory/MvPowerSeries/Equiv.lean
@@ -129,7 +129,7 @@ theorem mk_truncTotal_toAdicCompletionInv {n : ℕ}
       ← smul_eq_mul, ← Ideal.Quotient.eq]
     simp only [Submodule.mapQ_eq_factor, Submodule.factor_eq_factor, Ideal.Quotient.mk_out]
     rw [← AdicCompletion.transitionMap_ideal_mk _ (Nat.lt_iff_add_one_le.mp h), eq_comm]
-    convert f.prop h; simp
+    convert! f.prop h; simp
   simp
 
 /-- The isomorphism from multivariate power series to the adic completion of
diff --git a/Mathlib/RingTheory/MvPowerSeries/Evaluation.lean b/Mathlib/RingTheory/MvPowerSeries/Evaluation.lean
index b6271b491a475c..e8d9e970f0c47b 100644
--- a/Mathlib/RingTheory/MvPowerSeries/Evaluation.lean
+++ b/Mathlib/RingTheory/MvPowerSeries/Evaluation.lean
@@ -270,7 +270,7 @@ theorem hasSum_eval₂ (hφ : Continuous φ) (ha : HasEval a) (f : MvPowerSeries
     (fun (d : σ →₀ ℕ) ↦ φ (coeff d f) * (d.prod fun s e => (a s) ^ e))
     (MvPowerSeries.eval₂ φ a f) := by
   rw [← coe_eval₂Hom hφ ha, eval₂Hom_eq_extend hφ ha]
-  convert (hasSum_of_monomials_self f).map (eval₂Hom hφ ha) (?_) with d
+  convert! (hasSum_of_monomials_self f).map (eval₂Hom hφ ha) (?_) with d
   · simp only [Function.comp_apply, coe_eval₂Hom, ← MvPolynomial.coe_monomial,
       eval₂_coe, eval₂_monomial]
   · rw [coe_eval₂Hom]; exact continuous_eval₂ hφ ha
diff --git a/Mathlib/RingTheory/MvPowerSeries/GaussNorm.lean b/Mathlib/RingTheory/MvPowerSeries/GaussNorm.lean
index 20a9f26c05d19b..3cc3772f52a838 100644
--- a/Mathlib/RingTheory/MvPowerSeries/GaussNorm.lean
+++ b/Mathlib/RingTheory/MvPowerSeries/GaussNorm.lean
@@ -61,7 +61,7 @@ lemma gaussNorm_nonneg (vNonneg : ∀ a, v a ≥ 0) : 0 ≤ gaussNorm v c f := b
   by_cases h : HasGaussNorm v c f
   · trans v (constantCoeff f)
     · simp [vNonneg]
-    · convert (le_gaussNorm v c f h 0)
+    · convert! (le_gaussNorm v c f h 0)
       simp
   · simp [h]
 
diff --git a/Mathlib/RingTheory/MvPowerSeries/Inverse.lean b/Mathlib/RingTheory/MvPowerSeries/Inverse.lean
index a9083a5b70b841..ef53346a2f3738 100644
--- a/Mathlib/RingTheory/MvPowerSeries/Inverse.lean
+++ b/Mathlib/RingTheory/MvPowerSeries/Inverse.lean
@@ -93,7 +93,7 @@ theorem coeff_invOfUnit [DecidableEq σ] (n : σ →₀ ℕ) (φ : MvPowerSeries
         -↑u⁻¹ *
           ∑ x ∈ antidiagonal n,
             if x.2 < n then coeff x.1 φ * coeff x.2 (invOfUnit φ u) else 0 := by
-  convert coeff_inv_aux n (↑u⁻¹) φ
+  convert! coeff_inv_aux n (↑u⁻¹) φ
 
 @[simp]
 theorem constantCoeff_invOfUnit (φ : MvPowerSeries σ R) (u : Rˣ) :
diff --git a/Mathlib/RingTheory/MvPowerSeries/LinearTopology.lean b/Mathlib/RingTheory/MvPowerSeries/LinearTopology.lean
index 468dd004e88803..449d92e4eab269 100644
--- a/Mathlib/RingTheory/MvPowerSeries/LinearTopology.lean
+++ b/Mathlib/RingTheory/MvPowerSeries/LinearTopology.lean
@@ -125,7 +125,7 @@ lemma hasBasis_nhds_zero [IsLinearTopology R R] [IsLinearTopology Rᵐᵒᵖ R]
   · intro ⟨D, I⟩ ⟨hD, hI⟩
     refine ⟨⟨I, Finset.sup hD.toFinset id⟩, hI, fun f hf d hd ↦ ?_⟩
     rw [SetLike.mem_coe, mem_basis_iff] at hf
-    convert hf _ <| Finset.le_sup (hD.mem_toFinset.mpr hd)
+    convert! hf _ <| Finset.le_sup (hD.mem_toFinset.mpr hd)
   · intro ⟨I, d⟩ hI
     refine ⟨⟨Iic d, I⟩, ⟨finite_Iic d, hI⟩, ?_⟩
     simpa [basis, coeff_apply, Iic, Set.pi] using subset_rfl
diff --git a/Mathlib/RingTheory/MvPowerSeries/NoZeroDivisors.lean b/Mathlib/RingTheory/MvPowerSeries/NoZeroDivisors.lean
index 4bc05deee716f2..92710c44b43b68 100644
--- a/Mathlib/RingTheory/MvPowerSeries/NoZeroDivisors.lean
+++ b/Mathlib/RingTheory/MvPowerSeries/NoZeroDivisors.lean
@@ -61,7 +61,7 @@ theorem mem_nonZeroDivisorsRight_of_constantCoeff {φ : MvPowerSeries σ R}
   intro e he
   rw [map_zero, ← mul_right_mem_nonZeroDivisorsRight_eq_zero_iff hφ,
     ← map_zero (f := coeff e), ← hx]
-  convert (coeff_mul e x φ).symm
+  convert! (coeff_mul e x φ).symm
   rw [Finset.sum_eq_single (e, 0), coeff_zero_eq_constantCoeff]
   · rintro ⟨u, _⟩ huv _
     suffices u < e by simp only [he u this, zero_mul, map_zero]
@@ -82,7 +82,7 @@ theorem mem_nonZeroDivisorsLeft_of_constantCoeff {φ : MvPowerSeries σ R}
   intro e he
   rw [map_zero, ← mul_left_mem_nonZeroDivisorsLeft_eq_zero_iff hφ,
     ← map_zero (f := coeff e), ← hx]
-  convert (coeff_mul e φ x).symm
+  convert! (coeff_mul e φ x).symm
   rw [Finset.sum_eq_single (0, e), coeff_zero_eq_constantCoeff]
   · rintro ⟨_, u⟩ huv _
     suffices u < e by simp only [he u this, mul_zero, map_zero]
diff --git a/Mathlib/RingTheory/MvPowerSeries/Substitution.lean b/Mathlib/RingTheory/MvPowerSeries/Substitution.lean
index b9a86ed1598f08..7729dd918324e8 100644
--- a/Mathlib/RingTheory/MvPowerSeries/Substitution.lean
+++ b/Mathlib/RingTheory/MvPowerSeries/Substitution.lean
@@ -134,7 +134,7 @@ protected theorem HasSubst.map {a : σ → MvPowerSeries τ R} (ha : HasSubst a)
 
 theorem HasSubst.smul_X (a : σ → R) :
     HasSubst (a • X : σ → MvPowerSeries σ R) := by
-  convert HasSubst.X.mul_left (fun s ↦ algebraMap R (MvPowerSeries σ R) (a s))
+  convert! HasSubst.X.mul_left (fun s ↦ algebraMap R (MvPowerSeries σ R) (a s))
   simp [funext_iff, algebra_compatible_smul (MvPowerSeries σ R)]
 
 /-- Families of `MvPowerSeries` that can be substituted, as an `Ideal` -/
@@ -207,7 +207,7 @@ theorem substAlgHom_eq_aeval
     (ha : HasSubst a) :
     (substAlgHom ha : MvPowerSeries σ R → MvPowerSeries τ S) = MvPowerSeries.aeval ha.hasEval := by
   simp only [substAlgHom, coe_aeval ha.hasEval]
-  convert coe_aeval (R := R) (hasSubst_iff_hasEval_of_discreteTopology.mp ha) <;>
+  convert! coe_aeval (R := R) (hasSubst_iff_hasEval_of_discreteTopology.mp ha) <;>
   exact DiscreteUniformity.eq_bot.symm
 
 @[simp]
@@ -552,7 +552,7 @@ theorem rescale_zero :
   split_ifs with h
   · simp [h, coeff_apply, ← @coeff_zero_eq_constantCoeff_apply, coeff_apply]
   · simp only [coeff_apply]
-    convert zero_mul _
+    convert! zero_mul _
     simp only [DFunLike.ext_iff, not_forall, Finsupp.coe_zero, Pi.zero_apply] at h
     obtain ⟨s, h⟩ := h
     simp only [Finsupp.prod]
diff --git a/Mathlib/RingTheory/Noetherian/Defs.lean b/Mathlib/RingTheory/Noetherian/Defs.lean
index 66ddf1f73601e7..70d1d93cd80724 100644
--- a/Mathlib/RingTheory/Noetherian/Defs.lean
+++ b/Mathlib/RingTheory/Noetherian/Defs.lean
@@ -140,7 +140,7 @@ theorem isNoetherian_iff_fg_wellFounded :
     intro N
     obtain ⟨⟨N₀, h₁⟩, e : N₀ ≤ N, h₂⟩ :=
       WellFounded.has_min H.wf { N' : α | N'.1 ≤ N } ⟨⟨⊥, Submodule.fg_bot⟩, @bot_le _ _ _ N⟩
-    convert h₁
+    convert! h₁
     refine (e.antisymm ?_).symm
     by_contra h₃
     obtain ⟨x, hx₁ : x ∈ N, hx₂ : x ∉ N₀⟩ := Set.not_subset.mp h₃
diff --git a/Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean b/Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean
index aa2d134443da6e..4d9b88ed2cf504 100644
--- a/Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean
+++ b/Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean
@@ -392,7 +392,7 @@ variable [NonUnitalNonAssocSemiring S]
 
 theorem mem_map_equiv {f : R ≃+* S} {K : NonUnitalSubsemiring R} {x : S} :
     x ∈ K.map (f : R →ₙ+* S) ↔ f.symm x ∈ K := by
-  convert @Set.mem_image_equiv _ _ (↑K) f.toEquiv x
+  convert! @Set.mem_image_equiv _ _ (↑K) f.toEquiv x
 
 theorem map_equiv_eq_comap_symm (f : R ≃+* S) (K : NonUnitalSubsemiring R) :
     K.map (f : R →ₙ+* S) = K.comap f.symm :=
diff --git a/Mathlib/RingTheory/Norm/Transitivity.lean b/Mathlib/RingTheory/Norm/Transitivity.lean
index d573878929c064..298a5e942acb68 100644
--- a/Mathlib/RingTheory/Norm/Transitivity.lean
+++ b/Mathlib/RingTheory/Norm/Transitivity.lean
@@ -96,7 +96,7 @@ lemma det_mul_corner_pow :
     pow_one, det_one, smul_eq_mul, mul_one]
   -- `Decidable (P = Q)` diamond induced by `Prop.linearOrder`, which is classical, when `P` and `Q`
   -- are themselves decidable.
-  convert rfl
+  convert! rfl
 
 /-- A matrix with X added to the corner. -/
 noncomputable def cornerAddX : Matrix m m S[X] :=
diff --git a/Mathlib/RingTheory/Nullstellensatz.lean b/Mathlib/RingTheory/Nullstellensatz.lean
index 7022004ad776e4..104ec198650cdd 100644
--- a/Mathlib/RingTheory/Nullstellensatz.lean
+++ b/Mathlib/RingTheory/Nullstellensatz.lean
@@ -102,11 +102,11 @@ theorem mem_vanishingIdeal_singleton_iff (x : σ → K) (p : MvPolynomial σ k)
   ⟨fun h => h x rfl, fun hpx _ hy => hy.symm ▸ hpx⟩
 
 instance {x : σ → K} : (vanishingIdeal k {x} : Ideal (MvPolynomial σ k)).IsPrime := by
-  convert RingHom.ker_isPrime (aeval (R := k) x)
+  convert! RingHom.ker_isPrime (aeval (R := k) x)
   ext; simp
 
 instance {x : σ → K} : (vanishingIdeal K {x} : Ideal (MvPolynomial σ K)).IsMaximal := by
-  convert RingHom.ker_isMaximal_of_surjective (aeval (R := K) x) ?_
+  convert! RingHom.ker_isMaximal_of_surjective (aeval (R := K) x) ?_
   · ext; simp
   · intro z; use C z; simp
 
diff --git a/Mathlib/RingTheory/PicardGroup.lean b/Mathlib/RingTheory/PicardGroup.lean
index 0163b5490400ea..a6898ada1bd52f 100644
--- a/Mathlib/RingTheory/PicardGroup.lean
+++ b/Mathlib/RingTheory/PicardGroup.lean
@@ -683,8 +683,9 @@ set_option backward.privateInPublic.warn false in
 `I ⊗[R] J` to `I * J` induced by multiplication is an isomorphism. -/
 noncomputable def tensorEquivMul : I ⊗[R] J ≃ₗ[R] I * J := by
   refine .ofBijective _ ⟨.of_comp (f := Submodule.subtype _) ?_, mulMap'_surjective _ _⟩
-  convert (projective_units_and_mul'_comp_lTensor_bijective J).2.1.comp
-    (Flat.rTensor_preserves_injective_linearMap _ I.1.subtype_injective)
+  convert!
+    (projective_units_and_mul'_comp_lTensor_bijective J).2.1.comp
+      (Flat.rTensor_preserves_injective_linearMap _ I.1.subtype_injective)
   simp_rw [← LinearMap.coe_comp]
   congr 1; ext; rfl
 
@@ -774,7 +775,7 @@ instance [Module.Invertible R M] : Module.Invertible R (submoduleAlgebra e) :=
 the multiplication map induces an isomorphism `A ⊗[R] M ≃ₗ[A] A`. -/
 noncomputable def tensorSubmoduleAlgebraEquiv : A ⊗[R] submoduleAlgebra e ≃ₗ[A] A :=
   .ofBijective (.mul'' R A ∘ₗ AlgebraTensorModule.lTensor A A (Submodule.subtype _)) <| by
-    convert (AlgebraTensorModule.congr (.refl ..) (submoduleAlgebraEquiv e) ≪≫ₗ e).bijective
+    convert! (AlgebraTensorModule.congr (.refl ..) (submoduleAlgebraEquiv e) ≪≫ₗ e).bijective
     ext x
     refine x.induction_on (by simp) ?_ (by simp +contextual)
     intro a x
@@ -785,7 +786,8 @@ noncomputable def tensorSubmoduleAlgebraEquiv : A ⊗[R] submoduleAlgebra e ≃
 
 theorem top_mul_submoduleAlgebra : ⊤ * submoduleAlgebra e = ⊤ := by
   rw [← Submodule.mulMap_range]
-  convert (Submodule.topEquiv.rTensor _ ≪≫ₗ (tensorSubmoduleAlgebraEquiv e).restrictScalars R).range
+  convert!
+    (Submodule.topEquiv.rTensor _ ≪≫ₗ (tensorSubmoduleAlgebraEquiv e).restrictScalars R).range
   ext; rfl
 
 /-- When a flat `R`-module `M` is embedded as a submodule of a faithful `R`-algebra `A`,
@@ -793,8 +795,9 @@ we have `I ⊗[R] M ≃ₗ[R] I * M` for any `R`-submodule `I` of `A`. -/
 noncomputable def tensorSubmoduleAlgebraEquivMul (I : Submodule R A) :
     I ⊗[R] submoduleAlgebra e ≃ₗ[R] I * submoduleAlgebra e := by
   refine .ofBijective _ ⟨.of_comp (f := Submodule.subtype _) ?_, Submodule.mulMap'_surjective _ _⟩
-  convert ((tensorSubmoduleAlgebraEquiv e).restrictScalars R).injective.comp
-    (Flat.rTensor_preserves_injective_linearMap _ I.subtype_injective)
+  convert!
+    ((tensorSubmoduleAlgebraEquiv e).restrictScalars R).injective.comp
+      (Flat.rTensor_preserves_injective_linearMap _ I.subtype_injective)
   simp_rw [← LinearEquiv.coe_toLinearMap, ← LinearMap.coe_comp]
   congr 1; ext; rfl
 
@@ -900,7 +903,7 @@ theorem Ideal.eq_top_of_mk_tensor_eq_one [IsFractionRing R R] (I J : Ideal R)
   have : IsUnit (e 1 : R) := IsFractionRing.self_iff_nonZeroDivisors_le_isUnit.mp ‹_› <|
       IsRegular.mem_nonZeroDivisors <| isRightRegular_iff_isRegular.mp <| by
     rw [IsRightRegular]
-    convert Subtype.val_injective.comp e.injective using 2
+    convert! Subtype.val_injective.comp e.injective using 2
     rw [← smul_eq_mul, ← Submodule.coe_smul, ← map_smul, smul_eq_mul, mul_one, Function.comp_apply]
   constructor <;> refine eq_top_of_isUnit_mem _ ?_ this
   exacts [mul_le_right (e 1).2, mul_le_left (e 1).2]
diff --git a/Mathlib/RingTheory/Polynomial/Basic.lean b/Mathlib/RingTheory/Polynomial/Basic.lean
index acce808e31fc35..976ebdac86a394 100644
--- a/Mathlib/RingTheory/Polynomial/Basic.lean
+++ b/Mathlib/RingTheory/Polynomial/Basic.lean
@@ -575,7 +575,7 @@ theorem eq_zero_of_constant_mem_of_maximal (hR : IsField R) (I : Ideal R[X]) [hI
     (x : R) (hx : C x ∈ I) : x = 0 := by
   refine Classical.by_contradiction fun hx0 => hI.ne_top ((eq_top_iff_one I).2 ?_)
   obtain ⟨y, hy⟩ := hR.mul_inv_cancel hx0
-  convert I.mul_mem_left (C y) hx
+  convert! I.mul_mem_left (C y) hx
   rw [← C.map_mul, hR.mul_comm y x, hy, map_one]
 
 end Ring
@@ -593,7 +593,7 @@ theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
   constructor
   · intro H
     have := comap_isPrime C (map C P)
-    convert this using 1
+    convert! this using 1
     ext x
     simp only [mem_comap, mem_map_C_iff]
     constructor
@@ -683,7 +683,7 @@ theorem mem_span_C_coeff : f ∈ Ideal.span { g : R[X] | ∃ i : ℕ, g = C (coe
     rw [mem_setOf_eq]
     use n
   have : monomial n (1 : R) • C (coeff f n) ∈ p := p.smul_mem _ this
-  convert this using 1
+  convert! this using 1
   simp only [monomial_mul_C, one_mul, smul_eq_mul]
   rw [← C_mul_X_pow_eq_monomial]
 
@@ -727,7 +727,7 @@ private theorem prime_C_iff_of_fintype {R : Type u} (σ : Type v) {r : R} [CommR
   · induction Fintype.card σ with
     | zero => exact MulEquiv.prime_iff (isEmptyAlgEquiv R (Fin 0)).symm (p := r)
     | succ d hd =>
-      convert MulEquiv.prime_iff (finSuccEquiv R d).symm (p := Polynomial.C (C r))
+      convert! MulEquiv.prime_iff (finSuccEquiv R d).symm (p := Polynomial.C (C r))
       · simp [← finSuccEquiv_comp_C_eq_C]
       · simp [← hd, Polynomial.prime_C_iff]
 
@@ -744,7 +744,7 @@ theorem prime_C_iff : Prime (C r : MvPolynomial σ R) ↔ Prime r :=
       obtain ⟨s, a', b', rfl, rfl⟩ := exists_finset_rename₂ a b
       rw [← algebraMap_eq] at hd
       have : algebraMap R _ r ∣ a' * b' := by
-        convert _root_.map_dvd (killCompl Subtype.val_injective) hd
+        convert! _root_.map_dvd (killCompl Subtype.val_injective) hd
         · simp
         · simp
       rw [← rename_C ((↑) : s → σ)]
@@ -848,7 +848,7 @@ protected theorem Polynomial.isNoetherianRing [inst : IsNoetherianRing R] : IsNo
           have := Polynomial.degree_sub_lt h1 hp0 h2
           rw [Polynomial.degree_eq_natDegree hp0] at this
           rw [← sub_add_cancel p (q * Polynomial.X ^ (k - q.natDegree))]
-          convert (Ideal.span ↑s).add_mem _ ((Ideal.span (s : Set R[X])).mul_mem_right _ _)
+          convert! (Ideal.span ↑s).add_mem _ ((Ideal.span (s : Set R[X])).mul_mem_right _ _)
           · by_cases hpq : p - q * Polynomial.X ^ (k - q.natDegree) = 0
             · rw [hpq]
               exact Ideal.zero_mem _
diff --git a/Mathlib/RingTheory/Polynomial/Bernstein.lean b/Mathlib/RingTheory/Polynomial/Bernstein.lean
index afae82d695653c..21d772e327d470 100644
--- a/Mathlib/RingTheory/Polynomial/Bernstein.lean
+++ b/Mathlib/RingTheory/Polynomial/Bernstein.lean
@@ -120,8 +120,8 @@ theorem derivative_succ_aux (n ν : ℕ) :
     rw [mul_comm, ← mul_assoc, ← mul_assoc]; congr 1
     norm_cast
     congr 1
-    convert (Nat.choose_mul_succ_eq n (ν + 1)).symm using 1
-    · convert mul_comm _ _ using 2
+    convert! (Nat.choose_mul_succ_eq n (ν + 1)).symm using 1
+    · convert! mul_comm _ _ using 2
       simp
     · apply mul_comm
 
@@ -150,7 +150,7 @@ theorem iterate_derivative_at_0_eq_zero_of_lt (n : ℕ) {ν k : ℕ} :
       intro h
       apply mul_eq_zero_of_right
       rw [ih _ _ (Nat.le_of_succ_le h), sub_zero]
-      convert ih _ _ (Nat.pred_le_pred h)
+      convert! ih _ _ (Nat.pred_le_pred h)
       exact (Nat.succ_pred_eq_of_pos (k.succ_pos.trans_le h)).symm
 
 @[simp]
diff --git a/Mathlib/RingTheory/Polynomial/Chebyshev.lean b/Mathlib/RingTheory/Polynomial/Chebyshev.lean
index 6b7d48f52085da..76249e0a59852d 100644
--- a/Mathlib/RingTheory/Polynomial/Chebyshev.lean
+++ b/Mathlib/RingTheory/Polynomial/Chebyshev.lean
@@ -96,13 +96,13 @@ protected theorem induct' (motive : ℤ → Prop)
     ∀ (a : ℤ), motive a := by
   refine Chebyshev.induct motive zero one add_two ?_
   have neg' (n : ℤ) (h : motive (-n)) : motive n := by
-    convert neg (-n) h; rw [neg_neg]
+    convert! neg (-n) h; rw [neg_neg]
   intro n h₀ h₁
   cases n with
   | zero => exact neg 1 h₁
   | succ n =>
     apply neg (n + 2) (add_two n (neg' _ h₀) (neg' n ?_))
-    convert h₁ using 1; omega
+    convert! h₁ using 1; omega
 
 @[simp]
 theorem T_add_two : ∀ n, T R (n + 2) = 2 * X * T R (n + 1) - T R n
@@ -876,7 +876,7 @@ theorem T_derivative_mem_span_T (n : ℕ) :
   · simp [hn]
   rw [T_derivative_eq_U, ← smul_eq_mul]; norm_cast
   refine Submodule.smul_of_tower_mem _ n ?_
-  convert U_mem_span_T R (n - 1) using 2 <;> grind
+  convert! U_mem_span_T R (n - 1) using 2 <;> grind
 
 theorem T_iterate_derivative_mem_span_T (n k : ℕ) :
     derivative^[k] (T R n) ∈ Submodule.span ℕ ((fun m : ℕ => T R m) '' Set.Icc 0 (n - k)) := by
@@ -889,7 +889,7 @@ theorem T_iterate_derivative_mem_span_T (n k : ℕ) :
     suffices Submodule.span ℕ ((fun m : ℕ => derivative (T R m)) '' Set.Icc 0 (n - k)) ≤
       Submodule.span ℕ ((fun m : ℕ => T R m) '' Set.Icc 0 (n - (k + 1))) by
       apply this
-      convert Submodule.apply_mem_span_image_of_mem_span (derivative.restrictScalars ℕ) ih using 2
+      convert! Submodule.apply_mem_span_image_of_mem_span (derivative.restrictScalars ℕ) ih using 2
       simp [Set.image]
     refine Submodule.span_le.mpr (fun x hx => ?_)
     obtain ⟨m, hm, rfl⟩ := hx
diff --git a/Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean b/Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean
index 96b6cd1aac64ce..aa330d8e13e4ea 100644
--- a/Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean
+++ b/Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean
@@ -616,9 +616,9 @@ private theorem _root_.IsPrimitiveRoot.pow_sub_pow_eq_prod_sub_mul_field {K : Ty
   · simp only [hy, zero_pow (Nat.ne_zero_of_lt hpos), sub_zero, mul_zero, prod_const]
     congr
     rw [h.card_nthRootsFinset]
-  convert congr_arg (eval (x / y) · * y ^ card (nthRootsFinset n (1 : K)))
-    <| X_pow_sub_one_eq_prod hpos h
-    using 1
+  convert!
+    congr_arg (eval (x / y) · * y ^ card (nthRootsFinset n (1 : K))) <|
+      X_pow_sub_one_eq_prod hpos h using 1
   · simp [sub_mul, div_pow, hy, h.card_nthRootsFinset]
   · simp [eval_prod, prod_mul_pow_card, sub_mul, hy]
 
diff --git a/Mathlib/RingTheory/Polynomial/Cyclotomic/Eval.lean b/Mathlib/RingTheory/Polynomial/Cyclotomic/Eval.lean
index f95d087ecf9c20..6214c9b651a270 100644
--- a/Mathlib/RingTheory/Polynomial/Cyclotomic/Eval.lean
+++ b/Mathlib/RingTheory/Polynomial/Cyclotomic/Eval.lean
@@ -174,7 +174,7 @@ theorem sub_one_pow_totient_lt_cyclotomic_eval {n : ℕ} {q : ℝ} (hn' : 2 ≤
   have hfor : ∀ ζ' ∈ primitiveRoots n ℂ, q - 1 ≤ ‖↑q - ζ'‖ := by
     intro ζ' hζ'
     rw [mem_primitiveRoots hn] at hζ'
-    convert norm_sub_norm_le (↑q) ζ'
+    convert! norm_sub_norm_le (↑q) ζ'
     · rw [Complex.norm_real, Real.norm_of_nonneg hq.le]
     · rw [hζ'.norm'_eq_one hn.ne']
   let ζ := Complex.exp (2 * ↑Real.pi * Complex.I / ↑n)
@@ -182,7 +182,7 @@ theorem sub_one_pow_totient_lt_cyclotomic_eval {n : ℕ} {q : ℝ} (hn' : 2 ≤
   have hex : ∃ ζ' ∈ primitiveRoots n ℂ, q - 1 < ‖↑q - ζ'‖ := by
     refine ⟨ζ, (mem_primitiveRoots hn).mpr hζ, ?_⟩
     suffices ¬SameRay ℝ (q : ℂ) ζ by
-      convert lt_norm_sub_of_not_sameRay this <;>
+      convert! lt_norm_sub_of_not_sameRay this <;>
         simp only [hζ.norm'_eq_one hn.ne', Real.norm_of_nonneg hq.le, Complex.norm_real]
     rw [Complex.sameRay_iff]
     push Not
@@ -196,12 +196,12 @@ theorem sub_one_pow_totient_lt_cyclotomic_eval {n : ℕ} {q : ℝ} (hn' : 2 ≤
       Units.mk0 ‖(cyclotomic n ℂ).eval ↑q‖₊ (by simp_all) by
     simp only [← Units.val_lt_val, Units.val_pow_eq_pow_val, Units.val_mk0, ← NNReal.coe_lt_coe,
       hq'.le, coe_nnnorm, NNReal.coe_pow, Real.coe_toNNReal', sub_nonneg, sup_of_le_left] at this
-    convert this
+    convert! this
     rw [eq_comm]
     simp [cyclotomic_nonneg n hq'.le]
   simp only [cyclotomic_eq_prod_X_sub_primitiveRoots hζ, eval_prod, eval_C, eval_X, eval_sub,
     nnnorm_prod, Units.mk0_prod]
-  convert Finset.prod_lt_prod' (M := NNRealˣ) _ _
+  convert! Finset.prod_lt_prod' (M := NNRealˣ) _ _
   swap; · exact fun _ => Units.mk0 (Real.toNNReal (q - 1)) (by simp [hq'])
   · simp only [Complex.card_primitiveRoots, prod_const, card_attach]
   · simp only [Finset.mem_attach, forall_true_left, Subtype.forall, ←
@@ -226,7 +226,7 @@ theorem cyclotomic_eval_lt_add_one_pow_totient {n : ℕ} {q : ℝ} (hn' : 3 ≤
   have hfor : ∀ ζ' ∈ primitiveRoots n ℂ, ‖↑q - ζ'‖ ≤ q + 1 := by
     intro ζ' hζ'
     rw [mem_primitiveRoots hn] at hζ'
-    convert norm_sub_le (↑q) ζ'
+    convert! norm_sub_le (↑q) ζ'
     · rw [Complex.norm_real, Real.norm_of_nonneg (zero_le_one.trans_lt hq').le]
     · rw [hζ'.norm'_eq_one hn.ne']
   let ζ := Complex.exp (2 * ↑Real.pi * Complex.I / ↑n)
@@ -234,7 +234,7 @@ theorem cyclotomic_eval_lt_add_one_pow_totient {n : ℕ} {q : ℝ} (hn' : 3 ≤
   have hex : ∃ ζ' ∈ primitiveRoots n ℂ, ‖↑q - ζ'‖ < q + 1 := by
     refine ⟨ζ, (mem_primitiveRoots hn).mpr hζ, ?_⟩
     suffices ¬SameRay ℝ (q : ℂ) (-ζ) by
-      convert norm_add_lt_of_not_sameRay this using 2
+      convert! norm_add_lt_of_not_sameRay this using 2
       · rw [Complex.norm_real]
         symm
         exact abs_eq_self.mpr hq.le
@@ -261,14 +261,14 @@ theorem cyclotomic_eval_lt_add_one_pow_totient {n : ℕ} {q : ℝ} (hn' : 3 ≤
     simp only [← Units.val_lt_val, Units.val_pow_eq_pow_val, Units.val_mk0, ← NNReal.coe_lt_coe,
       coe_nnnorm, NNReal.coe_pow,
       Real.coe_toNNReal'] at this
-    convert this using 2
+    convert! this using 2
     · rw [eq_comm]
       simp [cyclotomic_nonneg n hq'.le]
     rw [eq_comm, max_eq_left_iff]
     linarith
   simp only [cyclotomic_eq_prod_X_sub_primitiveRoots hζ, eval_prod, eval_C, eval_X, eval_sub,
     nnnorm_prod, Units.mk0_prod]
-  convert Finset.prod_lt_prod' (M := NNRealˣ) _ _
+  convert! Finset.prod_lt_prod' (M := NNRealˣ) _ _
   swap; · exact fun _ => Units.mk0 (Real.toNNReal (q + 1)) (by positivity)
   · simp [Complex.card_primitiveRoots]
   · simp only [Finset.mem_attach, forall_true_left, Subtype.forall, ←
@@ -297,7 +297,7 @@ theorem sub_one_pow_totient_lt_natAbs_cyclotomic_eval {n : ℕ} {q : ℕ} (hn' :
     exact one_ne_zero
   rw [← @Nat.cast_lt ℝ, Nat.cast_pow, Nat.cast_sub hq'.le, Nat.cast_one, Nat.cast_natAbs]
   refine (sub_one_pow_totient_lt_cyclotomic_eval hn' (Nat.one_lt_cast.2 hq')).trans_le ?_
-  convert (cyclotomic.eval_apply (q : ℤ) n (algebraMap ℤ ℝ)).trans_le (le_abs_self _)
+  convert! (cyclotomic.eval_apply (q : ℤ) n (algebraMap ℤ ℝ)).trans_le (le_abs_self _)
   simp
 
 theorem sub_one_lt_natAbs_cyclotomic_eval {n : ℕ} {q : ℕ} (hn' : 1 < n) (hq : q ≠ 1) :
diff --git a/Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean b/Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean
index 0b8592fad60c6f..01a6f5ec86d5b5 100644
--- a/Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean
+++ b/Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean
@@ -59,7 +59,7 @@ theorem cyclotomic_expand_eq_cyclotomic_mul {p n : ℕ} (hp : Nat.Prime p) (hdiv
       refine minpoly.dvd ℚ _ ?_
       rw [← eval_map_algebraMap, map_expand, map_cyclotomic, expand_eval, ← IsRoot.def,
         @isRoot_cyclotomic_iff]
-      convert IsPrimitiveRoot.pow_of_dvd hprim hp.ne_zero (dvd_mul_left p n)
+      convert! IsPrimitiveRoot.pow_of_dvd hprim hp.ne_zero (dvd_mul_left p n)
       rw [Nat.mul_div_cancel _ (Nat.Prime.pos hp)]
     · have hprim := Complex.isPrimitiveRoot_exp _ hnpos.ne.symm
       rw [cyclotomic_eq_minpoly_rat hprim hnpos]
@@ -100,7 +100,7 @@ theorem cyclotomic_expand_eq_cyclotomic {p n : ℕ} (hp : Nat.Prime p) (hdiv : p
     refine minpoly.isIntegrallyClosed_dvd (hprim.isIntegral hpos) ?_
     rw [← eval_map_algebraMap, map_expand, map_cyclotomic, expand_eval, ← IsRoot.def,
       @isRoot_cyclotomic_iff]
-    convert IsPrimitiveRoot.pow_of_dvd hprim hp.ne_zero (dvd_mul_left p n)
+    convert! IsPrimitiveRoot.pow_of_dvd hprim hp.ne_zero (dvd_mul_left p n)
     rw [Nat.mul_div_cancel _ hp.pos]
   · rw [natDegree_expand, natDegree_cyclotomic, natDegree_cyclotomic, mul_comm n,
       Nat.totient_mul_of_prime_of_dvd hp hdiv, mul_comm]
diff --git a/Mathlib/RingTheory/Polynomial/Cyclotomic/Roots.lean b/Mathlib/RingTheory/Polynomial/Cyclotomic/Roots.lean
index 56167494b56579..34cec1230f631d 100644
--- a/Mathlib/RingTheory/Polynomial/Cyclotomic/Roots.lean
+++ b/Mathlib/RingTheory/Polynomial/Cyclotomic/Roots.lean
@@ -45,8 +45,8 @@ theorem isRoot_of_unity_of_root_cyclotomic {ζ : R} {i : ℕ} (hi : i ∈ n.divi
   · exact pow_zero _
   have := congr_arg (eval ζ) (prod_cyclotomic_eq_X_pow_sub_one hn R).symm
   rw [eval_sub, eval_X_pow, eval_one] at this
-  convert eq_add_of_sub_eq' this
-  convert (add_zero (M := R) _).symm
+  convert! eq_add_of_sub_eq' this
+  convert! (add_zero (M := R) _).symm
   apply eval_eq_zero_of_dvd_of_eval_eq_zero _ h
   exact Finset.dvd_prod_of_mem _ hi
 
diff --git a/Mathlib/RingTheory/Polynomial/Dickson.lean b/Mathlib/RingTheory/Polynomial/Dickson.lean
index ad1e6ab658618c..99c6d0c632f322 100644
--- a/Mathlib/RingTheory/Polynomial/Dickson.lean
+++ b/Mathlib/RingTheory/Polynomial/Dickson.lean
@@ -245,7 +245,7 @@ theorem dickson_one_one_zmod_p (p : ℕ) [Fact p.Prime] : dickson 1 (1 : ZMod p)
         simpa [φ, eval_X, eval_one, eval_pow, eval_sub, sub_zero, eval_add, eval_mul,
           mul_zero, sq, zero_add, one_ne_zero]
       classical
-        convert (φ.roots ∪ {0}).toFinset.finite_toSet using 1
+        convert! (φ.roots ∪ {0}).toFinset.finite_toSet using 1
         ext1 y
         simp only [φ, Multiset.mem_toFinset, Set.mem_setOf_eq, Finset.mem_coe, Multiset.mem_union,
           mem_roots hφ, IsRoot, eval_add, eval_sub, eval_pow, eval_mul, eval_X, eval_C, eval_one,
diff --git a/Mathlib/RingTheory/Polynomial/Eisenstein/Criterion.lean b/Mathlib/RingTheory/Polynomial/Eisenstein/Criterion.lean
index 5e29efdb448645..a59d1730a5c866 100644
--- a/Mathlib/RingTheory/Polynomial/Eisenstein/Criterion.lean
+++ b/Mathlib/RingTheory/Polynomial/Eisenstein/Criterion.lean
@@ -202,7 +202,7 @@ theorem irreducible_of_eisenstein_criterion {f : R[X]} {P : Ideal R} (hP : P.IsP
         · simp [Nat.lt_iff_le_and_ne, ← Nat.not_lt, hn', Ne.symm hn]
   · rw [modByMonic_X, map_C, ne_eq, C_eq_zero, Ideal.Quotient.eq_zero_iff_mem,
       ← coeff_zero_eq_eval_zero]
-    convert h0
+    convert! h0
     · rw [IsScalarTower.algebraMap_eq R (R ⧸ P) (FractionRing (R ⧸ P))]
       rw [ker_comp_of_injective]
       · ext a; simp
diff --git a/Mathlib/RingTheory/Polynomial/Eisenstein/IsIntegral.lean b/Mathlib/RingTheory/Polynomial/Eisenstein/IsIntegral.lean
index ccd9a5514f97b8..e48868808090f5 100644
--- a/Mathlib/RingTheory/Polynomial/Eisenstein/IsIntegral.lean
+++ b/Mathlib/RingTheory/Polynomial/Eisenstein/IsIntegral.lean
@@ -156,7 +156,7 @@ theorem dvd_coeff_zero_of_aeval_eq_prime_smul_of_minpoly_isEisensteinAt {B : Pow
     have hndiv : ¬p ^ 2 ∣ (minpoly R B.gen).coeff 0 := fun h =>
       hei.notMem ((span_singleton_pow p 2).symm ▸ Ideal.mem_span_singleton.2 h)
     refine hp.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvd (n := n) (?_ : _ ∣ _) hndiv
-    convert (IsUnit.dvd_mul_right ⟨(-1) ^ (n.succ * n), rfl⟩).mpr this using 1
+    convert! (IsUnit.dvd_mul_right ⟨(-1) ^ (n.succ * n), rfl⟩).mpr this using 1
     push_cast
     ring_nf
     simp
@@ -263,7 +263,7 @@ theorem mem_adjoin_of_smul_prime_smul_of_minpoly_isEisensteinAt {B : PowerBasis
     exact dvd_coeff_zero_of_aeval_eq_prime_smul_of_minpoly_isEisensteinAt hp hBint hQ hzint hei
   | hi j hind =>
     intro hj
-    convert hp.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvd (n := n) _ hndiv
+    convert! hp.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvd (n := n) _ hndiv
     -- Two technical results we will need about `P.natDegree` and `Q.natDegree`.
     have H := degree_modByMonic_lt Q₁ (minpoly.monic hBint)
     rw [← hQ₁, ← hP] at H
@@ -309,7 +309,7 @@ theorem mem_adjoin_of_smul_prime_smul_of_minpoly_isEisensteinAt {B : PowerBasis
     suffices
         p ^ n.succ ∣ Q.coeff (succ j) ^ n.succ *
           (minpoly R B.gen).coeff 0 ^ (succ j + (P.natDegree - (j + 2))) by
-      convert this
+      convert! this
       rw [Nat.succ_eq_add_one, add_assoc, ← Nat.add_sub_assoc H, add_comm (j + 1),
         Nat.add_sub_add_left, ← Nat.add_sub_assoc, Nat.add_sub_add_left, hP, ←
         (minpoly.monic hBint).natDegree_map (algebraMap R K), ←
diff --git a/Mathlib/RingTheory/Polynomial/GaussNorm.lean b/Mathlib/RingTheory/Polynomial/GaussNorm.lean
index 973e8cc85dd8f6..6a58cfb1633d34 100644
--- a/Mathlib/RingTheory/Polynomial/GaussNorm.lean
+++ b/Mathlib/RingTheory/Polynomial/GaussNorm.lean
@@ -125,8 +125,9 @@ only if the polynomial is zero. -/
 theorem gaussNorm_eq_zero_iff (h_eq_zero : ∀ x : R, v x = 0 → x = 0) (hc : 0 < c) :
     p.gaussNorm v c = 0 ↔ p = 0 := by
   rw [← gaussNorm_coe_powerSeries _ _ (le_of_lt hc)]
-  convert PowerSeries.gaussNorm_eq_zero_iff v c p (by grind) (by simp) h_eq_zero hc
-    (by simpa [PowerSeries.HasGaussNorm] using aux_bdd v p)
+  convert!
+    PowerSeries.gaussNorm_eq_zero_iff v c p (by grind) (by simp) h_eq_zero hc
+      (by simpa [PowerSeries.HasGaussNorm] using aux_bdd v p)
   exact Iff.symm coe_eq_zero_iff
 
 omit [ZeroHomClass F R ℝ] in
diff --git a/Mathlib/RingTheory/Polynomial/Hermite/Basic.lean b/Mathlib/RingTheory/Polynomial/Hermite/Basic.lean
index 82dc6c0255decc..ebc7dd98babcdf 100644
--- a/Mathlib/RingTheory/Polynomial/Hermite/Basic.lean
+++ b/Mathlib/RingTheory/Polynomial/Hermite/Basic.lean
@@ -143,7 +143,7 @@ theorem coeff_hermite_explicit :
     ∀ n k : ℕ, coeff (hermite (2 * n + k)) k = (-1) ^ n * (2 * n - 1)‼ * Nat.choose (2 * n + k) k
   | 0, _ => by simp
   | n + 1, 0 => by
-    convert coeff_hermite_succ_zero (2 * n + 1) using 1
+    convert! coeff_hermite_succ_zero (2 * n + 1) using 1
     rw [coeff_hermite_explicit n 1, (by grind : 2 * (n + 1) - 1 = 2 * n + 1),
       Nat.doubleFactorial_add_one, Nat.choose_zero_right,
       Nat.choose_one_right, pow_succ]
diff --git a/Mathlib/RingTheory/Polynomial/IsIntegral.lean b/Mathlib/RingTheory/Polynomial/IsIntegral.lean
index cbf2125c6bc6a3..a70f4023da5ff5 100644
--- a/Mathlib/RingTheory/Polynomial/IsIntegral.lean
+++ b/Mathlib/RingTheory/Polynomial/IsIntegral.lean
@@ -199,7 +199,7 @@ theorem MvPolynomial.isIntegral_iff_isIntegral_coeff.{w} {σ : Type w} {f : MvPo
     simp_rw [monomial_eq]
     refine IsIntegral.sum _ fun n _ ↦ .mul ((H n).map (Algebra.ofId _ _)).tower_top
       (.prod _ fun i _ ↦ .pow ?_ _)
-    convert isIntegral_algebraMap (x := MvPolynomial.X i)
+    convert! isIntegral_algebraMap (x := MvPolynomial.X i)
     simp only [algebraMap_def, map_X]
   unfold IsIntegral at H
   wlog hσ : Finite σ generalizing σ
@@ -212,8 +212,10 @@ theorem MvPolynomial.isIntegral_iff_isIntegral_coeff.{w} {σ : Type w} {f : MvPo
         (g := (rename ((↑) : f.vars → σ)).toRingHom) (rename_injective _ Subtype.val_injective)
         (.of_comp (f := (killCompl (f := ((↑) : f.vars → σ)) Subtype.val_injective).toRingHom) <| by
         simp only [AlgHom.toRingHom_eq_coe, algebraMap_def, RingHom.coe_coe, hg]
-        convert H.map ((rename Subtype.val).comp
-          (killCompl (f := ((↑) : f.vars → σ)) Subtype.val_injective)).toRingHom
+        convert!
+          H.map
+            ((rename Subtype.val).comp
+                (killCompl (f := ((↑) : f.vars → σ)) Subtype.val_injective)).toRingHom
         · exact RingHom.ext (by simp [MvPolynomial.killCompl_map])
         · nth_rw 1 12 [← hg]; simp)) n (.of_fintype _)
     · rw [← hg, coeff_rename_eq_zero _ _ _ (by grind)]
@@ -223,13 +225,13 @@ theorem MvPolynomial.isIntegral_iff_isIntegral_coeff.{w} {σ : Type w} {f : MvPo
   · intro α β e IH f H n
     have := @IH (rename e.symm f) (.of_map (g := (rename e).toRingHom)
       (rename_injective _ e.injective) <| .of_comp (f := (rename e.symm).toRingHom)
-        (by convert H <;> aesop)) (n.embDomain e.symm)
+        (by convert! H <;> aesop)) (n.embDomain e.symm)
     simpa [Finsupp.embDomain_eq_mapDomain, coeff_rename_mapDomain _ e.symm.injective] using this
   · intro f H n
     refine .of_map (g := (isEmptyAlgEquiv _ PEmpty).symm.toRingHom)
       (isEmptyAlgEquiv _ PEmpty).symm.injective
       (.of_comp (f := (isEmptyAlgEquiv _ PEmpty).toRingHom) ?_)
-    convert H
+    convert! H
     · aesop (add simp MvPolynomial.isEmptyAlgEquiv)
     · obtain rfl := Subsingleton.elim n 0
       have : constantCoeff = (isEmptyAlgEquiv S PEmpty).toRingHom := by aesop
@@ -240,7 +242,7 @@ theorem MvPolynomial.isIntegral_iff_isIntegral_coeff.{w} {σ : Type w} {f : MvPo
       (p := optionEquivLeft _ _ f) (.of_map
       (g := (optionEquivLeft _ _).symm.toRingHom) (optionEquivLeft _ _).symm.injective
       (.of_comp (f := (optionEquivLeft _ _).toRingHom) (by
-        convert H
+        convert! H
         · ext i m
           · aesop
           · cases i <;> aesop
diff --git a/Mathlib/RingTheory/Polynomial/Pochhammer.lean b/Mathlib/RingTheory/Polynomial/Pochhammer.lean
index 63a53ac347d62c..ae098f694678e6 100644
--- a/Mathlib/RingTheory/Polynomial/Pochhammer.lean
+++ b/Mathlib/RingTheory/Polynomial/Pochhammer.lean
@@ -445,7 +445,7 @@ theorem ascPochhammer_eval_eq_zero_iff [IsDomain R]
       | inr h =>
         exact ⟨n, lt_add_one n, eq_neg_of_add_eq_zero_right h⟩
   · obtain ⟨rn, hrn, rnn⟩ := hrn
-    convert ascPochhammer_eval_neg_coe_nat_of_lt hrn
+    convert! ascPochhammer_eval_neg_coe_nat_of_lt hrn
     simp [rnn]
 
 /-- `descPochhammer R n` is `0` for `0, 1, …, n-1`. -/
diff --git a/Mathlib/RingTheory/Polynomial/RationalRoot.lean b/Mathlib/RingTheory/Polynomial/RationalRoot.lean
index afc52ba5da0012..aac878274cb055 100644
--- a/Mathlib/RingTheory/Polynomial/RationalRoot.lean
+++ b/Mathlib/RingTheory/Polynomial/RationalRoot.lean
@@ -41,7 +41,7 @@ open Finsupp IsFractionRing IsLocalization Polynomial
 
 theorem scaleRoots_aeval_eq_zero_of_aeval_mk'_eq_zero {p : A[X]} {r : A} {s : M}
     (hr : aeval (mk' S r s) p = 0) : aeval (algebraMap A S r) (scaleRoots p s) = 0 := by
-  convert scaleRoots_eval₂_eq_zero (algebraMap A S) hr
+  convert! scaleRoots_eval₂_eq_zero (algebraMap A S) hr
   funext
   rw [aeval_def, mk'_spec' _ r s]
 
@@ -76,11 +76,11 @@ theorem num_dvd_of_is_root {p : A[X]} {r : K} (hr : aeval r p = 0) : num A r ∣
       intro q dvd_num dvd_denom_pow hq
       apply hq.not_unit
       exact num_den_reduced A r dvd_num (hq.dvd_of_dvd_pow dvd_denom_pow)
-  convert dvd_term_of_isRoot_of_dvd_terms 0 (num_isRoot_scaleRoots_of_aeval_eq_zero hr) _
+  convert! dvd_term_of_isRoot_of_dvd_terms 0 (num_isRoot_scaleRoots_of_aeval_eq_zero hr) _
   · rw [pow_zero, mul_one]
   intro j hj
   apply dvd_mul_of_dvd_right
-  convert pow_dvd_pow (num A r) (Nat.succ_le_of_lt (bot_lt_iff_ne_bot.mpr hj))
+  convert! pow_dvd_pow (num A r) (Nat.succ_le_of_lt (bot_lt_iff_ne_bot.mpr hj))
   exact (pow_one _).symm
 
 /-- Rational root theorem part 2:
@@ -101,7 +101,7 @@ theorem den_dvd_of_is_root {p : A[X]} {r : K} (hr : aeval r p = 0) :
   by_cases! h : j < p.natDegree
   · rw [coeff_scaleRoots]
     refine (dvd_mul_of_dvd_right ?_ _).mul_right _
-    convert pow_dvd_pow (den A r : A) (Nat.succ_le_iff.mpr (lt_tsub_iff_left.mpr _))
+    convert! pow_dvd_pow (den A r : A) (Nat.succ_le_iff.mpr (lt_tsub_iff_left.mpr _))
     · exact (pow_one _).symm
     simpa using h
   rw [← natDegree_scaleRoots p (den A r)] at *
diff --git a/Mathlib/RingTheory/Polynomial/Resultant/Basic.lean b/Mathlib/RingTheory/Polynomial/Resultant/Basic.lean
index 35f779049a94ad..c5db3b78562be0 100644
--- a/Mathlib/RingTheory/Polynomial/Resultant/Basic.lean
+++ b/Mathlib/RingTheory/Polynomial/Resultant/Basic.lean
@@ -659,17 +659,17 @@ lemma resultant_prod_right {ι : Type*} (s : Finset ι) (f : R[X]) (g : ι → R
 @[simp]
 lemma resultant_pow_left (hf : f.leadingCoeff ^ m ≠ 0) (hn : g.natDegree ≤ n) :
     (f ^ m).resultant g (f ^ m).natDegree n = (f.resultant g f.natDegree n) ^ m := by
-  convert resultant_prod_left (Finset.range m) (fun _ ↦ f) g n (by simpa) hn <;> simp
+  convert! resultant_prod_left (Finset.range m) (fun _ ↦ f) g n (by simpa) hn <;> simp
 
 @[simp]
 lemma resultant_pow_right (hm : f.natDegree ≤ m) (hg : g.leadingCoeff ^ n ≠ 0) :
     f.resultant (g ^ n) m (g ^ n).natDegree = (f.resultant g m g.natDegree) ^ n := by
-  convert resultant_prod_right (Finset.range n) f (fun _ ↦ g) m hm (by simpa) <;> simp
+  convert! resultant_prod_right (Finset.range n) f (fun _ ↦ g) m hm (by simpa) <;> simp
 
 lemma resultant_X_sub_C_pow_left (r : R) (g : R[X]) (m n : ℕ) (hn : g.natDegree ≤ n) :
     ((X - C r) ^ m).resultant g m n = eval r g ^ m := by
   nontriviality R
-  convert resultant_pow_left _ _ _ _ _ _ <;> simp [natDegree_pow', hn]
+  convert! resultant_pow_left _ _ _ _ _ _ <;> simp [natDegree_pow', hn]
 
 lemma resultant_X_sub_C_pow_right (f : R[X]) (r : R) (m n : ℕ) (hm : f.natDegree ≤ m) :
     f.resultant ((X - C r) ^ n) m n = (-1) ^ (m * n) * eval r f ^ n := by
@@ -677,11 +677,11 @@ lemma resultant_X_sub_C_pow_right (f : R[X]) (r : R) (m n : ℕ) (hm : f.natDegr
 
 lemma resultant_X_pow_left (g : R[X]) (m n : ℕ) (hn : g.natDegree ≤ n) :
     (X ^ m).resultant g m n = g.coeff 0 ^ m := by
-  convert resultant_X_sub_C_pow_left 0 g m n hn <;> simp [coeff_zero_eq_eval_zero]
+  convert! resultant_X_sub_C_pow_left 0 g m n hn <;> simp [coeff_zero_eq_eval_zero]
 
 lemma resultant_X_pow_right (f : R[X]) (m n : ℕ) (hm : f.natDegree ≤ m) :
     f.resultant (X ^ n) m n = (-1) ^ (m * n) * f.coeff 0 ^ n := by
-  convert resultant_X_sub_C_pow_right f 0 m n hm <;> simp [coeff_zero_eq_eval_zero]
+  convert! resultant_X_sub_C_pow_right f 0 m n hm <;> simp [coeff_zero_eq_eval_zero]
 
 nonrec lemma resultant_scaleRoots (f g : R[X]) (r : R) :
     resultant (f.scaleRoots r) (g.scaleRoots r) =
@@ -975,7 +975,7 @@ lemma resultant_deriv {f : R[X]} (hf : 0 < f.degree) :
   rw [resultant_comm, resultant, ← sylvesterDeriv_updateRow f hf, Matrix.det_updateRow_smul,
     Matrix.updateRow_eq_self, discr, mul_comm f.natDegree]
   ring_nf
-  rw [Nat.div_mul_cancel (by convert Nat.two_dvd_mul_add_one (f.natDegree - 1) using 2; lia)]
+  rw [Nat.div_mul_cancel (by convert! Nat.two_dvd_mul_add_one (f.natDegree - 1) using 2; lia)]
 
 set_option linter.style.whitespace false in -- manual alignment is not recognised
 private lemma sylvesterDeriv_of_natDegree_eq_three {f : R[X]} (hf : f.natDegree = 3) :
diff --git a/Mathlib/RingTheory/Polynomial/ScaleRoots.lean b/Mathlib/RingTheory/Polynomial/ScaleRoots.lean
index cf3db2ec59b8fc..1ba2255c027ed2 100644
--- a/Mathlib/RingTheory/Polynomial/ScaleRoots.lean
+++ b/Mathlib/RingTheory/Polynomial/ScaleRoots.lean
@@ -169,7 +169,7 @@ theorem scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero {p : S[X]} {f : S →+
     (hs : s ∈ nonZeroDivisors S) : eval₂ f (f r) (scaleRoots p s) = 0 := by
   -- if we don't specify the type with `(_ : S)`, the proof is much slower
   nontriviality S using Subsingleton.eq_zero (_ : S)
-  convert @scaleRoots_eval₂_eq_zero _ _ _ _ p f _ s hr
+  convert! @scaleRoots_eval₂_eq_zero _ _ _ _ p f _ s hr
   rw [← mul_div_assoc, mul_comm, mul_div_cancel_right₀]
   exact map_ne_zero_of_mem_nonZeroDivisors _ hf hs
 
diff --git a/Mathlib/RingTheory/Polynomial/SmallDegreeVieta.lean b/Mathlib/RingTheory/Polynomial/SmallDegreeVieta.lean
index 77fedfa207edad..6840b590e4ab53 100644
--- a/Mathlib/RingTheory/Polynomial/SmallDegreeVieta.lean
+++ b/Mathlib/RingTheory/Polynomial/SmallDegreeVieta.lean
@@ -32,7 +32,7 @@ lemma eq_neg_mul_add_of_roots_quadratic_eq_pair [CommRing R] [IsDomain R] {a b c
     b = -a * (x1 + x2) := by
   let p : R[X] := C a * X ^ 2 + C b * X + C c
   have hp_natDegree : p.natDegree = 2 := le_antisymm natDegree_quadratic_le
-    (by convert p.card_roots'; rw [hroots, Multiset.card_pair])
+    (by convert! p.card_roots'; rw [hroots, Multiset.card_pair])
   have hp_roots_card : p.roots.card = p.natDegree := by
     rw [hp_natDegree, hroots, Multiset.card_pair]
   simpa [leadingCoeff, hp_natDegree, p, hroots, mul_assoc, add_comm x1] using
@@ -44,7 +44,7 @@ lemma eq_mul_mul_of_roots_quadratic_eq_pair [CommRing R] [IsDomain R] {a b c x1
     c = a * x1 * x2 := by
   let p : R[X] := C a * X ^ 2 + C b * X + C c
   have hp_natDegree : p.natDegree = 2 := le_antisymm natDegree_quadratic_le
-    (by convert p.card_roots'; rw [hroots, Multiset.card_pair])
+    (by convert! p.card_roots'; rw [hroots, Multiset.card_pair])
   have hp_roots_card : p.roots.card = p.natDegree := by
     rw [hp_natDegree, hroots, Multiset.card_pair]
   simpa [leadingCoeff, hp_natDegree, p, hroots, mul_assoc, add_comm x1] using
diff --git a/Mathlib/RingTheory/Polynomial/UniversalFactorizationRing.lean b/Mathlib/RingTheory/Polynomial/UniversalFactorizationRing.lean
index a3a9e4b4f8cf49..b3936dabc82f22 100644
--- a/Mathlib/RingTheory/Polynomial/UniversalFactorizationRing.lean
+++ b/Mathlib/RingTheory/Polynomial/UniversalFactorizationRing.lean
@@ -587,7 +587,7 @@ def UniversalCoprimeFactorizationRing.homEquiv :
   toFun f :=
     letI q := UniversalFactorizationRing.homEquiv S m k hn p (f.comp (IsScalarTower.toAlgHom _ _ _))
     ⟨q.1, q.2, by
-      convert (isCoprime_factor₁_factor₂ m k hn p).map (Polynomial.mapRingHom f.toRingHom) <;>
+      convert! (isCoprime_factor₁_factor₂ m k hn p).map (Polynomial.mapRingHom f.toRingHom) <;>
         simp [q, UniversalFactorizationRing.homEquiv,
           AlgHom.comp_toRingHom, ← Polynomial.map_map] <;> rfl⟩
   invFun q := by
@@ -614,7 +614,7 @@ def UniversalCoprimeFactorizationRing.homEquiv :
     ext; simp
   right_inv q := by
     apply Subtype.ext
-    convert congr($((UniversalFactorizationRing.homEquiv S m k hn p).apply_symm_apply
+    convert! congr($((UniversalFactorizationRing.homEquiv S m k hn p).apply_symm_apply
       ⟨_, q.2.1⟩).1) using 1
     dsimp
     congr 2
diff --git a/Mathlib/RingTheory/Polynomial/Vieta.lean b/Mathlib/RingTheory/Polynomial/Vieta.lean
index 1a77f5434ad737..11cccb8d2bdc21 100644
--- a/Mathlib/RingTheory/Polynomial/Vieta.lean
+++ b/Mathlib/RingTheory/Polynomial/Vieta.lean
@@ -55,7 +55,7 @@ theorem prod_X_add_C_eq_sum_esymm (s : Multiset R) :
 through a multiset `s` : the `k`th coefficient is the symmetric function `esymm (card s - k) s`. -/
 theorem prod_X_add_C_coeff (s : Multiset R) {k : ℕ} (h : k ≤ Multiset.card s) :
     (s.map fun r => X + C r).prod.coeff k = s.esymm (Multiset.card s - k) := by
-  convert Polynomial.ext_iff.mp (prod_X_add_C_eq_sum_esymm s) k using 1
+  convert! Polynomial.ext_iff.mp (prod_X_add_C_eq_sum_esymm s) k using 1
   simp_rw [finsetSum_coeff, coeff_C_mul_X_pow]
   rw [Finset.sum_eq_single_of_mem (Multiset.card s - k) _] <;> grind
 
@@ -94,7 +94,7 @@ theorem prod_X_sub_X_eq_sum_esymm (s : Multiset R) :
     ext x
     rw [sub_eq_add_neg]
     rw [← map_neg C x]
-  convert prod_X_add_C_eq_sum_esymm (map (fun t => -t) s) using 1
+  convert! prod_X_add_C_eq_sum_esymm (map (fun t => -t) s) using 1
   · rw [map_map]; rfl
   · simp only [esymm_neg, card_map, mul_assoc, map_mul, map_pow, map_neg, map_one]
 
@@ -108,7 +108,7 @@ theorem prod_X_sub_C_coeff (s : Multiset R) {k : ℕ} (h : k ≤ Multiset.card s
     ext x
     rw [sub_eq_add_neg]
     rw [← map_neg C x]
-  convert prod_X_add_C_coeff (map (fun t => -t) s) _ using 1
+  convert! prod_X_add_C_coeff (map (fun t => -t) s) _ using 1
   · rw [map_map]; rfl
   · rw [esymm_neg, card_map]
   · rwa [card_map]
@@ -121,7 +121,7 @@ theorem _root_.Polynomial.coeff_eq_esymm_roots_of_card [IsDomain R] {p : R[X]}
   conv_lhs => rw [← C_leadingCoeff_mul_prod_multiset_X_sub_C hroots]
   rw [coeff_C_mul, mul_assoc]; congr
   have : k ≤ card (roots p) := by rw [hroots]; exact h
-  convert p.roots.prod_X_sub_C_coeff this using 3 <;> rw [hroots]
+  convert! p.roots.prod_X_sub_C_coeff this using 3 <;> rw [hroots]
 
 /-- Vieta's formula for split polynomials over a field. -/
 theorem _root_.Polynomial.coeff_eq_esymm_roots_of_splits {F} [Field F] {p : F[X]}
@@ -150,7 +150,7 @@ theorem MvPolynomial.prod_C_add_X_eq_sum_esymm :
   have : Fintype.card σ = Multiset.card s := by
     rw [Multiset.card_map, ← Finset.card_univ, Finset.card_def]
   simp_rw [this, MvPolynomial.esymm_eq_multiset_esymm σ R, Finset.prod_eq_multiset_prod]
-  convert Multiset.prod_X_add_C_eq_sum_esymm s
+  convert! Multiset.prod_X_add_C_eq_sum_esymm s
   simp_rw [s, Multiset.map_map, Function.comp_apply]
 
 theorem MvPolynomial.prod_X_add_C_coeff (k : ℕ) (h : k ≤ card σ) :
@@ -161,7 +161,7 @@ theorem MvPolynomial.prod_X_add_C_coeff (k : ℕ) (h : k ≤ card σ) :
     rw [Multiset.card_map, ← Finset.card_univ, Finset.card_def]
   rw [this] at h ⊢
   rw [MvPolynomial.esymm_eq_multiset_esymm σ R, Finset.prod_eq_multiset_prod]
-  convert Multiset.prod_X_add_C_coeff s h
+  convert! Multiset.prod_X_add_C_coeff s h
   dsimp
   simp_rw [s, Multiset.map_map, Function.comp_apply]
 
diff --git a/Mathlib/RingTheory/Polynomial/Wronskian.lean b/Mathlib/RingTheory/Polynomial/Wronskian.lean
index 2d59bba59302fb..591114a63e9ff7 100644
--- a/Mathlib/RingTheory/Polynomial/Wronskian.lean
+++ b/Mathlib/RingTheory/Polynomial/Wronskian.lean
@@ -113,7 +113,7 @@ theorem natDegree_wronskian_lt_add {a b : R[X]} (hw : wronskian a b ≠ 0) :
   have ha : a ≠ 0 := by intro h; subst h; rw [wronskian_zero_left] at hw; exact hw rfl
   have hb : b ≠ 0 := by intro h; subst h; rw [wronskian_zero_right] at hw; exact hw rfl
   rw [← WithBot.coe_lt_coe, WithBot.coe_add]
-  convert ← degree_wronskian_lt_add ha hb
+  convert! ← degree_wronskian_lt_add ha hb
   · exact Polynomial.degree_eq_natDegree hw
   · exact Polynomial.degree_eq_natDegree ha
   · exact Polynomial.degree_eq_natDegree hb
diff --git a/Mathlib/RingTheory/PolynomialLaw/Basic.lean b/Mathlib/RingTheory/PolynomialLaw/Basic.lean
index 428aacc7598da8..b2e6bc8fe2651c 100644
--- a/Mathlib/RingTheory/PolynomialLaw/Basic.lean
+++ b/Mathlib/RingTheory/PolynomialLaw/Basic.lean
@@ -235,7 +235,7 @@ instance : CoeFun (M →ₚₗ[R] N) (fun _ ↦ M → N) where
 theorem one_tmul_ground_apply' {S : Type u} [CommSemiring S] [Algebra R S] (x : M) :
     1 ⊗ₜ (f.ground x) = (f.toFun' S) (1 ⊗ₜ x) := by
   rw [ground_apply]
-  convert f.isCompat_apply' (Algebra.algHom R R S) (1 ⊗ₜ[R] x)
+  convert! f.isCompat_apply' (Algebra.algHom R R S) (1 ⊗ₜ[R] x)
   · simp only [includeRight_lid]
   · rw [rTensor_tmul, toLinearMap_apply, map_one]
 
@@ -584,7 +584,7 @@ variable {R : Type u} [CommSemiring R]
 theorem one_tmul_ground (x : M) :
     1 ⊗ₜ f.ground x = f.toFun S (1 ⊗ₜ x) := by
   simp only [ground, toFun'_eq_toFun]
-  convert f.isCompat_apply (Algebra.ofId R S) (1 ⊗ₜ[R] x)
+  convert! f.isCompat_apply (Algebra.ofId R S) (1 ⊗ₜ[R] x)
   · simp only [Function.comp_apply, TensorProduct.lid_symm_apply, TensorProduct.includeRight_lid]
     congr
   · rw [rTensor_tmul, toLinearMap_apply, _root_.map_one]
diff --git a/Mathlib/RingTheory/PowerBasis.lean b/Mathlib/RingTheory/PowerBasis.lean
index 53f0a417575ed6..28e97065e03cd6 100644
--- a/Mathlib/RingTheory/PowerBasis.lean
+++ b/Mathlib/RingTheory/PowerBasis.lean
@@ -235,7 +235,7 @@ protected theorem leftMulMatrix (pb : PowerBasis A S) : Algebra.leftMulMatrix pb
   apply (pow_succ' _ _).symm.trans
   split_ifs with h
   · simp_rw [h, neg_smul, Finset.sum_neg_distrib, eq_neg_iff_add_eq_zero]
-    convert pb.aeval_minpolyGen
+    convert! pb.aeval_minpolyGen
     rw [add_comm, aeval_eq_sum_range, Finset.sum_range_succ, ← leadingCoeff,
       pb.minpolyGen_monic.leadingCoeff, one_smul, natDegree_minpolyGen, Finset.sum_range]
   · rw [Fintype.sum_eq_single (⟨(k : ℕ) + 1, lt_of_le_of_ne k.2 h⟩ : Fin pb.dim), if_pos, one_smul]
@@ -270,11 +270,11 @@ theorem constr_pow_aeval (pb : PowerBasis A S) {y : S'} (hy : aeval y (minpoly A
 
 theorem constr_pow_gen (pb : PowerBasis A S) {y : S'} (hy : aeval y (minpoly A pb.gen) = 0) :
     pb.basis.constr A (fun i => y ^ (i : ℕ)) pb.gen = y := by
-  convert pb.constr_pow_aeval hy X <;> rw [aeval_X]
+  convert! pb.constr_pow_aeval hy X <;> rw [aeval_X]
 
 theorem constr_pow_algebraMap (pb : PowerBasis A S) {y : S'} (hy : aeval y (minpoly A pb.gen) = 0)
     (x : A) : pb.basis.constr A (fun i => y ^ (i : ℕ)) (algebraMap A S x) = algebraMap A S' x := by
-  convert pb.constr_pow_aeval hy (C x) <;> rw [aeval_C]
+  convert! pb.constr_pow_aeval hy (C x) <;> rw [aeval_C]
 
 theorem constr_pow_mul (pb : PowerBasis A S) {y : S'} (hy : aeval y (minpoly A pb.gen) = 0)
     (x x' : S) : pb.basis.constr A (fun i => y ^ (i : ℕ)) (x * x') =
@@ -291,8 +291,8 @@ See `PowerBasis.liftEquiv` for a bundled equiv sending `⟨y, hy⟩` to the alge
 noncomputable def lift (pb : PowerBasis A S) (y : S') (hy : aeval y (minpoly A pb.gen) = 0) :
     S →ₐ[A] S' :=
   { pb.basis.constr A fun i => y ^ (i : ℕ) with
-    map_one' := by convert pb.constr_pow_algebraMap hy 1 using 2 <;> rw [map_one]
-    map_zero' := by convert pb.constr_pow_algebraMap hy 0 using 2 <;> rw [map_zero]
+    map_one' := by convert! pb.constr_pow_algebraMap hy 1 using 2 <;> rw [map_one]
+    map_zero' := by convert! pb.constr_pow_algebraMap hy 0 using 2 <;> rw [map_zero]
     map_mul' := pb.constr_pow_mul hy
     commutes' := pb.constr_pow_algebraMap hy }
 
diff --git a/Mathlib/RingTheory/PowerSeries/Basic.lean b/Mathlib/RingTheory/PowerSeries/Basic.lean
index 881c5dbbeeab85..8c0bb47a5702c9 100644
--- a/Mathlib/RingTheory/PowerSeries/Basic.lean
+++ b/Mathlib/RingTheory/PowerSeries/Basic.lean
@@ -268,13 +268,13 @@ theorem smul_eq_C_mul (f : R⟦X⟧) (a : R) : a • f = C a * f := by
 @[simp]
 theorem coeff_succ_mul_X (n : ℕ) (φ : R⟦X⟧) : coeff (n + 1) (φ * X) = coeff n φ := by
   simp only [coeff, Finsupp.single_add]
-  convert φ.coeff_add_mul_monomial (single () n) (single () 1) _
+  convert! φ.coeff_add_mul_monomial (single () n) (single () 1) _
   rw [mul_one]
 
 @[simp]
 theorem coeff_succ_X_mul (n : ℕ) (φ : R⟦X⟧) : coeff (n + 1) (X * φ) = coeff n φ := by
   simp only [coeff, Finsupp.single_add, add_comm n 1]
-  convert φ.coeff_add_monomial_mul (single () 1) (single () n) _
+  convert! φ.coeff_add_monomial_mul (single () 1) (single () n) _
   rw [one_mul]
 
 theorem mul_X_cancel {φ ψ : R⟦X⟧} (h : φ * X = ψ * X) : φ = ψ := by
@@ -485,10 +485,10 @@ theorem map_eq_zero {R S : Type*} [DivisionSemiring R] [Semiring S] [Nontrivial
 
 theorem X_pow_dvd_iff {n : ℕ} {φ : R⟦X⟧} :
     (X : R⟦X⟧) ^ n ∣ φ ↔ ∀ m, m < n → coeff m φ = 0 := by
-  convert @MvPowerSeries.X_pow_dvd_iff Unit R _ () n φ
+  convert! @MvPowerSeries.X_pow_dvd_iff Unit R _ () n φ
   constructor <;> intro h m hm
   · rw [Finsupp.unique_single m]
-    convert h _ hm
+    convert! h _ hm
   · apply h
     simpa only [Finsupp.single_eq_same] using hm
 
@@ -595,7 +595,7 @@ theorem rescale_map {S : Type*} [CommSemiring S] (φ : R →+* S) (r : R) (f : R
 theorem rescale_algebraMap_map {A S : Type*} [CommSemiring A] [Algebra A R] [CommSemiring S]
     [Algebra A S] (φ : R →ₐ[A] S) (a : A) (f : R⟦X⟧) :
     rescale (algebraMap A S a) (f.map φ) = (rescale (algebraMap A R a) f).map φ := by
-  convert rescale_map (φ : R →+* S) _ _
+  convert! rescale_map (φ : R →+* S) _ _
   simp
 
 end CommSemiring
diff --git a/Mathlib/RingTheory/PowerSeries/Evaluation.lean b/Mathlib/RingTheory/PowerSeries/Evaluation.lean
index e2289d15a40ff7..c09f9380cc32d7 100644
--- a/Mathlib/RingTheory/PowerSeries/Evaluation.lean
+++ b/Mathlib/RingTheory/PowerSeries/Evaluation.lean
@@ -179,7 +179,7 @@ theorem hasSum_eval₂ (hφ : Continuous φ) (ha : HasEval a) (f : PowerSeries R
   have := MvPowerSeries.hasSum_eval₂ hφ (hasEval ha) f
   simp only [PowerSeries.eval₂]
   rw [← (Finsupp.single_injective ()).hasSum_iff] at this
-  · convert this; simp; congr
+  · convert! this; simp; congr
   · intro d hd
     exact False.elim (hd ⟨d (), by ext; simp⟩)
 
diff --git a/Mathlib/RingTheory/PowerSeries/Exp.lean b/Mathlib/RingTheory/PowerSeries/Exp.lean
index 1905c64609d6eb..f884c6491322a4 100644
--- a/Mathlib/RingTheory/PowerSeries/Exp.lean
+++ b/Mathlib/RingTheory/PowerSeries/Exp.lean
@@ -130,7 +130,7 @@ theorem exp_mul_exp_eq_exp_add [Algebra ℚ A] (a b : A) :
     a ^ x * b ^ (n - x) *
         (algebraMap ℚ A (1 / ↑x.factorial) * algebraMap ℚ A (1 / ↑(n - x).factorial)) =
       a ^ x * b ^ (n - x) * (↑(n.choose x) * (algebraMap ℚ A) (1 / ↑n.factorial))
-    by convert this using 1 <;> ring
+    by convert! this using 1 <;> ring
   congr 1
   rw [← map_natCast (algebraMap ℚ A) (n.choose x), ← map_mul, ← map_mul]
   refine RingHom.congr_arg _ ?_
@@ -147,7 +147,7 @@ theorem exp_mul_exp_eq_exp_add [Algebra ℚ A] (a b : A) :
 
 /-- Shows that $e^{x} * e^{-x} = 1$ -/
 theorem exp_mul_exp_neg_eq_one [Algebra ℚ A] : exp A * evalNegHom (exp A) = 1 := by
-  convert exp_mul_exp_eq_exp_add (1 : A) (-1) <;> simp
+  convert! exp_mul_exp_eq_exp_add (1 : A) (-1) <;> simp
 
 /-- Shows that $(e^{X})^k = e^{kX}$. -/
 theorem exp_pow_eq_rescale_exp [Algebra ℚ A] (k : ℕ) : exp A ^ k = rescale (k : A) (exp A) := by
diff --git a/Mathlib/RingTheory/PowerSeries/Order.lean b/Mathlib/RingTheory/PowerSeries/Order.lean
index 3081c69304e383..17000ebc4aebaf 100644
--- a/Mathlib/RingTheory/PowerSeries/Order.lean
+++ b/Mathlib/RingTheory/PowerSeries/Order.lean
@@ -116,7 +116,7 @@ theorem le_order (φ : R⟦X⟧) (n : ℕ∞) (h : ∀ i : ℕ, ↑i < n → coe
   cases n with
   | top => simpa using ext (by simpa using h)
   | coe n =>
-    convert nat_le_order φ n _
+    convert! nat_le_order φ n _
     simpa using h
 
 /-- The order of a formal power series is exactly `n` if the `n`th coefficient is nonzero,
diff --git a/Mathlib/RingTheory/PowerSeries/Substitution.lean b/Mathlib/RingTheory/PowerSeries/Substitution.lean
index b84d6cc55554e6..1e24436fb22b08 100644
--- a/Mathlib/RingTheory/PowerSeries/Substitution.lean
+++ b/Mathlib/RingTheory/PowerSeries/Substitution.lean
@@ -326,7 +326,7 @@ theorem le_weightedOrder_subst (w : τ → ℕ) (ha : HasSubst a) (f : PowerSeri
   simp only [ne_eq, Function.comp_const, le_iInf_iff]
   intro i hi
   trans i () * MvPowerSeries.weightedOrder w a
-  · exact mul_le_mul_left (f.order_le (i ()) (by delta PowerSeries.coeff; convert hi; aesop)) _
+  · exact mul_le_mul_left (f.order_le (i ()) (by delta PowerSeries.coeff; convert! hi; aesop)) _
   · simp [Finsupp.weight_apply, Finsupp.sum_fintype]
 
 theorem le_order_subst (a : MvPowerSeries τ S) (ha : HasSubst a) (f : PowerSeries R) :
diff --git a/Mathlib/RingTheory/PowerSeries/WeierstrassPreparation.lean b/Mathlib/RingTheory/PowerSeries/WeierstrassPreparation.lean
index 1c410073241183..a0dc12fa468ee4 100644
--- a/Mathlib/RingTheory/PowerSeries/WeierstrassPreparation.lean
+++ b/Mathlib/RingTheory/PowerSeries/WeierstrassPreparation.lean
@@ -478,8 +478,9 @@ noncomputable def _root_.Polynomial.IsDistinguishedAt.algEquivQuotient :
       rw [Eq.comm, Ideal.Quotient.mk_eq_mk_iff_sub_mem, Ideal.mem_span_singleton']
       exact ⟨f /ₘ g, by rw [Polynomial.modByMonic_eq_sub_mul_div]; ring⟩
     have h1 : g.degree = ((g : A⟦X⟧).map (Ideal.Quotient.mk I)).order.toNat := by
-      convert H.degree_eq_coe_lift_order_map g 1
-        (by rwa [constantCoeff_one, ← Ideal.ne_top_iff_one]) (by simp)
+      convert!
+        H.degree_eq_coe_lift_order_map g 1 (by rwa [constantCoeff_one, ← Ideal.ne_top_iff_one])
+          (by simp)
       exact (ENat.lift_eq_toNat_of_lt_top _).symm
     dsimp
     rw [Ideal.Quotient.mk_eq_mk_iff_sub_mem, Ideal.mem_span_singleton']
diff --git a/Mathlib/RingTheory/PrincipalIdealDomain.lean b/Mathlib/RingTheory/PrincipalIdealDomain.lean
index a34f34d6643154..f9191cf7a05d5e 100644
--- a/Mathlib/RingTheory/PrincipalIdealDomain.lean
+++ b/Mathlib/RingTheory/PrincipalIdealDomain.lean
@@ -94,7 +94,7 @@ theorem _root_.Ideal.span_singleton_generator (I : Ideal R) [I.IsPrincipal] :
 @[simp]
 theorem generator_mem (S : Submodule R M) [S.IsPrincipal] : generator S ∈ S := by
   have : generator S ∈ span R {generator S} := subset_span (mem_singleton _)
-  convert this
+  convert! this
   exact span_singleton_generator S |>.symm
 
 theorem mem_iff_eq_smul_generator (S : Submodule R M) [S.IsPrincipal] {x : M} :
diff --git a/Mathlib/RingTheory/QuasiFinite/Basic.lean b/Mathlib/RingTheory/QuasiFinite/Basic.lean
index 2dac2ef4953060..f66fbd78218bcc 100644
--- a/Mathlib/RingTheory/QuasiFinite/Basic.lean
+++ b/Mathlib/RingTheory/QuasiFinite/Basic.lean
@@ -85,7 +85,7 @@ lemma finite_primesOver [QuasiFinite R S] (I : Ideal R) : (I.primesOver S).Finit
   by_cases h : I.IsPrime
   · refine ((finite_comap_preimage_singleton ⟨I, h⟩).image PrimeSpectrum.asIdeal).subset ?_
     exact fun J hJ ↦ ⟨⟨_, hJ.1⟩, PrimeSpectrum.ext hJ.2.1.symm, rfl⟩
-  · convert Set.finite_empty
+  · convert! Set.finite_empty
     by_contra!
     obtain ⟨J, h₁, ⟨rfl⟩⟩ := this
     exact h inferInstance
@@ -326,7 +326,7 @@ lemma of_isIntegral_of_finiteType [Algebra.IsIntegral R S] [Algebra.FiniteType R
     obtain ⟨x, ⟨_, n, rfl⟩, rfl⟩ := IsLocalization.exists_mk'_eq (.powers s) x
     have : _root_.IsIntegral (Localization.Away sA) (algebraMap S T x) :=
       (Algebra.IsIntegral.isIntegral (R := R) x).algebraMap.tower_top
-    convert this.smul (Localization.Away.invSelf sA ^ n)
+    convert! this.smul (Localization.Away.invSelf sA ^ n)
     rw [IsLocalization.mk'_eq_iff_eq_mul]
     simp only [map_pow, Algebra.smul_mul_assoc]
     trans (sA • Localization.Away.invSelf sA) ^ n • (algebraMap S T x)
@@ -417,7 +417,7 @@ lemma QuasiFiniteAt.eq_of_le_of_under_eq {P Q : Ideal S} [P.IsPrime] [Q.IsPrime]
   have H := QuasiFinite.eq_of_le_of_under_eq (R := R)
     (Ideal.map (algebraMap S (Localization.AtPrime Q)) P) _
     (IsLocalRing.le_maximalIdeal_of_isPrime _) (by
-      convert h₂ <;> rw [← Ideal.under_under (B := S)]
+      convert! h₂ <;> rw [← Ideal.under_under (B := S)]
       · rw [IsLocalization.under_map_of_isPrime_disjoint Q.primeCompl _ ‹P.IsPrime› this]
       · rw [Localization.AtPrime.under_maximalIdeal])
   rw [← Localization.AtPrime.under_maximalIdeal (I := Q), ← H,
@@ -564,7 +564,7 @@ lemma _root_.Ideal.Fiber.lift_residueField_surjective [Algebra.FiniteType R S]
   refine .of_comp_left ?_
     (p.surjectiveOnStalks_residueField.baseChange'.residueFieldMap_bijective q q' hq').1
   rw [← AlgHom.coe_toRingHom, ← RingHom.coe_comp]
-  convert q'.algebraMap_residueField_surjective
+  convert! q'.algebraMap_residueField_surjective
   ext <;> simp [IsScalarTower.algebraMap_apply R S q.ResidueField]
 
 end QuasiFiniteAt
diff --git a/Mathlib/RingTheory/Radical/NatInt.lean b/Mathlib/RingTheory/Radical/NatInt.lean
index f57ac5eb13fe41..bb14afc78a1ea0 100644
--- a/Mathlib/RingTheory/Radical/NatInt.lean
+++ b/Mathlib/RingTheory/Radical/NatInt.lean
@@ -42,7 +42,7 @@ lemma UniqueFactorizationMonoid.primeFactors_eq_natPrimeFactors :
   ext n : 1
   rw [primeFactors, Nat.factors_eq, Nat.primeFactors]
   -- this convert is necessary because of the different DecidableEq instances
-  convert List.toFinset_coe _
+  convert! List.toFinset_coe _
 
 namespace Nat
 
diff --git a/Mathlib/RingTheory/RamificationInertia/Inertia.lean b/Mathlib/RingTheory/RamificationInertia/Inertia.lean
index ed00c8c3da8511..1832e595f5e45e 100644
--- a/Mathlib/RingTheory/RamificationInertia/Inertia.lean
+++ b/Mathlib/RingTheory/RamificationInertia/Inertia.lean
@@ -49,7 +49,7 @@ theorem inertiaDeg'_def [hq : q.IsPrime]
     [Algebra (Localization.AtPrime (q.under R)) (Localization.AtPrime q)]
     [Localization.AtPrime.IsLiesOverAlgebra (q.under R) q] :
     q.inertiaDeg' R = Module.finrank (q.under R).ResidueField q.ResidueField := by
-  convert dif_pos hq
+  convert! dif_pos hq
   simp [Algebra.algebra_ext_iff, Localization.AtPrime.IsLiesOverAlgebra.algebraMap_eq]
 
 theorem inertiaDeg'_of_not_isPrime (hq : ¬ q.IsPrime) : q.inertiaDeg' R = 0 :=
diff --git a/Mathlib/RingTheory/Regular/IsSMulRegular.lean b/Mathlib/RingTheory/Regular/IsSMulRegular.lean
index 14f7f6c78e1681..ce1fd7f8a89024 100644
--- a/Mathlib/RingTheory/Regular/IsSMulRegular.lean
+++ b/Mathlib/RingTheory/Regular/IsSMulRegular.lean
@@ -164,7 +164,7 @@ lemma isSMulRegular_of_ker_lsmul_eq_bot
 variable {N} in
 lemma smul_top_inf_eq_smul_of_isSMulRegular_on_quot :
     IsSMulRegular (M ⧸ N) r → r • ⊤ ⊓ N ≤ r • N := by
-  convert map_mono ∘ (isSMulRegular_on_quot_iff_lsmul_comap_le N r).mp using 2
+  convert! map_mono ∘ (isSMulRegular_on_quot_iff_lsmul_comap_le N r).mp using 2
   exact Eq.trans (congrArg (· ⊓ N) (map_top _)) (map_comap_eq _ _).symm
 
 -- Who knew this didn't rely on exactness at the right!?
diff --git a/Mathlib/RingTheory/Regular/LinearMap.lean b/Mathlib/RingTheory/Regular/LinearMap.lean
index 0bcb3f8785655a..9835b42022974a 100644
--- a/Mathlib/RingTheory/Regular/LinearMap.lean
+++ b/Mathlib/RingTheory/Regular/LinearMap.lean
@@ -81,7 +81,7 @@ lemma subsingleton_linearMap_iff [IsNoetherianRing R] [Module.Finite R M] [Modul
       __ := g
       map_smul' r x := by
         simp only [AddHom.toFun_eq_coe, coe_toAddHom, RingHom.id_apply]
-        convert g.map_smul (Ideal.Quotient.mk _ r) x }
+        convert! g.map_smul (Ideal.Quotient.mk _ r) x }
     let to_res : Nₚ →ₗ[Rₚ] p.ResidueField :=
       to_res'.comp ((maximalIdeal (Localization.AtPrime p)) • (⊤ : Submodule Rₚ Nₚ)).mkQ
     replace hx : maximalIdeal (Localization.AtPrime p) = (toSpanSingleton _ _ x).ker :=
diff --git a/Mathlib/RingTheory/Regular/RegularSequence.lean b/Mathlib/RingTheory/Regular/RegularSequence.lean
index 5b687feb3037a5..8b2559f6416cda 100644
--- a/Mathlib/RingTheory/Regular/RegularSequence.lean
+++ b/Mathlib/RingTheory/Regular/RegularSequence.lean
@@ -162,7 +162,7 @@ private lemma _root_.AddHom.map_smul_top_toAddSubgroup_of_surjective
       (Ideal.ofList bs • ⊤ : Submodule S M₂).toAddSubgroup := by
   induction h with
   | nil =>
-    convert AddSubgroup.map_bot f using 1 <;>
+    convert! AddSubgroup.map_bot f using 1 <;>
       rw [Ideal.ofList_nil, bot_smul, bot_toAddSubgroup]
   | @cons r s _ _ h _ ih =>
     conv => congr <;> rw [Ideal.ofList_cons, sup_smul, sup_toAddSubgroup,
diff --git a/Mathlib/RingTheory/RingHom/FinitePresentation.lean b/Mathlib/RingTheory/RingHom/FinitePresentation.lean
index 1e9b47c4270c24..a4e234ce2cce70 100644
--- a/Mathlib/RingTheory/RingHom/FinitePresentation.lean
+++ b/Mathlib/RingTheory/RingHom/FinitePresentation.lean
@@ -60,7 +60,7 @@ theorem finitePresentation_ofLocalizationSpanTarget :
   introv R hs H
   algebraize [f]
   replace H : ∀ r ∈ s, Algebra.FinitePresentation R (Localization.Away (r : S)) := by
-    intro r hr; simp_rw [RingHom.FinitePresentation] at H; convert H ⟨r, hr⟩; ext
+    intro r hr; simp_rw [RingHom.FinitePresentation] at H; convert! H ⟨r, hr⟩; ext
     simp_rw [Algebra.smul_def]; rfl
   exact Algebra.FinitePresentation.of_span_eq_top_target s hs H
 
diff --git a/Mathlib/RingTheory/RingHom/FiniteType.lean b/Mathlib/RingTheory/RingHom/FiniteType.lean
index b5f30344a7e5a5..2b94ddb5958f73 100644
--- a/Mathlib/RingTheory/RingHom/FiniteType.lean
+++ b/Mathlib/RingTheory/RingHom/FiniteType.lean
@@ -81,7 +81,7 @@ theorem finiteType_ofLocalizationSpanTarget : OfLocalizationSpanTarget @FiniteTy
   introv R hs H
   algebraize [f]
   replace H : ∀ r ∈ s, Algebra.FiniteType R (Localization.Away (r : S)) := by
-    intro r hr; simp_rw [RingHom.FiniteType] at H; convert H ⟨r, hr⟩; ext
+    intro r hr; simp_rw [RingHom.FiniteType] at H; convert! H ⟨r, hr⟩; ext
     simp_rw [Algebra.smul_def]; rfl
   exact Algebra.FiniteType.of_span_eq_top_target s hs H
 
diff --git a/Mathlib/RingTheory/RingHom/Flat.lean b/Mathlib/RingTheory/RingHom/Flat.lean
index a74bcf4c5242fd..721195176b5a4a 100644
--- a/Mathlib/RingTheory/RingHom/Flat.lean
+++ b/Mathlib/RingTheory/RingHom/Flat.lean
@@ -78,7 +78,7 @@ lemma ofLocalizationSpanTarget : OfLocalizationSpanTarget Flat := by
   refine Module.flat_of_isLocalized_span _ _ s hsp _
     (fun r ↦ Algebra.linearMap S <| Localization.Away r.1) ?_
   dsimp only [RingHom.Flat] at h
-  convert h; ext
+  convert! h; ext
   apply Algebra.smul_def
 
 /-- Flat is a local property of ring homomorphisms. -/
diff --git a/Mathlib/RingTheory/RingHom/Locally.lean b/Mathlib/RingTheory/RingHom/Locally.lean
index 60858fbbabb640..cc1a4f61fe5336 100644
--- a/Mathlib/RingTheory/RingHom/Locally.lean
+++ b/Mathlib/RingTheory/RingHom/Locally.lean
@@ -317,7 +317,7 @@ lemma locally_localizationAwayPreserves (hPl : LocalizationAwayPreserves P) :
     inferInstanceAs (IsLocalization.Away (rₐ a) (Sₐ a))
   haveI (a : s) : IsLocalization (Algebra.algebraMapSubmonoid (Localization.Away a.val)
     (Submonoid.map f (Submonoid.powers r))) (Sₐ a) := by
-    convert (inferInstance : IsLocalization.Away (rₐ a) (Sₐ a))
+    convert! (inferInstance : IsLocalization.Away (rₐ a) (Sₐ a))
     simp [rₐ, Algebra.algebraMapSubmonoid]
   have H (a : s) : Submonoid.powers (f r) ≤
       (Submonoid.powers (rₐ a)).comap (algebraMap S (Localization.Away a.val)) := by
@@ -329,8 +329,9 @@ lemma locally_localizationAwayPreserves (hPl : LocalizationAwayPreserves P) :
   refine ⟨s, fun a ↦ algebraMap S S' a.val, ?_, Sₐ,
       inferInstance, inferInstance, fun a ↦ ?_, fun a ↦ ?_⟩
   · rw [← Set.image_eq_range, ← Ideal.map_span, hsone, Ideal.map_top]
-  · convert IsLocalization.commutes (T := Sₐ a) (M₁ := (Submonoid.powers r).map f) (S₁ := S')
-      (S₂ := Localization.Away a.val) (M₂ := Submonoid.powers a.val)
+  · convert!
+    IsLocalization.commutes (T := Sₐ a) (M₁ := (Submonoid.powers r).map f) (S₁ := S') (S₂ :=
+      Localization.Away a.val) (M₂ := Submonoid.powers a.val)
     simp [Algebra.algebraMapSubmonoid]
   · rw [algebraMap_toAlgebra, IsLocalization.Away.map, IsLocalization.map_comp_map]
     exact hPl ((algebraMap _ (Localization.Away a.val)).comp f) r R' (Sₐ a) (hs _ a.2)
@@ -361,8 +362,9 @@ lemma locally_localizationPreserves (hPl : LocalizationPreserves P) :
   refine ⟨s, fun a ↦ algebraMap S S' a.val, ?_, Sₐ,
       inferInstance, inferInstance, fun a ↦ ?_, fun a ↦ ?_⟩
   · rw [← Set.image_eq_range, ← Ideal.map_span, hsone, Ideal.map_top]
-  · convert IsLocalization.commutes (T := Sₐ a) (M₁ := M.map f) (S₁ := S')
-      (S₂ := Localization.Away a.val) (M₂ := Submonoid.powers a.val)
+  · convert!
+    IsLocalization.commutes (T := Sₐ a) (M₁ := M.map f) (S₁ := S') (S₂ := Localization.Away a.val)
+      (M₂ := Submonoid.powers a.val)
     simp [Algebra.algebraMapSubmonoid]
   · rw [algebraMap_toAlgebra, IsLocalization.map_comp_map]
     apply hPl
diff --git a/Mathlib/RingTheory/RingHom/Smooth.lean b/Mathlib/RingTheory/RingHom/Smooth.lean
index 0ec5488e17835b..ca757ab5bba703 100644
--- a/Mathlib/RingTheory/RingHom/Smooth.lean
+++ b/Mathlib/RingTheory/RingHom/Smooth.lean
@@ -108,8 +108,9 @@ lemma stableUnderComposition : StableUnderComposition Smooth :=
   fun _ _ _ _ _ _ _ _ ↦ RingHom.Smooth.comp
 
 lemma isStableUnderBaseChange : IsStableUnderBaseChange Smooth := by
-  convert RingHom.FormallySmooth.isStableUnderBaseChange.and
-    RingHom.finitePresentation_isStableUnderBaseChange
+  convert!
+    RingHom.FormallySmooth.isStableUnderBaseChange.and
+      RingHom.finitePresentation_isStableUnderBaseChange
   rw [smooth_def]
 
 lemma holdsForLocalizationAway : HoldsForLocalizationAway Smooth := by
diff --git a/Mathlib/RingTheory/RingHom/StandardSmooth.lean b/Mathlib/RingTheory/RingHom/StandardSmooth.lean
index ec9fe9abc85930..72713dee616133 100644
--- a/Mathlib/RingTheory/RingHom/StandardSmooth.lean
+++ b/Mathlib/RingTheory/RingHom/StandardSmooth.lean
@@ -130,9 +130,9 @@ lemma isStandardSmooth_isStableUnderBaseChange :
   · exact isStandardSmooth_respectsIso
   · introv h
     replace h : Algebra.IsStandardSmooth R T := by
-      rw [RingHom.IsStandardSmooth] at h; convert h; ext; simp_rw [Algebra.smul_def]; rfl
+      rw [RingHom.IsStandardSmooth] at h; convert! h; ext; simp_rw [Algebra.smul_def]; rfl
     suffices Algebra.IsStandardSmooth S (S ⊗[R] T) by
-      rw [RingHom.IsStandardSmooth]; convert this; ext; simp_rw [Algebra.smul_def]; rfl
+      rw [RingHom.IsStandardSmooth]; convert! this; ext; simp_rw [Algebra.smul_def]; rfl
     infer_instance
 
 variable (n)
@@ -144,10 +144,10 @@ lemma isStandardSmoothOfRelativeDimension_isStableUnderBaseChange :
   · introv h
     replace h : Algebra.IsStandardSmoothOfRelativeDimension n R T := by
       rw [RingHom.IsStandardSmoothOfRelativeDimension] at h
-      convert h; ext; simp_rw [Algebra.smul_def]; rfl
+      convert! h; ext; simp_rw [Algebra.smul_def]; rfl
     suffices Algebra.IsStandardSmoothOfRelativeDimension n S (S ⊗[R] T) by
       rw [RingHom.IsStandardSmoothOfRelativeDimension]
-      convert this; ext; simp_rw [Algebra.smul_def]; rfl
+      convert! this; ext; simp_rw [Algebra.smul_def]; rfl
     infer_instance
 
 lemma IsStandardSmoothOfRelativeDimension.algebraMap_isLocalizationAway {Rᵣ : Type*} [CommRing Rᵣ]
@@ -223,7 +223,7 @@ theorem _root_.Algebra.IsStandardSmoothOfRelativeDimension.exists_etale_mvPolyno
     · simp [e]
   let P' : Algebra.PreSubmersivePresentation (MvPolynomial (Fin n) R) S σ σ :=
   { toGenerators := .ofSurjective (algebraMap _ _ <| e <| .X ·) <| by
-      convert P.algebraMap_surjective.comp e.surjective
+      convert! P.algebraMap_surjective.comp e.surjective
       exact congr($H)
     relation := e.symm ∘ P.relation
     span_range_relation_eq_ker := by
@@ -235,7 +235,7 @@ theorem _root_.Algebra.IsStandardSmoothOfRelativeDimension.exists_etale_mvPolyno
   let P' : Algebra.SubmersivePresentation (MvPolynomial (Fin n) R) S σ σ :=
   { __ := P'
     jacobian_isUnit := by
-      convert P.jacobian_isUnit using 1
+      convert! P.jacobian_isUnit using 1
       simp_rw [Algebra.PreSubmersivePresentation.jacobian_eq_jacobiMatrix_det, map_det]
       congr 1
       ext i j
diff --git a/Mathlib/RingTheory/RingHom/Unramified.lean b/Mathlib/RingTheory/RingHom/Unramified.lean
index 04b7e5a16f158a..bd73f63ea5d797 100644
--- a/Mathlib/RingTheory/RingHom/Unramified.lean
+++ b/Mathlib/RingTheory/RingHom/Unramified.lean
@@ -101,7 +101,7 @@ lemma ofLocalizationSpanTarget :
     simpa using (PrimeSpectrum.iSup_basicOpen_eq_top_iff'.mpr hs).ge
       (TopologicalSpace.Opens.mem_top x)
   refine Algebra.basicOpen_subset_unramifiedLocus_iff.mpr ?_ hrx
-  convert H ⟨r, hr⟩
+  convert! H ⟨r, hr⟩
   dsimp
   rw [← algebraMap_toAlgebra f, ← IsScalarTower.algebraMap_eq,
     formallyUnramified_algebraMap]
diff --git a/Mathlib/RingTheory/RingHomProperties.lean b/Mathlib/RingTheory/RingHomProperties.lean
index a5e6389153210b..ab50e47104778e 100644
--- a/Mathlib/RingTheory/RingHomProperties.lean
+++ b/Mathlib/RingTheory/RingHomProperties.lean
@@ -50,13 +50,13 @@ def RespectsIso : Prop :=
 theorem RespectsIso.cancel_left_isIso (hP : RespectsIso @P) {R S T : CommRingCat} (f : R ⟶ S)
     (g : S ⟶ T) [IsIso f] : P (g.hom.comp f.hom) ↔ P g.hom :=
   ⟨fun H => by
-    convert hP.2 (f ≫ g).hom (asIso f).symm.commRingCatIsoToRingEquiv H
+    convert! hP.2 (f ≫ g).hom (asIso f).symm.commRingCatIsoToRingEquiv H
     simp [← CommRingCat.hom_comp], hP.2 g.hom (asIso f).commRingCatIsoToRingEquiv⟩
 
 theorem RespectsIso.cancel_right_isIso (hP : RespectsIso @P) {R S T : CommRingCat} (f : R ⟶ S)
     (g : S ⟶ T) [IsIso g] : P (g.hom.comp f.hom) ↔ P f.hom :=
   ⟨fun H => by
-    convert hP.1 (f ≫ g).hom (asIso g).symm.commRingCatIsoToRingEquiv H
+    convert! hP.1 (f ≫ g).hom (asIso g).symm.commRingCatIsoToRingEquiv H
     simp [← CommRingCat.hom_comp],
    hP.1 f.hom (asIso g).commRingCatIsoToRingEquiv⟩
 
@@ -82,7 +82,7 @@ theorem RespectsIso.isLocalization_away_iff (hP : RingHom.RespectsIso @P) {R S :
                 (Submonoid.powers (f r)))) : Localization.Away r →+* Localization.Away (f r)).comp
                 (e₁ : R' →+* Localization.Away r))
   suffices e = IsLocalization.Away.map R' S' f r by
-    convert this
+    convert! this
   apply IsLocalization.ringHom_ext (Submonoid.powers r) _
   ext1 x
   dsimp [e, e₁, e₂, IsLocalization.Away.map]
@@ -148,7 +148,7 @@ theorem IsStableUnderBaseChange.mk (h₁ : RespectsIso @P)
     suffices e.toLinearMap.restrictScalars R = f'.toLinearMap from congr($this x)
     exact ext' fun x y ↦ by simp [e, f', IsBaseChange.equiv_tmul, Algebra.smul_def]
   have hemul (x y : _) : e (x * y) = e x * e y := by simp_rw [hef, map_mul]
-  convert h₁.1 _ { e with map_mul' := hemul } (h₂ H)
+  convert! h₁.1 _ { e with map_mul' := hemul } (h₂ H)
   ext x
   simp [e, h.symm.1.equiv_tmul, Algebra.smul_def]
 
diff --git a/Mathlib/RingTheory/RootsOfUnity/Complex.lean b/Mathlib/RingTheory/RootsOfUnity/Complex.lean
index b05a9d9b16e444..04e26b62c9db2b 100644
--- a/Mathlib/RingTheory/RootsOfUnity/Complex.lean
+++ b/Mathlib/RingTheory/RootsOfUnity/Complex.lean
@@ -54,26 +54,26 @@ theorem isPrimitiveRoot_exp_of_coprime (i n : ℕ) (h0 : n ≠ 0) (hi : i.Coprim
   isPrimitiveRoot_exp_of_isCoprime _ _ h0 hi.isCoprime
 
 theorem isPrimitiveRoot_exp_rat (q : ℚ) : IsPrimitiveRoot (exp (2 * π * I * q)) q.den := by
-  convert isPrimitiveRoot_exp_of_isCoprime _ _ q.den_nz <|
-    Int.isCoprime_iff_nat_coprime.mpr q.reduced
+  convert!
+    isPrimitiveRoot_exp_of_isCoprime _ _ q.den_nz <| Int.isCoprime_iff_nat_coprime.mpr q.reduced
   nth_rw 1 [← Rat.num_div_den q]
   simp
 
 theorem isPrimitiveRoot_exp_rat_of_even_num (q : ℚ) (h : Even q.num) :
     IsPrimitiveRoot (exp (π * I * q)) q.den := by
   have ⟨n, hn⟩ := even_iff_exists_two_nsmul _ |>.mp h
-  convert isPrimitiveRoot_exp_rat (n / q.den) using 1
+  convert! isPrimitiveRoot_exp_rat (n / q.den) using 1
   · nth_rw 1 [← q.num_div_den, hn, Int.nsmul_eq_mul]
     push_cast
     ring_nf
   · rw [← Int.cast_natCast, ← Rat.divInt_eq_div, ← Rat.mk_eq_divInt (nz := by simp)]
     apply Nat.Coprime.coprime_mul_left (k := 2)
-    convert q.reduced
+    convert! q.reduced
     grind
 
 theorem isPrimitiveRoot_exp_rat_of_odd_num (q : ℚ) (h : Odd q.num) :
     IsPrimitiveRoot (exp (π * I * q)) (2 * q.den) := by
-  convert isPrimitiveRoot_exp_rat (q / 2) using 1
+  convert! isPrimitiveRoot_exp_rat (q / 2) using 1
   · push_cast
     ring_nf
   · nth_rw 2 [← q.num_div_den]
@@ -163,10 +163,10 @@ theorem IsPrimitiveRoot.arg {n : ℕ} {ζ : ℂ} (h : IsPrimitiveRoot ζ n) (hn
     replace hin := Nat.isCoprime_iff_coprime.mpr hin
     split_ifs
     · exact hin
-    · convert hin.add_mul_left_left (-1) using 1
+    · convert! hin.add_mul_left_left (-1) using 1
       rw [mul_neg_one, sub_eq_add_neg]
   split_ifs with h₂
-  · convert Complex.arg_cos_add_sin_mul_I _
+  · convert! Complex.arg_cos_add_sin_mul_I _
     · push_cast; rfl
     · push_cast; rfl
     simp only [Int.cast_natCast, Set.mem_Ioc]
@@ -178,7 +178,7 @@ theorem IsPrimitiveRoot.arg {n : ℕ} {ζ : ℂ} (h : IsPrimitiveRoot ζ n) (hn
     exact mul_le_of_le_one_right Real.pi_pos.le
       ((div_le_iff₀' <| mod_cast pos_of_gt h).mpr <| mod_cast h₂)
   rw [← Complex.cos_sub_two_pi, ← Complex.sin_sub_two_pi]
-  convert Complex.arg_cos_add_sin_mul_I _
+  convert! Complex.arg_cos_add_sin_mul_I _
   · push_cast
     rw [← sub_one_mul, sub_div, div_self]
     exact mod_cast hn
diff --git a/Mathlib/RingTheory/RootsOfUnity/CyclotomicUnits.lean b/Mathlib/RingTheory/RootsOfUnity/CyclotomicUnits.lean
index 930b1dc7a3d7b9..04235887b02e7e 100644
--- a/Mathlib/RingTheory/RootsOfUnity/CyclotomicUnits.lean
+++ b/Mathlib/RingTheory/RootsOfUnity/CyclotomicUnits.lean
@@ -86,7 +86,7 @@ theorem associated_map_sub_one_map_sub_one {n : ℕ} [NeZero n] (hζ : IsPrimiti
 theorem geom_sum_isUnit (hζ : IsPrimitiveRoot ζ n) (hn : 2 ≤ n) (hj : j.Coprime n) :
     IsUnit (∑ i ∈ range j, ζ ^ i) := by
   obtain ⟨u, hu⟩ := hζ.associated_pow_sub_one_pow_of_coprime hj (coprime_one_left n)
-  convert u.isUnit
+  convert! u.isUnit
   apply mul_right_injective₀ (show 1 - ζ ≠ 0 by grind [sub_one_ne_zero])
   grind [mul_neg_geom_sum]
 
diff --git a/Mathlib/RingTheory/RootsOfUnity/Minpoly.lean b/Mathlib/RingTheory/RootsOfUnity/Minpoly.lean
index 66ac9aecc4f7ed..cee6484f6fc28b 100644
--- a/Mathlib/RingTheory/RootsOfUnity/Minpoly.lean
+++ b/Mathlib/RingTheory/RootsOfUnity/Minpoly.lean
@@ -61,8 +61,7 @@ theorem minpoly_dvd_x_pow_sub_one : minpoly ℤ μ ∣ X ^ n - 1 := by
 theorem separable_minpoly_mod {p : ℕ} [Fact p.Prime] (hdiv : ¬p ∣ n) :
     Separable (map (Int.castRingHom (ZMod p)) (minpoly ℤ μ)) := by
   have hdvd : map (Int.castRingHom (ZMod p)) (minpoly ℤ μ) ∣ X ^ n - 1 := by
-    convert _root_.map_dvd (mapRingHom (Int.castRingHom (ZMod p)))
-        (minpoly_dvd_x_pow_sub_one h)
+    convert! _root_.map_dvd (mapRingHom (Int.castRingHom (ZMod p))) (minpoly_dvd_x_pow_sub_one h)
     simp only [map_sub, map_pow, coe_mapRingHom, map_X, map_one]
   refine Separable.of_dvd (separable_X_pow_sub_C 1 ?_ one_ne_zero) hdvd
   by_contra hzero
@@ -199,7 +198,7 @@ theorem is_roots_of_minpoly [DecidableEq K] :
   intro x hx
   obtain ⟨m, _, hcop, rfl⟩ := (isPrimitiveRoot_iff h).1 ((mem_primitiveRoots hpos).1 hx)
   simp only [Multiset.mem_toFinset]
-  convert pow_isRoot_minpoly h hcop using 0
+  convert! pow_isRoot_minpoly h hcop using 0
   rw [← mem_roots]
   exact map_monic_ne_zero <| minpoly.monic <| isIntegral h hpos
 
diff --git a/Mathlib/RingTheory/RootsOfUnity/PrimitiveRoots.lean b/Mathlib/RingTheory/RootsOfUnity/PrimitiveRoots.lean
index 86ea593086cd71..590ce35e936184 100644
--- a/Mathlib/RingTheory/RootsOfUnity/PrimitiveRoots.lean
+++ b/Mathlib/RingTheory/RootsOfUnity/PrimitiveRoots.lean
@@ -228,9 +228,10 @@ theorem pow_mul_pow_lcm {ζ' : M} {k' : ℕ} (hζ : IsPrimitiveRoot ζ k) (hζ'
     IsPrimitiveRoot
       (ζ ^ (k / Nat.factorizationLCMLeft k k') * ζ' ^ (k' / Nat.factorizationLCMRight k k'))
       (Nat.lcm k k') := by
-  convert IsPrimitiveRoot.orderOf _
-  convert ((Commute.all ζ ζ').orderOf_mul_pow_eq_lcm
-    (by simpa [← hζ.eq_orderOf]) (by simpa [← hζ'.eq_orderOf])).symm using 2
+  convert! IsPrimitiveRoot.orderOf _
+  convert!
+    ((Commute.all ζ ζ').orderOf_mul_pow_eq_lcm (by simpa [← hζ.eq_orderOf])
+        (by simpa [← hζ'.eq_orderOf])).symm using 2
   all_goals simp [hζ.eq_orderOf, hζ'.eq_orderOf]
 
 theorem pow_of_dvd (h : IsPrimitiveRoot ζ k) {p : ℕ} (hp : p ≠ 0) (hdiv : p ∣ k) :
@@ -422,7 +423,7 @@ theorem eq_neg_one_of_two_right [NoZeroDivisors R] {ζ : R} (h : IsPrimitiveRoot
 
 theorem neg_one (p : ℕ) [Nontrivial R] [h : CharP R p] (hp : p ≠ 2) :
     IsPrimitiveRoot (-1 : R) 2 := by
-  convert IsPrimitiveRoot.orderOf (-1 : R)
+  convert! IsPrimitiveRoot.orderOf (-1 : R)
   rw [orderOf_neg_one, if_neg <| by rwa [ringChar.eq_iff.mpr h]]
 
 /-- If `1 < k` then `(∑ i ∈ range k, ζ ^ i) = 0`. -/
@@ -790,7 +791,7 @@ noncomputable def autToPow [NeZero n] : (S ≃ₐ[R] S) →* (ZMod n)ˣ :=
         replace h : μ' = μ' ^ h1.choose :=
           rootsOfUnity.coe_injective (by simpa only [rootsOfUnity.coe_pow] using h)
         nth_rw 1 [← pow_one μ'] at h
-        convert ho ▸ (ZMod.natCast_eq_natCast_iff ..).mpr (pow_eq_pow_iff_modEq.mp h).symm
+        convert! ho ▸ (ZMod.natCast_eq_natCast_iff ..).mpr (pow_eq_pow_iff_modEq.mp h).symm
         exact Nat.cast_one.symm
       map_mul' := by
         intro x y
@@ -804,7 +805,7 @@ noncomputable def autToPow [NeZero n] : (S ≃ₐ[R] S) →* (ZMod n)ˣ :=
         rw [← pow_mul] at hxy
         replace hxy : μ' ^ (hx'.choose * hy'.choose) = μ' ^ hxy'.choose :=
           rootsOfUnity.coe_injective (by simpa only [rootsOfUnity.coe_pow] using hxy)
-        convert ho ▸ (ZMod.natCast_eq_natCast_iff ..).mpr (pow_eq_pow_iff_modEq.mp hxy).symm
+        convert! ho ▸ (ZMod.natCast_eq_natCast_iff ..).mpr (pow_eq_pow_iff_modEq.mp hxy).symm
         exact (Nat.cast_mul ..).symm }
 
 -- We are not using @[simps] in `autToPow` to avoid a timeout.
diff --git a/Mathlib/RingTheory/SimpleModule/Basic.lean b/Mathlib/RingTheory/SimpleModule/Basic.lean
index 60aa65e964980a..9105cda93b03cf 100644
--- a/Mathlib/RingTheory/SimpleModule/Basic.lean
+++ b/Mathlib/RingTheory/SimpleModule/Basic.lean
@@ -170,7 +170,7 @@ theorem isSimpleModule_iff_quot_maximal :
     have ⟨m, hm⟩ := exists_ne (0 : M)
     exact ⟨_, ker_toSpanSingleton_isMaximal R hm,
       ⟨(LinearMap.quotKerEquivOfSurjective _ <| toSpanSingleton_surjective R hm).symm⟩⟩
-  · convert congr equiv; rwa [isSimpleModule_iff_isCoatom]
+  · convert! congr equiv; rwa [isSimpleModule_iff_isCoatom]
 
 /-- In general, the annihilator of a simple module is called a primitive ideal, and it is
 always a two-sided prime ideal, but mathlib's `Ideal.IsPrime` is not the correct definition
diff --git a/Mathlib/RingTheory/SimpleModule/Isotypic.lean b/Mathlib/RingTheory/SimpleModule/Isotypic.lean
index 66edd46678ae71..de62cf0c6ed01a 100644
--- a/Mathlib/RingTheory/SimpleModule/Isotypic.lean
+++ b/Mathlib/RingTheory/SimpleModule/Isotypic.lean
@@ -469,7 +469,7 @@ theorem isFullyInvariant_iff_sSup_isotypicComponents {m : Submodule R M} :
     m.IsFullyInvariant ↔ ∃ s ⊆ isotypicComponents R M, m = sSup s := by
   refine ⟨fun h ↦ ⟨OrderIso.setIsotypicComponents.symm ⟨m, h⟩, ⟨?_, ?_⟩⟩, ?_⟩
   · rintro _ ⟨c, _, rfl⟩; exact c.2
-  · convert Subtype.ext_iff.mp (OrderIso.setIsotypicComponents.right_inv ⟨m, h⟩).symm
+  · convert! Subtype.ext_iff.mp (OrderIso.setIsotypicComponents.right_inv ⟨m, h⟩).symm
     simp [sSup_image, OrderIso.setIsotypicComponents, OrderIso.symm]
   · rintro ⟨_, hs, rfl⟩
     exact (fullyInvariantSubmodule R M).sSupClosed fun _ h ↦ .of_mem_isotypicComponents (hs h)
diff --git a/Mathlib/RingTheory/Smooth/Basic.lean b/Mathlib/RingTheory/Smooth/Basic.lean
index c3fbf0a1423383..f64c55d51a53bf 100644
--- a/Mathlib/RingTheory/Smooth/Basic.lean
+++ b/Mathlib/RingTheory/Smooth/Basic.lean
@@ -293,8 +293,10 @@ theorem iff_split_injection
   rw [formallySmooth_iff, and_comm,
     Module.Projective.iff_split_of_projective (KaehlerDifferential.mapBaseChange R P A)
       (mapBaseChange_surjective R P A hf), ← kerCotangentToTensor_injective_iff hf]
-  convert (((exact_kerCotangentToTensor_mapBaseChange R _ _ hf).split_tfae'
-    (g := (KaehlerDifferential.mapBaseChange R P A).restrictScalars P)).out 0 1) using 2
+  convert!
+    (((exact_kerCotangentToTensor_mapBaseChange R _ _ hf).split_tfae' (g :=
+          (KaehlerDifferential.mapBaseChange R P A).restrictScalars P)).out
+      0 1) using 2
   · rw [← (LinearMap.extendScalarsOfSurjectiveEquiv hf).exists_congr_right]
     simp [LinearMap.ext_iff]
   · rw [and_iff_right (by exact mapBaseChange_surjective R P A hf)]
@@ -480,7 +482,7 @@ theorem of_isLocalization : FormallySmooth R Rₘ := by
   have : ∀ x : M, IsUnit (algebraMap R Q x) := by
     intro x
     apply (IsNilpotent.isUnit_quotient_mk_iff ⟨2, e⟩).mp
-    convert (IsLocalization.map_units Rₘ x).map f
+    convert! (IsLocalization.map_units Rₘ x).map f
     simp only [Ideal.Quotient.mk_algebraMap, AlgHom.commutes]
   let this : Rₘ →ₐ[R] Q :=
     { IsLocalization.lift this with commutes' := IsLocalization.lift_eq this }
diff --git a/Mathlib/RingTheory/Smooth/Fiber.lean b/Mathlib/RingTheory/Smooth/Fiber.lean
index d4ed4b2294e485..32fd91aa0ed1d4 100644
--- a/Mathlib/RingTheory/Smooth/Fiber.lean
+++ b/Mathlib/RingTheory/Smooth/Fiber.lean
@@ -125,7 +125,7 @@ private lemma FormallySmooth.of_formallySmooth_residueField_tensor_aux
     (AlgebraTensorModule.congr (.refl 𝓀[S] 𝓀[S]) e₁).restrictScalars S ≪≫ₗ
       (AlgebraTensorModule.cancelBaseChange P Pp Sp 𝓀[S] _).restrictScalars S
   -- It remains to check that the two maps are equal under the identifications above.
-  convert (eᵣ.injective.comp this).comp eₗ.symm.injective
+  convert! (eᵣ.injective.comp this).comp eₗ.symm.injective
   ext x
   dsimp
   induction x with
@@ -169,7 +169,7 @@ lemma FormallySmooth.of_formallySmooth_residueField_tensor (M : Submonoid P)
     simp [fP, IsLocalization.lift_mk', Units.mul_inv_eq_iff_eq_mul, IsUnit.liftRight]
   have hfP : (RingHom.ker fP).FG := by
     have := Algebra.FinitePresentation.ker_fG_of_surjective _ hf₀
-    convert this.map (algebraMap _ P')
+    convert! this.map (algebraMap _ P')
     refine le_antisymm ?_ (Ideal.map_le_iff_le_comap.mpr fun x hx ↦ by simp_all [fP])
     intro x hx
     obtain ⟨x, s, rfl⟩ := IsLocalization.exists_mk'_eq M' x
diff --git a/Mathlib/RingTheory/Smooth/Field.lean b/Mathlib/RingTheory/Smooth/Field.lean
index 2142daca169313..ca760870af23e6 100644
--- a/Mathlib/RingTheory/Smooth/Field.lean
+++ b/Mathlib/RingTheory/Smooth/Field.lean
@@ -54,5 +54,5 @@ instance (priority := low) Algebra.FormallySmooth.of_perfectField
     [PerfectField K] [Algebra.EssFiniteType K L] : Algebra.FormallySmooth K L := by
   obtain ⟨s, hs, H⟩ := exists_isTranscendenceBasis_and_isSeparable_of_perfectField K L
   have : Algebra.IsSeparable (↥(IntermediateField.adjoin K (Set.range ((↑) : s → L)))) L := by
-    convert H <;> simp
+    convert! H <;> simp
   exact .of_algebraicIndependent_of_isSeparable hs.1
diff --git a/Mathlib/RingTheory/Smooth/IntegralClosure.lean b/Mathlib/RingTheory/Smooth/IntegralClosure.lean
index e9b7e0852c36d9..667ceaa54a7970 100644
--- a/Mathlib/RingTheory/Smooth/IntegralClosure.lean
+++ b/Mathlib/RingTheory/Smooth/IntegralClosure.lean
@@ -44,8 +44,8 @@ def TensorProduct.toIntegralClosure
   | zero => simp
   | add x y _ _ => rw [map_add]; exact add_mem ‹_› ‹_›
   | tmul x y =>
-    convert ((y.2.map (Algebra.TensorProduct.includeRight
-      (R := R) (A := S))).tower_top (A := S)).smul x
+    convert!
+      ((y.2.map (Algebra.TensorProduct.includeRight (R := R) (A := S))).tower_top (A := S)).smul x
     simp [smul_tmul']
 
 lemma TensorProduct.toIntegralClosure_injective_of_flat [Module.Flat R S] :
@@ -65,7 +65,7 @@ lemma TensorProduct.toIntegralClosure_bijective_of_tower
       (Algebra.TensorProduct.congr (.refl (R := T) (A₁ := T)) (.ofBijective _ H)).trans <|
       (AlgEquiv.ofBijective _ H').trans <|
       (AlgEquiv.mapIntegralClosure (Algebra.TensorProduct.cancelBaseChange ..))
-  convert e.bijective
+  convert! e.bijective
   rw [← e.coe_algHom]
   congr 1
   ext; simp [e, toIntegralClosure]
@@ -109,8 +109,9 @@ lemma TensorProduct.toIntegralClosure_bijective_of_isLocalizationAway
     (fun r ↦ (Algebra.TensorProduct.map (Algebra.ofId _ _) (.id _ _)).toLinearMap)
     (fun r ↦ integralClosure (Sᵣ r) ((Sᵣ r) ⊗[R] B))
     (fun r ↦ (φ r).toLinearMap) fun r ↦ ?_
-  convert show Function.Bijective ((toIntegralClosure R (Sᵣ r) B).toLinearMap.restrictScalars S)
-    from H r using 1
+  convert!
+    show Function.Bijective ((toIntegralClosure R (Sᵣ r) B).toLinearMap.restrictScalars S) from
+      H r using 1
   congr!
   refine IsLocalizedModule.ext (.powers r.1) (Algebra.TensorProduct.map (Algebra.ofId S (Sᵣ r))
     (AlgHom.id R (integralClosure R B))).toLinearMap
@@ -162,16 +163,18 @@ lemma TensorProduct.toIntegralClosure_bijective_of_isLocalization
     AlgHom.codRestrict (Algebra.TensorProduct.includeRight.comp (integralClosure R B).val)
       ((integralClosure S (S ⊗[R] B)).restrictScalars R) fun ⟨x, hx⟩ ↦ by
     refine .of_comp (f := algebraMap R S) ?_
-    convert RingHom.IsIntegralElem.map hx
-      (Algebra.TensorProduct.includeRight : B →ₐ[R] S ⊗[R] B).toRingHom
+    convert!
+      RingHom.IsIntegralElem.map hx
+        (Algebra.TensorProduct.includeRight : B →ₐ[R] S ⊗[R] B).toRingHom
     simp [← IsScalarTower.algebraMap_eq]
   let := φ.toAlgebra
   have := IsScalarTower.of_algebraMap_eq' φ.comp_algebraMap.symm
   have : IsScalarTower (integralClosure R B) (integralClosure S (S ⊗[R] B)) (S ⊗[R] B) :=
     .of_algebraMap_eq' rfl
   have := IsLocalization.integralClosure (S := B) M (Rf := S) (Sf := S ⊗[R] B)
-  convert (IsLocalization.algEquiv (Algebra.algebraMapSubmonoid (integralClosure R B) M)
-    (S ⊗[R] integralClosure R B) (integralClosure S (S ⊗[R] B))).bijective
+  convert!
+    (IsLocalization.algEquiv (Algebra.algebraMapSubmonoid (integralClosure R B) M)
+        (S ⊗[R] integralClosure R B) (integralClosure S (S ⊗[R] B))).bijective
   rw [← AlgHom.coe_restrictScalars' R, ← AlgEquiv.coe_restrictScalars' R, ← AlgEquiv.coe_algHom]
   congr 1
   ext1
@@ -308,7 +311,7 @@ theorem mem_adjoin_map_integralClosure_of_isStandardEtale [Algebra.IsStandardEta
     have := 𝓟.monic_f.finite_adjoinRoot
     let e : AdjoinRoot 𝓟.f →ₐ[R] AdjoinRoot 𝓟'.f :=
       AdjoinRoot.mapAlgHom (Algebra.ofId _ _) _ _ (dvd_refl _)
-    convert (Algebra.IsIntegral.isIntegral (R := R) (AdjoinRoot.mk 𝓟.f 𝓟.g)).map e
+    convert! (Algebra.IsIntegral.isIntegral (R := R) (AdjoinRoot.mk 𝓟.f 𝓟.g)).map e
     have : (AdjoinRoot.mk 𝓟'.f).comp (mapRingHom (algebraMap R B)) =
         e.toRingHom.comp (AdjoinRoot.mk _) := by ext <;> simp [e]
     exact congr($this 𝓟.g)
@@ -323,7 +326,7 @@ theorem mem_adjoin_map_integralClosure_of_isStandardEtale [Algebra.IsStandardEta
   -- And `gᵏ • a` is still `R`-integral for `k` large enough.
   obtain ⟨k, hk⟩ : ∃ k, IsIntegral R (AdjoinRoot.mk 𝓟'.f 𝓟'.g ^ k * a) := by
     have H : ∀ k, e (1 ⊗ₜ (aeval 𝓟.x 𝓟.g ^ k)) = algebraMap _ _ (AdjoinRoot.mk 𝓟'.f 𝓟'.g ^ k) := by
-      intro k; convert congr($(heg 𝓟.g) ^ k) <;>
+      intro k; convert! congr($(heg 𝓟.g) ^ k) <;>
         simp [← map_pow, 𝓟', StandardEtalePresentation.baseChange]
     have := ((hx m).map (Algebra.TensorProduct.comm _ _ _).symm).map e
     simp only [Algebra.smul_def, Algebra.TensorProduct.algebraMap_apply, Algebra.algebraMap_self,
@@ -331,7 +334,7 @@ theorem mem_adjoin_map_integralClosure_of_isStandardEtale [Algebra.IsStandardEta
       AlgEquiv.apply_symm_apply] at this
     rw [H, pow_add, map_mul, mul_assoc, IsLocalization.mk'_spec'_mk, ← map_mul] at this
     obtain ⟨k, hk⟩ := IsLocalization.Away.exists_isIntegral_mul_of_isIntegral_algebraMap hfg this
-    refine ⟨k + n, by convert hk using 1; ring_nf⟩
+    refine ⟨k + n, by convert! hk using 1; ring_nf⟩
   -- We now use the key lemma `exists_derivative_mul_eq_and_isIntegral_coeff` to get a `y : B[X]`
   -- with `R`-integral coefficients such that `f' * gᵏ * a = y` in `S ⊗[R] B`.
   obtain ⟨y, hy, hRy⟩ := exists_derivative_mul_eq_and_isIntegral_coeff
@@ -343,7 +346,7 @@ theorem mem_adjoin_map_integralClosure_of_isStandardEtale [Algebra.IsStandardEta
   rw [← Subalgebra.mem_toSubmodule, ← Submodule.smul_mem_iff_of_isUnit _
     (𝓟.hasMap.isUnit_derivative_f.mul <| (𝓟.hasMap.2.pow k).mul (𝓟.hasMap.2.pow m))]
   convert_to eval₂ Algebra.TensorProduct.includeRight.toRingHom (𝓟.x ⊗ₜ[R] 1) y ∈ _ using 1
-  · convert congr(Algebra.TensorProduct.comm _ _ _ <| e.symm (algebraMap _ _ $hy))
+  · convert! congr(Algebra.TensorProduct.comm _ _ _ <| e.symm (algebraMap _ _ $hy))
     · apply (Algebra.TensorProduct.comm R B S).symm.injective
       apply e.injective
       simp only [Algebra.smul_def, Algebra.TensorProduct.algebraMap_apply, Algebra.algebraMap_self,
diff --git a/Mathlib/RingTheory/Smooth/NoetherianDescent.lean b/Mathlib/RingTheory/Smooth/NoetherianDescent.lean
index fadae704bac92d..864beb323b18d2 100644
--- a/Mathlib/RingTheory/Smooth/NoetherianDescent.lean
+++ b/Mathlib/RingTheory/Smooth/NoetherianDescent.lean
@@ -211,7 +211,7 @@ public theorem exists_subalgebra_fg [Smooth A B] :
     algHom_ext (by simp [hh])
   have (j : _) : Ideal.Quotient.mk (RingHom.ker f ^ 2) (aeval h (P.relation j)) = 0 := by
     suffices ho : σ (aeval P.val (P.relation j)) = 0 by
-      convert ho
+      convert! ho
       exact congr($hdiag _)
     simp
   simp_rw [Ideal.Quotient.eq_zero_iff_mem, hkerf,
diff --git a/Mathlib/RingTheory/Smooth/Pi.lean b/Mathlib/RingTheory/Smooth/Pi.lean
index abec27b5624ac3..a9154eef777ce2 100644
--- a/Mathlib/RingTheory/Smooth/Pi.lean
+++ b/Mathlib/RingTheory/Smooth/Pi.lean
@@ -37,7 +37,7 @@ theorem of_pi [FormallySmooth R (Π i, A i)] (i) :
         Ideal.Quotient.eq_zero_iff_mem]
       have : Pi.single i 1 - 1 ∈ RingHom.ker (Pi.evalAlgHom R A i).toRingHom := by
         simp [RingHom.mem_ker]
-      convert neg_mem (Ideal.pow_mem_pow this 2) using 1
+      convert! neg_mem (Ideal.pow_mem_pow this 2) using 1
       simp [pow_two, sub_mul, mul_sub, ← Pi.single_mul]
     · intro x y
       change Ideal.Quotient.mk _ _ = Ideal.Quotient.mk _ _ * Ideal.Quotient.mk _ _
diff --git a/Mathlib/RingTheory/Smooth/StandardSmoothCotangent.lean b/Mathlib/RingTheory/Smooth/StandardSmoothCotangent.lean
index 826a96cb9a3f91..c5dc4f58a4b88b 100644
--- a/Mathlib/RingTheory/Smooth/StandardSmoothCotangent.lean
+++ b/Mathlib/RingTheory/Smooth/StandardSmoothCotangent.lean
@@ -204,7 +204,7 @@ noncomputable def basisKaehlerOfIsCompl {κ : Type*} {f : κ → ι}
     simp [← hcompl.compl_eq]
   · simp only [sectionCotangent, LinearMap.coe_comp, Function.comp_assoc, LinearEquiv.coe_coe]
     apply LinearIndependent.map' _ _ P.cotangentEquiv.symm.ker
-    convert (Pi.basisFun S σ).linearIndependent
+    convert! (Pi.basisFun S σ).linearIndependent
     classical
     ext i j
     simp only [Function.comp_apply, Basis.repr_self, Finsupp.linearEquivFunOnFinite_apply,
diff --git a/Mathlib/RingTheory/Spectrum/Prime/Chevalley.lean b/Mathlib/RingTheory/Spectrum/Prime/Chevalley.lean
index bb6bfeb6a899f5..9297286dbe9a34 100644
--- a/Mathlib/RingTheory/Spectrum/Prime/Chevalley.lean
+++ b/Mathlib/RingTheory/Spectrum/Prime/Chevalley.lean
@@ -80,8 +80,9 @@ theorem isOpenMap_comap_algebraMap_tensorProduct_of_field
   obtain ⟨B', hB, f, rfl⟩ := exists_fg_and_mem_baseChange f
   have : Algebra.FinitePresentation K B' :=
     Algebra.FinitePresentation.of_finiteType.mp ⟨B'.fg_top.mpr hB⟩
-  convert isOpenMap_comap_of_hasGoingDown_of_finitePresentation (R := A) (S := A ⊗[K] B') _
-    (basicOpen f).isOpen using 1
+  convert!
+    isOpenMap_comap_of_hasGoingDown_of_finitePresentation (R := A) (S := A ⊗[K] B') _
+      (basicOpen f).isOpen using 1
   ext x
   rw [PrimeSpectrum.mem_image_comap_basicOpen, PrimeSpectrum.mem_image_comap_basicOpen,
     not_iff_not]
diff --git a/Mathlib/RingTheory/Spectrum/Prime/ChevalleyComplexity.lean b/Mathlib/RingTheory/Spectrum/Prime/ChevalleyComplexity.lean
index 72ba82d2dbecce..7dea7041a84cfa 100644
--- a/Mathlib/RingTheory/Spectrum/Prime/ChevalleyComplexity.lean
+++ b/Mathlib/RingTheory/Spectrum/Prime/ChevalleyComplexity.lean
@@ -203,7 +203,7 @@ private lemma induction_structure (n : ℕ)
     by_cases he0 : e = ⟨0⟩
     · exact he0 ▸ hP₁ R
     cases subsingleton_or_nontrivial R
-    · convert hP₁ R; ext; exact Subsingleton.elim _ _
+    · convert! hP₁ R; ext; exact Subsingleton.elim _ _
     simp only [InductionObj.ext_iff, funext_iff, Pi.zero_apply, not_forall] at he0
     -- Case I : The `e i ≠ 0` with minimal degree has invertible leading coefficient
     by_cases H : (∃ i, (e.1 i).Monic ∧ ∀ j, e.1 j ≠ 0 → (e.1 i).degree ≤ (e.1 j).degree)
@@ -357,7 +357,7 @@ private lemma induction_aux (R : Type*) [CommRing R] [Algebra R₀ R]
       _ = ⋃ C ∈ S₁ ∪ S₂, C.toSet := by
         simpa using (Set.biUnion_union (SetLike.coe S₁) S₂ _).symm
     congr 1
-    · convert congr(comap q₁.toRingHom '' $hT₁)
+    · convert! congr(comap q₁.toRingHom '' $hT₁)
       · dsimp only [e₁]
         rw [Set.preimage_diff, preimage_comap_zeroLocus, preimage_comap_zeroLocus,
           Set.image_singleton, Pi.smul_def, ← Set.smul_set_range, Set.range_comp]
@@ -384,7 +384,7 @@ private lemma induction_aux (R : Type*) [CommRing R] [Algebra R₀ R]
             ← pow_succ']
           simp only [← smul_eq_mul, ← Set.smul_set_range, ← Set.smul_set_singleton,
             zeroLocus_smul_of_isUnit ((isUnit_of_invertible (q₁ c)).pow _)]
-    · convert congr(comap q₂.toRingHom '' $hT₂)
+    · convert! congr(comap q₂.toRingHom '' $hT₂)
       · rw [Set.preimage_diff, preimage_comap_zeroLocus, preimage_comap_zeroLocus,
           Set.image_singleton, Set.range_comp, AlgHom.toRingHom_eq_coe]
       · rw [ConstructibleSetData.toSet, Set.image_iUnion₂]
@@ -436,7 +436,7 @@ private lemma statement : ∀ S : InductionObj R n, Statement R₀ R n S := by
   apply induction_structure
   · intro R _ R₀ _ _ f
     refine ⟨(Finset.range (f.natDegree + 2)).image fun j ↦ ⟨f.coeff j, 0, 0⟩, ?_, ?_⟩
-    · convert image_comap_C_basicOpen f
+    · convert! image_comap_C_basicOpen f
       · simp only [basicOpen_eq_zeroLocus_compl, Set.compl_eq_univ_diff]
         congr 1
         rw [← Set.univ_subset_iff]
@@ -535,7 +535,8 @@ private lemma statement : ∀ S : InductionObj R n, Statement R₀ R n S := by
       · intro l m
         rw [update_apply]
         split_ifs with hlj
-        · convert coeff_modByMonic_mem_pow_natDegree_mul _ _ _ (fun _ ↦ coeff_mem_coeffSubmodule)
+        · convert!
+          coeff_modByMonic_mem_pow_natDegree_mul _ _ _ (fun _ ↦ coeff_mem_coeffSubmodule)
             one_mem_coeffSubmodule _ (fun _ ↦ coeff_mem_coeffSubmodule) one_mem_coeffSubmodule _
           rw [← pow_succ, Polynomial.degree_eq_natDegree, WithBot.succ_natCast, Nat.cast_id]
           intro e
diff --git a/Mathlib/RingTheory/Spectrum/Prime/FreeLocus.lean b/Mathlib/RingTheory/Spectrum/Prime/FreeLocus.lean
index 0e2381c60c53ba..83c797ec9e1c5a 100644
--- a/Mathlib/RingTheory/Spectrum/Prime/FreeLocus.lean
+++ b/Mathlib/RingTheory/Spectrum/Prime/FreeLocus.lean
@@ -229,7 +229,7 @@ lemma isLocallyConstant_rankAtStalk [Module.FinitePresentation R M] [Module.Flat
     IsLocallyConstant (rankAtStalk (R := R) M) := by
   let e : freeLocus R M ≃ₜ PrimeSpectrum R :=
     (Homeomorph.setCongr freeLocus_eq_univ).trans (Homeomorph.Set.univ (PrimeSpectrum R))
-  convert isLocallyConstant_rankAtStalk_freeLocus.comp_continuous e.symm.continuous
+  convert! isLocallyConstant_rankAtStalk_freeLocus.comp_continuous e.symm.continuous
 
 @[simp]
 lemma rankAtStalk_eq_zero_of_subsingleton [Subsingleton M] :
diff --git a/Mathlib/RingTheory/Spectrum/Prime/Homeomorph.lean b/Mathlib/RingTheory/Spectrum/Prime/Homeomorph.lean
index a29c94296b7765..40f4e96484d595 100644
--- a/Mathlib/RingTheory/Spectrum/Prime/Homeomorph.lean
+++ b/Mathlib/RingTheory/Spectrum/Prime/Homeomorph.lean
@@ -66,7 +66,7 @@ lemma PrimeSpectrum.isHomeomorph_comap_of_isPurelyInseparable [IsPurelyInseparab
     IsHomeomorph (comap <| algebraMap R (R ⊗[k] K)) := by
   let q := ringExpChar k
   refine isHomeomorph_comap _ (IsPurelyInseparable.exists_pow_mem_range_tensorProduct) ?_
-  convert bot_le
+  convert! bot_le
   rw [← RingHom.injective_iff_ker_eq_bot]
   exact Algebra.TensorProduct.includeLeft_injective (S := R) (algebraMap k K).injective
 
diff --git a/Mathlib/RingTheory/Spectrum/Prime/RingHom.lean b/Mathlib/RingTheory/Spectrum/Prime/RingHom.lean
index acb9925c1b1633..3592cf2015d84b 100644
--- a/Mathlib/RingTheory/Spectrum/Prime/RingHom.lean
+++ b/Mathlib/RingTheory/Spectrum/Prime/RingHom.lean
@@ -192,7 +192,7 @@ lemma exists_comap_evalRingHom_eq
   let h₁ : Function.Surjective (Pi.evalRingHom R i) := RingHomSurjective.is_surjective
   have h₂ : RingHom.ker (Pi.evalRingHom R i) ≤ p.asIdeal := by
     intro x hx
-    convert p.asIdeal.mul_mem_left x hi
+    convert! p.asIdeal.mul_mem_left x hi
     ext j
     by_cases hj : i = j
     · subst hj; simpa [e]
@@ -258,7 +258,7 @@ alias image_specComap_zeroLocus_eq_zeroLocus_comap := image_comap_zeroLocus_eq_z
 theorem range_comap_of_surjective (hf : Surjective f) :
     Set.range (comap f) = zeroLocus (ker f) := by
   rw [← Set.image_univ]
-  convert image_comap_zeroLocus_eq_zeroLocus_comap _ _ hf _
+  convert! image_comap_zeroLocus_eq_zeroLocus_comap _ _ hf _
   rw [zeroLocus_bot]
 
 @[deprecated (since := "2025-12-10")]
diff --git a/Mathlib/RingTheory/Spectrum/Prime/Topology.lean b/Mathlib/RingTheory/Spectrum/Prime/Topology.lean
index 49a274abcc0296..55ca991f27bf7e 100644
--- a/Mathlib/RingTheory/Spectrum/Prime/Topology.lean
+++ b/Mathlib/RingTheory/Spectrum/Prime/Topology.lean
@@ -196,7 +196,7 @@ theorem vanishingIdeal_anti_mono_iff {s t : Set (PrimeSpectrum R)} (ht : IsClose
     s ⊆ t ↔ vanishingIdeal t ≤ vanishingIdeal s :=
   ⟨vanishingIdeal_anti_mono, fun h => by
     rw [← ht.closure_subset_iff, ← ht.closure_eq]
-    convert ← zeroLocus_anti_mono_ideal h <;> apply zeroLocus_vanishingIdeal_eq_closure⟩
+    convert! ← zeroLocus_anti_mono_ideal h <;> apply zeroLocus_vanishingIdeal_eq_closure⟩
 
 theorem vanishingIdeal_strict_anti_mono_iff {s t : Set (PrimeSpectrum R)} (hs : IsClosed s)
     (ht : IsClosed t) : s ⊂ t ↔ vanishingIdeal t < vanishingIdeal s := by
@@ -586,7 +586,7 @@ theorem eq_biUnion_of_isOpen {s : Set (PrimeSpectrum R)} (hs : IsOpen s) :
 
 theorem isBasis_basic_opens : TopologicalSpace.Opens.IsBasis (Set.range (@basicOpen R _)) := by
   unfold TopologicalSpace.Opens.IsBasis
-  convert isTopologicalBasis_basic_opens (R := R)
+  convert! isTopologicalBasis_basic_opens (R := R)
   rw [← Set.range_comp]
   rfl
 
@@ -925,7 +925,7 @@ lemma isQuotientMap_of_generalizingMap (h₂ : GeneralizingMap (comap f)) :
     fun hsc ↦ Set.image_preimage_eq s h₁ ▸ ?_⟩⟩
   apply isClosed_image_of_stableUnderSpecialization _ _ hsc
   rw [Set.image_preimage_eq s h₁, ← stableUnderGeneralization_compl_iff]
-  convert h₂.stableUnderGeneralization_image hsc.isOpen_compl.stableUnderGeneralization
+  convert! h₂.stableUnderGeneralization_image hsc.isOpen_compl.stableUnderGeneralization
   rw [← Set.preimage_compl, Set.image_preimage_eq _ h₁]
 
 end IsQuotientMap
@@ -959,7 +959,7 @@ lemma denseRange_comap_iff_minimalPrimes :
     have : I ∈ (RingHom.ker f).minimalPrimes := by
       rw [denseRange_comap_iff_ker_le_nilRadical] at H
       simp only [Set.mem_setOf, Ideal.IsMinimalPrime] at hI ⊢
-      convert hI using 2 with p
+      convert! hI using 2 with p
       exact ⟨fun h ↦ ⟨h.1, bot_le⟩, fun h ↦ ⟨h.1, H.trans (h.1.radical_le_iff.mpr bot_le)⟩⟩
     obtain ⟨p, hp, _, rfl⟩ := Ideal.exists_comap_eq_of_mem_minimalPrimes f (I := ⊥) I this
     exact ⟨⟨p, hp⟩, rfl⟩
diff --git a/Mathlib/RingTheory/SurjectiveOnStalks.lean b/Mathlib/RingTheory/SurjectiveOnStalks.lean
index 8467d695ce4e59..7c1ee5de1a3fbb 100644
--- a/Mathlib/RingTheory/SurjectiveOnStalks.lean
+++ b/Mathlib/RingTheory/SurjectiveOnStalks.lean
@@ -62,7 +62,7 @@ lemma surjective_localRingHom_iff (P : Ideal S) [P.IsPrime] :
         IsLocalization.mk'_eq_iff_eq, IsLocalization.eq_iff_exists P.primeCompl]
       refine ⟨⟨yc, hyc⟩ * ⟨yt, hyt⟩, ?_⟩
       simp only [Submonoid.coe_mul]
-      convert congr($(ey.symm) * $(et)) using 1 <;> ring
+      convert! congr($(ey.symm) * $(et)) using 1 <;> ring
 
 lemma surjectiveOnStalks_iff_forall_ideal :
     f.SurjectiveOnStalks ↔
@@ -189,8 +189,11 @@ lemma SurjectiveOnStalks.baseChange
 lemma SurjectiveOnStalks.baseChange' [Algebra R T] [Algebra R S]
     (hf : (algebraMap R S).SurjectiveOnStalks) :
     (Algebra.TensorProduct.includeRight (R := R) (A := S) (B := T)).SurjectiveOnStalks := by
-  convert (surjectiveOnStalks_of_surjective (Algebra.TensorProduct.comm R T S).surjective).comp
-    (hf.baseChange (S := T))
+  convert!
+    (surjectiveOnStalks_of_surjective (Algebra.TensorProduct.comm R T S).surjective).comp
+      (hf.baseChange (S := T))
+        -- Subsumed by `RingHom.SurjectiveOnStalks.tensorProductMap`.
+
 
 -- Subsumed by `RingHom.SurjectiveOnStalks.tensorProductMap`.
 private lemma SurjectiveOnStalks.tensorProductMap_id
@@ -211,10 +214,11 @@ lemma SurjectiveOnStalks.tensorProductMap
     [Algebra R S] [Algebra R T] [Algebra R S'] [Algebra R T']
     {f : S →ₐ[R] S'} (Hf : f.SurjectiveOnStalks) {g : T →ₐ[R] T'} (Hg : g.SurjectiveOnStalks) :
     (Algebra.TensorProduct.map f g).SurjectiveOnStalks := by
-  convert RingHom.SurjectiveOnStalks.tensorProductMap_id (T := T') Hf |>.comp <|
-    (Algebra.TensorProduct.comm _ _ _).toRingEquiv.surjectiveOnStalks |>.comp <|
-    RingHom.SurjectiveOnStalks.tensorProductMap_id (T := S) Hg |>.comp <|
-    (Algebra.TensorProduct.comm _ _ _).toRingEquiv.surjectiveOnStalks
+  convert!
+    RingHom.SurjectiveOnStalks.tensorProductMap_id (T := T') Hf |>.comp <|
+      (Algebra.TensorProduct.comm _ _ _).toRingEquiv.surjectiveOnStalks |>.comp <|
+        RingHom.SurjectiveOnStalks.tensorProductMap_id (T := S) Hg |>.comp <|
+          (Algebra.TensorProduct.comm _ _ _).toRingEquiv.surjectiveOnStalks
   simp only [AlgHom.toRingHom_eq_coe, RingEquiv.toRingHom_eq_coe,
     AlgEquiv.toRingEquiv_toRingHom, ← AlgEquiv.toAlgHom_toRingHom, ← AlgHom.comp_toRingHom]
   congr
diff --git a/Mathlib/RingTheory/TensorProduct/Finite.lean b/Mathlib/RingTheory/TensorProduct/Finite.lean
index 5af22a0009c55b..9a44ca5362dbec 100644
--- a/Mathlib/RingTheory/TensorProduct/Finite.lean
+++ b/Mathlib/RingTheory/TensorProduct/Finite.lean
@@ -176,10 +176,11 @@ lemma RingHom.Finite.tensorProductMap
     [Algebra R S] [Algebra R T] [Algebra R S'] [Algebra R T']
     {f : S →ₐ[R] S'} (Hf : f.Finite) {g : T →ₐ[R] T'} (Hg : g.Finite) :
     (Algebra.TensorProduct.map f g).toRingHom.Finite := by
-  convert RingHom.Finite.tensorProductMap_id (T := T') Hf |>.comp <|
-    (Algebra.TensorProduct.comm _ _ _).toRingEquiv.finite |>.comp <|
-    RingHom.Finite.tensorProductMap_id (T := S) Hg |>.comp <|
-    (Algebra.TensorProduct.comm _ _ _).toRingEquiv.finite
+  convert!
+    RingHom.Finite.tensorProductMap_id (T := T') Hf |>.comp <|
+      (Algebra.TensorProduct.comm _ _ _).toRingEquiv.finite |>.comp <|
+        RingHom.Finite.tensorProductMap_id (T := S) Hg |>.comp <|
+          (Algebra.TensorProduct.comm _ _ _).toRingEquiv.finite
   simp only [AlgHom.toRingHom_eq_coe, RingEquiv.toRingHom_eq_coe,
     AlgEquiv.toRingEquiv_toRingHom, ← AlgEquiv.toAlgHom_toRingHom, ← AlgHom.comp_toRingHom]
   congr
diff --git a/Mathlib/RingTheory/Trace/Defs.lean b/Mathlib/RingTheory/Trace/Defs.lean
index b0df6d1c0df6fd..20bbbbb9f42612 100644
--- a/Mathlib/RingTheory/Trace/Defs.lean
+++ b/Mathlib/RingTheory/Trace/Defs.lean
@@ -93,7 +93,7 @@ theorem trace_algebraMap_of_basis (b : Basis ι R S) (x : R) :
     trace R S (algebraMap R S x) = Fintype.card ι • x := by
   haveI := Classical.decEq ι
   rw [trace_apply, LinearMap.trace_eq_matrix_trace R b, Matrix.trace]
-  convert Finset.sum_const x
+  convert! Finset.sum_const x
   simp [-coe_lmul_eq_mul]
 
 
diff --git a/Mathlib/RingTheory/TwoSidedIdeal/Basic.lean b/Mathlib/RingTheory/TwoSidedIdeal/Basic.lean
index 76662f764e151d..8419925a8c28a2 100644
--- a/Mathlib/RingTheory/TwoSidedIdeal/Basic.lean
+++ b/Mathlib/RingTheory/TwoSidedIdeal/Basic.lean
@@ -61,10 +61,10 @@ instance setLike : SetLike (TwoSidedIdeal R) R where
     refine RingCon.ext fun a b ↦ ⟨fun H ↦ ?_, fun H ↦ ?_⟩
     · have H' : a - b ∈ {x | t₁ x 0} := sub_self b ▸ t₁.sub H (t₁.refl b)
       rw [h] at H'
-      convert t₂.add H' (t₂.refl b) using 1 <;> abel
+      convert! t₂.add H' (t₂.refl b) using 1 <;> abel
     · have H' : a - b ∈ {x | t₂ x 0} := sub_self b ▸ t₂.sub H (t₂.refl b)
       rw [← h] at H'
-      convert t₁.add H' (t₁.refl b) using 1 <;> abel
+      convert! t₁.add H' (t₁.refl b) using 1 <;> abel
 
 instance : PartialOrder (TwoSidedIdeal R) := .ofSetLike (TwoSidedIdeal R) R
 
@@ -79,8 +79,8 @@ lemma coe_mk {c : RingCon R} : (mk c : Set R) = {x | c x 0} := rfl
 lemma rel_iff (x y : R) : I.ringCon x y ↔ x - y ∈ I := by
   rw [mem_iff]
   constructor
-  · intro h; convert I.ringCon.sub h (I.ringCon.refl y); abel
-  · intro h; convert I.ringCon.add h (I.ringCon.refl y) <;> abel
+  · intro h; convert! I.ringCon.sub h (I.ringCon.refl y); abel
+  · intro h; convert! I.ringCon.add h (I.ringCon.refl y) <;> abel
 
 /--
 the coercion from two-sided-ideals to sets is an order embedding
diff --git a/Mathlib/RingTheory/TwoSidedIdeal/Lattice.lean b/Mathlib/RingTheory/TwoSidedIdeal/Lattice.lean
index 92c59e730f9879..11406844dcf195 100644
--- a/Mathlib/RingTheory/TwoSidedIdeal/Lattice.lean
+++ b/Mathlib/RingTheory/TwoSidedIdeal/Lattice.lean
@@ -52,7 +52,7 @@ lemma mem_sup {I J : TwoSidedIdeal R} {x : R} :
       (by rintro r _ ⟨x, ⟨hx, ⟨y, ⟨hy, rfl⟩⟩⟩⟩
           exact ⟨_, ⟨mul_mem_right _ _ _ hx, ⟨_, ⟨mul_mem_right _ _ _ hy, add_mul _ _ _ |>.symm⟩⟩⟩⟩)
     suffices (I.ringCon ⊔ J.ringCon) ≤ s.ringCon by
-      intro h; convert this h; rw [rel_iff, sub_zero, mem_mk']; rfl
+      intro h; convert! this h; rw [rel_iff, sub_zero, mem_mk']; rfl
     refine sup_le (fun x y h => ?_) (fun x y h => ?_) <;> rw [rel_iff] at h ⊢ <;> rw [mem_mk']
     exacts [⟨_, ⟨h, ⟨0, ⟨zero_mem _, add_zero _⟩⟩⟩⟩, ⟨0, ⟨zero_mem _, ⟨_, ⟨h, zero_add _⟩⟩⟩⟩]
   · rintro ⟨y, ⟨hy, ⟨z, ⟨hz, rfl⟩⟩⟩⟩; exact add_mem _ (mem_sup_left hy) (mem_sup_right hz)
diff --git a/Mathlib/RingTheory/UniqueFactorizationDomain/Basic.lean b/Mathlib/RingTheory/UniqueFactorizationDomain/Basic.lean
index 87469bc1bb6ccb..a1ad2b43565bc1 100644
--- a/Mathlib/RingTheory/UniqueFactorizationDomain/Basic.lean
+++ b/Mathlib/RingTheory/UniqueFactorizationDomain/Basic.lean
@@ -58,7 +58,7 @@ theorem WfDvdMonoid.of_wellFoundedLT_associates [CommMonoidWithZero α] [IsCance
     (h : WellFoundedLT (Associates α)) : WfDvdMonoid α :=
   WfDvdMonoid.of_wfDvdMonoid_associates
     ⟨by
-      convert h.wf
+      convert! h.wf
       ext
       exact Associates.dvdNotUnit_iff_lt⟩
 
@@ -345,7 +345,7 @@ theorem WfDvdMonoid.of_exists_prime_factors : WfDvdMonoid α :=
           _ = Multiset.card (Classical.choose (pf b h)) :=
             Multiset.card_eq_card_of_rel
             (prime_factors_unique ?_ (Classical.choose_spec (pf _ h)).1 ?_)
-        · convert (Classical.choose_spec (pf c cne0)).2.symm
+        · convert! (Classical.choose_spec (pf c cne0)).2.symm
           rw [con, Multiset.prod_zero]
         · intro x hadd
           rw [Multiset.mem_add] at hadd
@@ -390,7 +390,7 @@ theorem MulEquiv.uniqueFactorizationMonoid (e : α ≃* β) (hα : UniqueFactori
   obtain ⟨w, hp, u, h⟩ :=
     hα (e.symm a) fun h =>
       ha <| by
-        convert ← map_zero e
+        convert! ← map_zero e
         simp [← h]
   exact
     ⟨w.map e, fun b hb =>
@@ -418,7 +418,7 @@ theorem of_existsUnique_irreducible_factors [CommMonoidWithZero α] [IsCancelMul
     UniqueFactorizationMonoid α :=
   UniqueFactorizationMonoid.of_exists_prime_factors
     (by
-      convert eif using 7
+      convert! eif using 7
       simp_rw [irreducible_iff_prime_of_existsUnique_irreducible_factors eif uif])
 
 variable {R : Type*} [CommMonoidWithZero R] [UniqueFactorizationMonoid R]
diff --git a/Mathlib/RingTheory/UniqueFactorizationDomain/FactorSet.lean b/Mathlib/RingTheory/UniqueFactorizationDomain/FactorSet.lean
index e1a9d462999c1f..ee203370d34d5e 100644
--- a/Mathlib/RingTheory/UniqueFactorizationDomain/FactorSet.lean
+++ b/Mathlib/RingTheory/UniqueFactorizationDomain/FactorSet.lean
@@ -244,7 +244,7 @@ theorem prod_factors [Nontrivial α] (s : FactorSet α) : s.prod.factors = s :=
 @[nontriviality]
 theorem factors_subsingleton [Subsingleton α] {a : Associates α} : a.factors = ⊤ := by
   have : Subsingleton (Associates α) := inferInstance
-  convert factors_zero
+  convert! factors_zero
 
 theorem factors_eq_top_iff_zero {a : Associates α} : a.factors = ⊤ ↔ a = 0 := by
   nontriviality α
@@ -581,7 +581,7 @@ theorem eq_pow_count_factors_of_dvd_pow {p a : Associates α}
   apply eq_of_eq_counts ha (pow_ne_zero _ hp.ne_zero)
   have eq_zero_of_ne : ∀ q : Associates α, Irreducible q → q ≠ p → _ = 0 := fun q hq h' =>
     Nat.eq_zero_of_le_zero <| by
-      convert count_le_count_of_le hph hq h
+      convert! count_le_count_of_le hph hq h
       symm
       rw [count_pow hp.ne_zero hq, count_eq_zero_of_ne hq hp h', mul_zero]
   intro q hq
@@ -601,7 +601,7 @@ theorem count_factors_eq_find_of_dvd_pow {a p : Associates α}
   · have hph := pow_ne_zero (@Nat.find (fun n => a ∣ p ^ n) _ ⟨n, h⟩) hp.ne_zero
     rcases subsingleton_or_nontrivial α with hα | hα
     · simp [eq_iff_true_of_subsingleton] at hph
-    convert count_le_count_of_le hph hp (@Nat.find_spec (fun n => a ∣ p ^ n) _ ⟨n, h⟩)
+    convert! count_le_count_of_le hph hp (@Nat.find_spec (fun n => a ∣ p ^ n) _ ⟨n, h⟩)
     rw [count_pow hp.ne_zero hp, count_self hp, mul_one]
 
 end count
diff --git a/Mathlib/RingTheory/UniqueFactorizationDomain/Ideal.lean b/Mathlib/RingTheory/UniqueFactorizationDomain/Ideal.lean
index 3fdc18c86c5d45..4a392091aa3b51 100644
--- a/Mathlib/RingTheory/UniqueFactorizationDomain/Ideal.lean
+++ b/Mathlib/RingTheory/UniqueFactorizationDomain/Ideal.lean
@@ -44,7 +44,7 @@ lemma Ideal.setOf_isPrincipal_wellFoundedOn_gt [CommSemiring α] [WfDvdMonoid α
     ext
     simp [Submodule.isPrincipal_iff, eq_comm]
   rw [this, Set.wellFoundedOn_image, Set.wellFoundedOn_univ]
-  convert wellFounded_dvdNotUnit (α := α)
+  convert! wellFounded_dvdNotUnit (α := α)
   ext
   exact Ideal.span_singleton_lt_span_singleton
 
@@ -55,7 +55,7 @@ lemma WfDvdMonoid.of_setOf_isPrincipal_wellFoundedOn_gt [CommSemiring α] [IsDom
     WfDvdMonoid α := by
   have : WellFounded (α := {I : Ideal α // I.IsPrincipal}) (· > ·) := h
   constructor
-  convert InvImage.wf (fun a => ⟨Ideal.span ({a} : Set α), _, rfl⟩) this
+  convert! InvImage.wf (fun a => ⟨Ideal.span ({ a } : Set α), _, rfl⟩) this
   ext
   exact Ideal.span_singleton_lt_span_singleton.symm
 
diff --git a/Mathlib/RingTheory/UniqueFactorizationDomain/Multiplicative.lean b/Mathlib/RingTheory/UniqueFactorizationDomain/Multiplicative.lean
index e1510b203ba187..19dca9ea9ba773 100644
--- a/Mathlib/RingTheory/UniqueFactorizationDomain/Multiplicative.lean
+++ b/Mathlib/RingTheory/UniqueFactorizationDomain/Multiplicative.lean
@@ -45,7 +45,7 @@ theorem prime_pow_coprime_prod_of_coprime_insert [DecidableEq α] {s : Finset α
   obtain ⟨q, q_mem, rfl⟩ := Multiset.mem_map.mp q_mem'
   replace hdq := hd.dvd_of_dvd_pow hdq
   have : p ∣ q := dvd_trans (hd.irreducible.dvd_symm hp.irreducible hdp) hdq
-  convert q_mem using 0
+  convert! q_mem using 0
   rw [Finset.mem_val,
     is_coprime _ (Finset.mem_insert_self p s) _ (Finset.mem_insert_of_mem q_mem) this]
 
diff --git a/Mathlib/RingTheory/UniqueFactorizationDomain/Multiplicity.lean b/Mathlib/RingTheory/UniqueFactorizationDomain/Multiplicity.lean
index ce1f6523fc9704..0efb9ee6f31af1 100644
--- a/Mathlib/RingTheory/UniqueFactorizationDomain/Multiplicity.lean
+++ b/Mathlib/RingTheory/UniqueFactorizationDomain/Multiplicity.lean
@@ -118,7 +118,7 @@ theorem count_normalizedFactors_eq {p x : R} (hp : Irreducible p) (hnorm : norma
   by_cases hx0 : x = 0
   · simp [hx0] at hlt
   apply Nat.cast_injective (R := ℕ∞)
-  convert (emultiplicity_eq_count_normalizedFactors hp hx0).symm
+  convert! (emultiplicity_eq_count_normalizedFactors hp hx0).symm
   · exact hnorm.symm
   exact (emultiplicity_eq_coe.mpr ⟨hle, hlt⟩).symm
 
diff --git a/Mathlib/RingTheory/UniqueFactorizationDomain/NormalizedFactors.lean b/Mathlib/RingTheory/UniqueFactorizationDomain/NormalizedFactors.lean
index 0cfdef04a98dd6..d02f959aebbcb2 100644
--- a/Mathlib/RingTheory/UniqueFactorizationDomain/NormalizedFactors.lean
+++ b/Mathlib/RingTheory/UniqueFactorizationDomain/NormalizedFactors.lean
@@ -41,7 +41,7 @@ if `M` has a trivial group of units. -/
 theorem factors_eq_normalizedFactors {M : Type*} [CommMonoidWithZero M]
     [UniqueFactorizationMonoid M] [Subsingleton Mˣ] (x : M) : factors x = normalizedFactors x := by
   unfold normalizedFactors
-  convert (Multiset.map_id (factors x)).symm
+  convert! (Multiset.map_id (factors x)).symm
   ext p
   exact normalize_eq p
 
@@ -87,15 +87,16 @@ theorem normalizedFactors_irreducible {a : α} (ha : Irreducible a) :
   have p_mem : p ∈ normalizedFactors a := by
     rw [hp]
     exact Multiset.mem_singleton_self _
-  convert hp
+  convert! hp
   rwa [← normalize_normalized_factor p p_mem, normalize_eq_normalize_iff, dvd_dvd_iff_associated]
 
 theorem normalizedFactors_eq_of_dvd (a : α) :
     ∀ᵉ (p ∈ normalizedFactors a) (q ∈ normalizedFactors a), p ∣ q → p = q := by
   intro p hp q hq hdvd
-  convert normalize_eq_normalize hdvd
-          ((prime_of_normalized_factor _ hp).irreducible.dvd_symm
-            (prime_of_normalized_factor _ hq).irreducible hdvd) <;>
+  convert!
+    normalize_eq_normalize hdvd
+      ((prime_of_normalized_factor _ hp).irreducible.dvd_symm
+        (prime_of_normalized_factor _ hq).irreducible hdvd) <;>
     apply (normalize_normalized_factor _ ‹_›).symm
 
 theorem exists_mem_normalizedFactors_of_dvd {a p : α} (ha0 : a ≠ 0) (hp : Irreducible p) :
@@ -325,7 +326,7 @@ theorem normalizedFactors_multiset_prod (s : Multiset α) (hs : 0 ∉ s) :
   · obtain rfl : s = 0 := by
       apply Multiset.eq_zero_of_forall_notMem
       intro _
-      convert hs
+      convert! hs
     simp
   induction s using Multiset.induction with
   | empty => simp
diff --git a/Mathlib/RingTheory/Unramified/LocalStructure.lean b/Mathlib/RingTheory/Unramified/LocalStructure.lean
index 4cacf107d92c77..18a73ec56aae7e 100644
--- a/Mathlib/RingTheory/Unramified/LocalStructure.lean
+++ b/Mathlib/RingTheory/Unramified/LocalStructure.lean
@@ -90,7 +90,7 @@ private theorem exists_hasStandardEtaleSurjectionOn_of_exists_adjoin_singleton_e
       P.ResidueField[X] ⧸ I.map (mapRingHom (algebraMap _ P.ResidueField)) :=
     Polynomial.fiberEquivQuotient (aeval (R := R) x) hx' _
   rw [← RingHom.ker_comp_of_injective _ (f := e.toRingHom) e.injective]
-  convert Ideal.mk_ker.symm
+  convert! Ideal.mk_ker.symm
   ext a
   · dsimp [-TensorProduct.algebraMap_apply]
     rw [aeval_C, AlgEquiv.commutes]
@@ -119,7 +119,7 @@ private theorem exists_hasStandardEtaleSurjectionOn_of_exists_adjoin_singleton_e
   have : Function.Surjective (aeval (R := P.ResidueField) ((1 : P.ResidueField) ⊗ₜ[R] x)) := by
     rw [← AlgHom.range_eq_top, ← adjoin_singleton_eq_range_aeval]
     simpa using TensorProduct.adjoin_one_tmul_image_eq_top (A := P.ResidueField) _ hp₂
-  convert IsUnramifiedAt.not_minpoly_sq_dvd (A := P.Fiber S) Q' (1 ⊗ₜ x) _ hp₁ this
+  convert! IsUnramifiedAt.not_minpoly_sq_dvd (A := P.Fiber S) Q' (1 ⊗ₜ x) _ hp₁ this
   rw [← minpoly.algHom_eq _
     (IsScalarTower.toAlgHom P.ResidueField Q.ResidueField Q'.ResidueField).injective]
   congr 1
@@ -233,7 +233,7 @@ lemma exists_notMem_forall_ne_mem_and_adjoin_eq_top
     have : Ideal.ResidueField.mapₐ p Q (ofId R S) (Ideal.over_def Q p) =
       AlgHom.restrictScalars R (ofId p.ResidueField Q.ResidueField) := by ext
     rw [← AlgHom.restrictScalars_apply R, Algebra.TensorProduct.restrictScalars_lift]
-    convert hrQ
+    convert! hrQ
     rw [← SetLike.mem_coe, PrimeSpectrum.coe_primesOverOrderIsoFiber_apply_asIdeal]
     simp [this]
   have hsQ' : algebraMap R Q.ResidueField s ≠ 0 := by
diff --git a/Mathlib/RingTheory/Unramified/Pi.lean b/Mathlib/RingTheory/Unramified/Pi.lean
index 02866761f98d13..0dcaf171bbf480 100644
--- a/Mathlib/RingTheory/Unramified/Pi.lean
+++ b/Mathlib/RingTheory/Unramified/Pi.lean
@@ -48,12 +48,12 @@ theorem pi_iff :
     have h₁ : (f₁ e) * (1 - f₂ e) = 0 := by
       rw [← Ideal.mem_bot, ← hJ, ← ((he.map f₁).mul (he.map f₂).one_sub).eq, ← pow_two]
       apply Ideal.pow_mem_pow
-      convert Ideal.mul_mem_left _ (f₁ e) (hf e) using 1
+      convert! Ideal.mul_mem_left _ (f₁ e) (hf e) using 1
       rw [mul_sub, mul_sub, mul_one, (he.map f₁).eq]
     have h₂ : (f₂ e) * (1 - f₁ e) = 0 := by
       rw [← Ideal.mem_bot, ← hJ, ← ((he.map f₂).mul (he.map f₁).one_sub).eq, ← pow_two]
       apply Ideal.pow_mem_pow
-      convert Ideal.mul_mem_left _ (-f₂ e) (hf e) using 1
+      convert! Ideal.mul_mem_left _ (-f₂ e) (hf e) using 1
       rw [neg_mul, mul_sub, mul_sub, mul_one, neg_sub, (he.map f₂).eq]
     have H : f₁ e = f₂ e := by
       trans f₁ e * f₂ e
diff --git a/Mathlib/RingTheory/Valuation/Basic.lean b/Mathlib/RingTheory/Valuation/Basic.lean
index 034cc67b75f7e8..26570c1f8394cc 100644
--- a/Mathlib/RingTheory/Valuation/Basic.lean
+++ b/Mathlib/RingTheory/Valuation/Basic.lean
@@ -889,7 +889,7 @@ theorem orderMonoidIso_spec (h : v.IsEquiv w) (a : R) :
   · rw [← restrict₀_eq_zero_iff] at ha
     rwa [restrict_def, ha, map_zero, Eq.comm, ← h_res.eq_zero]
   · rw [(v.restrict_eq_mk ha)]
-    convert valueGroup₀Fun_spec (h := h) (hs := ha) (r := 1) (by simp)
+    convert! valueGroup₀Fun_spec (h := h) (hs := ha) (r := 1) (by simp)
     exact w.restrict_eq_mk ((eq_zero h.symm).ne.mpr ha)
 
 theorem orderMonoidIso_symm (h : v.IsEquiv w) (h' : w.IsEquiv v) :
diff --git a/Mathlib/RingTheory/Valuation/ExtendToLocalization.lean b/Mathlib/RingTheory/Valuation/ExtendToLocalization.lean
index 904eae8ec5c268..4c6b5fe08c4708 100644
--- a/Mathlib/RingTheory/Valuation/ExtendToLocalization.lean
+++ b/Mathlib/RingTheory/Valuation/ExtendToLocalization.lean
@@ -31,7 +31,7 @@ noncomputable def Valuation.extendToLocalization : Valuation B Γ :=
   let f := IsLocalization.toLocalizationMap S B
   let h : ∀ s : S, IsUnit (v.1.toMonoidHom s) := fun s => isUnit_iff_ne_zero.2 (hS s.2)
   { f.lift h with
-    map_zero' := by convert f.lift_eq (P := Γ) _ 0 <;> simp [f]
+    map_zero' := by convert! f.lift_eq (P := Γ) _ 0 <;> simp [f]
     map_add_le_max' := fun x y => by
       obtain ⟨a, b, s, rfl, rfl⟩ : ∃ (a b : A) (s : S), f.mk' a s = x ∧ f.mk' b s = y := by
         obtain ⟨a, s, rfl⟩ := f.mk'_surjective x
diff --git a/Mathlib/RingTheory/Valuation/Integers.lean b/Mathlib/RingTheory/Valuation/Integers.lean
index 6672e0b355fe44..de9982a5402457 100644
--- a/Mathlib/RingTheory/Valuation/Integers.lean
+++ b/Mathlib/RingTheory/Valuation/Integers.lean
@@ -433,7 +433,7 @@ lemma leIdeal_v_le_of_mem {K : Type*} [Field K] (v : Valuation K Γ₀)
   · simp
   intro y hy
   have : v ((y : K) / x) ≤ 1 := by simpa using div_le_one_of_le₀ hy zero_le'
-  convert I.smul_mem ⟨_, this⟩ hx using 1
+  convert! I.smul_mem ⟨_, this⟩ hx using 1
   simp [Subtype.ext_iff, div_mul_cancel₀ _ (ZeroMemClass.coe_eq_zero.not.mpr hx0)]
 
 lemma ltIdeal_v_le_of_mem {K : Type*} [Field K] {v : Valuation K Γ₀}
diff --git a/Mathlib/RingTheory/Valuation/LocalSubring.lean b/Mathlib/RingTheory/Valuation/LocalSubring.lean
index 68a9ac5adf29e6..4d5dcc292ac35c 100644
--- a/Mathlib/RingTheory/Valuation/LocalSubring.lean
+++ b/Mathlib/RingTheory/Valuation/LocalSubring.lean
@@ -224,7 +224,7 @@ lemma bijective_rangeRestrict_comp_of_valuationRing [IsDomain R] [ValuationRing
     (f : R →+* S) (g : S →+* K) (h : g.comp f = algebraMap R K) [IsLocalHom f] :
     Function.Bijective (g.rangeRestrict.comp f) := by
   refine ⟨?_, ?_⟩
-  · exact .of_comp (f := Subtype.val) (by convert (IsFractionRing.injective R K); rw [← h]; rfl)
+  · exact .of_comp (f := Subtype.val) (by convert! (IsFractionRing.injective R K); rw [← h]; rfl)
   · let V : ValuationSubring K :=
       ⟨(algebraMap R K).range, ValuationRing.isInteger_or_isInteger R⟩
     suffices LocalSubring.range g ≤ V.toLocalSubring by
@@ -238,7 +238,7 @@ lemma bijective_rangeRestrict_comp_of_valuationRing [IsDomain R] [ValuationRing
     suffices IsUnit a from this.map (algebraMap R K).rangeRestrict
     apply IsUnit.of_map f
     apply (IsLocalHom.of_surjective g.rangeRestrict g.rangeRestrict_surjective).1
-    convert ha
+    convert! ha
     simp [← h]
 
 lemma IsLocalRing.exists_factor_valuationRing [IsLocalRing R] (f : R →+* K) :
diff --git a/Mathlib/RingTheory/Valuation/RankOne.lean b/Mathlib/RingTheory/Valuation/RankOne.lean
index 33263f3ff6c1b1..dcf66cb8d5c942 100644
--- a/Mathlib/RingTheory/Valuation/RankOne.lean
+++ b/Mathlib/RingTheory/Valuation/RankOne.lean
@@ -158,7 +158,7 @@ theorem exists_val_lt {γ : ℝ≥0} (hγ : γ ≠ 0) : ∃ x ≠ 0, RankOne.hom
     by_contra h0
     rw [dif_pos (by rw [dif_pos ((zero_iff v).mpr h0)]), eq_comm] at hk
     simp at hk
-  · convert h
+  · convert! h
     simp only [restrict_RankOne_hom_eq, coe_comp, Function.comp_apply, ← hk]
     congr 1
     exact (embedding_restrict₀ k).symm
diff --git a/Mathlib/RingTheory/Valuation/ValuationRing.lean b/Mathlib/RingTheory/Valuation/ValuationRing.lean
index 721dcf75bdf8bb..bc71ae1e143939 100644
--- a/Mathlib/RingTheory/Valuation/ValuationRing.lean
+++ b/Mathlib/RingTheory/Valuation/ValuationRing.lean
@@ -398,7 +398,7 @@ instance (priority := 100) [IsLocalRing R] [IsBezout R] : ValuationRing R := by
   rcases eq_or_ne g 0 with h | h
   · simp [h]
   have : x * a + y * b = 1 := by
-    apply mul_left_injective₀ h; convert e' using 1 <;> ring
+    apply mul_left_injective₀ h; convert! e' using 1 <;> ring
   rcases IsLocalRing.isUnit_or_isUnit_of_add_one this with h' | h' <;> [left; right]
   all_goals exact mul_dvd_mul_right (isUnit_iff_forall_dvd.mp (isUnit_of_mul_isUnit_right h') _) _
 
diff --git a/Mathlib/RingTheory/Valuation/ValuativeRel/Basic.lean b/Mathlib/RingTheory/Valuation/ValuativeRel/Basic.lean
index 86c75c364db366..3645bd7fcad779 100644
--- a/Mathlib/RingTheory/Valuation/ValuativeRel/Basic.lean
+++ b/Mathlib/RingTheory/Valuation/ValuativeRel/Basic.lean
@@ -1147,7 +1147,7 @@ where the first row is the map `v` factored through its image group (with zero)
 @[simp]
 lemma embed_valuation_eq_restrict₀ [v.Compatible] (x : R) :
     embed v (valuation R x) = ValueGroup₀.restrict₀ v x := by
-  convert embed_mk v x 1
+  convert! embed_mk v x 1
   simp
 
 /--
diff --git a/Mathlib/RingTheory/Valuation/ValuativeRel/Trivial.lean b/Mathlib/RingTheory/Valuation/ValuativeRel/Trivial.lean
index a1ac9361766878..d1923deefbe89f 100644
--- a/Mathlib/RingTheory/Valuation/ValuativeRel/Trivial.lean
+++ b/Mathlib/RingTheory/Valuation/ValuativeRel/Trivial.lean
@@ -53,7 +53,7 @@ lemma eq_trivialRel_of_compatible_one [h : ValuativeRel R]
 
 lemma trivialRel_eq_ofValuation_one :
     trivialRel = ValuativeRel.ofValuation (1 : Valuation R Γ) := by
-  convert (eq_trivialRel_of_compatible_one (Γ := Γ)).symm
+  convert! (eq_trivialRel_of_compatible_one (Γ := Γ)).symm
   exact Valuation.Compatible.ofValuation 1
 
 variable (R Γ) in
diff --git a/Mathlib/RingTheory/WittVector/DiscreteValuationRing.lean b/Mathlib/RingTheory/WittVector/DiscreteValuationRing.lean
index ef571e47200128..8ea43e8cd2eebd 100644
--- a/Mathlib/RingTheory/WittVector/DiscreteValuationRing.lean
+++ b/Mathlib/RingTheory/WittVector/DiscreteValuationRing.lean
@@ -127,7 +127,7 @@ theorem exists_eq_pow_p_mul (a : 𝕎 k) (ha : a ≠ 0) :
   · contrapose hc
     simp [hc, zero_pow <| pow_ne_zero _ hp.out.ne_zero]
   · simp_rw [← mul_left_iterate (p : 𝕎 k) m]
-    convert hcm using 2
+    convert! hcm using 2
     ext1 x
     rw [mul_comm, ← WittVector.verschiebung_frobenius x]; rfl
 
diff --git a/Mathlib/RingTheory/WittVector/FrobeniusFractionField.lean b/Mathlib/RingTheory/WittVector/FrobeniusFractionField.lean
index 7341fdcf59e801..25380ba5a64305 100644
--- a/Mathlib/RingTheory/WittVector/FrobeniusFractionField.lean
+++ b/Mathlib/RingTheory/WittVector/FrobeniusFractionField.lean
@@ -131,7 +131,7 @@ theorem succNthVal_spec' (n : ℕ) (a₁ a₂ : 𝕎 k) (bs : Fin (n + 1) → k)
     Polynomial.eval_pow, succNthDefiningPoly, Polynomial.eval_mul, Polynomial.eval_add,
     Polynomial.eval_sub, Polynomial.IsRoot.def]
     at this
-  convert this using 1
+  convert! this using 1
   ring
 
 end IsAlgClosed
@@ -207,7 +207,7 @@ theorem frobenius_frobeniusRotation {a₁ a₂ : 𝕎 k} (ha₁ : a₁.coeff 0 
       succNthVal_spec' p n a₁ a₂ (fun i : Fin (n + 1) => frobeniusRotationCoeff p ha₁ ha₂ i.val)
         ha₁ ha₂
     simp only [frobeniusRotationCoeff, Fin.val_zero] at this
-    convert this using 3; clear this
+    convert! this using 3; clear this
     apply TruncatedWittVector.ext
     intro i
     simp only [WittVector.coeff_truncateFun, WittVector.coeff_frobenius_charP]
@@ -236,7 +236,7 @@ theorem exists_frobenius_solution_fractionRing_aux (m n : ℕ) (r' q' : 𝕎 k)
       (IsFractionRing.injective (𝕎 k) (FractionRing (𝕎 k))).ne hq'''
   rw [zpow_sub₀ (FractionRing.p_nonzero p k)]
   simp [field, FractionRing.p_nonzero p k]
-  convert congr_arg (fun x => algebraMap (𝕎 k) (FractionRing (𝕎 k)) x) key using 1
+  convert! congr_arg (fun x => algebraMap (𝕎 k) (FractionRing (𝕎 k)) x) key using 1
   · simp only [map_mul]
   · simp only [map_mul]
 
diff --git a/Mathlib/RingTheory/WittVector/Identities.lean b/Mathlib/RingTheory/WittVector/Identities.lean
index 5bef05ead1f40b..9ba6ce06ae5bc2 100644
--- a/Mathlib/RingTheory/WittVector/Identities.lean
+++ b/Mathlib/RingTheory/WittVector/Identities.lean
@@ -214,7 +214,7 @@ theorem iterate_verschiebung_mul_coeff (x y : 𝕎 R) (i j : ℕ) :
     _ = (frobenius^[j] x).coeff 0 * (frobenius^[i] y).coeff 0 := ?_
     _ = _ := ?_
   · rw [iterate_verschiebung_mul]
-  · convert iterate_verschiebung_coeff (p := p) (R := R) _ _ _ using 2
+  · convert! iterate_verschiebung_coeff (p := p) (R := R) _ _ _ using 2
     rw [zero_add]
   · apply mul_coeff_zero
   · simp only [iterate_frobenius_coeff]
diff --git a/Mathlib/RingTheory/WittVector/IsPoly.lean b/Mathlib/RingTheory/WittVector/IsPoly.lean
index 18db959d3218d4..902cfc16d982c3 100644
--- a/Mathlib/RingTheory/WittVector/IsPoly.lean
+++ b/Mathlib/RingTheory/WittVector/IsPoly.lean
@@ -184,7 +184,7 @@ theorem ext [Fact p.Prime] {f g} (hf : IsPoly p f) (hg : IsPoly p g)
   simp only [ghostComponent_apply, aeval_eq_eval₂Hom] at h
   apply (ULift.ringEquiv.symm : ℤ ≃+* _).injective
   simp only [← RingEquiv.coe_toRingHom, map_eval₂Hom]
-  convert h using 1
+  convert! h using 1
   all_goals
     simp only [hf, hg, MvPolynomial.eval, map_eval₂Hom]
     apply eval₂Hom_congr (RingHom.ext_int _ _) _ rfl
@@ -344,7 +344,7 @@ theorem ext [Fact p.Prime] {f g} (hf : IsPoly₂ p f) (hg : IsPoly₂ p g)
   simp only [ghostComponent_apply, aeval_eq_eval₂Hom] at h
   apply (ULift.ringEquiv.symm : ℤ ≃+* _).injective
   simp only [← RingEquiv.coe_toRingHom, map_eval₂Hom]
-  convert h using 1
+  convert! h using 1
   all_goals
     simp only [hf, hg, MvPolynomial.eval, map_eval₂Hom]
     apply eval₂Hom_congr (RingHom.ext_int _ _) _ rfl
diff --git a/Mathlib/RingTheory/WittVector/Isocrystal.lean b/Mathlib/RingTheory/WittVector/Isocrystal.lean
index 65c3c23f8203ec..a91b60b777cdcc 100644
--- a/Mathlib/RingTheory/WittVector/Isocrystal.lean
+++ b/Mathlib/RingTheory/WittVector/Isocrystal.lean
@@ -191,7 +191,7 @@ theorem isocrystal_classification (k : Type*) [Field k] [IsAlgClosed k] [CharP k
     apply this
     simp only [← ha, ha', zero_smul]
   obtain ⟨b, hb, m, hmb⟩ := WittVector.exists_frobenius_solution_fractionRing p ha
-  replace hmb : φ(p, k) b * a = (p : K(p, k)) ^ m * b := by convert hmb
+  replace hmb : φ(p, k) b * a = (p : K(p, k)) ^ m * b := by convert! hmb
   use m
   let F₀ : StandardOneDimIsocrystal p k m →ₗ[K(p, k)] V := LinearMap.toSpanSingleton K(p, k) V x
   let F : StandardOneDimIsocrystal p k m ≃ₗ[K(p, k)] V := by
diff --git a/Mathlib/RingTheory/WittVector/MulCoeff.lean b/Mathlib/RingTheory/WittVector/MulCoeff.lean
index af5114c453fd08..741a27a70778d5 100644
--- a/Mathlib/RingTheory/WittVector/MulCoeff.lean
+++ b/Mathlib/RingTheory/WittVector/MulCoeff.lean
@@ -113,7 +113,7 @@ def polyOfInterest (n : ℕ) : 𝕄 :=
 theorem mul_polyOfInterest_aux1 (n : ℕ) :
     ∑ i ∈ range (n + 1), (p : 𝕄) ^ i * wittMul p i ^ p ^ (n - i) = wittPolyProd p n := by
   simp only [wittPolyProd]
-  convert wittStructureInt_prop p (X (0 : Fin 2) * X 1) n using 1
+  convert! wittStructureInt_prop p (X (0 : Fin 2) * X 1) n using 1
   · simp only [wittPolynomial, wittMul]
     rw [map_sum]
     congr 1 with i
@@ -128,7 +128,7 @@ theorem mul_polyOfInterest_aux1 (n : ℕ) :
 
 theorem mul_polyOfInterest_aux2 (n : ℕ) :
     (p : 𝕄) ^ n * wittMul p n + wittPolyProdRemainder p n = wittPolyProd p n := by
-  convert mul_polyOfInterest_aux1 p n
+  convert! mul_polyOfInterest_aux1 p n
   rw [sum_range_succ, add_comm, Nat.sub_self, pow_zero, pow_one]
   rfl
 
diff --git a/Mathlib/RingTheory/WittVector/StructurePolynomial.lean b/Mathlib/RingTheory/WittVector/StructurePolynomial.lean
index dbe3ac979f9098..c75019e2c4122c 100644
--- a/Mathlib/RingTheory/WittVector/StructurePolynomial.lean
+++ b/Mathlib/RingTheory/WittVector/StructurePolynomial.lean
@@ -322,7 +322,7 @@ theorem wittStructureInt_existsUnique (Φ : MvPolynomial idx ℤ) :
 theorem witt_structure_prop (Φ : MvPolynomial idx ℤ) (n) :
     aeval (fun i => map (Int.castRingHom R) (wittStructureInt p Φ i)) (wittPolynomial p ℤ n) =
       aeval (fun i => rename (Prod.mk i) (W n)) Φ := by
-  convert congr_arg (map (Int.castRingHom R)) (wittStructureInt_prop p Φ n) using 1 <;>
+  convert! congr_arg (map (Int.castRingHom R)) (wittStructureInt_prop p Φ n) using 1 <;>
       rw [hom_bind₁] <;>
     apply eval₂Hom_congr (RingHom.ext_int _ _) _ rfl
   · rfl
diff --git a/Mathlib/RingTheory/ZMod/UnitsCyclic.lean b/Mathlib/RingTheory/ZMod/UnitsCyclic.lean
index 79e5082f07e949..140332f7e2e47d 100644
--- a/Mathlib/RingTheory/ZMod/UnitsCyclic.lean
+++ b/Mathlib/RingTheory/ZMod/UnitsCyclic.lean
@@ -181,13 +181,13 @@ theorem orderOf_one_add_mul_prime_pow {p : ℕ} (hp : p.Prime) (m : ℕ) (hm0 :
 theorem orderOf_one_add_mul_prime {p : ℕ} (hp : p.Prime) (hp2 : p ≠ 2) (a : ℤ)
     (ha : ¬ (p : ℤ) ∣ a) (n : ℕ) :
     orderOf (1 + p * a : ZMod (p ^ (n + 1))) = p ^ n := by
-  convert orderOf_one_add_mul_prime_pow hp 1 one_ne_zero _ a ha n using 1
+  convert! orderOf_one_add_mul_prime_pow hp 1 one_ne_zero _ a ha n using 1
   · rw [pow_one]
   · have := hp.two_le; lia
 
 theorem orderOf_one_add_prime {p : ℕ} (hp : p.Prime) (hp2 : p ≠ 2) (n : ℕ) :
     orderOf (1 + p : ZMod (p ^ (n + 1))) = p ^ n := by
-  convert orderOf_one_add_mul_prime hp hp2 1 _ n
+  convert! orderOf_one_add_mul_prime hp hp2 1 _ n
   · simp
   · intro H
     apply hp.ne_one
@@ -242,13 +242,13 @@ theorem isCyclic_units_two_pow_iff (n : ℕ) :
 
 lemma orderOf_one_add_four_mul (a : ℤ) (ha : Odd a) (n : ℕ) :
     orderOf (1 + 4 * a : ZMod (2 ^ (n + 2))) = 2 ^ n := by
-  convert orderOf_one_add_mul_prime_pow Nat.prime_two 2 two_ne_zero le_rfl a ?_ n using 1
+  convert! orderOf_one_add_mul_prime_pow Nat.prime_two 2 two_ne_zero le_rfl a ?_ n using 1
   · norm_num
   · rwa [← Int.not_even_iff_odd, even_iff_two_dvd] at ha
 
 theorem orderOf_five (n : ℕ) :
     orderOf (5 : ZMod (2 ^ (n + 2))) = 2 ^ n := by
-  convert orderOf_one_add_four_mul 1 (by simp) n
+  convert! orderOf_one_add_four_mul 1 (by simp) n
   norm_num
 
 end PrimePow
diff --git a/Mathlib/RingTheory/ZariskisMainTheorem.lean b/Mathlib/RingTheory/ZariskisMainTheorem.lean
index e8f3322e52d1d9..12cf49175b301e 100644
--- a/Mathlib/RingTheory/ZariskisMainTheorem.lean
+++ b/Mathlib/RingTheory/ZariskisMainTheorem.lean
@@ -224,7 +224,7 @@ lemma exists_isIntegral_leadingCoeff_pow_smul_sub_of_isIntegralElem_of_mul_mem_r
   simp only [Algebra.smul_def, Submonoid.smul_def, algebraMap_apply R S S', ← map_mul] at hm
   obtain ⟨_, ⟨k, rfl⟩, hk⟩ := IsLocalization.exists_isIntegral_smul_of_isIntegral_map (.powers a) hm
   refine ⟨C a ^ (k + m) * q', k + m + n, ?_⟩
-  convert hk using 1
+  convert! hk using 1
   simp only [Algebra.smul_def, map_pow, ← Polynomial.algebraMap_eq, map_mul, AlgHom.commutes]
   ring
 
@@ -239,7 +239,7 @@ lemma exists_leadingCoeff_pow_smul_mem_conductor
     have : φ p * t * x ∈ φ.range := by simpa [← AlgHom.map_adjoin_singleton] using hp x
     obtain ⟨q, n, hn⟩ :=
       exists_isIntegral_leadingCoeff_pow_smul_sub_of_isIntegralElem_of_mul_mem_range φ _ p
-        (hφ.to_isIntegral (t * x)) (by convert this using 1; ring)
+        (hφ.to_isIntegral (t * x)) (by convert! this using 1; ring)
     obtain ⟨r, hr : algebraMap _ _ r = _⟩ := hRS.le hn
     exact ⟨n, (C r + q), by simp [← Polynomial.algebraMap_eq, - Polynomial.algebraMap_apply, hr]⟩
   choose n hn using this
@@ -384,16 +384,18 @@ private lemma not_isStronglyTranscendental_of_weaklyQuasiFiniteAt_of_isDomain_au
     rw [show algebraMap S' L (f x) = algebraMap _ _ x from congr($hf₂ x)]
     exact ((hx.of_isLocalization S⁰).of_isLocalization_left R⁰).restrictScalars (S := K)
   have H₂ : (aeval (R := R') (f x)).toRingHom.Finite := by
-    convert ((RingHom.Finite.of_surjective g.toRingHom hf₁).comp
-      (RingHom.Finite.tensorProductMap (f := AlgHom.id R R') (RingEquiv.refl _).finite hx')).comp
-      (polyEquivTensor R R').toRingEquiv.finite using 1
+    convert!
+      ((RingHom.Finite.of_surjective g.toRingHom hf₁).comp
+            (RingHom.Finite.tensorProductMap (f := AlgHom.id R R') (RingEquiv.refl _).finite
+              hx')).comp
+        (polyEquivTensor R R').toRingEquiv.finite using 1
     ext <;> simp [g]
   obtain ⟨⟨Q, _⟩, hQ⟩ := hf₄.comap_surjective hf₃ ⟨P, ‹_›⟩
   suffices WeaklyQuasiFiniteAt R' Q from
     not_isStronglyTranscendental_of_weaklyQuasiFiniteAt_of_isIntegrallyClosed H₂ Q H₁
   have : Algebra.WeaklyQuasiFiniteAt R' (Q.comap g.toRingHom) := .baseChange P _ <| by
     rw [Ideal.comap_comap]
-    convert congr(($hQ.symm).1)
+    convert! congr(($hQ.symm).1)
     ext; simp [g]
   exact .of_surjectiveOnStalks (Q.comap g.toRingHom) _ g
     (RingHom.surjectiveOnStalks_of_surjective hf₁) rfl
@@ -420,7 +422,7 @@ nonrec lemma not_isStronglyTranscendental_of_weaklyQuasiFiniteAt [IsReduced S]
       ((isStronglyTranscendental_mk_of_mem_minimalPrimes hx p hp).of_surjective_left
         Ideal.Quotient.mk_surjective)
     refine RingHom.Finite.of_comp_finite (f := mapRingHom (Ideal.Quotient.mk _)) ?_
-    convert (RingHom.Finite.of_surjective _ (Ideal.Quotient.mk_surjective (I := p))).comp hx'
+    convert! (RingHom.Finite.of_surjective _ (Ideal.Quotient.mk_surjective (I := p))).comp hx'
     ext <;> simp
   cases hS
   have : IsDomain R := (FaithfulSMul.algebraMap_injective R S).isDomain
@@ -493,7 +495,7 @@ private lemma ZariskisMainProperty.of_adjoin_eq_top
         simpa [eraseLead_coeff, show n ≠ f.natDegree by rintro rfl; exact hfn (by simpa)]
       rwa [Ideal.add_mem_iff_left]
       split_ifs
-      · convert p.mul_mem_right x Hfp
+      · convert! p.mul_mem_right x Hfp
         simpa [Algebra.smul_def] using ha
       · simp
   · refine zariskisMainProperty_iff_exists_saturation_eq_top.mpr ⟨_, Hfp, isIntegral_algebraMap, ?_⟩
@@ -512,7 +514,7 @@ private lemma ZariskisMainProperty.of_algHom_polynomial
       .of_restrictScalars R (integralClosure R S) _
     refine .restrictScalars (this p (aeval (f X)) ?_ (integralClosure_idem (R := R)))
     refine RingHom.Finite.of_comp_finite (f := mapRingHom (algebraMap R _)) ?_
-    convert (show f.toRingHom.Finite from hf)
+    convert! (show f.toRingHom.Finite from hf)
     ext <;> simp [show ∀ x, f (C x) = algebraMap _ _ x from f.commutes]
   replace hf : ¬ conductor R (f X) ≤ p := by
     intro hp
@@ -528,8 +530,9 @@ private lemma ZariskisMainProperty.of_algHom_polynomial
         ((Ideal.comap_map_of_surjective _ Ideal.Quotient.mk_surjective p).trans ?_).symm
       simpa [← RingHom.ker_eq_comap_bot]
     refine not_isStronglyTranscendental_of_weaklyQuasiFiniteAt ?_ (p.map (Ideal.Quotient.mk J))
-      (isStronglyTranscendental_mk_radical_conductor H (f X) (by convert hf; ext; simp))
-    convert (RingHom.Finite.of_surjective _ (Ideal.Quotient.mk_surjective (I := J))).comp hf using 1
+      (isStronglyTranscendental_mk_radical_conductor H (f X) (by convert! hf; ext; simp))
+    convert! (RingHom.Finite.of_surjective _ (Ideal.Quotient.mk_surjective (I := J))).comp hf
+      using 1
     ext <;> simp [show ∀ x, f (C x) = algebraMap _ _ x from f.commutes, J]
   obtain ⟨x, hx, hxp⟩ := SetLike.not_le_iff_exists.mp hf
   replace hx (a : _) : x * a ∈ f.range := by simpa [← AlgHom.map_adjoin_singleton f] using hx a
@@ -557,7 +560,7 @@ private lemma ZariskisMainProperty.of_algHom_mvPolynomial
   | zero =>
     have : Module.Finite R S := by
       rw [← RingHom.finite_algebraMap]
-      convert RingHom.Finite.comp hf (RingHom.Finite.of_surjective _ (MvPolynomial.C_surjective _))
+      convert! RingHom.Finite.comp hf (RingHom.Finite.of_surjective _ (MvPolynomial.C_surjective _))
       exact f.comp_algebraMap.symm
     exact .of_isIntegral _
   | succ n IH =>
@@ -610,7 +613,7 @@ private lemma ZariskisMainProperty.of_algHom_mvPolynomial
             ← isIntegral_algebraMap_iff (FaithfulSMul.algebraMap_injective R' S),
             forall_and, hr, or_imp, Finset.mem_smul_finset]
         refine ⟨fun i ↦ ?_, fun a has ↦ ?_⟩
-        · convert isIntegral_algebraMap (x := MvPolynomial.X i)
+        · convert! isIntegral_algebraMap (x := MvPolynomial.X i)
           simp [RingHom.algebraMap_toAlgebra, f', MvPolynomial.finSuccEquiv,
             MvPolynomial.optionEquivLeft]
         · rw [← Nat.sub_add_cancel (s.le_sup has), pow_add, mul_assoc]
diff --git a/Mathlib/SetTheory/Cardinal/Arithmetic.lean b/Mathlib/SetTheory/Cardinal/Arithmetic.lean
index 5056b45cf12646..c11b1336a233ff 100644
--- a/Mathlib/SetTheory/Cardinal/Arithmetic.lean
+++ b/Mathlib/SetTheory/Cardinal/Arithmetic.lean
@@ -121,7 +121,7 @@ theorem mul_lt_of_lt {a b c : Cardinal} (hc : ℵ₀ ≤ c) (ha : a < c) (hb : b
     exact max_lt ha hb
 
 theorem mul_le_max_of_aleph0_le_left {a b : Cardinal} (h : ℵ₀ ≤ a) : a * b ≤ max a b := by
-  convert mul_le_mul' (le_max_left a b) (le_max_right a b) using 1
+  convert! mul_le_mul' (le_max_left a b) (le_max_right a b) using 1
   rw [mul_eq_self]
   exact h.trans (le_max_left a b)
 
@@ -132,7 +132,7 @@ theorem mul_eq_max_of_aleph0_le_left {a b : Cardinal} (h : ℵ₀ ≤ a) (h' : b
   refine (mul_le_max_of_aleph0_le_left h).antisymm ?_
   have : b ≤ a := hb.le.trans h
   rw [max_eq_left this]
-  convert mul_le_mul_right (Cardinal.one_le_iff_ne_zero.mpr h') a
+  convert! mul_le_mul_right (Cardinal.one_le_iff_ne_zero.mpr h') a
   rw [mul_one]
 
 theorem mul_le_max_of_aleph0_le_right {a b : Cardinal} (h : ℵ₀ ≤ b) : a * b ≤ max a b := by
@@ -166,7 +166,7 @@ theorem mul_eq_right {a b : Cardinal} (hb : ℵ₀ ≤ b) (ha : a ≤ b) (ha' :
   rw [mul_comm, mul_eq_left hb ha ha']
 
 theorem le_mul_left {a b : Cardinal} (h : b ≠ 0) : a ≤ b * a := by
-  convert mul_le_mul_left (Cardinal.one_le_iff_ne_zero.mpr h) a
+  convert! mul_le_mul_left (Cardinal.one_le_iff_ne_zero.mpr h) a
   rw [one_mul]
 
 theorem le_mul_right {a b : Cardinal} (h : b ≠ 0) : a ≤ a * b := by
@@ -428,7 +428,7 @@ theorem sum_eq_lift_iSup_of_lift_mk_le_lift_iSup [Small.{v} ι] {f : ι → Card
     (h : lift.{v} #ι ≤ lift.{u} (⨆ i, f i)) : sum f = lift (⨆ i, f i) := by
   rw [lift_iSup bddAbove_of_small] at h
   apply (lift_iSup_le_sum f).antisymm'
-  convert sum_le_lift_mk_mul_iSup_lift f
+  convert! sum_le_lift_mk_mul_iSup_lift f
   rw [mul_eq_max (aleph0_le_lift.mpr hι) ((aleph0_le_lift.mpr hι).trans h), max_eq_right h,
     lift_iSup bddAbove_of_small]
 
@@ -598,7 +598,7 @@ theorem powerlt_aleph0 {c : Cardinal} (h : ℵ₀ ≤ c) : c ^< ℵ₀ = c := by
   apply le_antisymm
   · rw [powerlt_le]
     exact fun _ a ↦ pow_le h a
-  convert le_powerlt c one_lt_aleph0; rw [power_one]
+  convert! le_powerlt c one_lt_aleph0; rw [power_one]
 
 theorem powerlt_aleph0_le (c : Cardinal) : c ^< ℵ₀ ≤ max c ℵ₀ := by
   rcases le_or_gt ℵ₀ c with h | h
diff --git a/Mathlib/SetTheory/Cardinal/Basic.lean b/Mathlib/SetTheory/Cardinal/Basic.lean
index b45d98e570313b..a487a36c7b89d4 100644
--- a/Mathlib/SetTheory/Cardinal/Basic.lean
+++ b/Mathlib/SetTheory/Cardinal/Basic.lean
@@ -133,7 +133,7 @@ theorem lift_sInf (s : Set Cardinal) : lift.{u, v} (sInf s) = sInf (lift.{u, v}
 @[simp]
 theorem lift_iInf {ι} (f : ι → Cardinal) : lift.{u, v} (iInf f) = ⨅ i, lift.{u, v} (f i) := by
   unfold iInf
-  convert lift_sInf (range f)
+  convert! lift_sInf (range f)
   simp_rw [← comp_apply (f := lift), range_comp]
 
 end Cardinal
@@ -285,7 +285,7 @@ lemma lt_natCast_add_one_iff {n : ℕ} {c : Cardinal} : c < n + 1 ↔ c ≤ n :=
   rw [← Order.lt_succ_iff, succ_natCast]
 
 lemma two_le_iff_one_lt {c : Cardinal} : 2 ≤ c ↔ 1 < c := by
-  convert natCast_add_one_le_iff
+  convert! natCast_add_one_le_iff
   norm_cast
 
 @[simp]
@@ -919,7 +919,7 @@ theorem mk_preimage_of_injective_of_subset_range_lift {β : Type v} (f : α →
 
 theorem mk_preimage_of_injective_of_subset_range (f : α → β) (s : Set β) (h : Injective f)
     (h2 : s ⊆ range f) : #(f ⁻¹' s) = #s := by
-  convert mk_preimage_of_injective_of_subset_range_lift.{u, u} f s h h2 using 1 <;> rw [lift_id]
+  convert! mk_preimage_of_injective_of_subset_range_lift.{u, u} f s h h2 using 1 <;> rw [lift_id]
 
 @[simp]
 theorem mk_preimage_equiv_lift {β : Type v} (f : α ≃ β) (s : Set β) :
@@ -945,14 +945,14 @@ theorem mk_preimage_of_subset_range (f : α → β) (s : Set β) (h : s ⊆ rang
 theorem mk_subset_ge_of_subset_image_lift {α : Type u} {β : Type v} (f : α → β) {s : Set α}
     {t : Set β} (h : t ⊆ f '' s) : lift.{u} #t ≤ lift.{v} #({ x ∈ s | f x ∈ t } : Set α) := by
   rw [image_eq_range] at h
-  convert mk_preimage_of_subset_range_lift _ _ h using 1
+  convert! mk_preimage_of_subset_range_lift _ _ h using 1
   rw [mk_sep]
   rfl
 
 theorem mk_subset_ge_of_subset_image (f : α → β) {s : Set α} {t : Set β} (h : t ⊆ f '' s) :
     #t ≤ #({ x ∈ s | f x ∈ t } : Set α) := by
   rw [image_eq_range] at h
-  convert mk_preimage_of_subset_range _ _ h using 1
+  convert! mk_preimage_of_subset_range _ _ h using 1
   rw [mk_sep]
   rfl
 
@@ -1053,7 +1053,7 @@ theorem zero_powerlt {a : Cardinal} (h : a ≠ 0) : 0 ^< a = 1 := by
 
 @[simp]
 theorem powerlt_zero {a : Cardinal} : a ^< 0 = 0 := by
-  convert Cardinal.iSup_of_empty _
+  convert! Cardinal.iSup_of_empty _
   exact Subtype.isEmpty_of_false fun x => mem_Iio.not.mpr not_lt_zero
 
 /-- The cardinality of a set is an upper-bound for the amount of elements before the set's mex
diff --git a/Mathlib/SetTheory/Cardinal/Cofinality/Ordinal.lean b/Mathlib/SetTheory/Cardinal/Cofinality/Ordinal.lean
index a3fbe3edf236a9..7fbb74e6cd1928 100644
--- a/Mathlib/SetTheory/Cardinal/Cofinality/Ordinal.lean
+++ b/Mathlib/SetTheory/Cardinal/Cofinality/Ordinal.lean
@@ -255,7 +255,7 @@ theorem sSup_add_one_lt_of_lt_cof {s : Set Ordinal.{u}} {a : Ordinal.{u}}
     refine small_of_injective (β := Iio a) (f := fun x ↦ ⟨f x, hs _ (f x).2⟩) fun _ ↦ ?_
     simp [Subtype.val_inj]
   have : range (fun i ↦ (f i).1 + 1) = (· + 1) '' s := by
-    convert range_comp (· + 1) (fun i ↦ (f i).1)
+    convert! range_comp (· + 1) (fun i ↦ (f i).1)
     rw [range_comp', f.range_eq]
     simp
   rw [← this, sSup_range]
diff --git a/Mathlib/SetTheory/Cardinal/CountableCover.lean b/Mathlib/SetTheory/Cardinal/CountableCover.lean
index d9700f654ffc97..5d850d5e75e65c 100644
--- a/Mathlib/SetTheory/Cardinal/CountableCover.lean
+++ b/Mathlib/SetTheory/Cardinal/CountableCover.lean
@@ -51,7 +51,7 @@ lemma mk_subtype_le_of_countable_eventually_mem_aux {α ι : Type u} {a : Cardin
       have : s ⊆ u := fun x hx ↦ by simpa only [u, Set.mem_toFinset] using hi x hx
       exact Finset.card_le_card this
     have I2 : (u.card : Cardinal) ≤ n := by
-      convert h'f i; simp only [u, Set.toFinset_card, mk_fintype]
+      convert! h'f i; simp only [u, Set.toFinset_card, mk_fintype]
     exact I1.trans (Nat.cast_le.1 I2)
   -- case `a` infinite:
   · have : t ⊆ ⋃ i, f i := by
diff --git a/Mathlib/SetTheory/Cardinal/HasCardinalLT.lean b/Mathlib/SetTheory/Cardinal/HasCardinalLT.lean
index 3ca5cefec78842..99db04260f81fc 100644
--- a/Mathlib/SetTheory/Cardinal/HasCardinalLT.lean
+++ b/Mathlib/SetTheory/Cardinal/HasCardinalLT.lean
@@ -172,7 +172,7 @@ lemma hasCardinalLT_iUnion
     {ι : Type*} {X : Type*} (S : ι → Set X) {κ : Cardinal} [Fact κ.IsRegular]
     (hι : HasCardinalLT ι κ) (hS : ∀ i, HasCardinalLT (S i) κ) :
     HasCardinalLT (⋃ i, S i) κ := by
-  convert show HasCardinalLT (setOf ((⨆ i, S i))) κ from hasCardinalLT_subtype_iSup S hι hS
+  convert! show HasCardinalLT (setOf ((⨆ i, S i))) κ from hasCardinalLT_subtype_iSup S hι hS
   aesop
 
 /-- The particular case of `hasCardinalLT_prod` when all the inputs are in the
diff --git a/Mathlib/SetTheory/Cardinal/Order.lean b/Mathlib/SetTheory/Cardinal/Order.lean
index fa292d6f22482c..7852ac1273b299 100644
--- a/Mathlib/SetTheory/Cardinal/Order.lean
+++ b/Mathlib/SetTheory/Cardinal/Order.lean
@@ -330,7 +330,7 @@ theorem power_le_power_left : ∀ {a b c : Cardinal}, a ≠ 0 → b ≤ c → a
 theorem self_le_power (a : Cardinal) {b : Cardinal} (hb : 1 ≤ b) : a ≤ a ^ b := by
   rcases eq_or_ne a 0 with (rfl | ha)
   · exact zero_le
-  · convert power_le_power_left ha hb
+  · convert! power_le_power_left ha hb
     exact (power_one a).symm
 
 /-- **Cantor's theorem** -/
diff --git a/Mathlib/SetTheory/Cardinal/Ordinal.lean b/Mathlib/SetTheory/Cardinal/Ordinal.lean
index 4f6ace67a5b457..eb9fe0c8b127b4 100644
--- a/Mathlib/SetTheory/Cardinal/Ordinal.lean
+++ b/Mathlib/SetTheory/Cardinal/Ordinal.lean
@@ -79,7 +79,7 @@ theorem card_iSup_Iio_le_sum_card {o : Ordinal.{u}} (f : Iio o → Ordinal.{max
 theorem card_iSup_Iio_le_card_mul_iSup {o : Ordinal.{u}} (f : Iio o → Ordinal.{max u v}) :
     (⨆ a : Iio o, f a).card ≤ Cardinal.lift.{v} o.card * ⨆ a : Iio o, (f a).card := by
   apply (card_iSup_Iio_le_sum_card f).trans
-  convert ← sum_le_lift_mk_mul_iSup _
+  convert! ← sum_le_lift_mk_mul_iSup _
   · exact mk_toType o
   · exact ToType.mk.symm.iSup_comp (g := fun x ↦ (f x).card)
 
diff --git a/Mathlib/SetTheory/Cardinal/Subfield.lean b/Mathlib/SetTheory/Cardinal/Subfield.lean
index 695fc393a77e41..cbaec6024adf50 100644
--- a/Mathlib/SetTheory/Cardinal/Subfield.lean
+++ b/Mathlib/SetTheory/Cardinal/Subfield.lean
@@ -72,7 +72,7 @@ open Cardinal
 
 lemma cardinalMk_closure_le_max : #(closure s) ≤ max #s ℵ₀ :=
   (Cardinal.mk_le_of_surjective <| surjective_ofWType s).trans <| by
-    convert WType.cardinalMk_le_max_aleph0_of_finite' using 1
+    convert! WType.cardinalMk_le_max_aleph0_of_finite' using 1
     · rw [lift_uzero, mk_sum, lift_uzero]
       have : lift.{u, 0} #(Fin 6) < ℵ₀ := lift_lt_aleph0.mpr (lt_aleph0_of_finite _)
       obtain h | h := lt_or_ge #s ℵ₀
diff --git a/Mathlib/SetTheory/Ordinal/Arithmetic.lean b/Mathlib/SetTheory/Ordinal/Arithmetic.lean
index d04d39abb922cf..4c72cc6aaefef8 100644
--- a/Mathlib/SetTheory/Ordinal/Arithmetic.lean
+++ b/Mathlib/SetTheory/Ordinal/Arithmetic.lean
@@ -233,7 +233,7 @@ theorem enum_succ_eq_top {o : Ordinal} :
 theorem has_succ_of_type_succ_lt {α} {r : α → α → Prop} [wo : IsWellOrder α r]
     (h : ∀ a < type r, succ a < type r) (x : α) : ∃ y, r x y := by
   use enum r ⟨succ (typein r x), h _ (typein_lt_type r x)⟩
-  convert enum_lt_enum.mpr _
+  convert! enum_lt_enum.mpr _
   · rw [enum_typein]
   · rw [Subtype.mk_lt_mk, lt_succ_iff]
 
@@ -592,11 +592,11 @@ instance mulRightMono : MulRightMono Ordinal.{u} :=
       · exact Prod.Lex.right _ (f.toRelEmbedding.map_rel_iff.2 h')⟩
 
 theorem le_mul_left (a : Ordinal) {b : Ordinal} (hb : 0 < b) : a ≤ a * b := by
-  convert mul_le_mul_right (one_le_iff_pos.2 hb) a
+  convert! mul_le_mul_right (one_le_iff_pos.2 hb) a
   rw [mul_one a]
 
 theorem le_mul_right (a : Ordinal) {b : Ordinal} (hb : 0 < b) : a ≤ b * a := by
-  convert mul_le_mul_left (one_le_iff_pos.2 hb) a
+  convert! mul_le_mul_left (one_le_iff_pos.2 hb) a
   rw [one_mul a]
 
 private theorem mul_le_of_limit_aux {α β r s} [IsWellOrder α r] [IsWellOrder β s] {c}
@@ -796,7 +796,7 @@ theorem mul_add_div_mul {a c : Ordinal} (hc : c < a) (b d : Ordinal) :
     · grw [← mul_le_iff_le_div H, mul_assoc, mul_div_le b d, ← le_self_add]
 
 theorem mul_div_mul_cancel {a : Ordinal} (ha : a ≠ 0) (b c) : a * b / (a * c) = b / c := by
-  convert mul_add_div_mul (pos_iff_ne_zero.2 ha) b c using 1
+  convert! mul_add_div_mul (pos_iff_ne_zero.2 ha) b c using 1
   rw [add_zero]
 
 theorem div_eq {a b c : Ordinal} (hle : b * c ≤ a) (hlt : a < b * (c + 1)) : a / b = c := by
@@ -938,7 +938,7 @@ theorem mul_add_mod_mul {w x : Ordinal} (hw : w < x) (y z : Ordinal) :
 theorem mul_mod_mul (x y z : Ordinal) : (x * y) % (x * z) = x * (y % z) := by
   obtain rfl | hx := eq_zero_or_pos x
   · simp
-  · convert mul_add_mod_mul hx y z using 1 <;>
+  · convert! mul_add_mod_mul hx y z using 1 <;>
     rw [add_zero]
 
 theorem mod_mod_of_dvd (a : Ordinal) {b c : Ordinal} (h : c ∣ b) : a % b % c = a % c := by
diff --git a/Mathlib/SetTheory/Ordinal/Exponential.lean b/Mathlib/SetTheory/Ordinal/Exponential.lean
index f43661c24a209a..d33e3d383cfecf 100644
--- a/Mathlib/SetTheory/Ordinal/Exponential.lean
+++ b/Mathlib/SetTheory/Ordinal/Exponential.lean
@@ -301,7 +301,7 @@ theorem log_zero_right (b : Ordinal) : log b 0 = 0 := by
   obtain rfl | hb := eq_or_ne b 0
   · exact log_zero_left 0
   · rw [log]
-    convert csSup_empty
+    convert! csSup_empty
     aesop
 
 /-- `opow b` and `log b` (almost) form a Galois connection.
@@ -445,7 +445,7 @@ theorem log_opow_mul {b v : Ordinal} (hb : 1 < b) (u : Ordinal) (hv : v ≠ 0) :
   simpa using log_opow_mul_add hb hv (opow_pos u (bot_lt_of_lt hb))
 
 theorem log_opow {b : Ordinal} (hb : 1 < b) (x : Ordinal) : log b (b ^ x) = x := by
-  convert log_opow_mul hb x zero_ne_one.symm using 1
+  convert! log_opow_mul hb x zero_ne_one.symm using 1
   · rw [mul_one]
   · rw [log_one_right, add_zero]
 
@@ -465,7 +465,7 @@ theorem div_two_opow_log {o : Ordinal} (ho : o ≠ 0) : o / 2 ^ log 2 o = 1 := b
   · simpa [one_le_iff_ne_zero, pos_iff_ne_zero] using div_opow_log_pos 2 ho
 
 theorem two_opow_log_add {o : Ordinal} (ho : o ≠ 0) : 2 ^ log 2 o + o % 2 ^ log 2 o = o := by
-  convert div_add_mod .. using 2
+  convert! div_add_mod .. using 2
   rw [div_two_opow_log ho, mul_one]
 
 theorem add_log_le_log_mul {x y : Ordinal} (b : Ordinal) (hx : x ≠ 0) (hy : y ≠ 0) :
diff --git a/Mathlib/SetTheory/Ordinal/Family.lean b/Mathlib/SetTheory/Ordinal/Family.lean
index 28865f56d343f8..748e7cda02fe64 100644
--- a/Mathlib/SetTheory/Ordinal/Family.lean
+++ b/Mathlib/SetTheory/Ordinal/Family.lean
@@ -665,7 +665,7 @@ set_option linter.deprecated false in
 @[deprecated "lsub is deprecated" (since := "2026-03-27")]
 theorem lsub_le_of_range_subset {ι ι'} {f : ι → Ordinal} {g : ι' → Ordinal}
     (h : Set.range f ⊆ Set.range g) : lsub.{u, max v w} f ≤ lsub.{v, max u w} g :=
-  csSup_le_csSup' bddAbove_of_small (by convert Set.image_mono h <;> apply Set.range_comp)
+  csSup_le_csSup' bddAbove_of_small (by convert! Set.image_mono h <;> apply Set.range_comp)
 
 set_option linter.deprecated false in
 @[deprecated "lsub is deprecated" (since := "2026-03-27")]
@@ -782,7 +782,7 @@ set_option linter.deprecated false in
 @[deprecated "blsub is deprecated" (since := "2026-03-23")]
 theorem blsub_le_iff {o : Ordinal.{u}} {f : ∀ a < o, Ordinal.{max u v}} {a} :
     blsub.{_, v} o f ≤ a ↔ ∀ i h, f i h < a := by
-  convert bsup_le_iff.{_, v} (f := fun a ha => succ (f a ha)) (a := a) using 2
+  convert! bsup_le_iff.{_, v} (f := fun a ha => succ (f a ha)) (a := a) using 2
   simp_rw [succ_le_iff]
 
 set_option linter.deprecated false in
diff --git a/Mathlib/SetTheory/Ordinal/FixedPoint.lean b/Mathlib/SetTheory/Ordinal/FixedPoint.lean
index b5f91a07c49ef1..2baa6623a71731 100644
--- a/Mathlib/SetTheory/Ordinal/FixedPoint.lean
+++ b/Mathlib/SetTheory/Ordinal/FixedPoint.lean
@@ -328,7 +328,7 @@ theorem nfp_eq_self {a} (h : f a = a) : nfp f a = a :=
 /-- The fixed point lemma for normal functions: any normal function has an unbounded set of
 fixed points. -/
 theorem not_bddAbove_fp (H : IsNormal f) : ¬ BddAbove (Function.fixedPoints f) := by
-  convert not_bddAbove_fp_family fun _ : Unit => H
+  convert! not_bddAbove_fp_family fun _ : Unit => H
   exact (Set.iInter_const _).symm
 
 /-- The derivative of a normal function `f` is the sequence of fixed points of `f`.
@@ -379,7 +379,7 @@ theorem mem_range_deriv (H : IsNormal f) {a} : a ∈ Set.range (deriv f) ↔ f a
 
 /-- `Ordinal.deriv` enumerates the fixed points of a normal function. -/
 theorem deriv_eq_enumOrd (H : IsNormal f) : deriv f = enumOrd (Function.fixedPoints f) := by
-  convert derivFamily_eq_enumOrd fun _ : Unit => H
+  convert! derivFamily_eq_enumOrd fun _ : Unit => H
   exact (Set.iInter_const _).symm
 
 @[deprecated "do not depend on the junk values of `nfp`" (since := "2026-05-13")]
diff --git a/Mathlib/SetTheory/Ordinal/Principal.lean b/Mathlib/SetTheory/Ordinal/Principal.lean
index 7ee3e2edd64876..225bacaf8298d3 100644
--- a/Mathlib/SetTheory/Ordinal/Principal.lean
+++ b/Mathlib/SetTheory/Ordinal/Principal.lean
@@ -385,7 +385,7 @@ theorem isPrincipal_mul_iff_mul_left_eq :
     IsPrincipal (· * ·) o ↔ ∀ a, 0 < a → a < o → a * o = o := by
   refine ⟨fun h a ha₀ hao => ?_, fun h a b hao hbo => ?_⟩
   · rcases le_or_gt o 2 with ho | ho
-    · convert one_mul o
+    · convert! one_mul o
       apply le_antisymm
       · rw [← lt_add_one_iff, one_add_one_eq_two]
         exact hao.trans_le ho
diff --git a/Mathlib/SetTheory/Ordinal/Veblen.lean b/Mathlib/SetTheory/Ordinal/Veblen.lean
index 5f3115ba14f3cd..8d6a66f96a7009 100644
--- a/Mathlib/SetTheory/Ordinal/Veblen.lean
+++ b/Mathlib/SetTheory/Ordinal/Veblen.lean
@@ -510,7 +510,7 @@ theorem invVeblen₂_lt (x : Ordinal) : invVeblen₂ x < ω ^ x := by
 theorem invVeblen₂_le (x : Ordinal) : invVeblen₂ x ≤ x := by
   obtain h | h := eq_zero_or_pos (invVeblen₁ x)
   · rw [invVeblen₂_le_iff, h, veblen_zero]
-  · convert (invVeblen₂_lt x).le
+  · convert! (invVeblen₂_lt x).le
     rw [← veblen_zero_apply, veblen_eq_of_lt_invVeblen₁ h]
 
 theorem invVeblen₂_of_lt_opow (h : a < ω ^ a) : invVeblen₂ a = a := by
@@ -536,7 +536,7 @@ theorem veblen_eq_opow_iff (h : a < veblen o a) :
     · rw [← veblen_veblen_of_lt ho, veblen_zero_apply, opow_right_inj one_lt_omega0]
       rintro rfl
       simp [invVeblen₁_veblen h, invVeblen₂_veblen ho.ne' h]
-  · convert ← veblen_invVeblen₁_invVeblen₂ x
+  · convert! ← veblen_invVeblen₁_invVeblen₂ x
 
 /-! ### Epsilon function -/
 
diff --git a/Mathlib/SetTheory/ZFC/Cardinal.lean b/Mathlib/SetTheory/ZFC/Cardinal.lean
index 79322c59496a21..5f95e3b55cae00 100644
--- a/Mathlib/SetTheory/ZFC/Cardinal.lean
+++ b/Mathlib/SetTheory/ZFC/Cardinal.lean
@@ -57,7 +57,7 @@ theorem card_singleton : card {x} = 1 := by
   simpa [notMem_singleton] using card_insert (notMem_empty x)
 
 theorem card_pair_of_ne (h : x ≠ y) : card {x, y} = 2 := by
-  convert card_insert (notMem_singleton.2 h)
+  convert! card_insert (notMem_singleton.2 h)
   rw [card_singleton, one_add_one_eq_two]
 
 theorem card_union_le : card (x ∪ y) ≤ card x + card y := by
diff --git a/Mathlib/SetTheory/ZFC/Ordinal.lean b/Mathlib/SetTheory/ZFC/Ordinal.lean
index d88a4c560ec4a5..00ccaf89956172 100644
--- a/Mathlib/SetTheory/ZFC/Ordinal.lean
+++ b/Mathlib/SetTheory/ZFC/Ordinal.lean
@@ -296,7 +296,7 @@ theorem mem_toPSet_iff {o : Ordinal} {x : PSet} : x ∈ o.toPSet ↔ ∃ a < o,
 theorem rank_toPSet (o : Ordinal) : o.toPSet.rank = o := by
   rw [toPSet, PSet.rank]
   conv_rhs => rw [← _root_.iSup_succ o]
-  convert ToType.mk.symm.iSup_comp (g := fun x ↦ Order.succ x.1.toPSet.rank)
+  convert! ToType.mk.symm.iSup_comp (g := fun x ↦ Order.succ x.1.toPSet.rank)
   rw [rank_toPSet]
 termination_by o
 decreasing_by rename_i x; exact x.2
diff --git a/Mathlib/Tactic/ComputeAsymptotics/Lemmas.lean b/Mathlib/Tactic/ComputeAsymptotics/Lemmas.lean
index 5fafd73e902048..48065c7c5d6236 100644
--- a/Mathlib/Tactic/ComputeAsymptotics/Lemmas.lean
+++ b/Mathlib/Tactic/ComputeAsymptotics/Lemmas.lean
@@ -61,7 +61,7 @@ theorem tendsto_nhdsNE_of_tendsto_atTop_nhds_of_eq [TopologicalSpace α] {a b :
     (h_pos : Tendsto (fun x ↦ f (c + x⁻¹)) atTop (𝓝 b)) (h_eq : a = b) :
     Tendsto f (𝓝[≠] c) (𝓝 a) := by
   apply tendsto_nhdsNE_of_tendsto_atTop _ _ h_neg
-  convert h_pos
+  convert! h_pos
 
 theorem isBigOWith_of_tendsto_top {C : ℝ} {f g : ℝ → ℝ} {l : Filter ℝ}
     (h : Tendsto (fun x ↦ g x / f x) l atTop) (hC : 0 < C) :
diff --git a/Mathlib/Tactic/ComputeAsymptotics/Multiseries/Corecursion.lean b/Mathlib/Tactic/ComputeAsymptotics/Multiseries/Corecursion.lean
index dfde0e05295698..3ef27c26e30b22 100644
--- a/Mathlib/Tactic/ComputeAsymptotics/Multiseries/Corecursion.lean
+++ b/Mathlib/Tactic/ComputeAsymptotics/Multiseries/Corecursion.lean
@@ -135,7 +135,7 @@ theorem dist_cons_cons (x : α) (s t : Seq α) : dist (cons x s) (cons x t) = 2
   · contrapose! h'
     apply_fun Subtype.val using Subtype.val_injective
     simpa
-  · convert Nat.find_comp_succ _ _ _
+  · convert! Nat.find_comp_succ _ _ _
     simp [Stream'.cons]
 
 theorem dist_eq_half_of_head {s t : Seq α} (h : s.head = t.head) :
@@ -145,7 +145,7 @@ theorem dist_eq_half_of_head {s t : Seq α} (h : s.head = t.head) :
 set_option backward.isDefEq.respectTransparency false in
 theorem dist_eq_one_of_head {s t : Seq α} (h : s.head ≠ t.head) : dist s t = 1 := by
   rw [Subtype.dist_eq, PiNat.dist_eq_of_ne]
-  · convert pow_zero _
+  · convert! pow_zero _
     simp only [PiNat.firstDiff, ne_eq, Classical.dite_not, dite_eq_left_iff,
       Nat.find_eq_zero]
     intro h'
@@ -197,7 +197,7 @@ theorem FriendlyOperation.comp {op op' : Seq α → Seq α}
     (h : FriendlyOperation op) (h' : FriendlyOperation op') :
     FriendlyOperation (op ∘ op') := by
   rw [FriendlyOperation] at h h' ⊢
-  convert h.comp h'
+  convert! h.comp h'
   simp
 
 theorem FriendlyOperation.const {s : Seq α} : FriendlyOperation (fun _ ↦ s) := by
diff --git a/Mathlib/Tactic/ComputeAsymptotics/Multiseries/Majorized.lean b/Mathlib/Tactic/ComputeAsymptotics/Multiseries/Majorized.lean
index 1df2b486954207..e8f42bca27387e 100644
--- a/Mathlib/Tactic/ComputeAsymptotics/Multiseries/Majorized.lean
+++ b/Mathlib/Tactic/ComputeAsymptotics/Multiseries/Majorized.lean
@@ -119,7 +119,7 @@ theorem mul_bounded {f g basis_hd : ℝ → ℝ} {exp : ℝ} (hf : Majorized f b
     (hg : g =O[atTop] (fun _ ↦ (1 : ℝ))) :
     Majorized (f * g) basis_hd exp := by
   intro exp h_exp
-  convert IsLittleO.mul_isBigO (hf _ h_exp) hg using 1
+  convert! IsLittleO.mul_isBigO (hf _ h_exp) hg using 1
   simp
   rfl
 
diff --git a/Mathlib/Tactic/Convert.lean b/Mathlib/Tactic/Convert.lean
index eae981dc3385ee..9d3cf8b7982e5e 100644
--- a/Mathlib/Tactic/Convert.lean
+++ b/Mathlib/Tactic/Convert.lean
@@ -172,8 +172,8 @@ example (p q : Nat → Prop) (h : ∀ ε > 0, p ε) :
   sorry
 ```
 -/
-syntax (name := convert) "convert" Lean.Parser.Tactic.optConfig " ←"? ppSpace term (" using " num)?
-  (" with" (ppSpace colGt rintroPat)*)? : tactic
+syntax (name := convert) "convert" "!"? Lean.Parser.Tactic.optConfig " ←"? ppSpace term
+  (" using " num)? (" with" (ppSpace colGt rintroPat)*)? : tactic
 
 @[tactic_alt convert]
 syntax (name := convert!) "convert!" Lean.Parser.Tactic.optConfig " ←"? ppSpace term
@@ -181,7 +181,7 @@ syntax (name := convert!) "convert!" Lean.Parser.Tactic.optConfig " ←"? ppSpac
 
 macro_rules
 | `(tactic| convert! $cfg $[←%$l]? $t $[using $n]? $[with $[$w]*]?) =>
-    `(tactic| convert $cfg $[←%$l]? $t:term $[using $n]? $[with $[$w]*]?)
+    `(tactic| convert ! $cfg $[←%$l]? $t:term $[using $n]? $[with $[$w]*]?)
 
 /--
 Elaborates `term` ensuring the expected type, allowing stuck metavariables.
@@ -200,7 +200,7 @@ def elabTermForConvert (term : Syntax) (expectedType? : Option Expr) :
       return t
 
 elab_rules : tactic
-| `(tactic| convert $cfg $[←%$sym]? $term $[using $n]? $[with $ps?*]?) =>
+| `(tactic| convert $[!]? $cfg $[←%$sym]? $term $[using $n]? $[with $ps?*]?) =>
   withMainContext do
     let config ← Congr!.elabConfig (mkOptionalNode cfg)
     let patterns := (ps?.getD #[]).toList
diff --git a/Mathlib/Tactic/NormNum/NatFactorial.lean b/Mathlib/Tactic/NormNum/NatFactorial.lean
index d0cbe76f5eb0ef..e7bb3afd199ae7 100644
--- a/Mathlib/Tactic/NormNum/NatFactorial.lean
+++ b/Mathlib/Tactic/NormNum/NatFactorial.lean
@@ -55,7 +55,7 @@ partial def proveAscFactorial (n l : ℕ) (en el : Q(ℕ)) :
     let ⟨b, eb, b_prf⟩ := proveAscFactorial (n + m) r enm er
     have eab : Q(ℕ) := mkRawNatLit (a * b)
     have : $eab =Q $ea * $eb := ⟨⟩
-    ⟨a * b, eab, q(by convert asc_factorial_aux $en $em $er $ea $eb $a_prf $b_prf)⟩
+    ⟨a * b, eab, q(by convert! asc_factorial_aux «$en» «$em» «$er» «$ea» «$eb» «$a_prf» «$b_prf»)⟩
 
 lemma isNat_factorial {n x : ℕ} (h₁ : IsNat n x) (a : ℕ) (h₂ : (1).ascFactorial x = a) :
     IsNat (n !) a := by
diff --git a/Mathlib/Topology/Algebra/Algebra.lean b/Mathlib/Topology/Algebra/Algebra.lean
index 9ace4389aa5b0f..d735a9f8763010 100644
--- a/Mathlib/Topology/Algebra/Algebra.lean
+++ b/Mathlib/Topology/Algebra/Algebra.lean
@@ -609,7 +609,7 @@ theorem Subalgebra.le_topologicalClosure (s : Subalgebra R A) : s ≤ s.topologi
   subset_closure
 
 theorem Subalgebra.isClosed_topologicalClosure (s : Subalgebra R A) :
-    IsClosed (s.topologicalClosure : Set A) := by convert @isClosed_closure A _ s
+    IsClosed (s.topologicalClosure : Set A) := by convert! @isClosed_closure A _ s
 
 theorem Subalgebra.topologicalClosure_minimal {s t : Subalgebra R A} (h : s ≤ t)
     (ht : IsClosed (t : Set A)) : s.topologicalClosure ≤ t :=
diff --git a/Mathlib/Topology/Algebra/Category/ProfiniteGrp/Limits.lean b/Mathlib/Topology/Algebra/Category/ProfiniteGrp/Limits.lean
index eb5eeed67da128..8c314bc61cabf3 100644
--- a/Mathlib/Topology/Algebra/Category/ProfiniteGrp/Limits.lean
+++ b/Mathlib/Topology/Algebra/Category/ProfiniteGrp/Limits.lean
@@ -73,7 +73,7 @@ lemma toLimitFun_continuous (P : ProfiniteGrp.{u}) : Continuous (toLimitFun P) :
   intro s _
   rw [← (Set.biUnion_preimage_singleton QuotientGroup.mk s)]
   refine isOpen_iUnion (fun i ↦ isOpen_iUnion (fun _ ↦ ?_))
-  convert IsOpen.leftCoset H.toOpenSubgroup.isOpen' (Quotient.out i)
+  convert! IsOpen.leftCoset H.toOpenSubgroup.isOpen' (Quotient.out i)
   ext x
   simp only [Set.mem_preimage, Set.mem_singleton_iff]
   nth_rw 1 [← QuotientGroup.out_eq' i, eq_comm, QuotientGroup.eq]
diff --git a/Mathlib/Topology/Algebra/ConstMulAction.lean b/Mathlib/Topology/Algebra/ConstMulAction.lean
index 72020ad7c9d75f..0ebae3e977eda3 100644
--- a/Mathlib/Topology/Algebra/ConstMulAction.lean
+++ b/Mathlib/Topology/Algebra/ConstMulAction.lean
@@ -470,7 +470,7 @@ nonrec theorem smul_mem_nhds_smul_iff (hc : IsUnit c) {s : Set α} {a : α} :
 theorem isQuotientMap_smul {S β} [SMul S M] [SMul S α] [IsScalarTower S M α]
     [SMul S β] (f : α →[S] β) [TopologicalSpace β] (hf : IsQuotientMap f)
     (c : S) (hc : IsUnit (c • 1 : M)) : IsQuotientMap (c • · : β → β) :=
-  hf.of_comp_isQuotientMap <| by convert hf.comp hc.isHomeomorph_smul.isQuotientMap; ext; simp
+  hf.of_comp_isQuotientMap <| by convert! hf.comp hc.isHomeomorph_smul.isQuotientMap; ext; simp
 
 theorem isQuotientMap_nsmul {M β} [Semiring M] [AddCommMonoid α] [Module M α]
     [ContinuousConstSMul M α] [AddMonoid β] (f : α →+ β) [TopologicalSpace β]
@@ -542,7 +542,7 @@ variable [T2Space T] [LocallyCompactSpace T] [ContinuousConstSMul Γ T] (x : T)
 
 @[to_additive] lemma ProperlyDiscontinuousSMul.exists_nhds_disjoint_image :
     ∃ U ∈ 𝓝 x, ∀ γ : Γ, γ • x ≠ x → Disjoint ((γ • ·) '' U) U := by
-  convert exists_nhds_image_smul_eq_self Γ x using 4
+  convert! exists_nhds_image_smul_eq_self Γ x using 4
   rw [← not_imp_not]
   simp [Set.not_disjoint_iff_nonempty_inter]
 
diff --git a/Mathlib/Topology/Algebra/ContinuousMonoidHom.lean b/Mathlib/Topology/Algebra/ContinuousMonoidHom.lean
index a7d19908ba5858..19e62997f3e074 100644
--- a/Mathlib/Topology/Algebra/ContinuousMonoidHom.lean
+++ b/Mathlib/Topology/Algebra/ContinuousMonoidHom.lean
@@ -141,11 +141,11 @@ theorem ext {f g : A →ₜ* B} (h : ∀ x, f x = g x) : f = g :=
 
 @[to_additive]
 theorem toContinuousMap_injective : Injective (toContinuousMap : _ → C(A, B)) := fun f g h =>
-  ext <| by convert DFunLike.ext_iff.1 h
+  ext <| by convert! DFunLike.ext_iff.1 h
 
 @[to_additive]
 theorem toMonoidHom_injective : Injective (toMonoidHom : _ → A →* B) := fun f g h =>
-  ext <| by convert DFunLike.ext_iff.1 h
+  ext <| by convert! DFunLike.ext_iff.1 h
 
 /-- Composition of two continuous homomorphisms. -/
 @[to_additive (attr := simps!) /-- Composition of two continuous homomorphisms. -/]
@@ -524,8 +524,8 @@ variable {L : Type*} [Mul L] [TopologicalSpace L]
 @[to_additive /-- The composition of two ContinuousAddEquiv. -/]
 def trans (cme1 : M ≃ₜ* N) (cme2 : N ≃ₜ* L) : M ≃ₜ* L where
   __ := cme1.toMulEquiv.trans cme2.toMulEquiv
-  continuous_toFun := by convert Continuous.comp cme2.continuous_toFun cme1.continuous_toFun
-  continuous_invFun := by convert Continuous.comp cme1.continuous_invFun cme2.continuous_invFun
+  continuous_toFun := by convert! Continuous.comp cme2.continuous_toFun cme1.continuous_toFun
+  continuous_invFun := by convert! Continuous.comp cme1.continuous_invFun cme2.continuous_invFun
 
 @[to_additive (attr := simp)]
 theorem coe_trans (e₁ : M ≃ₜ* N) (e₂ : N ≃ₜ* L) : ↑(e₁.trans e₂) = e₂ ∘ e₁ := rfl
@@ -594,7 +594,7 @@ lemma toMulEquiv_toContinuousMulEquiv : (e.toContinuousMulEquiv he : G ≃* H) =
 @[to_additive]
 lemma symm_toContinuousMulEquiv :
     (e.toContinuousMulEquiv he).symm = e.symm.toContinuousMulEquiv
-      (fun s ↦ by convert (he _).symm; exact (e.preimage_symm_preimage s).symm) :=
+      (fun s ↦ by convert! (he _).symm; exact (e.preimage_symm_preimage s).symm) :=
   rfl
 
 end MulEquiv
diff --git a/Mathlib/Topology/Algebra/Group/Basic.lean b/Mathlib/Topology/Algebra/Group/Basic.lean
index 9348c7d88a3bf6..6b132b67820f16 100644
--- a/Mathlib/Topology/Algebra/Group/Basic.lean
+++ b/Mathlib/Topology/Algebra/Group/Basic.lean
@@ -96,7 +96,7 @@ theorem IsClosed.leftCoset {U : Set G} (h : IsClosed U) (x : G) : IsClosed (x 
 @[to_additive (attr := simp)]
 theorem Filter.map_mul_left_nhdsNE {c a : G} :
     map (c * ·) (𝓝[≠] a) = (𝓝[≠] (c * a)) := by
-  convert (Homeomorph.mulLeft c).isEmbedding.map_nhdsWithin_eq .. using 2
+  convert! (Homeomorph.mulLeft c).isEmbedding.map_nhdsWithin_eq .. using 2
   simp
 
 /-- Multiplication from the right in a topological group as a homeomorphism. -/
@@ -132,7 +132,7 @@ theorem IsClosed.rightCoset {U : Set G} (h : IsClosed U) (x : G) : IsClosed (op
 @[to_additive (attr := simp)]
 theorem Filter.map_mul_right_nhdsNE {c a : G} :
     map (· * c) (𝓝[≠] a) = (𝓝[≠] (a * c)) := by
-  convert (Homeomorph.mulRight c).isEmbedding.map_nhdsWithin_eq .. using 2
+  convert! (Homeomorph.mulRight c).isEmbedding.map_nhdsWithin_eq .. using 2
   simp
 
 @[to_additive]
@@ -159,13 +159,13 @@ theorem totallyDisconnectedSpace_iff_connectedComponent_one :
 lemma Filter.tendsto_mul_const_iff (b : G) {c : G} {f : α → G} {l : Filter α} :
     Tendsto (f · * b) l (𝓝 (c * b)) ↔ Tendsto f l (𝓝 c) := by
   refine ⟨?_, Tendsto.mul_const b⟩
-  convert Tendsto.mul_const b⁻¹ using 3 <;> rw [mul_inv_cancel_right]
+  convert! Tendsto.mul_const b⁻¹ using 3 <;> rw [mul_inv_cancel_right]
 
 @[to_additive]
 lemma Filter.tendsto_const_mul_iff (b : G) {c : G} {f : α → G} {l : Filter α} :
     Tendsto (b * f ·) l (𝓝 (b * c)) ↔ Tendsto f l (𝓝 c) := by
   refine ⟨?_, Tendsto.const_mul b⟩
-  convert Tendsto.const_mul b⁻¹ using 3 <;> rw [inv_mul_cancel_left]
+  convert! Tendsto.const_mul b⁻¹ using 3 <;> rw [inv_mul_cancel_left]
 
 end ContinuousMulGroup
 
@@ -374,7 +374,7 @@ lemma continuousOn_inv_iff : ContinuousOn f⁻¹ s ↔ ContinuousOn f s :=
 
 @[to_additive (attr := simp)]
 theorem Filter.inv_nhdsNE {a : G} : (𝓝[≠] a)⁻¹ = (𝓝[≠] (a⁻¹)) := by
-  convert (Homeomorph.inv G).isEmbedding.map_nhdsWithin_eq .. using 2
+  convert! (Homeomorph.inv G).isEmbedding.map_nhdsWithin_eq .. using 2
   simp
 
 end ContinuousInvolutiveInv
@@ -518,22 +518,22 @@ variable [ContinuousMul H]
 
 @[to_additive (attr := simp)]
 theorem Filter.map_mul_left_nhdsGT {c a : H} : map (c * ·) (𝓝[>] a) = (𝓝[>] (c * a)) := by
-  convert (Homeomorph.mulLeft c).isEmbedding.map_nhdsWithin_eq .. using 2
+  convert! (Homeomorph.mulLeft c).isEmbedding.map_nhdsWithin_eq .. using 2
   simp [mul_comm]
 
 @[to_additive (attr := simp)]
 theorem Filter.map_mul_left_nhdsLT {c a : H} : map (c * ·) (𝓝[<] a) = (𝓝[<] (c * a)) := by
-  convert (Homeomorph.mulLeft c).isEmbedding.map_nhdsWithin_eq .. using 2
+  convert! (Homeomorph.mulLeft c).isEmbedding.map_nhdsWithin_eq .. using 2
   simp [mul_comm]
 
 @[to_additive (attr := simp)]
 theorem Filter.map_mul_right_nhdsGT {c a : H} : map (· * c) (𝓝[>] a) = (𝓝[>] (a * c)) := by
-  convert (Homeomorph.mulRight c).isEmbedding.map_nhdsWithin_eq .. using 2
+  convert! (Homeomorph.mulRight c).isEmbedding.map_nhdsWithin_eq .. using 2
   simp
 
 @[to_additive (attr := simp)]
 theorem Filter.map_mul_right_nhdsLT {c a : H} : map (· * c) (𝓝[<] a) = (𝓝[<] (a * c)) := by
-  convert (Homeomorph.mulRight c).isEmbedding.map_nhdsWithin_eq .. using 2
+  convert! (Homeomorph.mulRight c).isEmbedding.map_nhdsWithin_eq .. using 2
   simp
 
 end mul
@@ -544,12 +544,12 @@ variable [ContinuousInv H]
 
 @[to_additive (attr := simp)]
 theorem Filter.inv_nhdsGT {a : H} : (𝓝[>] a)⁻¹ = (𝓝[<] (a⁻¹)) := by
-  convert (Homeomorph.inv H).isEmbedding.map_nhdsWithin_eq .. using 2
+  convert! (Homeomorph.inv H).isEmbedding.map_nhdsWithin_eq .. using 2
   simp
 
 @[to_additive (attr := simp)]
 theorem Filter.inv_nhdsLT {a : H} : (𝓝[<] a)⁻¹ = (𝓝[>] (a⁻¹)) := by
-  convert (Homeomorph.inv H).isEmbedding.map_nhdsWithin_eq .. using 2
+  convert! (Homeomorph.inv H).isEmbedding.map_nhdsWithin_eq .. using 2
   simp
 
 @[to_additive]
@@ -1013,7 +1013,7 @@ lemma Filter.tendsto_div_const_iff {G : Type*}
     {b : G} (hb : b ≠ 0) {c : G} {f : α → G} {l : Filter α} :
     Tendsto (f · / b) l (𝓝 (c / b)) ↔ Tendsto f l (𝓝 c) := by
   refine ⟨fun h ↦ ?_, fun h ↦ Filter.Tendsto.div_const' h b⟩
-  convert h.div_const' b⁻¹ with k <;> rw [← div_mul_eq_div_div_swap, inv_mul_cancel₀ hb, div_one]
+  convert! h.div_const' b⁻¹ with k <;> rw [← div_mul_eq_div_div_swap, inv_mul_cancel₀ hb, div_one]
 
 @[to_additive tendsto_sub_const_iff]
 lemma Filter.tendsto_div_const_iff' {G : Type*}
@@ -1021,7 +1021,7 @@ lemma Filter.tendsto_div_const_iff' {G : Type*}
     (b : G) {c : G} {f : α → G} {l : Filter α} :
     Tendsto (f · / b) l (𝓝 (c / b)) ↔ Tendsto f l (𝓝 c) := by
   refine ⟨fun h ↦ ?_, fun h ↦ Filter.Tendsto.div_const' h b⟩
-  convert h.div_const' b⁻¹ with k <;> rw [← div_mul_eq_div_div_swap, inv_mul_cancel, div_one]
+  convert! h.div_const' b⁻¹ with k <;> rw [← div_mul_eq_div_div_swap, inv_mul_cancel, div_one]
 
 @[to_additive const_sub]
 theorem Filter.Tendsto.const_div' (b : G) {c : G} {f : α → G} {l : Filter α}
@@ -1044,7 +1044,7 @@ variable [Group G] [TopologicalSpace G] [IsTopologicalGroup G]
 lemma Filter.tendsto_const_div_iff' (b : G) {c : G} {f : α → G} {l : Filter α} :
     Tendsto (fun k : α ↦ b / f k) l (𝓝 (b / c)) ↔ Tendsto f l (𝓝 c) := by
   refine ⟨fun h ↦ ?_, Filter.Tendsto.const_div' b⟩
-  convert h.inv.mul_const b with k <;> rw [inv_div, div_mul_cancel]
+  convert! h.inv.mul_const b with k <;> rw [inv_div, div_mul_cancel]
 
 @[deprecated (since := "2026-02-03")]
 alias Filter.tendsto_const_div_iff := Filter.tendsto_const_div_iff'
@@ -1119,7 +1119,7 @@ theorem Subgroup.properlyDiscontinuousSMul_of_tendsto_cofinite (S : Subgroup G)
       intro K L hK hL
       have H : Set.Finite _ := hS ((hL.prod hK).image continuous_div').compl_mem_cocompact
       rw [preimage_compl, compl_compl] at H
-      convert H
+      convert! H
       ext x
       simp only [image_smul, mem_setOf_eq, coe_subtype, mem_preimage, mem_image, Prod.exists]
       exact Set.smul_inter_nonempty_iff' }
@@ -1146,7 +1146,7 @@ theorem Subgroup.properlyDiscontinuousSMul_opposite_of_tendsto_cofinite (S : Sub
         hS ((hK.prod hL).image (continuous_mul.comp this)).compl_mem_cocompact
       simp only [preimage_compl, compl_compl, coe_subtype, comp_apply] at H
       apply Finite.of_preimage _ (equivOp S).surjective
-      convert H using 1
+      convert! H using 1
       ext x
       simp only [image_smul, mem_setOf_eq, mem_preimage, mem_image, Prod.exists]
       exact Set.op_smul_inter_nonempty_iff }
diff --git a/Mathlib/Topology/Algebra/Group/ClosedSubgroup.lean b/Mathlib/Topology/Algebra/Group/ClosedSubgroup.lean
index fb683cedd07a04..e0ae8b75fbc4c4 100644
--- a/Mathlib/Topology/Algebra/Group/ClosedSubgroup.lean
+++ b/Mathlib/Topology/Algebra/Group/ClosedSubgroup.lean
@@ -102,7 +102,7 @@ lemma normalCore_isClosed (H : Subgroup G) (h : IsClosed (H : Set G)) :
   push_cast
   apply isClosed_iInter
   intro g
-  convert IsClosed.preimage (IsTopologicalGroup.continuous_conj (ConjAct.ofConjAct g⁻¹)) h using 1
+  convert! IsClosed.preimage (IsTopologicalGroup.continuous_conj (ConjAct.ofConjAct g⁻¹)) h using 1
   exact Set.ext (fun t ↦ Set.mem_smul_set_iff_inv_smul_mem)
 
 @[to_additive]
diff --git a/Mathlib/Topology/Algebra/Group/DiscontinuousSubgroup.lean b/Mathlib/Topology/Algebra/Group/DiscontinuousSubgroup.lean
index 8b4093b9da32dc..9299ba695f52ea 100644
--- a/Mathlib/Topology/Algebra/Group/DiscontinuousSubgroup.lean
+++ b/Mathlib/Topology/Algebra/Group/DiscontinuousSubgroup.lean
@@ -26,7 +26,7 @@ protected lemma Subgroup.properlyDiscontinuousSMul_iff
       IsCompact K → IsCompact L →  {g : Γ | g ∈ S ∧ (g • K ∩ L).Nonempty}.Finite := by
   rw [properlyDiscontinuousSMul_iff]
   congr! with K L hK hL
-  convert injOn_subtype_val (s := {m : S | (m • K ∩ L).Nonempty}) |>.bijOn_image.finite_iff_finite
+  convert! injOn_subtype_val (s := {m : S | (m • K ∩ L).Nonempty}) |>.bijOn_image.finite_iff_finite
   ext g
   simp [Set.subtype_smul_set, and_comm]
 
diff --git a/Mathlib/Topology/Algebra/Group/Pointwise.lean b/Mathlib/Topology/Algebra/Group/Pointwise.lean
index 505e63bcab00ef..0052f83df123fa 100644
--- a/Mathlib/Topology/Algebra/Group/Pointwise.lean
+++ b/Mathlib/Topology/Algebra/Group/Pointwise.lean
@@ -83,7 +83,7 @@ theorem MulAction.isClosedMap_quotient [CompactSpace α] :
   intro t ht
   rw [← isQuotientMap_quotient_mk'.isClosed_preimage,
     MulAction.quotient_preimage_image_eq_union_mul]
-  convert ht.smul_left_of_isCompact (isCompact_univ (X := α))
+  convert! ht.smul_left_of_isCompact (isCompact_univ (X := α))
   rw [← biUnion_univ, ← iUnion_smul_left_image]
   simp only [image_smul]
 
diff --git a/Mathlib/Topology/Algebra/InfiniteSum/Basic.lean b/Mathlib/Topology/Algebra/InfiniteSum/Basic.lean
index c680957af672d5..917957abae71b0 100644
--- a/Mathlib/Topology/Algebra/InfiniteSum/Basic.lean
+++ b/Mathlib/Topology/Algebra/InfiniteSum/Basic.lean
@@ -44,11 +44,11 @@ theorem hasProd_one : HasProd (fun _ ↦ 1 : β → α) 1 L := by simp [HasProd,
 
 @[to_additive (attr := simp)]
 theorem hasProd_empty [IsEmpty β] : HasProd f 1 L := by
-  convert hasProd_one
+  convert! hasProd_one
 
 @[to_additive (attr := nontriviality)]
 theorem HasProd.of_subsingleton_cod [Subsingleton α] : HasProd f 1 L := by
-  convert hasProd_one
+  convert! hasProd_one
 
 @[to_additive (attr := simp)]
 theorem multipliable_one : Multipliable (fun _ ↦ 1 : β → α) L :=
@@ -169,7 +169,7 @@ lemma hasProd_singleton (m : β) (f : β → α) : HasProd (({m} : Set β).restr
 @[to_additive]
 theorem hasProd_ite_eq (b : β) [DecidablePred (· = b)] (a : α) (L := unconditional β) [L.LeAtTop] :
     HasProd (fun b' ↦ if b' = b then a else 1) a L := by
-  convert hasProd_single b (hf := fun b' hb' ↦ if_neg hb') (L := L)
+  convert! hasProd_single b (hf := fun b' hb' ↦ if_neg hb') (L := L)
   exact (if_pos rfl).symm
 
 @[to_additive]
@@ -418,7 +418,7 @@ theorem eq_mul_of_hasProd_ite [L.LeAtTop] [L.NeBot] {α : Type*} [TopologicalSpa
     [T2Space α] [ContinuousMul α] [DecidableEq β] {f : β → α} {a : α} (hf : HasProd f a L) (b : β)
     (a' : α) (hf' : HasProd (fun n ↦ ite (n = b) 1 (f n)) a' L) : a = a' * f b := by
   refine (mul_one a).symm.trans (hf.update' b 1 ?_)
-  convert hf'
+  convert! hf'
   apply update_apply
 
 end HasProd
@@ -459,7 +459,7 @@ theorem tprod_one : ∏'[L] _, (1 : α) = 1 := by
 
 @[to_additive (attr := simp)]
 theorem tprod_empty [IsEmpty β] : ∏'[L] b, f b = 1 := by
-  convert tprod_one (L := L)
+  convert! tprod_one (L := L)
 
 @[to_additive]
 theorem tprod_congr {f g : β → α}
diff --git a/Mathlib/Topology/Algebra/InfiniteSum/ConditionalInt.lean b/Mathlib/Topology/Algebra/InfiniteSum/ConditionalInt.lean
index 2332fbcb5f4897..df3018e330b7be 100644
--- a/Mathlib/Topology/Algebra/InfiniteSum/ConditionalInt.lean
+++ b/Mathlib/Topology/Algebra/InfiniteSum/ConditionalInt.lean
@@ -118,7 +118,7 @@ lemma symmetricIcc_eq_symmetricIoo_int : symmetricIcc ℤ = symmetricIoo ℤ :=
   simp only [← Nat.map_cast_int_atTop, Filter.map_map, Filter.mem_map, mem_atTop_sets, ge_iff_le,
     Set.mem_preimage, comp_apply]
   refine ⟨fun ⟨a, ha⟩ ↦ ⟨a + 1, fun b hb ↦ ?_⟩, fun ⟨a, ha⟩ ↦ ⟨a - 1, fun b hb ↦ ?_⟩⟩ <;>
-  [convert ha (b - 1) (by grind) using 1; convert ha (b + 1) (by grind) using 1] <;>
+  [convert! ha (b - 1) (by grind) using 1; convert! ha (b + 1) (by grind) using 1] <;>
   simp [Finset.ext_iff] <;> grind
 
 @[to_additive]
@@ -182,7 +182,7 @@ lemma _root_.Summable.tendsto_zero_of_even_summable_symmetricIcc {F : Type*} [No
   filter_upwards [eventually_ge_atTop 1] with x hx
   have : Finset.Icc (-x) x = Icc (-(x - 1)) (x - 1) ∪ {-x, x} := by
     lift x to ℕ using by positivity
-    convert Finset.Icc_succ_succ (x - 1) (x - 1) <;> grind
+    convert! Finset.Icc_succ_succ (x - 1) (x - 1) <;> grind
   rw [this, Finset.sum_union, Finset.sum_insert, Finset.sum_singleton,
     hs x, add_comm, add_sub_cancel_right, ← two_zsmul, norm_smul, Int.norm_eq_abs,
     Int.cast_two, abs_two, inv_mul_cancel_left₀ two_ne_zero] <;>
diff --git a/Mathlib/Topology/Algebra/InfiniteSum/Constructions.lean b/Mathlib/Topology/Algebra/InfiniteSum/Constructions.lean
index 0f29cf7e430d4e..96a5615e2aa861 100644
--- a/Mathlib/Topology/Algebra/InfiniteSum/Constructions.lean
+++ b/Mathlib/Topology/Algebra/InfiniteSum/Constructions.lean
@@ -36,7 +36,7 @@ variable [CommMonoid α] [TopologicalSpace α]
 
 @[to_additive]
 theorem hasProd_pi_single [DecidableEq β] (b : β) (a : α) : HasProd (Pi.mulSingle b a) a := by
-  convert hasProd_ite_eq (L := .unconditional β) b a
+  convert! hasProd_ite_eq (L := .unconditional β) b a
   simp [Pi.mulSingle_apply]
 
 @[to_additive (attr := simp)]
@@ -85,7 +85,7 @@ lemma HasProd.sum {α β M : Type*} [CommMonoid M] [TopologicalSpace M] [Continu
     (h₁ : HasProd (f ∘ Sum.inl) a) (h₂ : HasProd (f ∘ Sum.inr) b) : HasProd f (a * b) := by
   have : Tendsto ((∏ b ∈ ·, f b) ∘ sumEquiv.symm) (atTop.map sumEquiv) (nhds (a * b)) := by
     rw [Finset.sumEquiv.map_atTop, ← prod_atTop_atTop_eq]
-    convert (tendsto_mul.comp (nhds_prod_eq (x := a) (y := b) ▸ Tendsto.prodMap h₁ h₂))
+    convert! (tendsto_mul.comp (nhds_prod_eq (x := a) (y := b) ▸ Tendsto.prodMap h₁ h₂))
     ext s
     simp
   simpa [Tendsto, ← Filter.map_map] using this
diff --git a/Mathlib/Topology/Algebra/InfiniteSum/Defs.lean b/Mathlib/Topology/Algebra/InfiniteSum/Defs.lean
index 4f54a5f41226d2..01c9ccbcfcd3fa 100644
--- a/Mathlib/Topology/Algebra/InfiniteSum/Defs.lean
+++ b/Mathlib/Topology/Algebra/InfiniteSum/Defs.lean
@@ -309,7 +309,7 @@ theorem Multipliable.hasProd (ha : Multipliable f L) : HasProd f (∏'[L] b, f b
   classical
   rw [tprod_def, dif_pos ha]
   split_ifs with h h'
-  · convert hasProd_prod_support_of_ne_finset_one (s := h.2.toFinset) (L := L) _ using 2
+  · convert! hasProd_prod_support_of_ne_finset_one (s := h.2.toFinset) (L := L) _ using 2
     · simp only [Set.inter_eq_left.mpr (show ↑h.2.toFinset ⊆ L.support by simp)]
       simp only [Set.Finite.coe_toFinset, Finset.toFinset_coe]
       rw [finprod_eq_prod_of_mulSupport_subset (s := h.2.toFinset)]
diff --git a/Mathlib/Topology/Algebra/InfiniteSum/ENNReal.lean b/Mathlib/Topology/Algebra/InfiniteSum/ENNReal.lean
index 75b5aae84a67ad..6d23b702f40b31 100644
--- a/Mathlib/Topology/Algebra/InfiniteSum/ENNReal.lean
+++ b/Mathlib/Topology/Algebra/InfiniteSum/ENNReal.lean
@@ -234,7 +234,7 @@ space. This does not need a summability assumption, as otherwise all sums are ze
 theorem tendsto_tsum_compl_atTop_zero {α : Type*} {f : α → ℝ≥0∞} (hf : ∑' x, f x ≠ ∞) :
     Tendsto (fun s : Finset α => ∑' b : { x // x ∉ s }, f b) atTop (𝓝 0) := by
   lift f to α → ℝ≥0 using ENNReal.ne_top_of_tsum_ne_top hf
-  convert ENNReal.tendsto_coe.2 (NNReal.tendsto_tsum_compl_atTop_zero f)
+  convert! ENNReal.tendsto_coe.2 (NNReal.tendsto_tsum_compl_atTop_zero f)
   rw [ENNReal.coe_tsum]
   exact NNReal.summable_comp_injective (tsum_coe_ne_top_iff_summable.1 hf) Subtype.coe_injective
 
@@ -444,7 +444,7 @@ open Finset
 assumption on `f`, as otherwise all sums are zero. -/
 theorem tendsto_sum_nat_add (f : ℕ → ℝ≥0) : Tendsto (fun i => ∑' k, f (k + i)) atTop (𝓝 0) := by
   rw [← tendsto_coe]
-  convert _root_.tendsto_sum_nat_add fun i => (f i : ℝ)
+  convert! _root_.tendsto_sum_nat_add fun i => (f i : ℝ)
   norm_cast
 
 nonrec theorem hasSum_lt {f g : α → ℝ≥0} {sf sg : ℝ≥0} {i : α} (h : ∀ a : α, f a ≤ g a)
diff --git a/Mathlib/Topology/Algebra/InfiniteSum/Group.lean b/Mathlib/Topology/Algebra/InfiniteSum/Group.lean
index e28f041c119434..067c2f87f3925a 100644
--- a/Mathlib/Topology/Algebra/InfiniteSum/Group.lean
+++ b/Mathlib/Topology/Algebra/InfiniteSum/Group.lean
@@ -73,7 +73,7 @@ theorem multipliable_iff_of_multipliable_div (hfg : Multipliable (fun b ↦ f b
 @[to_additive]
 theorem HasProd.update [L.LeAtTop] (hf : HasProd f a₁ L) (b : β) [DecidableEq β] (a : α) :
     HasProd (update f b a) (a / f b * a₁) L := by
-  convert (hasProd_ite_eq b (a / f b) (L := L)).mul hf with b'
+  convert! (hasProd_ite_eq b (a / f b) (L := L)).mul hf with b'
   by_cases h : b' = b
   · rw [h, update_self]
     simp
@@ -126,7 +126,7 @@ theorem Set.Finite.multipliable_compl_iff {s : Set β} (hs : s.Finite) :
 @[to_additive]
 theorem hasProd_ite_div_hasProd [L.LeAtTop] [DecidableEq β] (hf : HasProd f a L) (b : β) :
     HasProd (fun n ↦ ite (n = b) 1 (f n)) (a / f b) L := by
-  convert hf.update b 1 using 1
+  convert! hf.update b 1 using 1
   · ext n
     rw [Function.update_apply]
   · rw [div_mul_eq_mul_div, one_mul]
diff --git a/Mathlib/Topology/Algebra/InfiniteSum/Module.lean b/Mathlib/Topology/Algebra/InfiniteSum/Module.lean
index f032067ed1cf50..93ddd5f754cb60 100644
--- a/Mathlib/Topology/Algebra/InfiniteSum/Module.lean
+++ b/Mathlib/Topology/Algebra/InfiniteSum/Module.lean
@@ -192,7 +192,7 @@ noncomputable def MulAction.automorphize [Group α] [MulAction α β] (f : β 
   intro b₁ b₂ ⟨a, (ha : a • b₂ = b₁)⟩
   simp only
   rw [← ha]
-  convert (Equiv.mulRight a).tsum_eq (fun a' ↦ f (a' • b₂)) using 1
+  convert! (Equiv.mulRight a).tsum_eq (fun a' ↦ f (a' • b₂)) using 1
   simp only [Equiv.coe_mulRight]
   congr
   ext
diff --git a/Mathlib/Topology/Algebra/InfiniteSum/NatInt.lean b/Mathlib/Topology/Algebra/InfiniteSum/NatInt.lean
index dc52aef2bbd369..e0dbc3df77b3fe 100644
--- a/Mathlib/Topology/Algebra/InfiniteSum/NatInt.lean
+++ b/Mathlib/Topology/Algebra/InfiniteSum/NatInt.lean
@@ -173,7 +173,7 @@ theorem rel_iSup_prod [CompleteLattice α] (m : α → M) (m0 : m ⊥ = 1) (R :
 theorem rel_sup_mul [CompleteLattice α] (m : α → M) (m0 : m ⊥ = 1) (R : M → M → Prop)
     (m_iSup : ∀ s : ℕ → α, R (m (⨆ i, s i)) (∏' i, m (s i))) (s₁ s₂ : α) :
     R (m (s₁ ⊔ s₂)) (m s₁ * m s₂) := by
-  convert rel_iSup_tprod m m0 R m_iSup fun b ↦ cond b s₁ s₂
+  convert! rel_iSup_tprod m m0 R m_iSup fun b ↦ cond b s₁ s₂
   · simp only [iSup_bool_eq, cond]
   · rw [tprod_fintype, Fintype.prod_bool, cond, cond]
 
diff --git a/Mathlib/Topology/Algebra/InfiniteSum/Ring.lean b/Mathlib/Topology/Algebra/InfiniteSum/Ring.lean
index a81c1ec803c300..24ea336c752619 100644
--- a/Mathlib/Topology/Algebra/InfiniteSum/Ring.lean
+++ b/Mathlib/Topology/Algebra/InfiniteSum/Ring.lean
@@ -328,13 +328,13 @@ theorem tprod_one_add_ordered [ContinuousAdd α]
   · simp
   obtain ⟨x, hx⟩ := hprod
   obtain ⟨a, ha⟩ := hsum
-  convert hx.tprod_eq
+  convert! hx.tprod_eq
   unfold HasProd at hx
   conv at hx in fun _ ↦ _ => ext _; rw [prod_one_add_ordered] -- simp_rw would cause loop
   rw [ha.tsum_eq]
   refine (tendsto_nhds_unique (hx.comp tendsto_finset_Iic_atTop_atTop) ?_).symm
   apply Tendsto.const_add
-  convert ha.comp tendsto_finset_Iic_atTop_atTop using 2 with s
+  convert! ha.comp tendsto_finset_Iic_atTop_atTop using 2 with s
   refine sum_congr rfl (fun i hi ↦ ?_)
   congr
   grind
diff --git a/Mathlib/Topology/Algebra/InfiniteSum/SummationFilter.lean b/Mathlib/Topology/Algebra/InfiniteSum/SummationFilter.lean
index 49f3f3912dcf63..3d23c163809747 100644
--- a/Mathlib/Topology/Algebra/InfiniteSum/SummationFilter.lean
+++ b/Mathlib/Topology/Algebra/InfiniteSum/SummationFilter.lean
@@ -252,7 +252,7 @@ lemma conditional_filter_eq_map_range : (conditional ℕ).filter = atTop.map Fin
       simp only [tendsto_atTop', mem_map, mem_atTop_sets, mem_preimage] <;>
       rintro s ⟨a, ha⟩
   · exact ⟨a + 1, fun b hb ↦ ha (b + 1) (by lia)⟩
-  · exact ⟨a + 1, fun b hb ↦ by convert ha (b - 1) (by lia); lia⟩
+  · exact ⟨a + 1, fun b hb ↦ by convert! ha (b - 1) (by lia); lia⟩
 
 end conditionalTop
 
diff --git a/Mathlib/Topology/Algebra/IsOpenUnits.lean b/Mathlib/Topology/Algebra/IsOpenUnits.lean
index c8e91978ce8452..9c84f5cb5ec4cc 100644
--- a/Mathlib/Topology/Algebra/IsOpenUnits.lean
+++ b/Mathlib/Topology/Algebra/IsOpenUnits.lean
@@ -54,7 +54,7 @@ instance (priority := 900) {M : Type*} [GroupWithZero M]
     [TopologicalSpace M] [ContinuousInv₀ M] [T1Space M] : IsOpenUnits M where
   isOpenEmbedding_unitsVal := by
     refine ⟨Units.isEmbedding_val₀, ?_⟩
-    convert (isClosed_singleton (X := M) (x := 0)).isOpen_compl
+    convert! (isClosed_singleton (X := M) (x := 0)).isOpen_compl
     ext
     simp only [Set.mem_range, Set.mem_compl_iff, Set.mem_singleton_iff]
     exact isUnit_iff_ne_zero
diff --git a/Mathlib/Topology/Algebra/IsUniformGroup/Basic.lean b/Mathlib/Topology/Algebra/IsUniformGroup/Basic.lean
index d1152d6b71e53a..812dc6c398e1e4 100644
--- a/Mathlib/Topology/Algebra/IsUniformGroup/Basic.lean
+++ b/Mathlib/Topology/Algebra/IsUniformGroup/Basic.lean
@@ -138,7 +138,7 @@ theorem totallyBounded_iff_subset_finite_iUnion_nhds_one {s : Set α} :
 
 @[to_additive]
 theorem totallyBounded_inv {s : Set α} (hs : TotallyBounded s) : TotallyBounded (s⁻¹) := by
-  convert TotallyBounded.image hs uniformContinuous_inv
+  convert! TotallyBounded.image hs uniformContinuous_inv
   aesop
 
 section UniformConvergence
@@ -697,7 +697,7 @@ instance QuotientGroup.completeSpace_right' (G : Type u) [Group G] [TopologicalS
     ⟨↑x₀,
       tendsto_nhds_of_cauchySeq_of_subseq hx
         (strictMono_nat_of_lt_succ fun n => (hφ (n + 1)).1).tendsto_atTop ?_⟩
-  convert ((continuous_coinduced_rng : Continuous ((↑) : G → G ⧸ N)).tendsto x₀).comp hx₀
+  convert! ((continuous_coinduced_rng : Continuous ((↑) : G → G ⧸ N)).tendsto x₀).comp hx₀
   exact funext fun n => (x' n).snd
 
 /-- The quotient `G ⧸ N` of a complete first countable uniform group `G` by a normal subgroup
diff --git a/Mathlib/Topology/Algebra/IsUniformGroup/Defs.lean b/Mathlib/Topology/Algebra/IsUniformGroup/Defs.lean
index 9e592b3779255f..a8318593f8ef4d 100644
--- a/Mathlib/Topology/Algebra/IsUniformGroup/Defs.lean
+++ b/Mathlib/Topology/Algebra/IsUniformGroup/Defs.lean
@@ -456,7 +456,7 @@ theorem Filter.Tendsto.conj_nhds_one {ι : Type*} {l : Filter ι} {x : ι → β
   have : Tendsto (fun i ↦ (g i, x i)) l (comap Prod.snd (𝓝 1)) := by
     rwa [tendsto_comap_iff]
   -- `exact` works but is quite slow...
-  convert tendsto_conj_nhds_one.comp this
+  convert! tendsto_conj_nhds_one.comp this
 
 theorem IsUniformGroup.of_left_right : IsUniformGroup β where
   uniformContinuous_div := by
diff --git a/Mathlib/Topology/Algebra/Module/Alternating/Basic.lean b/Mathlib/Topology/Algebra/Module/Alternating/Basic.lean
index 2fe0ff95b01983..3d10a520a2569e 100644
--- a/Mathlib/Topology/Algebra/Module/Alternating/Basic.lean
+++ b/Mathlib/Topology/Algebra/Module/Alternating/Basic.lean
@@ -101,7 +101,7 @@ theorem ext {f g : M [⋀^ι]→L[R] N} (H : ∀ x, f x = g x) : f = g :=
 
 theorem toAlternatingMap_injective :
     Injective (toAlternatingMap : (M [⋀^ι]→L[R] N) → (M [⋀^ι]→ₗ[R] N)) := fun f g h =>
-  DFunLike.ext' <| by convert DFunLike.ext'_iff.1 h
+  DFunLike.ext' <| by convert! DFunLike.ext'_iff.1 h
 
 @[simp]
 theorem range_toAlternatingMap :
diff --git a/Mathlib/Topology/Algebra/Module/Basic.lean b/Mathlib/Topology/Algebra/Module/Basic.lean
index ef874d64733656..e2cd9a9f25d672 100644
--- a/Mathlib/Topology/Algebra/Module/Basic.lean
+++ b/Mathlib/Topology/Algebra/Module/Basic.lean
@@ -90,7 +90,7 @@ theorem Module.punctured_nhds_neBot [Nontrivial M] [NeBot (𝓝[≠] (0 : R))] [
   rcases exists_ne (0 : M) with ⟨y, hy⟩
   suffices Tendsto (fun c : R => x + c • y) (𝓝[≠] 0) (𝓝[≠] x) from this.neBot
   refine Tendsto.inf ?_ (tendsto_principal_principal.2 <| ?_)
-  · convert tendsto_const_nhds.add ((@tendsto_id R _).smul_const y)
+  · convert! tendsto_const_nhds.add ((@tendsto_id R _).smul_const y)
     rw [zero_smul, add_zero]
   · intro c hc
     simpa [hy] using hc
diff --git a/Mathlib/Topology/Algebra/Module/Equiv.lean b/Mathlib/Topology/Algebra/Module/Equiv.lean
index c33c0c379f411f..a34700f66eb647 100644
--- a/Mathlib/Topology/Algebra/Module/Equiv.lean
+++ b/Mathlib/Topology/Algebra/Module/Equiv.lean
@@ -1215,7 +1215,7 @@ lemma IsInvertible.inverse_comp_apply_of_right {g : M₂ →L[R] M₃} {f : M 
 @[simp]
 theorem ringInverse_equiv (e : M ≃L[R] M) : (↑e)⁻¹ʳ = inverse (e : M →L[R] M) := by
   suffices ((ContinuousLinearEquiv.unitsEquiv _ _).symm e : M →L[R] M)⁻¹ʳ = inverse ↑e by
-    convert this
+    convert! this
   simp
   rfl
 
diff --git a/Mathlib/Topology/Algebra/Module/Multilinear/Topology.lean b/Mathlib/Topology/Algebra/Module/Multilinear/Topology.lean
index cae0a409413142..c82b6758a559b1 100644
--- a/Mathlib/Topology/Algebra/Module/Multilinear/Topology.lean
+++ b/Mathlib/Topology/Algebra/Module/Multilinear/Topology.lean
@@ -53,7 +53,7 @@ lemma range_toUniformOnFun [DecidableEq ι] [TopologicalSpace F] :
   · rintro ⟨f, rfl⟩
     exact ⟨f.cont, f.map_update_add, f.map_update_smul⟩
   · rintro ⟨hcont, hadd, hsmul⟩
-    exact ⟨⟨⟨f, by intro; convert hadd, by intro; convert hsmul⟩, hcont⟩, rfl⟩
+    exact ⟨⟨⟨f, by intro; convert! hadd, by intro; convert! hsmul⟩, hcont⟩, rfl⟩
 
 @[simp]
 lemma toUniformOnFun_toFun [TopologicalSpace F] (f : ContinuousMultilinearMap 𝕜 E F) :
@@ -161,7 +161,7 @@ theorem isUniformEmbedding_restrictScalars :
   letI : NontriviallyNormedField 𝕜 :=
     ⟨let ⟨x, hx⟩ := @NontriviallyNormedField.non_trivial 𝕜' _; ⟨algebraMap 𝕜' 𝕜 x, by simpa⟩⟩
   rw [← isUniformEmbedding_toUniformOnFun.of_comp_iff]
-  convert isUniformEmbedding_toUniformOnFun using 4 with s
+  convert! isUniformEmbedding_toUniformOnFun using 4 with s
   exact ⟨fun h ↦ h.extend_scalars _, fun h ↦ h.restrict_scalars _⟩
 
 theorem uniformContinuous_restrictScalars :
diff --git a/Mathlib/Topology/Algebra/Module/Spaces/ContinuousLinearMap.lean b/Mathlib/Topology/Algebra/Module/Spaces/ContinuousLinearMap.lean
index efeec28683bac1..f0a3681fab4122 100644
--- a/Mathlib/Topology/Algebra/Module/Spaces/ContinuousLinearMap.lean
+++ b/Mathlib/Topology/Algebra/Module/Spaces/ContinuousLinearMap.lean
@@ -383,7 +383,7 @@ set_option backward.isDefEq.respectTransparency false in
 theorem isUniformEmbedding_restrictScalars :
     IsUniformEmbedding (restrictScalars 𝕜' : (E →L[𝕜] F) → (E →L[𝕜'] F)) := by
   rw [← isUniformEmbedding_toUniformOnFun.of_comp_iff]
-  convert isUniformEmbedding_toUniformOnFun using 4 with s
+  convert! isUniformEmbedding_toUniformOnFun using 4 with s
   exact ⟨fun h ↦ h.extend_scalars _, fun h ↦ h.restrict_scalars _⟩
 
 theorem uniformContinuous_restrictScalars :
diff --git a/Mathlib/Topology/Algebra/Module/Spaces/UniformConvergenceCLM.lean b/Mathlib/Topology/Algebra/Module/Spaces/UniformConvergenceCLM.lean
index cd8b3bef764a1d..8dc08ebe38c81e 100644
--- a/Mathlib/Topology/Algebra/Module/Spaces/UniformConvergenceCLM.lean
+++ b/Mathlib/Topology/Algebra/Module/Spaces/UniformConvergenceCLM.lean
@@ -378,8 +378,10 @@ theorem completeSpace [UniformSpace F] [IsUniformAddGroup F] [ContinuousSMul 
   apply IsClosed.isComplete
   have H₁ : IsClosed {f : E →ᵤ[𝔖] F | Continuous ((UniformOnFun.toFun 𝔖) f)} :=
     UniformOnFun.isClosed_setOf_continuous h𝔖
-  convert H₁.inter <| (LinearMap.isClosed_range_coe E F σ).preimage
-    (UniformOnFun.uniformContinuous_toFun h𝔖U).continuous
+  convert!
+    H₁.inter <|
+      (LinearMap.isClosed_range_coe E F σ).preimage
+        (UniformOnFun.uniformContinuous_toFun h𝔖U).continuous
   exact ContinuousLinearMap.range_coeFn_eq
 
 variable {𝔖₁ 𝔖₂ : Set (Set E)}
diff --git a/Mathlib/Topology/Algebra/Monoid.lean b/Mathlib/Topology/Algebra/Monoid.lean
index 5f381c40f0b7d6..81929aa3d61b25 100644
--- a/Mathlib/Topology/Algebra/Monoid.lean
+++ b/Mathlib/Topology/Algebra/Monoid.lean
@@ -731,7 +731,7 @@ inverse images of compact sets are compact. -/
 theorem Filter.tendsto_cocompact_mul_left {a b : M} (ha : b * a = 1) :
     Filter.Tendsto (fun x : M => a * x) (Filter.cocompact M) (Filter.cocompact M) := by
   refine Filter.Tendsto.of_tendsto_comp ?_ (Filter.comap_cocompact_le (continuous_const_mul b))
-  convert Filter.tendsto_id
+  convert! Filter.tendsto_id
   ext x
   simp [← mul_assoc, ha]
 
diff --git a/Mathlib/Topology/Algebra/MulAction.lean b/Mathlib/Topology/Algebra/MulAction.lean
index d2149b7e268771..5dde5946dbe3fd 100644
--- a/Mathlib/Topology/Algebra/MulAction.lean
+++ b/Mathlib/Topology/Algebra/MulAction.lean
@@ -257,7 +257,7 @@ theorem continuousSMul_iff_stabilizer_isOpen [DiscreteTopology X] :
   have hU : IsOpen U := by
     by_cases hU' : U ≠ ∅
     · obtain ⟨m, (hm : m • y = x)⟩ := Set.nonempty_iff_empty_ne.mpr hU'.symm
-      convert (h x).preimage (by fun_prop : Continuous fun m' : M ↦ m' * m⁻¹)
+      convert! (h x).preimage (by fun_prop : Continuous fun m' : M ↦ m' * m⁻¹)
       ext; simp [← smul_smul, U, eq_inv_smul_iff.mpr hm]
     simp_all
   simpa using hU
@@ -349,7 +349,7 @@ include G in
 it loops for a group as a torsor over itself. -/
 protected theorem AddTorsor.connectedSpace : ConnectedSpace P :=
   { isPreconnected_univ := by
-      convert
+      convert!
         isPreconnected_univ.image (Equiv.vaddConst (Classical.arbitrary P) : G → P)
           (continuous_id.vadd continuous_const).continuousOn
       rw [Set.image_univ, Equiv.range_eq_univ]
diff --git a/Mathlib/Topology/Algebra/Nonarchimedean/AdicTopology.lean b/Mathlib/Topology/Algebra/Nonarchimedean/AdicTopology.lean
index a80cf958305cf2..37e7a4839ce8a7 100644
--- a/Mathlib/Topology/Algebra/Nonarchimedean/AdicTopology.lean
+++ b/Mathlib/Topology/Algebra/Nonarchimedean/AdicTopology.lean
@@ -143,7 +143,7 @@ on an `R`-module `M`, seen as open additive subgroups of `M`. -/
 def openAddSubgroup (n : ℕ) : @OpenAddSubgroup R _ I.adicTopology := by
   letI := I.adicTopology
   refine ⟨(I ^ n).toAddSubgroup, ?_⟩
-  convert (I.adic_basis.toRing_subgroups_basis.openAddSubgroup n).isOpen
+  convert! (I.adic_basis.toRing_subgroups_basis.openAddSubgroup n).isOpen
   change (↑(I ^ n) : Set R) = ↑(I ^ n • (⊤ : Ideal R))
   simp
 
diff --git a/Mathlib/Topology/Algebra/Order/Field.lean b/Mathlib/Topology/Algebra/Order/Field.lean
index e5924455049a57..6d6f2c656bd3ec 100644
--- a/Mathlib/Topology/Algebra/Order/Field.lean
+++ b/Mathlib/Topology/Algebra/Order/Field.lean
@@ -68,7 +68,7 @@ theorem tendsto_inv_atTop_nhdsGT_zero : Tendsto (fun r : 𝕜 => r⁻¹) atTop (
 theorem tendsto_nhdsGT_zero_of_comp_inv_tendsto_atTop {f : 𝕜 → α}
     (h : Tendsto (fun x ↦ f x⁻¹) atTop l) :
     Tendsto f (𝓝[>] 0) l := by
-  convert h.comp tendsto_inv_nhdsGT_zero
+  convert! h.comp tendsto_inv_nhdsGT_zero
   grind [inv_inv]
 
 theorem tendsto_inv_atTop_zero : Tendsto (fun r : 𝕜 => r⁻¹) atTop (𝓝 0) :=
@@ -199,7 +199,7 @@ theorem tendsto_inv_nhdsLT_zero : Tendsto (fun x : 𝕜 => x⁻¹) (𝓝[<] (0 :
 theorem tendsto_nhdsLT_zero_of_comp_inv_tendsto_atBot {f : 𝕜 → α}
     (h : Tendsto (fun x ↦ f x⁻¹) atBot l) :
     Tendsto f (𝓝[<] 0) l := by
-  convert h.comp tendsto_inv_nhdsLT_zero
+  convert! h.comp tendsto_inv_nhdsLT_zero
   grind
 
 /-- The function `r ↦ r⁻¹` tends to `0` on the left as `r → -∞`. -/
@@ -239,7 +239,7 @@ theorem bdd_le_mul_tendsto_zero' {f g : α → 𝕜} (C : 𝕜) (hf : ∀ᶠ x i
     (hg : Tendsto g l (𝓝 0)) : Tendsto (fun x ↦ f x * g x) l (𝓝 0) := by
   rw [tendsto_zero_iff_abs_tendsto_zero]
   have hC : Tendsto (fun x ↦ |C * g x|) l (𝓝 0) := by
-    convert (hg.const_mul C).abs
+    convert! (hg.const_mul C).abs
     simp_rw [mul_zero, abs_zero]
   apply tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_const_nhds hC
   · filter_upwards [hf] with x _ using abs_nonneg _
diff --git a/Mathlib/Topology/Algebra/Order/Floor.lean b/Mathlib/Topology/Algebra/Order/Floor.lean
index 32f79177081880..fca55d68eb8cb1 100644
--- a/Mathlib/Topology/Algebra/Order/Floor.lean
+++ b/Mathlib/Topology/Algebra/Order/Floor.lean
@@ -53,7 +53,7 @@ theorem tendsto_mul_pow_div_factorial_sub_atTop (a c : K) (d : ℕ) :
 
 theorem tendsto_pow_div_factorial_atTop (c : K) :
     Tendsto (fun n ↦ c ^ n / n !) atTop (𝓝 0) := by
-  convert tendsto_mul_pow_div_factorial_sub_atTop 1 c 0
+  convert! tendsto_mul_pow_div_factorial_sub_atTop 1 c 0
   rw [one_mul]
 
 end FloorSemiring
diff --git a/Mathlib/Topology/Algebra/ProperAction/Basic.lean b/Mathlib/Topology/Algebra/ProperAction/Basic.lean
index 5760e5f9441d43..494afe211b3fb6 100644
--- a/Mathlib/Topology/Algebra/ProperAction/Basic.lean
+++ b/Mathlib/Topology/Algebra/ProperAction/Basic.lean
@@ -119,7 +119,7 @@ instance t2Space_quotient_mulAction_of_properSMul [ProperSMul G X] :
   have : IsOpenQuotientMap (Prod.map π π) :=
     MulAction.isOpenQuotientMap_quotientMk.prodMap MulAction.isOpenQuotientMap_quotientMk
   rw [← this.isQuotientMap.isClosed_preimage]
-  convert ProperSMul.isProperMap_smul_pair.isClosedMap.isClosed_range
+  convert! ProperSMul.isProperMap_smul_pair.isClosedMap.isClosed_range
   · ext ⟨x₁, x₂⟩
     simp only [mem_preimage, map_apply, mem_diagonal_iff, mem_range, Prod.mk.injEq, Prod.exists,
       exists_eq_right]
@@ -271,8 +271,9 @@ lemma ProperSMul.isCompact_setOf_inter_nonempty
     {G : Type*} [Group G] [MulAction G X] [TopologicalSpace G] [ProperSMul G X]
     {U V : Set X} (hU : IsCompact U) (hV : IsCompact V) :
     IsCompact {g : G | (g • U ∩ V).Nonempty} := by
-  convert ((ProperSMul.isProperMap_smul_pair (G := G)).isCompact_preimage
-    (hV.prod hU)).image continuous_fst
+  convert!
+    ((ProperSMul.isProperMap_smul_pair (G := G)).isCompact_preimage (hV.prod hU)).image
+      continuous_fst
   ext g
   suffices (∃ v, v ∈ g • U ∧ v ∈ V) ↔ ∃ u, g • u ∈ V ∧ u ∈ U by simpa
   rw [← (MulAction.toPerm g).exists_congr_right]
diff --git a/Mathlib/Topology/Algebra/RestrictedProduct/TopologicalSpace.lean b/Mathlib/Topology/Algebra/RestrictedProduct/TopologicalSpace.lean
index bda5e04f0ef950..47b0e8187ea3cc 100644
--- a/Mathlib/Topology/Algebra/RestrictedProduct/TopologicalSpace.lean
+++ b/Mathlib/Topology/Algebra/RestrictedProduct/TopologicalSpace.lean
@@ -344,7 +344,8 @@ include hAopen in
 theorem isOpen_forall_imp_mem_of_principal {S : Set ι} (hS : cofinite ≤ 𝓟 S) {p : ι → Prop} :
     IsOpen {f : Πʳ i, [R i, A i]_[𝓟 S] | ∀ i, p i → f.1 i ∈ A i} := by
   rw [le_principal_iff] at hS
-  convert isOpen_set_pi (hS.inter_of_left {i | p i}) (fun i _ ↦ hAopen i) |>.preimage continuous_coe
+  convert!
+    isOpen_set_pi (hS.inter_of_left {i | p i}) (fun i _ ↦ hAopen i) |>.preimage continuous_coe
   ext f
   refine ⟨fun H i hi ↦ H i hi.2, fun H i hiT ↦ ?_⟩
   by_cases hiS : i ∈ S
@@ -354,7 +355,7 @@ theorem isOpen_forall_imp_mem_of_principal {S : Set ι} (hS : cofinite ≤ 𝓟
 include hAopen in
 theorem isOpen_forall_mem_of_principal {S : Set ι} (hS : cofinite ≤ 𝓟 S) :
     IsOpen {f : Πʳ i, [R i, A i]_[𝓟 S] | ∀ i, f.1 i ∈ A i} := by
-  convert isOpen_forall_imp_mem_of_principal hAopen hS (p := fun _ ↦ True)
+  convert! isOpen_forall_imp_mem_of_principal hAopen hS (p := fun _ ↦ True)
   simp
 
 include hAopen in
diff --git a/Mathlib/Topology/Algebra/Semigroup.lean b/Mathlib/Topology/Algebra/Semigroup.lean
index 0aaa3d7c90a1bd..98f129280c3c51 100644
--- a/Mathlib/Topology/Algebra/Semigroup.lean
+++ b/Mathlib/Topology/Algebra/Semigroup.lean
@@ -63,7 +63,7 @@ theorem exists_idempotent_of_compact_t2_of_continuous_mul_left {M} [Nonempty M]
   · obtain rfl | hcnemp := c.eq_empty_or_nonempty
     · rw [Set.sInter_empty]
       apply Set.univ_nonempty
-    convert
+    convert!
       @IsCompact.nonempty_iInter_of_directed_nonempty_isCompact_isClosed _ _ _ hcnemp.coe_sort
         ((↑) : c → Set M) ?_ ?_ ?_ ?_
     · exact Set.sInter_eq_iInter
diff --git a/Mathlib/Topology/Algebra/StarSubalgebra.lean b/Mathlib/Topology/Algebra/StarSubalgebra.lean
index a1df756c6cb8d1..577713e2e042a2 100644
--- a/Mathlib/Topology/Algebra/StarSubalgebra.lean
+++ b/Mathlib/Topology/Algebra/StarSubalgebra.lean
@@ -52,7 +52,7 @@ theorem isClosedEmbedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ 
   { IsEmbedding.inclusion h with
     isClosed_range := isClosed_induced_iff.2
       ⟨S₁, hS₁, by
-          convert (Set.range_subtype_map id _).symm
+          convert! (Set.range_subtype_map id _).symm
           · rw [Set.image_id]; rfl
           · intro _ h'
             apply h h' ⟩ }
diff --git a/Mathlib/Topology/Algebra/UniformConvergence.lean b/Mathlib/Topology/Algebra/UniformConvergence.lean
index 74bc74023f6069..3b3a3eb462d10d 100644
--- a/Mathlib/Topology/Algebra/UniformConvergence.lean
+++ b/Mathlib/Topology/Algebra/UniformConvergence.lean
@@ -223,7 +223,7 @@ instance : IsUniformGroup (α →ᵤ G) :=
 protected theorem UniformFun.hasBasis_nhds_one_of_basis {p : ι → Prop} {b : ι → Set G}
     (h : (𝓝 1 : Filter G).HasBasis p b) :
     (𝓝 1 : Filter (α →ᵤ G)).HasBasis p fun i => { f : α →ᵤ G | ∀ x, toFun f x ∈ b i } := by
-  convert UniformFun.hasBasis_nhds_of_basis α _ (1 : α →ᵤ G) h.uniformity_of_nhds_one
+  convert! UniformFun.hasBasis_nhds_of_basis α _ (1 : α →ᵤ G) h.uniformity_of_nhds_one
   simp
 
 @[to_additive]
@@ -251,8 +251,9 @@ protected theorem UniformOnFun.hasBasis_nhds_one_of_basis (𝔖 : Set <| Set α)
     (h : (𝓝 1 : Filter G).HasBasis p b) :
     (𝓝 1 : Filter (α →ᵤ[𝔖] G)).HasBasis (fun Si : Set α × ι => Si.1 ∈ 𝔖 ∧ p Si.2) fun Si =>
       { f : α →ᵤ[𝔖] G | ∀ x ∈ Si.1, toFun 𝔖 f x ∈ b Si.2 } := by
-  convert UniformOnFun.hasBasis_nhds_of_basis α _ 𝔖 (1 : α →ᵤ[𝔖] G) h𝔖₁ h𝔖₂ <|
-    h.uniformity_of_nhds_one_swapped
+  convert!
+    UniformOnFun.hasBasis_nhds_of_basis α _ 𝔖 (1 : α →ᵤ[𝔖] G) h𝔖₁ h𝔖₂ <|
+      h.uniformity_of_nhds_one_swapped
   simp [UniformOnFun.gen]
 
 @[to_additive]
diff --git a/Mathlib/Topology/Algebra/UniformRing.lean b/Mathlib/Topology/Algebra/UniformRing.lean
index b5bec753989c7f..4457f3024d4e62 100644
--- a/Mathlib/Topology/Algebra/UniformRing.lean
+++ b/Mathlib/Topology/Algebra/UniformRing.lean
@@ -271,10 +271,10 @@ noncomputable def IsDenseInducing.extendRingHom {i : α →+* β} {f : α →+*
     (ue : IsUniformInducing i) (dr : DenseRange i) (hf : UniformContinuous f) : β →+* γ where
   toFun := (ue.isDenseInducing dr).extend f
   map_one' := by
-    convert IsDenseInducing.extend_eq (ue.isDenseInducing dr) hf.continuous 1
+    convert! IsDenseInducing.extend_eq (ue.isDenseInducing dr) hf.continuous 1
     exacts [i.map_one.symm, f.map_one.symm]
   map_zero' := by
-    convert IsDenseInducing.extend_eq (ue.isDenseInducing dr) hf.continuous 0 <;>
+    convert! IsDenseInducing.extend_eq (ue.isDenseInducing dr) hf.continuous 0 <;>
     simp only [map_zero]
   map_add' := by
     have h := (uniformContinuous_uniformly_extend ue dr hf).continuous
diff --git a/Mathlib/Topology/Algebra/ValuativeRel/ValuativeTopology.lean b/Mathlib/Topology/Algebra/ValuativeRel/ValuativeTopology.lean
index 546119a05d24e6..4f98bf5ca7c270 100644
--- a/Mathlib/Topology/Algebra/ValuativeRel/ValuativeTopology.lean
+++ b/Mathlib/Topology/Algebra/ValuativeRel/ValuativeTopology.lean
@@ -48,7 +48,7 @@ lemma Valuation.exists_setOf_restrict_le_iff {Γ₀ : Type*} [LinearOrderedCommG
     ∃ γ : (ValueGroupWithZero R)ˣ, {a | valuation R (a - x) < γ} ⊆ s := by
   refine ⟨fun ⟨r, hr⟩ ↦ ⟨r.mapEquiv (orderMonoidIso v).symm, ?_⟩,
     fun ⟨r, hr⟩ ↦ ⟨r.mapEquiv (orderMonoidIso v), ?_⟩⟩
-  all_goals convert hr; simp
+  all_goals convert! hr; simp
 
 /-- We say that a topology on `R` is valuative if the neighborhoods of `0` in `R`
 are determined by the valuative relation `· ≤ᵥ ·`. -/
@@ -97,7 +97,7 @@ namespace IsValuativeTopology
 /-- A variant of `IsValuativeTopology.mem_nhds_iff` using subtraction. -/
 lemma mem_nhds_iff' {s : Set R} {x : R} :
     s ∈ 𝓝 x ↔ ∃ γ : (ValueGroupWithZero R)ˣ, { z | valuation R (z - x) < γ } ⊆ s := by
-  convert mem_nhds_iff (s := s) using 4
+  convert! mem_nhds_iff (s := s) using 4
   simp [neg_add_eq_sub]
 
 lemma mem_nhds_zero_iff (s : Set R) :
@@ -119,7 +119,7 @@ variable (R) in
 theorem hasBasis_nhds_zero :
     (𝓝 0).HasBasis (fun _ ↦ True)
       fun γ : (ValueGroupWithZero R)ˣ ↦ { x | valuation R x < γ } := by
-  convert hasBasis_nhds (0 : R)
+  convert! hasBasis_nhds (0 : R)
   rw [sub_zero]
 
 variable (R) in
@@ -137,7 +137,7 @@ namespace Valuation
 
 lemma mem_nhds_iff {s : Set R} {x : R} : s ∈ 𝓝 x ↔
     ∃ γ : (MonoidWithZeroHom.ValueGroup₀ v)ˣ, { z | v.restrict (z - x) < γ.val } ⊆ s := by
-  convert IsValuativeTopology.mem_nhds_iff (s := s) using 4
+  convert! IsValuativeTopology.mem_nhds_iff (s := s) using 4
   simpa [neg_add_eq_sub] using v.exists_setOf_restrict_le_iff _ _
 
 lemma mem_nhds_zero_iff (s : Set R) : s ∈ 𝓝 0 ↔
@@ -207,7 +207,7 @@ theorem hasBasis_uniformity : (𝓤 R).HasBasis (fun _ ↦ True)
 theorem toUniformSpace_eq : _u =
     @IsTopologicalAddGroup.rightUniformSpace R _ v.subgroups_basis.topology _ := by
   refine UniformSpace.ext (v.hasBasis_uniformity.eq_of_same_basis ?_)
-  convert v.subgroups_basis.hasBasis_nhds_zero.comap _
+  convert! v.subgroups_basis.hasBasis_nhds_zero.comap _
   simp [restrict_lt_iff_lt_embedding, sub_eq_add_neg]
 
 theorem cauchy_iff {F : Filter R} : Cauchy F ↔
@@ -238,7 +238,7 @@ theorem toTopologicalSpace_eq :
   exact congrArg (fun u ↦ @UniformSpace.toTopologicalSpace R u) v.toUniformSpace_eq
 
 instance (priority := low) _root_.IsValuativeTopology.isTopologicalRing : IsTopologicalRing R := by
-  convert (ValuativeRel.nonarchimedeanRing R).toIsTopologicalRing
+  convert! (ValuativeRel.nonarchimedeanRing R).toIsTopologicalRing
   exact toTopologicalSpace_eq _
 
 section Discrete
@@ -336,7 +336,7 @@ theorem isOpen_sphere {r : ValueGroup₀ v} (hr : r ≠ 0) :
 around zero `{x | v.restrict x = r}` is closed in the valuative topology. -/
 theorem isClosed_sphere (r : ValueGroup₀ v) : IsClosed (X := R) {x | v.restrict x = r} := by
   rcases eq_or_ne r 0 with rfl | hr
-  · convert v.isClosed_closedBall 0 using 3
+  · convert! v.isClosed_closedBall 0 using 3
     exact (le_zero_iff (α := ValueGroup₀ v)).symm
   exact isClopen_sphere hr |>.isClosed
 
diff --git a/Mathlib/Topology/Algebra/Valued/LocallyCompact.lean b/Mathlib/Topology/Algebra/Valued/LocallyCompact.lean
index 9a5e8a36c19b7e..2898d75d54ac16 100644
--- a/Mathlib/Topology/Algebra/Valued/LocallyCompact.lean
+++ b/Mathlib/Topology/Algebra/Valued/LocallyCompact.lean
@@ -144,7 +144,11 @@ lemma totallyBounded_iff_finite_residueField [(Valued.v : Valuation K Γ₀).Ran
     simp only [Submodule.Quotient.quot_mk_eq_mk, Ideal.Quotient.mk_eq_mk, Set.mem_univ,
       IsLocalRing.residue, Set.mem_image, true_implies]
     refine ⟨y, hy, ?_⟩
-    convert (Ideal.Quotient.mk_eq_mk_iff_sub_mem (I := 𝓂[K]) y x).mpr _
+    convert!
+      (Ideal.Quotient.mk_eq_mk_iff_sub_mem (I := 𝓂[K]) y x).mpr
+        _
+          -- TODO: make Valued.maximalIdeal abbreviations instead of def
+
     -- TODO: make Valued.maximalIdeal abbreviations instead of def
     rw [Valued.maximalIdeal, hp.maximalIdeal_eq, ← SetLike.mem_coe,
       (Valuation.integer.integers _).coe_span_singleton_eq_setOf_le_v_algebraMap]
diff --git a/Mathlib/Topology/Algebra/Valued/ValuationTopology.lean b/Mathlib/Topology/Algebra/Valued/ValuationTopology.lean
index ff7ee313d70d76..1d6fa7bce51937 100644
--- a/Mathlib/Topology/Algebra/Valued/ValuationTopology.lean
+++ b/Mathlib/Topology/Algebra/Valued/ValuationTopology.lean
@@ -167,7 +167,7 @@ theorem hasBasis_uniformity : (𝓤 R).HasBasis (fun _ ↦ True)
 theorem toUniformSpace_eq : toUniformSpace =
     @IsTopologicalAddGroup.rightUniformSpace R _ v.subgroups_basis.topology _ := by
   refine UniformSpace.ext ((hasBasis_uniformity R Γ₀).eq_of_same_basis ?_)
-  convert v.subgroups_basis.hasBasis_nhds_zero.comap _
+  convert! v.subgroups_basis.hasBasis_nhds_zero.comap _
   simp_rw [restrict_lt_iff_lt_embedding, sub_eq_add_neg]
   simp
 
diff --git a/Mathlib/Topology/Algebra/Valued/ValuativeRel.lean b/Mathlib/Topology/Algebra/Valued/ValuativeRel.lean
index 57ff65b5a27e0e..6dd6eb229c9ea1 100644
--- a/Mathlib/Topology/Algebra/Valued/ValuativeRel.lean
+++ b/Mathlib/Topology/Algebra/Valued/ValuativeRel.lean
@@ -57,7 +57,7 @@ instance (priority := low) {R : Type*} [CommRing R] [ValuativeRel R] [UniformSpa
   «v» := valuation R
   is_topological_valuation := by
     simp_rw [Valuation.restrict_lt_iff_lt_embedding]
-    convert mem_nhds_zero_iff (R := R)
+    convert! mem_nhds_zero_iff (R := R)
     simpa [← Valuation.restrict_lt_iff_lt_embedding] using
       (valuation R).exists_setOf_restrict_le_iff 0 _
 
diff --git a/Mathlib/Topology/Algebra/Valued/ValuedField.lean b/Mathlib/Topology/Algebra/Valued/ValuedField.lean
index dcfb36ad592e1c..6cd1e903fbc472 100644
--- a/Mathlib/Topology/Algebra/Valued/ValuedField.lean
+++ b/Mathlib/Topology/Algebra/Valued/ValuedField.lean
@@ -242,7 +242,7 @@ theorem continuous_extension : Continuous (Valued.extension : hat K → ValueGro
       have : (v (1 : K) : Γ₀) ≠ 0 := by
         rw [Valuation.map_one]
         exact zero_ne_one.symm
-      convert Valued.locally_const this
+      convert! Valued.locally_const this
       ext x
       rw [Valuation.map_one, mem_preimage, mem_singleton_iff, mem_setOf_eq]
     obtain ⟨V, V_in, hV⟩ : ∃ V ∈ 𝓝 (1 : hat K), ∀ x : K, (x : hat K) ∈ V → (v x : Γ₀) = 1 := by
@@ -258,7 +258,7 @@ theorem continuous_extension : Continuous (Valued.extension : hat K → ValueGro
           rw [← one_mul (1 : hat K)]
         refine
           Tendsto.mul continuous_fst.continuousAt (Tendsto.comp ?_ continuous_snd.continuousAt)
-        convert (continuousAt_inv₀ (zero_ne_one.symm : 1 ≠ (0 : hat K))).tendsto
+        convert! (continuousAt_inv₀ (zero_ne_one.symm : 1 ≠ (0 : hat K))).tendsto
         exact inv_one.symm
       rcases tendsto_prod_self_iff.mp this V V_in with ⟨U, U_in, hU⟩
       let hatKstar := ({0}ᶜ : Set <| hat K)
@@ -370,7 +370,7 @@ lemma exists_coe_eq_v (x : hat K) : ∃ r : K, extensionValuation x = v r := by
       have h (a b : ValueGroup₀ hv.v) : ValueGroup₀.embedding a = ValueGroup₀.embedding b ↔
           a = b := by rw [embedding_strictMono.injective.eq_iff]
       simp_rw [← hr, ← Valuation.restrict_def, h]
-      convert valuation_isClosedMap.isClosed_range.preimage (continuous_extension (hv := hv))
+      convert! valuation_isClosedMap.isClosed_range.preimage (continuous_extension (hv := hv))
       simp_rw [eq_comm (a := extension _)]
       #adaptation_note /-- Before https://github.com/leanprover/lean4/pull/13166
       (replacing grind's canonicalizer with a type-directed normalizer), `grind` closed this
@@ -416,7 +416,7 @@ theorem closure_coe_completion_v_mul_v_lt {r s : K} (hr : r ≠ 0) (hs : s ≠ 0
     closure ((↑) '' { x : K | v x * v r < v s }) =
     { x : hat K | extensionValuation x * v r < v s } := by
   have hrs : v s / v r ≠ 0 := by simp [hr, hs]
-  convert closure_coe_completion_v_lt (γ := .mk0 _ hrs) using 3
+  convert! closure_coe_completion_v_lt (γ := .mk0 _ hrs) using 3
   all_goals simp [← lt_div_iff₀, zero_lt_iff, hr]
 
 set_option backward.isDefEq.respectTransparency false in
@@ -561,14 +561,14 @@ noncomputable instance valuedCompletion : Valued (hat K) Γ₀ where
               simp
       refine ⟨fun ⟨γ, h⟩ ↦ ?_, fun ⟨γ, h⟩ ↦ ?_⟩
       · use Units.map valueGroup₀_equiv_extensionValuation.toMonoidHom γ
-        convert h
+        convert! h
         apply this
       · use Units.map valueGroup₀_equiv_extensionValuation.symm.toMonoidHom γ
-        convert h
+        convert! h
         rw [← this]
         simp [Valuation.restrict_def, restrict₀_apply]
     simp_rw [← closure_coe_completion_v_lt, Units.coe_map]
-    convert (hasBasis_nhds_zero K Γ₀).hasBasis_of_isDenseInducing Completion.isDenseInducing_coe
+    convert! (hasBasis_nhds_zero K Γ₀).hasBasis_of_isDenseInducing Completion.isDenseInducing_coe
     rw [Valuation.restrict_lt_iff_lt_embedding]; rfl
 
 @[simp]
@@ -590,7 +590,7 @@ lemma valuedCompletion_surjective_iff :
             erw [ne_eq, ← embedding_strictMono.injective.eq_iff, embedding_restrict₀ r, hr,
               map_zero]
             exact hγ
-          convert isClosed_univ.sdiff (isOpen_sphere (hat K) hr') using 1
+          convert! isClosed_univ.sdiff (isOpen_sphere (hat K) hr') using 1
           ext x
           simp only [← hr, mem_setOf_eq, mem_diff, mem_univ, true_and, ← v.restrict_def,
             v.restrict_inj]
diff --git a/Mathlib/Topology/Algebra/Valued/WithVal.lean b/Mathlib/Topology/Algebra/Valued/WithVal.lean
index 8279da9be3bb9d..4da736b6ee90e8 100644
--- a/Mathlib/Topology/Algebra/Valued/WithVal.lean
+++ b/Mathlib/Topology/Algebra/Valued/WithVal.lean
@@ -615,8 +615,9 @@ theorem IsEquiv.valuedCompletion_le_one_iff {K : Type*} [Field K] {v : Valuation
     have h1 (x : UniformSpace.Completion (WithVal v)) :
       Valued.v x ≤ 1 ↔ Valued.v.restrict x ≤ 1 := by rw [restrict_le_one_iff]
     simp_rw [h1]
-    convert (mapEquiv h.uniformEquiv).toHomeomorph.isClosed_setOf_iff
-      (Valued.isClopen_closedBall _ one_ne_zero) (Valued.isClopen_closedBall _ one_ne_zero)
+    convert!
+      (mapEquiv h.uniformEquiv).toHomeomorph.isClosed_setOf_iff
+        (Valued.isClopen_closedBall _ one_ne_zero) (Valued.isClopen_closedBall _ one_ne_zero)
     rw [restrict_le_one_iff]
     rfl
   | ih a =>
diff --git a/Mathlib/Topology/Baire/LocallyCompactRegular.lean b/Mathlib/Topology/Baire/LocallyCompactRegular.lean
index f6a4948b0702f3..b186ca315b7fff 100644
--- a/Mathlib/Topology/Baire/LocallyCompactRegular.lean
+++ b/Mathlib/Topology/Baire/LocallyCompactRegular.lean
@@ -61,7 +61,7 @@ instance (priority := 100) BaireSpace.of_t2Space_locallyCompactSpace : BaireSpac
 /-- A Gδ subset of a locally compact R₁ space is Baire. -/
 theorem IsGδ.of_t2Space_locallyCompactSpace (hG : IsGδ s) : BaireSpace s := by
   have : BaireSpace (closure s) := by
-    convert BaireSpace.of_t2Space_locallyCompactSpace using 1
+    convert! BaireSpace.of_t2Space_locallyCompactSpace using 1
     · infer_instance
     · exact isClosed_closure.locallyCompactSpace
   have : BaireSpace ((↑) ⁻¹' s : Set (closure s)) :=
diff --git a/Mathlib/Topology/Bases.lean b/Mathlib/Topology/Bases.lean
index f451752d9ede71..d46e549da524a9 100644
--- a/Mathlib/Topology/Bases.lean
+++ b/Mathlib/Topology/Bases.lean
@@ -95,7 +95,7 @@ theorem isTopologicalBasis_of_subbasis {s : Set (Set α)} (hs : t = generateFrom
 
 theorem isTopologicalBasis_of_subbasis_of_finiteInter {s : Set (Set α)} (hsg : t = generateFrom s)
     (hsi : FiniteInter s) : IsTopologicalBasis s := by
-  convert isTopologicalBasis_of_subbasis hsg
+  convert! isTopologicalBasis_of_subbasis hsg
   refine le_antisymm (fun t ht ↦ ⟨{t}, by simpa using ht⟩) ?_
   rintro _ ⟨g, ⟨hg, hgs⟩, rfl⟩
   lift g to Finset (Set α) using hg
@@ -248,7 +248,7 @@ theorem isTopologicalBasis_opens : IsTopologicalBasis { U : Set α | IsOpen U }
 protected lemma IsTopologicalBasis.isInducing [TopologicalSpace β] {f : α → β} {T : Set (Set β)}
     (hf : IsInducing f) (h : IsTopologicalBasis T) : IsTopologicalBasis ((preimage f) '' T) :=
   .of_hasBasis_nhds fun a ↦ by
-    convert (hf.basis_nhds (h.nhds_hasBasis (a := f a))).to_image_id with s
+    convert! (hf.basis_nhds (h.nhds_hasBasis (a := f a))).to_image_id with s
     aesop
 
 protected theorem IsTopologicalBasis.induced {α} [s : TopologicalSpace β] (f : α → β)
@@ -261,7 +261,7 @@ protected theorem IsTopologicalBasis.inf {t₁ t₂ : TopologicalSpace β} {B₁
     IsTopologicalBasis (t := t₁ ⊓ t₂) (image2 (· ∩ ·) B₁ B₂) := by
   refine .of_hasBasis_nhds (t := ?_) fun a ↦ ?_
   rw [nhds_inf (t₁ := t₁)]
-  convert ((h₁.nhds_hasBasis (t := t₁)).inf (h₂.nhds_hasBasis (t := t₂))).to_image_id
+  convert! ((h₁.nhds_hasBasis (t := t₁)).inf (h₂.nhds_hasBasis (t := t₂))).to_image_id
   aesop
 
 theorem IsTopologicalBasis.inf_induced {γ} [s : TopologicalSpace β] {B₁ : Set (Set α)}
@@ -606,7 +606,7 @@ theorem IsTopologicalBasis.iInf_induced {β : Type*} {ι : Type*} {X : ι → Ty
     IsTopologicalBasis (t := ⨅ i, induced (f i) (t i))
       { S | ∃ (U : ∀ i, Set (X i)) (F : Finset ι),
         (∀ i, i ∈ F → U i ∈ T i) ∧ S = ⋂ (i) (_ : i ∈ F), f i ⁻¹' U i } := by
-  convert IsTopologicalBasis.iInf (fun i ↦ (cond i).induced (f i)) with S
+  convert! IsTopologicalBasis.iInf (fun i ↦ (cond i).induced (f i)) with S
   constructor <;> rintro ⟨U, F, hUT, hSU⟩
   · exact ⟨fun i ↦ (f i) ⁻¹' (U i), F, fun i hi ↦ mem_image_of_mem _ (hUT i hi), hSU⟩
   · choose! U' hU' hUU' using hUT
@@ -991,7 +991,7 @@ lemma IsTopologicalBasis.exists_countable
     obtain ⟨u, u_mem, xu, uv⟩ : ∃ u ∈ countableBasis α, x ∈ u ∧ u ⊆ v :=
       (isBasis_countableBasis α).isOpen_iff.1 hv _ hx
     have : x ∈ ⋃ a ∈ s u, a := by
-      convert xu
+      convert! xu
       exact (hs u u_mem).symm
     obtain ⟨w, ws, xw⟩ : ∃ w ∈ s u, x ∈ w := by simpa using this
     refine ⟨w, ⟨u, u_mem, ws⟩, xw, ?_⟩
@@ -1045,7 +1045,7 @@ theorem IsTopologicalBasis.sigma {s : ∀ i : ι, Set (Set (E i))}
     IsTopologicalBasis (⋃ i : ι, (fun u => (Sigma.mk i '' u : Set (Σ i, E i))) '' s i) := by
   refine .of_hasBasis_nhds fun a ↦ ?_
   rw [Sigma.nhds_eq]
-  convert (((hs a.1).nhds_hasBasis).map _).to_image_id
+  convert! (((hs a.1).nhds_hasBasis).map _).to_image_id
   aesop
 
 /-- A countable disjoint union of second countable spaces is second countable. -/
diff --git a/Mathlib/Topology/Bornology/BoundedOperation.lean b/Mathlib/Topology/Bornology/BoundedOperation.lean
index e7d163c2dcbb38..1d43bfb49c720f 100644
--- a/Mathlib/Topology/Bornology/BoundedOperation.lean
+++ b/Mathlib/Topology/Bornology/BoundedOperation.lean
@@ -65,7 +65,7 @@ lemma boundedSub_of_lipschitzWith_sub [PseudoMetricSpace R] [Sub R] {K : NNReal}
     BoundedSub R where
   isBounded_sub {s t} s_bdd t_bdd := by
     have bdd : Bornology.IsBounded (s ×ˢ t) := Bornology.IsBounded.prod s_bdd t_bdd
-    convert lip.isBounded_image bdd
+    convert! lip.isBounded_image bdd
     simp
 
 end bounded_sub
@@ -137,7 +137,7 @@ instance [PseudoMetricSpace R] [Monoid R] [LipschitzMul R] : BoundedMul R where
   isBounded_mul {s t} s_bdd t_bdd := by
     have bdd : Bornology.IsBounded (s ×ˢ t) := Bornology.IsBounded.prod s_bdd t_bdd
     obtain ⟨C, mul_lip⟩ := ‹LipschitzMul R›.lipschitz_mul
-    convert mul_lip.isBounded_image bdd
+    convert! mul_lip.isBounded_image bdd
     ext p
     simp only [Set.mem_image, Set.mem_prod, Prod.exists]
     constructor
@@ -157,7 +157,7 @@ variable {R : Type*} [SeminormedAddCommGroup R]
 
 lemma SeminormedAddCommGroup.lipschitzWith_sub :
     LipschitzWith 2 (fun (p : R × R) ↦ p.1 - p.2) := by
-  convert LipschitzWith.prod_fst.sub LipschitzWith.prod_snd
+  convert! LipschitzWith.prod_fst.sub LipschitzWith.prod_snd
   norm_num
 
 instance : BoundedSub R := boundedSub_of_lipschitzWith_sub SeminormedAddCommGroup.lipschitzWith_sub
@@ -177,7 +177,7 @@ lemma tendsto_add_const_cobounded (x : R) :
   rw [mem_map]
   rw [← isCobounded_def, ← isBounded_compl_iff] at hs ⊢
   rw [← Set.preimage_compl]
-  convert isBounded_sub hs (t := {x}) isBounded_singleton using 1
+  convert! isBounded_sub hs (t := { x }) isBounded_singleton using 1
   ext y
   simp [sub_eq_iff_eq_add]
 
@@ -188,7 +188,7 @@ lemma tendsto_const_add_cobounded (x : R) :
   rw [mem_map]
   rw [← isCobounded_def, ← isBounded_compl_iff] at hs ⊢
   rw [← Set.preimage_compl]
-  convert isBounded_add isBounded_singleton (s := {-x}) hs using 1
+  convert! isBounded_add isBounded_singleton (s := {-x}) hs using 1
   ext y
   simp
 
diff --git a/Mathlib/Topology/CWComplex/Classical/Finite.lean b/Mathlib/Topology/CWComplex/Classical/Finite.lean
index 81fb550da38fa2..b4c1d87a7f7862 100644
--- a/Mathlib/Topology/CWComplex/Classical/Finite.lean
+++ b/Mathlib/Topology/CWComplex/Classical/Finite.lean
@@ -215,7 +215,7 @@ def RelCWComplex.mkFinite.{u} {X : Type u} [TopologicalSpace X] (C : Set X)
     simp_rw [Filter.eventually_atTop, ge_iff_le] at eventually_isEmpty_cell
     obtain ⟨N, hN⟩ := eventually_isEmpty_cell
     suffices IsClosed (A ∩ (D ∪ ⋃ (n : {n : ℕ // n < N}), ⋃ j, ↑(map n j) '' closedBall 0 1)) by
-      convert this using 2
+      convert! this using 2
       rw [← union', iUnion_subtype]
       congrm D ∪ ⋃ n, ?_
       refine subset_antisymm ?_ (iUnion_subset (fun i ↦ by rfl))
diff --git a/Mathlib/Topology/Category/CompHaus/Projective.lean b/Mathlib/Topology/Category/CompHaus/Projective.lean
index 01a01dee8e3e4f..7e0935185e3be8 100644
--- a/Mathlib/Topology/Category/CompHaus/Projective.lean
+++ b/Mathlib/Topology/Category/CompHaus/Projective.lean
@@ -48,7 +48,11 @@ instance projective_ultrafilter (X : Type*) : Projective (of <| Ultrafilter X) w
     use CompHausLike.ofHom _ ⟨h, hh⟩
     apply ConcreteCategory.coe_ext
     have : g.hom ∘ g' = id := hg'.comp_eq_id
-    convert denseRange_pure.equalizer (g.hom.hom.continuous.comp hh) f.hom.hom.continuous _
+    convert!
+      denseRange_pure.equalizer (g.hom.hom.continuous.comp hh) f.hom.hom.continuous
+        _
+          -- This used to be `rw`, but we need `rw; rfl` after https://github.com/leanprover/lean4/pull/2644
+
     -- This used to be `rw`, but we need `rw; rfl` after https://github.com/leanprover/lean4/pull/2644
     rw [comp_assoc, ultrafilter_extend_extends, ← comp_assoc, this, id_comp]
     rfl
diff --git a/Mathlib/Topology/Category/CompHausLike/Limits.lean b/Mathlib/Topology/Category/CompHausLike/Limits.lean
index d816f67ee06f81..b35aa2b4442b12 100644
--- a/Mathlib/Topology/Category/CompHausLike/Limits.lean
+++ b/Mathlib/Topology/Category/CompHausLike/Limits.lean
@@ -162,7 +162,7 @@ lemma Sigma.isOpenEmbedding_ι (a : α) :
     IsOpenEmbedding (Sigma.ι X a) := by
   refine IsOpenEmbedding.of_comp _ (homeoOfIso ((colimit.isColimit _).coconePointUniqueUpToIso
     (finiteCoproduct.isColimit X))).isOpenEmbedding ?_
-  convert finiteCoproduct.isOpenEmbedding_ι X a
+  convert! finiteCoproduct.isOpenEmbedding_ι X a
   ext x
   change (Sigma.ι X a ≫ _) x = _
   simp
diff --git a/Mathlib/Topology/Category/LightProfinite/Injective.lean b/Mathlib/Topology/Category/LightProfinite/Injective.lean
index 8d5ba576412a97..061b1b2f7108a1 100644
--- a/Mathlib/Topology/Category/LightProfinite/Injective.lean
+++ b/Mathlib/Topology/Category/LightProfinite/Injective.lean
@@ -104,7 +104,7 @@ lemma exists_lift_of_finite_of_injective_of_surjective {X Y S T : Type*}
   refine ⟨liftCover C (fun i _ ↦ i) h_glue C_cover_univ, IsLocallyConstant.continuous ?_, ?_, ?_⟩
   · rw [IsLocallyConstant.iff_isOpen_fiber]
     intro s
-    convert (C_clopen s).2
+    convert! (C_clopen s).2
     ext y
     simp [preimage_liftCover]
   · ext y
diff --git a/Mathlib/Topology/Category/Profinite/CofilteredLimit.lean b/Mathlib/Topology/Category/Profinite/CofilteredLimit.lean
index 9b09b85cd308de..eaf75ca1a848ba 100644
--- a/Mathlib/Topology/Category/Profinite/CofilteredLimit.lean
+++ b/Mathlib/Topology/Category/Profinite/CofilteredLimit.lean
@@ -195,7 +195,7 @@ theorem exists_locallyConstant {α : Type*} (hC : IsLimit C) (f : LocallyConstan
   · suffices ∃ j, IsEmpty (F.obj j) by
       refine this.imp fun j hj => ?_
       refine ⟨⟨hj.elim, fun A => ?_⟩, ?_⟩
-      · convert isOpen_empty
+      · convert! isOpen_empty
         ext x
         exact hj.elim x
       · ext x
diff --git a/Mathlib/Topology/Category/Profinite/Nobeling/Basic.lean b/Mathlib/Topology/Category/Profinite/Nobeling/Basic.lean
index c60fd18e70b1c2..93873c0c7c3ada 100644
--- a/Mathlib/Topology/Category/Profinite/Nobeling/Basic.lean
+++ b/Mathlib/Topology/Category/Profinite/Nobeling/Basic.lean
@@ -392,7 +392,7 @@ theorem eval_eq (l : Products I) (x : C) :
     exact if_pos (h i hi)
   · simp only [List.map_map, List.prod_eq_zero_iff, List.mem_map, Function.comp_apply]
     push Not at h
-    convert h with i
+    convert! h with i
     dsimp [LocallyConstant.evalMonoidHom, e]
     simp only [ite_eq_right_iff, one_ne_zero]
 
diff --git a/Mathlib/Topology/Category/Profinite/Nobeling/Induction.lean b/Mathlib/Topology/Category/Profinite/Nobeling/Induction.lean
index 65843652742314..4289fc17787723 100644
--- a/Mathlib/Topology/Category/Profinite/Nobeling/Induction.lean
+++ b/Mathlib/Topology/Category/Profinite/Nobeling/Induction.lean
@@ -130,11 +130,11 @@ theorem Nobeling.isClosedEmbedding : IsClosedEmbedding (Nobeling.ι S) := by
     refine ((IsLocallyConstant.tfae _).out 0 3).mpr ?_
     rintro ⟨⟩
     · refine IsClopen.isOpen (isClopen_compl_iff.mp ?_)
-      convert C.2
+      convert! C.2
       ext x
       simp
     · refine IsClopen.isOpen ?_
-      convert C.2
+      convert! C.2
       ext x
       simp only [Set.mem_preimage, Set.mem_singleton_iff, decide_eq_true_eq]
   · intro a b h
diff --git a/Mathlib/Topology/Category/Profinite/Nobeling/Successor.lean b/Mathlib/Topology/Category/Profinite/Nobeling/Successor.lean
index e1de02ccb8ae70..42ddb5eeda8e98 100644
--- a/Mathlib/Topology/Category/Profinite/Nobeling/Successor.lean
+++ b/Mathlib/Topology/Category/Profinite/Nobeling/Successor.lean
@@ -150,7 +150,7 @@ include hsC in
 theorem swapTrue_mem_C1 (f : π (C1 C ho) (ord I · < o)) :
     SwapTrue o f.val ∈ C1 C ho := by
   obtain ⟨f, g, hg, rfl⟩ := f
-  convert hg
+  convert! hg
   dsimp +unfoldPartialApp [SwapTrue]
   ext i
   split_ifs with h
diff --git a/Mathlib/Topology/Category/Profinite/Projective.lean b/Mathlib/Topology/Category/Profinite/Projective.lean
index 22d548d5a59ecb..4a0091b41978cc 100644
--- a/Mathlib/Topology/Category/Profinite/Projective.lean
+++ b/Mathlib/Topology/Category/Profinite/Projective.lean
@@ -46,7 +46,7 @@ instance projective_ultrafilter (X : Type u) : Projective (of <| Ultrafilter X)
     use CompHausLike.ofHom _ ⟨h, hh⟩
     apply ConcreteCategory.coe_ext
     simp only [h]
-    convert denseRange_pure.equalizer (g.hom.hom.continuous.comp hh) f.hom.hom.continuous _
+    convert! denseRange_pure.equalizer (g.hom.hom.continuous.comp hh) f.hom.hom.continuous _
     have : g.hom ∘ g' = id := hg'.comp_eq_id
     rw [comp_assoc, ultrafilter_extend_extends, ← comp_assoc, this, id_comp]
     rfl
diff --git a/Mathlib/Topology/Category/TopCat/Basic.lean b/Mathlib/Topology/Category/TopCat/Basic.lean
index b13caf15fff8d6..5e6e87949bf89a 100644
--- a/Mathlib/Topology/Category/TopCat/Basic.lean
+++ b/Mathlib/Topology/Category/TopCat/Basic.lean
@@ -250,7 +250,7 @@ theorem isOpenEmbedding_iff_isIso_comp {X Y Z : TopCat.{u}} (f : X ⟶ Y) (g : Y
     IsOpenEmbedding (f ≫ g) ↔ IsOpenEmbedding g := by
   constructor
   · intro h
-    convert h.comp (TopCat.homeoOfIso (asIso f).symm).isOpenEmbedding
+    convert! h.comp (TopCat.homeoOfIso (asIso f).symm).isOpenEmbedding
     exact congr_arg (DFunLike.coe ∘ ConcreteCategory.hom) (IsIso.inv_hom_id_assoc f g).symm
   · exact fun h => h.comp (TopCat.homeoOfIso (asIso f)).isOpenEmbedding
 
diff --git a/Mathlib/Topology/Category/TopCat/Limits/Basic.lean b/Mathlib/Topology/Category/TopCat/Limits/Basic.lean
index 4c489941c12fbf..69dc595eac1c48 100644
--- a/Mathlib/Topology/Category/TopCat/Limits/Basic.lean
+++ b/Mathlib/Topology/Category/TopCat/Limits/Basic.lean
@@ -111,7 +111,7 @@ def isLimitConeOfForget (c : Cone (F ⋙ forget)) (hc : IsLimit c) :
   rw [le_iInf_iff]
   intro j
   rw [coinduced_le_iff_le_induced, induced_compose]
-  convert continuous_iff_le_induced.1 (s.π.app j).hom.continuous
+  convert! continuous_iff_le_induced.1 (s.π.app j).hom.continuous
   ext x
   exact ConcreteCategory.hom_ext_iff.mp (hc.fac ((forget).mapCone s) j) x
 
@@ -224,7 +224,7 @@ def isColimitCoconeOfForget (c : Cocone (F ⋙ forget)) (hc : IsColimit c) :
   rw [iSup_le_iff]
   intro j
   rw [coinduced_le_iff_le_induced, induced_compose]
-  convert continuous_iff_le_induced.1 (s.ι.app j).hom.continuous
+  convert! continuous_iff_le_induced.1 (s.ι.app j).hom.continuous
   ext x
   exact ConcreteCategory.hom_ext_iff.mp (hc.fac ((forget).mapCocone s) j) x
 
diff --git a/Mathlib/Topology/Category/TopCat/Limits/Cofiltered.lean b/Mathlib/Topology/Category/TopCat/Limits/Cofiltered.lean
index 764fdb83bce6d3..a45dbd86b2fd49 100644
--- a/Mathlib/Topology/Category/TopCat/Limits/Cofiltered.lean
+++ b/Mathlib/Topology/Category/TopCat/Limits/Cofiltered.lean
@@ -47,7 +47,7 @@ theorem isTopologicalBasis_cofiltered_limit (hC : IsLimit C) (T : ∀ j, Set (Se
     IsTopologicalBasis
       {U : Set C.pt | ∃ (j : _) (V : Set (F.obj j)), V ∈ T j ∧ U = C.π.app j ⁻¹' V} := by
   classical
-  convert IsTopologicalBasis.iInf_induced hT fun j (x : C.pt) => C.π.app j x using 1
+  convert! IsTopologicalBasis.iInf_induced hT fun j (x : C.pt) => C.π.app j x using 1
   · exact induced_of_isLimit C hC
   ext U0
   constructor
diff --git a/Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean b/Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean
index 49881b17a94fe2..f555405a1f9fe6 100644
--- a/Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean
+++ b/Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean
@@ -156,13 +156,13 @@ def pullbackHomeoPreimage
     intro x
     ext <;> dsimp
     apply hg.injective
-    convert x.prop
+    convert! x.prop
     exact Exists.choose_spec (p := fun y ↦ g y = f (↑x : X × Y).1) _
   continuous_toFun := by fun_prop
   continuous_invFun := by
     apply Continuous.subtype_mk
     refine continuous_subtype_val.prodMk <| hg.isInducing.continuous_iff.mpr ?_
-    convert hf.comp continuous_subtype_val
+    convert! hf.comp continuous_subtype_val
     ext x
     exact Exists.choose_spec x.2
 
@@ -280,29 +280,32 @@ theorem pullback_map_isOpenEmbedding {W X Y Z S T : TopCat.{u}} (f₁ : W ⟶ S)
 set_option backward.isDefEq.respectTransparency false in
 lemma snd_isEmbedding_of_left {X Y S : TopCat.{u}} {f : X ⟶ S} (H : IsEmbedding f) (g : Y ⟶ S) :
     IsEmbedding <| ⇑(pullback.snd f g) := by
-  convert (homeoOfIso (asIso (pullback.snd (𝟙 S) g))).isEmbedding.comp
-      (pullback_map_isEmbedding (i₂ := 𝟙 Y)
-        f g (𝟙 S) g H (homeoOfIso (Iso.refl _)).isEmbedding (𝟙 _) rfl (by simp))
+  convert!
+    (homeoOfIso (asIso (pullback.snd (𝟙 S) g))).isEmbedding.comp
+      (pullback_map_isEmbedding (i₂ := 𝟙 Y) f g (𝟙 S) g H (homeoOfIso (Iso.refl _)).isEmbedding
+        (𝟙 _) rfl (by simp))
   simp [homeoOfIso, ← coe_comp]
 
 set_option backward.isDefEq.respectTransparency false in
 theorem fst_isEmbedding_of_right {X Y S : TopCat.{u}} (f : X ⟶ S) {g : Y ⟶ S}
     (H : IsEmbedding g) : IsEmbedding <| ⇑(pullback.fst f g) := by
-  convert (homeoOfIso (asIso (pullback.fst f (𝟙 S)))).isEmbedding.comp
-      (pullback_map_isEmbedding (i₁ := 𝟙 X)
-        f g f (𝟙 _) (homeoOfIso (Iso.refl _)).isEmbedding H (𝟙 _) rfl (by simp))
+  convert!
+    (homeoOfIso (asIso (pullback.fst f (𝟙 S)))).isEmbedding.comp
+      (pullback_map_isEmbedding (i₁ := 𝟙 X) f g f (𝟙 _) (homeoOfIso (Iso.refl _)).isEmbedding H
+        (𝟙 _) rfl (by simp))
   simp [homeoOfIso, ← coe_comp]
 
 theorem isEmbedding_of_pullback {X Y S : TopCat.{u}} {f : X ⟶ S} {g : Y ⟶ S} (H₁ : IsEmbedding f)
     (H₂ : IsEmbedding g) : IsEmbedding (limit.π (cospan f g) WalkingCospan.one) := by
-  convert H₂.comp (snd_isEmbedding_of_left H₁ g)
+  convert! H₂.comp (snd_isEmbedding_of_left H₁ g)
   rw [← coe_comp, ← limit.w _ WalkingCospan.Hom.inr]
   rfl
 
 set_option backward.isDefEq.respectTransparency false in
 theorem snd_isOpenEmbedding_of_left {X Y S : TopCat.{u}} {f : X ⟶ S} (H : IsOpenEmbedding f)
     (g : Y ⟶ S) : IsOpenEmbedding <| ⇑(pullback.snd f g) := by
-  convert (homeoOfIso (asIso (pullback.snd (𝟙 S) g))).isOpenEmbedding.comp
+  convert!
+    (homeoOfIso (asIso (pullback.snd (𝟙 S) g))).isOpenEmbedding.comp
       (pullback_map_isOpenEmbedding (i₂ := 𝟙 Y) f g (𝟙 _) g H
         (homeoOfIso (Iso.refl _)).isOpenEmbedding (𝟙 _) rfl (by simp))
   simp [homeoOfIso, ← coe_comp]
@@ -310,7 +313,8 @@ theorem snd_isOpenEmbedding_of_left {X Y S : TopCat.{u}} {f : X ⟶ S} (H : IsOp
 set_option backward.isDefEq.respectTransparency false in
 theorem fst_isOpenEmbedding_of_right {X Y S : TopCat.{u}} (f : X ⟶ S) {g : Y ⟶ S}
     (H : IsOpenEmbedding g) : IsOpenEmbedding <| ⇑(pullback.fst f g) := by
-  convert (homeoOfIso (asIso (pullback.fst f (𝟙 S)))).isOpenEmbedding.comp
+  convert!
+    (homeoOfIso (asIso (pullback.fst f (𝟙 S)))).isOpenEmbedding.comp
       (pullback_map_isOpenEmbedding (i₁ := 𝟙 X) f g f (𝟙 _)
         (homeoOfIso (Iso.refl _)).isOpenEmbedding H (𝟙 _) rfl (by simp))
   simp [homeoOfIso, ← coe_comp]
@@ -319,7 +323,7 @@ theorem fst_isOpenEmbedding_of_right {X Y S : TopCat.{u}} (f : X ⟶ S) {g : Y 
 theorem isOpenEmbedding_of_pullback {X Y S : TopCat.{u}} {f : X ⟶ S} {g : Y ⟶ S}
     (H₁ : IsOpenEmbedding f) (H₂ : IsOpenEmbedding g) :
     IsOpenEmbedding (limit.π (cospan f g) WalkingCospan.one) := by
-  convert H₂.comp (snd_isOpenEmbedding_of_left H₁ g)
+  convert! H₂.comp (snd_isOpenEmbedding_of_left H₁ g)
   rw [← coe_comp, ← limit.w _ WalkingCospan.Hom.inr]
   rfl
 
@@ -333,7 +337,7 @@ theorem fst_iso_of_right_embedding_range_subset {X Y S : TopCat.{u}} (f : X ⟶
           ⟨x, by
             rw [pullback_fst_range]
             exact ⟨_, (H (Set.mem_range_self x)).choose_spec.symm⟩⟩ }
-  convert (isoOfHomeo esto).isIso_hom
+  convert! (isoOfHomeo esto).isIso_hom
 
 theorem snd_iso_of_left_embedding_range_subset {X Y S : TopCat.{u}} {f : X ⟶ S} (hf : IsEmbedding f)
     (g : Y ⟶ S) (H : Set.range g ⊆ Set.range f) : IsIso (pullback.snd f g) := by
@@ -344,7 +348,7 @@ theorem snd_iso_of_left_embedding_range_subset {X Y S : TopCat.{u}} {f : X ⟶ S
           ⟨x, by
             rw [pullback_snd_range]
             exact ⟨_, (H (Set.mem_range_self x)).choose_spec⟩⟩ }
-  convert (isoOfHomeo esto).isIso_hom
+  convert! (isoOfHomeo esto).isIso_hom
 
 theorem pullback_snd_image_fst_preimage (f : X ⟶ Z) (g : Y ⟶ Z) (U : Set X) :
     (pullback.snd f g) '' (pullback.fst f g) ⁻¹' U =
@@ -359,7 +363,7 @@ theorem pullback_snd_image_fst_preimage (f : X ⟶ Z) (g : Y ⟶ Z) (U : Set X)
   -- `exact ⟨(TopCat.pullbackIsoProdSubtype f g).inv ⟨⟨_, _⟩, eq⟩, by simpa, by simp⟩` before https://github.com/leanprover-community/mathlib4/pull/13170
     refine ⟨(TopCat.pullbackIsoProdSubtype f g).inv ⟨⟨_, _⟩, eq⟩, ?_, ?_⟩
     · simp only [coe_of, Set.mem_preimage]
-      convert hy
+      convert! hy
       rw [pullbackIsoProdSubtype_inv_fst_apply]
     · rw [pullbackIsoProdSubtype_inv_snd_apply]
 
@@ -378,7 +382,7 @@ theorem pullback_fst_image_snd_preimage (f : X ⟶ Z) (g : Y ⟶ Z) (U : Set Y)
     -- before https://github.com/leanprover-community/mathlib4/pull/13170
     refine ⟨(TopCat.pullbackIsoProdSubtype f g).inv ⟨⟨_, _⟩, eq.symm⟩, ?_, ?_⟩
     · simp only [coe_of, Set.mem_preimage]
-      convert hy
+      convert! hy
       rw [pullbackIsoProdSubtype_inv_snd_apply]
     · rw [pullbackIsoProdSubtype_inv_fst_apply]
 
diff --git a/Mathlib/Topology/Category/TopCat/Sphere.lean b/Mathlib/Topology/Category/TopCat/Sphere.lean
index 5edecbd2bee763..05a0ef143b1efb 100644
--- a/Mathlib/Topology/Category/TopCat/Sphere.lean
+++ b/Mathlib/Topology/Category/TopCat/Sphere.lean
@@ -83,11 +83,11 @@ instance {n : ℕ} : Mono (ballInclusion n) := TopCat.mono_iff_injective _ |>.mp
   congr
 
 instance (n : ℕ) : CompactSpace (𝔻 n) := by
-  convert Homeomorph.compactSpace Homeomorph.ulift.symm
+  convert! Homeomorph.compactSpace Homeomorph.ulift.symm
   infer_instance
 
 instance (n : ℕ) : CompactSpace (∂𝔻 n) := by
-  convert Homeomorph.compactSpace Homeomorph.ulift.symm
+  convert! Homeomorph.compactSpace Homeomorph.ulift.symm
   infer_instance
 
 end TopCat
diff --git a/Mathlib/Topology/Clopen.lean b/Mathlib/Topology/Clopen.lean
index d1c6a65fa37f1a..0d21251cbe4fe1 100644
--- a/Mathlib/Topology/Clopen.lean
+++ b/Mathlib/Topology/Clopen.lean
@@ -101,7 +101,7 @@ theorem isClopen_inter_of_disjoint_cover_clopen {s a b : Set X} (h : IsClopen s)
     (ha : IsOpen a) (hb : IsOpen b) (hab : Disjoint a b) : IsClopen (s ∩ a) := by
   refine ⟨?_, IsOpen.inter h.2 ha⟩
   have : IsClosed (s ∩ bᶜ) := IsClosed.inter h.1 (isClosed_compl_iff.2 hb)
-  convert this using 1
+  convert! this using 1
   refine (inter_subset_inter_right s hab.subset_compl_right).antisymm ?_
   rintro x ⟨hx₁, hx₂⟩
   exact ⟨hx₁, by simpa [notMem_of_mem_compl hx₂] using cover hx₁⟩
diff --git a/Mathlib/Topology/CompactOpen.lean b/Mathlib/Topology/CompactOpen.lean
index 05eae8f49e1193..e470152c297db6 100644
--- a/Mathlib/Topology/CompactOpen.lean
+++ b/Mathlib/Topology/CompactOpen.lean
@@ -339,7 +339,7 @@ theorem compactOpen_eq_iInf_induced :
   refine le_antisymm (le_iInf₂ fun s _ ↦ compactOpen_le_induced s) ?_
   refine le_generateFrom <| forall_mem_image2.2 fun K (hK : IsCompact K) U hU ↦ ?_
   refine TopologicalSpace.le_def.1 (iInf₂_le K hK) _ ?_
-  convert isOpen_induced (isOpen_setOf_mapsTo (isCompact_iff_isCompact_univ.1 hK) hU)
+  convert! isOpen_induced (isOpen_setOf_mapsTo (isCompact_iff_isCompact_univ.1 hK) hU)
   simp [Subtype.forall, MapsTo]
 
 theorem nhds_compactOpen_eq_iInf_nhds_induced (f : C(X, Y)) :
diff --git a/Mathlib/Topology/Compactification/StoneCech.lean b/Mathlib/Topology/Compactification/StoneCech.lean
index 48a69aa742890c..d2e261792e3636 100644
--- a/Mathlib/Topology/Compactification/StoneCech.lean
+++ b/Mathlib/Topology/Compactification/StoneCech.lean
@@ -74,7 +74,7 @@ theorem ultrafilter_isOpen_basic (s : Set α) : IsOpen { u : Ultrafilter α | s
 /-- The basic open sets for the topology on ultrafilters are also closed. -/
 theorem ultrafilter_isClosed_basic (s : Set α) : IsClosed { u : Ultrafilter α | s ∈ u } := by
   rw [← isOpen_compl_iff]
-  convert ultrafilter_isOpen_basic sᶜ using 1
+  convert! ultrafilter_isOpen_basic sᶜ using 1
   ext u
   exact Ultrafilter.compl_mem_iff_notMem.symm
 
@@ -252,7 +252,7 @@ theorem continuous_preStoneCechUnit : Continuous (preStoneCechUnit : α → PreS
       rfl
     have : (map preStoneCechUnit g : Filter (PreStoneCech α)) ≤ 𝓝 (Quot.mk _ g) :=
       (map_mono this).trans (continuous_quot_mk.tendsto _)
-    convert this
+    convert! this
     exact Quot.sound ⟨x, pure_le_nhds x, gx⟩
 
 theorem denseRange_preStoneCechUnit : DenseRange (preStoneCechUnit : α → PreStoneCech α) :=
diff --git a/Mathlib/Topology/Compactness/Compact.lean b/Mathlib/Topology/Compactness/Compact.lean
index e92f082402486e..b9f0f85f820727 100644
--- a/Mathlib/Topology/Compactness/Compact.lean
+++ b/Mathlib/Topology/Compactness/Compact.lean
@@ -113,7 +113,7 @@ theorem IsCompact.image_of_continuousOn {f : X → Y} (hs : IsCompact s) (hf : C
   haveI := hx.neBot
   use f x, mem_image_of_mem f hxs
   have : Tendsto f (𝓝 x ⊓ (comap f l ⊓ 𝓟 s)) (𝓝 (f x) ⊓ l) := by
-    convert (hf x hxs).inf (@tendsto_comap _ _ f l) using 1
+    convert! (hf x hxs).inf (@tendsto_comap _ _ f l) using 1
     rw [nhdsWithin]
     ac_rfl
   exact this.neBot
@@ -1155,7 +1155,7 @@ theorem isCompact_pi_infinite {s : ∀ i, Set (X i)} :
 /-- **Tychonoff's theorem** formulated using `Set.pi`: product of compact sets is compact. -/
 theorem isCompact_univ_pi {s : ∀ i, Set (X i)} (h : ∀ i, IsCompact (s i)) :
     IsCompact (pi univ s) := by
-  convert isCompact_pi_infinite h
+  convert! isCompact_pi_infinite h
   simp only [← mem_univ_pi, setOf_mem_eq]
 
 instance Pi.compactSpace [∀ i, CompactSpace (X i)] : CompactSpace (∀ i, X i) :=
diff --git a/Mathlib/Topology/Compactness/CompactSystem.lean b/Mathlib/Topology/Compactness/CompactSystem.lean
index a7dccf8b717d84..11e01cc117c7a1 100644
--- a/Mathlib/Topology/Compactness/CompactSystem.lean
+++ b/Mathlib/Topology/Compactness/CompactSystem.lean
@@ -172,7 +172,7 @@ theorem isCompactSystem_isCompact_isClosed (α : Type*) [TopologicalSpace α] :
 /-- In a `T2Space` the set of compact sets is a compact system. -/
 theorem isCompactSystem_isCompact (α : Type*) [TopologicalSpace α] [T2Space α] :
     IsCompactSystem {s : Set α | IsCompact s} := by
-  convert isCompactSystem_isCompact_isClosed α with s
+  convert! isCompactSystem_isCompact_isClosed α with s
   simpa using IsCompact.isClosed
 
 /-- The set of sets which are either compact and closed, or `univ`, is a compact system. -/
diff --git a/Mathlib/Topology/Compactness/Lindelof.lean b/Mathlib/Topology/Compactness/Lindelof.lean
index f2d29cca699945..78b8fdaf7ef8b7 100644
--- a/Mathlib/Topology/Compactness/Lindelof.lean
+++ b/Mathlib/Topology/Compactness/Lindelof.lean
@@ -108,7 +108,7 @@ theorem IsLindelof.image_of_continuousOn {f : X → Y} (hs : IsLindelof s) (hf :
   haveI := hx.neBot
   use f x, mem_image_of_mem f hxs
   have : Tendsto f (𝓝 x ⊓ (comap f l ⊓ 𝓟 s)) (𝓝 (f x) ⊓ l) := by
-    convert (hf x hxs).inf (@tendsto_comap _ _ f l) using 1
+    convert! (hf x hxs).inf (@tendsto_comap _ _ f l) using 1
     rw [nhdsWithin]
     ac_rfl
   exact this.neBot
diff --git a/Mathlib/Topology/Connected/CardComponents.lean b/Mathlib/Topology/Connected/CardComponents.lean
index 34224be42638e1..19185b97ebdb50 100644
--- a/Mathlib/Topology/Connected/CardComponents.lean
+++ b/Mathlib/Topology/Connected/CardComponents.lean
@@ -64,7 +64,7 @@ lemma IsOpenMap.enatCard_connectedComponents_le_encard_preimage_singleton [Conne
   · simp
   · rw [finsum_eq_sum_of_fintype]
     refine Fintype.sum_mono fun i ↦ Set.one_le_encard_iff_nonempty.mpr (show y ∈ f '' (U i) from ?_)
-    convert Set.mem_univ y
+    convert! Set.mem_univ y
     exact IsClopen.eq_univ ⟨hf₂ _ (hU1 i).1, hf₁ _ (hU1 i).2⟩ ((hU2 i).image f)
 
 lemma IsOpenMap.finite_connectedComponents_of_finite_preimage_singleton_of_connectedSpace
@@ -93,7 +93,7 @@ lemma IsOpenMap.finite_connectedComponents_of_finite_preimage_singleton
     (hf₁.restrictPreimage (connectedComponent y)) (hf₂.restrictPreimage (connectedComponent y))
     (y := ⟨y, mem_connectedComponent⟩) ?_
   rw [← Set.finite_image_iff Subtype.val_injective.injOn]
-  convert h y
+  convert! h y
   aesop (add safe mem_connectedComponent)
 
 end
diff --git a/Mathlib/Topology/Connected/TotallyDisconnected.lean b/Mathlib/Topology/Connected/TotallyDisconnected.lean
index f6fba4876114c5..d3db5708dc348c 100644
--- a/Mathlib/Topology/Connected/TotallyDisconnected.lean
+++ b/Mathlib/Topology/Connected/TotallyDisconnected.lean
@@ -258,7 +258,7 @@ def Continuous.connectedComponentsLift (h : Continuous f) : ConnectedComponents
 @[continuity]
 theorem Continuous.connectedComponentsLift_continuous (h : Continuous f) :
     Continuous h.connectedComponentsLift :=
-  h.quotient_liftOn' <| by convert h.image_eq_of_connectedComponent_eq
+  h.quotient_liftOn' <| by convert! h.image_eq_of_connectedComponent_eq
 
 @[simp]
 theorem Continuous.connectedComponentsLift_apply_coe (h : Continuous f) (x : α) :
diff --git a/Mathlib/Topology/Constructible.lean b/Mathlib/Topology/Constructible.lean
index e8fe3c95171a0c..ba2cb248d539fb 100644
--- a/Mathlib/Topology/Constructible.lean
+++ b/Mathlib/Topology/Constructible.lean
@@ -304,8 +304,10 @@ lemma _root_.QuasiSeparatedSpace.of_isOpenCover {ι : Type*} {U : ι → Opens X
     QuasiSeparatedSpace X where
   inter_isCompact V₁ V₂ ho₁ hc₁ ho₂ hc₂ := by
     obtain ⟨t, ht⟩ := hc₁.elim_finite_subcover _ (fun i ↦ (U i).2) (by simp [hU.iSup_set_eq_univ])
-    convert t.isCompact_biUnion fun i _ ↦ h₂ i _ _ Set.inter_subset_left ((U i).2.inter ho₁)
-      (h₁ i hc₁ ho₁) Set.inter_subset_left ((U i).2.inter ho₂) (h₁ i hc₂ ho₂)
+    convert!
+      t.isCompact_biUnion fun i _ ↦
+        h₂ i _ _ Set.inter_subset_left ((U i).2.inter ho₁) (h₁ i hc₁ ho₁) Set.inter_subset_left
+          ((U i).2.inter ho₂) (h₁ i hc₂ ho₂)
     apply subset_antisymm
     · rintro x ⟨hx₁, hx₂⟩
       obtain ⟨i, hi, hxi⟩ := Set.mem_iUnion₂.mp (ht hx₁)
@@ -477,7 +479,7 @@ lemma IsLocallyConstructible.isConstructible_of_subset_of_isCompact
     ⟨V, hV₁, hV₂, hxV, this⟩
   choose U hU hU' hxU hUs using this
   obtain ⟨σ, hσ, htσ⟩ := ht.elim_nhds_subcover U (fun x _ ↦ (hU x).mem_nhds (hxU x))
-  convert IsConstructible.biUnion σ.finite_toSet (fun x _ ↦ hUs x)
+  convert! IsConstructible.biUnion σ.finite_toSet (fun x _ ↦ hUs x)
   apply subset_antisymm
   · rw [← Set.iUnion₂_inter, Set.subset_inter_iff]
     exact ⟨hst.trans htσ, subset_rfl⟩
@@ -509,7 +511,7 @@ lemma IsLocallyConstructible.of_isOpenCover
   let e : V ≃ₜ Subtype.val '' V :=
     (Equiv.Set.image _ V Subtype.val_injective).toHomeomorphOfIsInducing
       ((U i).2.isOpenEmbedding_subtypeVal.restrict (by simp [MapsTo]) hV).isInducing
-  convert hV'.preimage_of_isOpenEmbedding e.symm.isOpenEmbedding
+  convert! hV'.preimage_of_isOpenEmbedding e.symm.isOpenEmbedding
   ext ⟨_, x, hx, rfl⟩
   simp [e, Equiv.toHomeomorphOfIsInducing]
 
diff --git a/Mathlib/Topology/Constructions.lean b/Mathlib/Topology/Constructions.lean
index 6c2daa06e4a9dc..03c4a57177fd18 100644
--- a/Mathlib/Topology/Constructions.lean
+++ b/Mathlib/Topology/Constructions.lean
@@ -415,12 +415,12 @@ theorem Continuous.subtype_mk {f : Y → X} (h : Continuous f) (hp : ∀ x, p (f
 
 theorem IsOpenMap.subtype_mk {f : Y → X} (hf : IsOpenMap f) (hp : ∀ x, p (f x)) :
     IsOpenMap fun x ↦ (⟨f x, hp x⟩ : Subtype p) := fun u hu ↦ by
-  convert (hf u hu).preimage continuous_subtype_val
+  convert! (hf u hu).preimage continuous_subtype_val
   exact Set.ext fun _ ↦ exists_congr fun _ ↦ and_congr_right' Subtype.ext_iff
 
 theorem IsClosedMap.subtype_mk {f : Y → X} (hf : IsClosedMap f) (hp : ∀ x, p (f x)) :
     IsClosedMap fun x ↦ (⟨f x, hp x⟩ : Subtype p) := fun u hu ↦ by
-  convert (hf u hu).preimage continuous_subtype_val
+  convert! (hf u hu).preimage continuous_subtype_val
   exact Set.ext fun _ ↦ exists_congr fun _ ↦ and_congr_right' Subtype.ext_iff
 
 @[fun_prop]
diff --git a/Mathlib/Topology/Constructions/SumProd.lean b/Mathlib/Topology/Constructions/SumProd.lean
index d311151fb14adf..47f5604db505be 100644
--- a/Mathlib/Topology/Constructions/SumProd.lean
+++ b/Mathlib/Topology/Constructions/SumProd.lean
@@ -812,7 +812,7 @@ theorem isClosedMap_sum {f : X ⊕ Y → Z} :
     exact ⟨h.comp IsClosedEmbedding.inl.isClosedMap, h.comp IsClosedEmbedding.inr.isClosedMap⟩
   · rintro h Z hZ
     rw [isClosed_sum_iff] at hZ
-    convert (h.1 _ hZ.1).union (h.2 _ hZ.2)
+    convert! (h.1 _ hZ.1).union (h.2 _ hZ.2)
     ext
     simp only [mem_image, Sum.exists, mem_union, mem_preimage]
 
@@ -951,7 +951,7 @@ theorem Topology.IsInducing.sumElim (hf : IsInducing f) (hg : IsInducing g)
   obtain x | x := x <;>
   simp only [comap_sumElim_eq, nhds_inl, nhds_inr, elim_inl, elim_inr, ← hf.nhds_eq_comap,
     ← hg.nhds_eq_comap, sup_le_iff, le_rfl, true_and, and_true] <;>
-  convert bot_le (α := Filter (X ⊕ Y)) <;>
+  convert! bot_le (α := Filter (X ⊕ Y)) <;>
   rw [map_eq_bot_iff, comap_eq_bot_iff_compl_range]
   · rw [← disjoint_principal_right]
     exact hfG.mono_left (nhds_le_nhdsSet (mem_range_self x))
diff --git a/Mathlib/Topology/ContinuousMap/Basic.lean b/Mathlib/Topology/ContinuousMap/Basic.lean
index f9aee2b0b3522a..876e093cb0da1c 100644
--- a/Mathlib/Topology/ContinuousMap/Basic.lean
+++ b/Mathlib/Topology/ContinuousMap/Basic.lean
@@ -442,7 +442,7 @@ noncomputable def homeomorph (hf : IsQuotientMap f) : Quotient (Setoid.ker f) 
   continuous_toFun := isQuotientMap_quot_mk.continuous_iff.mpr hf.continuous
   continuous_invFun := by
     rw [hf.continuous_iff]
-    convert continuous_quotient_mk'
+    convert! continuous_quotient_mk'
     ext
     simp only [Equiv.invFun_as_coe, Function.comp_apply,
       (Setoid.quotientKerEquivOfSurjective f hf.surjective).symm_apply_eq]
diff --git a/Mathlib/Topology/ContinuousMap/Bounded/Basic.lean b/Mathlib/Topology/ContinuousMap/Bounded/Basic.lean
index db450514f732aa..08c2ea4fe0598d 100644
--- a/Mathlib/Topology/ContinuousMap/Bounded/Basic.lean
+++ b/Mathlib/Topology/ContinuousMap/Bounded/Basic.lean
@@ -179,7 +179,7 @@ theorem dist_lt_iff_of_compact [CompactSpace α] (C0 : (0 : ℝ) < C) :
   · by_cases h : Nonempty α
     · exact dist_lt_of_nonempty_compact
     · rintro -
-      convert C0
+      convert! C0
       apply le_antisymm _ dist_nonneg'
       rw [dist_eq]
       exact csInf_le ⟨0, fun C => And.left⟩ ⟨le_rfl, fun x => False.elim (h (Nonempty.intro x))⟩
diff --git a/Mathlib/Topology/ContinuousMap/Ideals.lean b/Mathlib/Topology/ContinuousMap/Ideals.lean
index 57a7446e8ad7ac..459d6dee6c7e11 100644
--- a/Mathlib/Topology/ContinuousMap/Ideals.lean
+++ b/Mathlib/Topology/ContinuousMap/Ideals.lean
@@ -102,7 +102,7 @@ variable {R}
 
 theorem mem_idealOfSet {s : Set X} {f : C(X, R)} :
     f ∈ idealOfSet R s ↔ ∀ ⦃x : X⦄, x ∈ sᶜ → f x = 0 := by
-  convert Iff.rfl
+  convert! Iff.rfl
 
 theorem notMem_idealOfSet {s : Set X} {f : C(X, R)} : f ∉ idealOfSet R s ↔ ∃ x ∈ sᶜ, f x ≠ 0 := by
   simp_rw [mem_idealOfSet]; push Not; rfl
@@ -244,13 +244,13 @@ theorem idealOfSet_ofIdeal_eq_closure (I : Ideal C(X, 𝕜)) :
   have : ∃ g' : C(X, ℝ≥0), (algebraMapCLM ℝ≥0 𝕜 : C(ℝ≥0, 𝕜)).comp g' ∈ I ∧ ∀ x ∈ t, 0 < g' x := by
     refine ht.isCompact.induction_on ?_ ?_ ?_ ?_
     · refine ⟨0, ?_, fun x hx => False.elim hx⟩
-      convert I.zero_mem
+      convert! I.zero_mem
       ext
       simp only [comp_apply, zero_apply, ContinuousMap.coe_coe, map_zero]
     · rintro s₁ s₂ hs ⟨g, hI, hgt⟩; exact ⟨g, hI, fun x hx => hgt x (hs hx)⟩
     · rintro s₁ s₂ ⟨g₁, hI₁, hgt₁⟩ ⟨g₂, hI₂, hgt₂⟩
       refine ⟨g₁ + g₂, ?_, fun x hx => ?_⟩
-      · convert I.add_mem hI₁ hI₂
+      · convert! I.add_mem hI₁ hI₂
         ext y
         simp
       · rcases hx with (hx | hx)
@@ -266,7 +266,7 @@ theorem idealOfSet_ofIdeal_eq_closure (I : Ideal C(X, 𝕜)) :
           mem_nhdsWithin_iff_exists_mem_nhds_inter.mpr ⟨_, this, Set.Subset.rfl⟩,
           ⟨⟨fun x => ‖g x‖₊ ^ 2, (map_continuous g).nnnorm.pow 2⟩, ?_, fun x hx =>
             pow_pos (norm_pos_iff.mpr hx.1) 2⟩⟩
-      convert I.mul_mem_left (star g) hI
+      convert! I.mul_mem_left (star g) hI
       ext
       simp only [comp_apply, ContinuousMap.coe_coe, coe_mk, algebraMapCLM_apply, map_pow,
         mul_apply, star_apply, star_def]
@@ -283,7 +283,7 @@ theorem idealOfSet_ofIdeal_eq_closure (I : Ideal C(X, 𝕜)) :
       ⟨g' x, hgt' x hx, hx'⟩
   obtain ⟨g, hg, hgc⟩ := exists_mul_le_one_eqOn_ge g' hc
   refine ⟨g * g', ?_, hg, hgc.mono hgc'⟩
-  convert I.mul_mem_left ((algebraMapCLM ℝ≥0 𝕜 : C(ℝ≥0, 𝕜)).comp g) hI'
+  convert! I.mul_mem_left ((algebraMapCLM ℝ≥0 𝕜 : C(ℝ≥0, 𝕜)).comp g) hI'
   ext
   simp only [coe_algebraMapCLM, comp_apply, mul_apply, ContinuousMap.coe_coe, map_mul]
 
diff --git a/Mathlib/Topology/ContinuousMap/Periodic.lean b/Mathlib/Topology/ContinuousMap/Periodic.lean
index 345c409eefe8e1..d06265a3841a15 100644
--- a/Mathlib/Topology/ContinuousMap/Periodic.lean
+++ b/Mathlib/Topology/ContinuousMap/Periodic.lean
@@ -32,7 +32,9 @@ theorem periodic_tsum_comp_add_zsmul [AddCommGroup X] [ContinuousAdd X] [AddComm
     Function.Periodic (⇑(∑' n : ℤ, f.comp (ContinuousMap.addRight (n • p)))) p := by
   intro x
   by_cases h : Summable fun n : ℤ => f.comp (ContinuousMap.addRight (n • p))
-  · convert congr_arg (fun f : C(X, Y) => f x) ((Equiv.addRight (1 : ℤ)).tsum_eq _) using 1
+  · convert! congr_arg (fun f : C(X, Y) => f x) ((Equiv.addRight (1 : ℤ)).tsum_eq _) using 1
+    -- This `have` unfolds the function composition in `Equiv.summable_iff`.
+
     -- This `have` unfolds the function composition in `Equiv.summable_iff`.
     have : Summable fun (c : ℤ) => f.comp (ContinuousMap.addRight (Equiv.addRight 1 c • p)) :=
       (Equiv.addRight (1 : ℤ)).summable_iff.mpr h
diff --git a/Mathlib/Topology/ContinuousMap/Polynomial.lean b/Mathlib/Topology/ContinuousMap/Polynomial.lean
index 5be1a5f611d5b5..cd74e882e79f05 100644
--- a/Mathlib/Topology/ContinuousMap/Polynomial.lean
+++ b/Mathlib/Topology/ContinuousMap/Polynomial.lean
@@ -184,7 +184,7 @@ theorem polynomialFunctions.comap_compRightAlgHom_iccHomeoI (a b : ℝ) (h : a <
         smul_eq_mul, Polynomial.eval_mul, Polynomial.eval_add,
         Polynomial.eval_comp, Polynomial.toContinuousMapOnAlgHom_apply,
         Polynomial.toContinuousMapOn_apply, Polynomial.toContinuousMap_apply]
-      convert w ⟨_, _⟩
+      convert! w ⟨_, _⟩
       · ext
         simp only [iccHomeoI_symm_apply_coe]
         replace h : b - a ≠ 0 := sub_ne_zero_of_ne h.ne.symm
diff --git a/Mathlib/Topology/ContinuousMap/StoneWeierstrass.lean b/Mathlib/Topology/ContinuousMap/StoneWeierstrass.lean
index 4c5edb995054cf..c311a9ddb11d85 100644
--- a/Mathlib/Topology/ContinuousMap/StoneWeierstrass.lean
+++ b/Mathlib/Topology/ContinuousMap/StoneWeierstrass.lean
@@ -134,7 +134,7 @@ theorem inf_mem_subalgebra_closure (A : Subalgebra ℝ C(X, ℝ)) (f g : A) :
 
 theorem inf_mem_closed_subalgebra (A : Subalgebra ℝ C(X, ℝ)) (h : IsClosed (A : Set C(X, ℝ)))
     (f g : A) : (f : C(X, ℝ)) ⊓ (g : C(X, ℝ)) ∈ A := by
-  convert inf_mem_subalgebra_closure A f g
+  convert! inf_mem_subalgebra_closure A f g
   apply SetLike.ext'
   symm
   rw [Subalgebra.topologicalClosure_coe, closure_eq_iff_isClosed]
@@ -154,7 +154,7 @@ theorem sup_mem_subalgebra_closure (A : Subalgebra ℝ C(X, ℝ)) (f g : A) :
 
 theorem sup_mem_closed_subalgebra (A : Subalgebra ℝ C(X, ℝ)) (h : IsClosed (A : Set C(X, ℝ)))
     (f g : A) : (f : C(X, ℝ)) ⊔ (g : C(X, ℝ)) ∈ A := by
-  convert sup_mem_subalgebra_closure A f g
+  convert! sup_mem_subalgebra_closure A f g
   apply SetLike.ext'
   simp
 
@@ -270,7 +270,7 @@ theorem subalgebra_topologicalClosure_eq_top_of_separatesPoints (A : Subalgebra
   apply SetLike.ext'
   let L := A.topologicalClosure
   have n : Set.Nonempty (L : Set C(X, ℝ)) := ⟨(1 : C(X, ℝ)), A.le_topologicalClosure A.one_mem⟩
-  convert
+  convert!
     sublattice_closure_eq_top (L : Set C(X, ℝ)) n
       (fun f fm g gm => inf_mem_closed_subalgebra L A.isClosed_topologicalClosure ⟨f, fm⟩ ⟨g, gm⟩)
       (fun f fm g gm => sup_mem_closed_subalgebra L A.isClosed_topologicalClosure ⟨f, fm⟩ ⟨g, gm⟩)
@@ -385,7 +385,7 @@ theorem Subalgebra.SeparatesPoints.rclike_to_real {A : StarSubalgebra 𝕜 C(X,
   refine ⟨_, ⟨⟨(‖F ·‖ ^ 2), by fun_prop⟩, ?_, rfl⟩, ?_⟩
   · -- This is also an element of the subalgebra, and takes only real values
     rw [SetLike.mem_coe, Subalgebra.mem_comap]
-    convert (A.restrictScalars ℝ).mul_mem hFA (star_mem hFA : star F ∈ A)
+    convert! (A.restrictScalars ℝ).mul_mem hFA (star_mem hFA : star F ∈ A)
     ext1
     simp [← RCLike.mul_conj]
   · -- And it also separates the points `x₁`, `x₂`
@@ -428,7 +428,7 @@ theorem ContinuousMap.starSubalgebra_topologicalClosure_eq_top_of_separatesPoint
   -- So `f_re + I • f_im` is in the closure of `A`
   have := A.topologicalClosure.add_mem h_f_re (A.topologicalClosure.smul_mem h_f_im RCLike.I)
   rw [StarSubalgebra.mem_toSubalgebra] at this
-  convert this
+  convert! this
   -- And this, of course, is just `f`
   ext
   apply Eq.symm
@@ -613,7 +613,7 @@ lemma ker_evalStarAlgHom_eq_closure_adjoin_id (s : Set 𝕜) (h0 : 0 ∈ s) [Com
       closure (adjoin 𝕜 {(restrict s (.id 𝕜))}) := by
   rw [← ker_evalStarAlgHom_inter_adjoin_id s h0,
     AlgHom.closure_ker_inter (φ := evalStarAlgHom 𝕜 𝕜 (X := s) ⟨0, h0⟩) (continuous_eval_const _) _]
-  convert (Set.univ_inter _).symm
+  convert! (Set.univ_inter _).symm
   rw [← Polynomial.toContinuousMapOn_X_eq_restrict_id, ← Polynomial.toContinuousMapOnAlgHom_apply,
     ← polynomialFunctions.starClosure_eq_adjoin_X s]
   congrm (($(polynomialFunctions.starClosure_topologicalClosure s) : Set C(s, 𝕜)))
diff --git a/Mathlib/Topology/ContinuousMap/T0Sierpinski.lean b/Mathlib/Topology/ContinuousMap/T0Sierpinski.lean
index 3271ee7a3bf687..77c27b073bb658 100644
--- a/Mathlib/Topology/ContinuousMap/T0Sierpinski.lean
+++ b/Mathlib/Topology/ContinuousMap/T0Sierpinski.lean
@@ -49,7 +49,7 @@ def productOfMemOpens : C(X, Opens X → Prop) where
   continuous_toFun := continuous_pi_iff.2 fun u => continuous_Prop.2 u.isOpen
 
 theorem productOfMemOpens_isInducing : IsInducing (productOfMemOpens X) := by
-  convert inducing_iInf_to_pi fun (u : Opens X) (x : X) => x ∈ u
+  convert! inducing_iInf_to_pi fun (u : Opens X) (x : X) => x ∈ u
   apply eq_induced_by_maps_to_sierpinski
 
 theorem productOfMemOpens_injective [T0Space X] : Function.Injective (productOfMemOpens X) := by
diff --git a/Mathlib/Topology/ContinuousOn.lean b/Mathlib/Topology/ContinuousOn.lean
index f1a9f9c1334284..01fc94ed52bc8a 100644
--- a/Mathlib/Topology/ContinuousOn.lean
+++ b/Mathlib/Topology/ContinuousOn.lean
@@ -183,7 +183,7 @@ theorem ContinuousOn.isOpen_inter_preimage {t : Set β}
 
 theorem ContinuousOn.isOpen_preimage {t : Set β} (h : ContinuousOn f s)
     (hs : IsOpen s) (hp : f ⁻¹' t ⊆ s) (ht : IsOpen t) : IsOpen (f ⁻¹' t) := by
-  convert (continuousOn_open_iff hs).mp h t ht
+  convert! (continuousOn_open_iff hs).mp h t ht
   rw [inter_comm, inter_eq_self_of_subset_left hp]
 
 theorem ContinuousOn.preimage_isClosed_of_isClosed {t : Set β}
diff --git a/Mathlib/Topology/Convenient/OpenClosed.lean b/Mathlib/Topology/Convenient/OpenClosed.lean
index 747461c4ad0076..cf54c8355aa24f 100644
--- a/Mathlib/Topology/Convenient/OpenClosed.lean
+++ b/Mathlib/Topology/Convenient/OpenClosed.lean
@@ -47,7 +47,7 @@ lemma IsOpen.isGeneratedBy [IsGeneratedBy X Y] {U : Set Y} (hU : IsOpen U) :
   refine continuous_subtype_val.isOpen_preimage _ ?_
   rw [IsGeneratedBy.isOpen_iff X]
   intro i f
-  convert (W ⟨i, f⟩).isOpen.isOpenMap_subtype_val _ (hV ⟨i, f⟩)
+  convert! (W ⟨i, f⟩).isOpen.isOpenMap_subtype_val _ (hV ⟨i, f⟩)
   aesop
 
 lemma Topology.IsOpenEmbedding.isGeneratedBy [IsGeneratedBy X Y]
@@ -80,7 +80,7 @@ lemma IsClosed.isGeneratedBy [IsGeneratedBy X Y] {F : Set Y} (hF : IsClosed F) :
   refine IsClosed.preimage continuous_subtype_val ?_
   rw [IsGeneratedBy.isClosed_iff X]
   intro i f
-  convert (W ⟨i, f⟩).isClosed.isClosedMap_subtype_val _ (hV ⟨i, f⟩)
+  convert! (W ⟨i, f⟩).isClosed.isClosedMap_subtype_val _ (hV ⟨i, f⟩)
   aesop
 
 lemma Topology.IsClosedEmbedding.isGeneratedBy [IsGeneratedBy X Y]
diff --git a/Mathlib/Topology/Covering/AddCircle.lean b/Mathlib/Topology/Covering/AddCircle.lean
index 735711e09f6c02..300abb208c1e92 100644
--- a/Mathlib/Topology/Covering/AddCircle.lean
+++ b/Mathlib/Topology/Covering/AddCircle.lean
@@ -62,20 +62,20 @@ theorem isAddQuotientCoveringMap_zsmul {n : ℤ} (hn : IsUnit (n : 𝕜)) :
 theorem isAddQuotientCoveringMap_nsmul {n : ℕ} (hn : IsUnit (n : 𝕜)) :
     IsAddQuotientCoveringMap (n • · : AddCircle p → _)
       (nsmulAddMonoidHom (α := AddCircle p) n).ker := by
-  convert isAddQuotientCoveringMap_zsmul p (n := n) (mod_cast hn)
+  convert! isAddQuotientCoveringMap_zsmul p (n := n) (mod_cast hn)
   all_goals ext; simp
 
 theorem isAddQuotientCoveringMap_zsmul_of_ne_zero [Algebra ℚ 𝕜] (n : ℤ) [NeZero n] :
     IsAddQuotientCoveringMap (n • · : AddCircle p → _)
       (zsmulAddGroupHom (α := AddCircle p) n).ker :=
   isAddQuotientCoveringMap_zsmul p (n := n) <| by
-    convert (Int.cast_ne_zero.mpr <| NeZero.ne n).isUnit.map (algebraMap ℚ 𝕜); simp
+    convert! (Int.cast_ne_zero.mpr <| NeZero.ne n).isUnit.map (algebraMap ℚ 𝕜); simp
 
 theorem isAddQuotientCoveringMap_nsmul_of_ne_zero [Algebra ℚ 𝕜] (n : ℕ) [NeZero n] :
     IsAddQuotientCoveringMap (n • · : AddCircle p → _)
       (nsmulAddMonoidHom (α := AddCircle p) n).ker :=
   isAddQuotientCoveringMap_nsmul p (n := n) <| by
-    convert (Nat.cast_ne_zero.mpr <| NeZero.ne n).isUnit.map (algebraMap ℚ 𝕜); simp
+    convert! (Nat.cast_ne_zero.mpr <| NeZero.ne n).isUnit.map (algebraMap ℚ 𝕜); simp
 
 end Field
 
diff --git a/Mathlib/Topology/Covering/Basic.lean b/Mathlib/Topology/Covering/Basic.lean
index 6b8d5c739538e6..f920a421ae0246 100644
--- a/Mathlib/Topology/Covering/Basic.lean
+++ b/Mathlib/Topology/Covering/Basic.lean
@@ -161,11 +161,11 @@ theorem comp_subtypeVal (hs : IsOpen s) (hfs : IsOpen (f ⁻¹' s)) {x : X} (hx
   (isEmpty_or_nonempty I).elim (fun _ ↦ .of_preimage_eq_empty _ ((hs.inter hU).mem_nhds ⟨hx, hxU⟩)
     <| Set.not_nonempty_iff_eq_empty.mp fun ⟨e, he⟩ ↦ isEmptyElim (H ⟨⟨e, he.1⟩, he.2⟩).2) fun _ ↦
   have hUs : U ⊆ s := fun y hy ↦ by
-    convert Set.mem_preimage.mp (H.symm (⟨y, hy⟩, Classical.arbitrary I)).1.2; simp [← hH]
+    convert! Set.mem_preimage.mp (H.symm (⟨y, hy⟩, Classical.arbitrary I)).1.2; simp [← hH]
   have : Subtype.val '' (fun e : f ⁻¹' s ↦ f e) ⁻¹' U = f ⁻¹' U := by ext; simpa using @hUs _
   ⟨inst, U, hxU, hU, this ▸ hfs.isOpenMap_subtype_val _ hfU, .trans (.symm <| .trans
     (IsEmbedding.subtypeVal.homeomorphImage _) <| .setCongr this) H, fun x ↦ by
-    dsimp; convert hH ⟨⟨x, hUs x.2⟩, x.2⟩ using 4; rw [Homeomorph.symm_apply_eq]; rfl⟩
+    dsimp; convert! hH ⟨⟨x, hUs x.2⟩, x.2⟩ using 4; rw [Homeomorph.symm_apply_eq]; rfl⟩
 
 theorem comp_homeomorph {x : X} (h : IsEvenlyCovered f x I) {E'} [TopologicalSpace E']
     (g : E' ≃ₜ E) : IsEvenlyCovered (f ∘ g) x I :=
@@ -175,7 +175,7 @@ theorem comp_homeomorph {x : X} (h : IsEvenlyCovered f x I) {E'} [TopologicalSpa
 
 @[simp] theorem comp_homeomorph_iff {x : X} {E'} [TopologicalSpace E'] (g : E' ≃ₜ E) :
     IsEvenlyCovered (f ∘ g) x I ↔ IsEvenlyCovered f x I where
-  mp h := by convert h.comp_homeomorph g.symm; ext; simp
+  mp h := by convert! h.comp_homeomorph g.symm; ext; simp
   mpr h := h.comp_homeomorph g
 
 theorem homeomorph_comp {x : X} (h : IsEvenlyCovered f x I) {Y} [TopologicalSpace Y] (g : X ≃ₜ Y) :
@@ -187,7 +187,7 @@ theorem homeomorph_comp {x : X} (h : IsEvenlyCovered f x I) {Y} [TopologicalSpac
 
 @[simp] theorem homeomorph_comp_iff {x : X} {Y} [TopologicalSpace Y] (g : X ≃ₜ Y) :
     IsEvenlyCovered (g ∘ f) (g x) I ↔ IsEvenlyCovered f x I where
-  mp h := by convert h.homeomorph_comp g.symm <;> ((try ext); simp)
+  mp h := by convert! h.homeomorph_comp g.symm <;> ((try ext); simp)
   mpr h := h.homeomorph_comp g
 
 end IsEvenlyCovered
@@ -268,7 +268,7 @@ theorem comp_homeomorph (hf : IsCoveringMapOn f s) {E'} [TopologicalSpace E'] (g
 
 @[simp] theorem comp_homeomorph_iff {E'} [TopologicalSpace E'] (g : E' ≃ₜ E) :
     IsCoveringMapOn (f ∘ g) s ↔ IsCoveringMapOn f s where
-  mp h := by convert h.comp_homeomorph g.symm; ext; simp
+  mp h := by convert! h.comp_homeomorph g.symm; ext; simp
   mpr h := h.comp_homeomorph g
 
 theorem homeomorph_comp (hf : IsCoveringMapOn f s) {Y} [TopologicalSpace Y] (g : X ≃ₜ Y) :
@@ -277,7 +277,7 @@ theorem homeomorph_comp (hf : IsCoveringMapOn f s) {Y} [TopologicalSpace Y] (g :
 
 @[simp] theorem homeomorph_comp_iff {Y} [TopologicalSpace Y] (g : X ≃ₜ Y) :
     IsCoveringMapOn (g ∘ f) (g.symm ⁻¹' s) ↔ IsCoveringMapOn f s where
-  mp h := by convert h.homeomorph_comp g.symm <;> (ext; simp)
+  mp h := by convert! h.homeomorph_comp g.symm <;> (ext; simp)
   mpr h := h.homeomorph_comp g
 
 end IsCoveringMapOn
@@ -397,12 +397,12 @@ omit hf
 
 theorem comp_homeomorph_iff {E'} [TopologicalSpace E'] (g : E' ≃ₜ E) :
     IsCoveringMap (f ∘ g) ↔ IsCoveringMap f where
-  mp h := by convert h.comp_homeomorph g.symm; ext; simp
+  mp h := by convert! h.comp_homeomorph g.symm; ext; simp
   mpr h := h.comp_homeomorph g
 
 theorem homeomorph_comp_iff {Y} [TopologicalSpace Y] (g : X ≃ₜ Y) :
     IsCoveringMap (g ∘ f) ↔ IsCoveringMap f where
-  mp h := by convert h.homeomorph_comp g.symm; ext; simp
+  mp h := by convert! h.homeomorph_comp g.symm; ext; simp
   mpr h := h.homeomorph_comp g
 
 end IsCoveringMap
@@ -462,7 +462,7 @@ Then `f` admits a `Bundle.Trivialization` over the base set `V`. -/
       rw [dif_pos ((f_inv _ hx.1).symm ▸ hx.1)]
       by_contra h; exact (disjoint h).le_bot ⟨idx_U .., inv_U _ _⟩ }
   have open_preim {W} (hWV : W ⊆ V) (open_W : IsOpen W) : IsOpen (f ⁻¹' W) := by
-    convert isOpen_iUnion (fun i ↦ (open_iff i hWV).mp open_W)
+    convert! isOpen_iUnion (fun i ↦ (open_iff i hWV).mp open_W)
     rw [← Set.inter_iUnion, eq_comm, Set.inter_eq_left]
     exact (Set.preimage_mono hWV).trans exhaustive'
   have open_source : IsOpen F.source := open_preim subset_rfl open_V
@@ -487,7 +487,7 @@ Then `f` admits a `Bundle.Trivialization` over the base set `V`. -/
   · simp_rw [F, Set.prodMk_mem_set_prod_eq, Set.mem_univ, and_true]
     refine (continuousOn_open_iff open_V).mpr fun W open_W ↦ ?_
     rw [open_iff i Set.inter_subset_left]
-    convert ((open_iff i subset_rfl).mp open_V).inter open_W using 1
+    convert! ((open_iff i subset_rfl).mp open_V).inter open_W using 1
     refine Set.ext fun e ↦ and_right_comm.trans (and_congr_right fun ⟨hV, hU⟩ ↦ ?_)
     rw [Set.mem_preimage, dif_pos hV, inj i (inv_U i _) hU (f_inv i _)]
 
@@ -531,7 +531,7 @@ theorem IsClosedMap.isEvenlyCovered_of_openPartialHomeomorph [T2Space E] {x : X}
   let U' := U ∩ ⋂ e : f ⁻¹' {x}, f '' (V' e)
   have : Finite (f ⁻¹' {x}) := fin
   have hU' : IsOpen U' := hU.inter <| isOpen_iInter_of_finite fun e ↦ by
-    convert ← (φ e).isOpen_image_of_subset_source (hV' _) inter_subset_right; exact (hφ e).2
+    convert! ← (φ e).isOpen_image_of_subset_source (hV' _) inter_subset_right; exact (hφ e).2
   have hUV e : U' ⊆ f '' V' e := inter_subset_right.trans (iInter_subset ..)
   have : Nonempty E := ⟨Classical.arbitrary (f ⁻¹' {x})⟩
   refine .of_trivialization (t := hU'.trivializationDiscrete _ _
@@ -540,17 +540,17 @@ theorem IsClosedMap.isEvenlyCovered_of_openPartialHomeomorph [T2Space E] {x : X}
     (pairwise_disjoint_mono disj.subtype fun e ↦ inter_subset_left)
     ((preimage_mono (inter_subset_left.trans hUW)).trans hWV))
     ⟨hxU, Set.mem_iInter.mpr fun e ↦ ⟨e, ⟨(hV e).1, (hφ e).1⟩, e.2⟩⟩
-  · convert ((φ e).isOpen_inter_preimage h).inter (hV e).2 using 1
+  · convert! ((φ e).isOpen_inter_preimage h).inter (hV e).2 using 1
     simp_rw [(hφ e).2, V']; ac_rfl
   · have : s ⊆ (φ e).target := hs.trans <| (hUV e).trans <| by
       rw [← (φ e).image_source_eq_target, (hφ e).2]; exact image_mono inter_subset_right
     rw [← (φ e).isOpen_symm_image_iff_of_subset_target this,
       (φ e).symm_image_eq_source_inter_preimage this, (hφ e).2, inter_comm]
-    convert h using 1
+    convert! h using 1
     refine inter_eq_inter_iff_left.mpr ⟨fun e' h ↦ h.2.2, fun e' h ↦ ⟨?_ , h.2⟩⟩
     have ⟨e'', ⟨_, mem⟩, eq⟩ := mem_iInter.mp (hs h.1).2 e
     rwa [← (φ e).injOn mem h.2 (by rwa [(hφ e).2])]
-  · convert ← (φ e).injOn.mono inter_subset_right; exact (hφ e).2
+  · convert! ← (φ e).injOn.mono inter_subset_right; exact (hφ e).2
 
 /-- If `f : E → X` is a closed map between topological spaces with `E` Hausdorff, and `s` is
 a subset of `X` on which `f` has finite fibers, such that `f` restricts to a homeomorphism on
diff --git a/Mathlib/Topology/Covering/Quotient.lean b/Mathlib/Topology/Covering/Quotient.lean
index 3aafe45fc9009e..18ec7fc50a48f7 100644
--- a/Mathlib/Topology/Covering/Quotient.lean
+++ b/Mathlib/Topology/Covering/Quotient.lean
@@ -64,7 +64,7 @@ variable {f G}
 
 @[to_additive (attr := simp)] theorem homeomorph_comp_iff {Y} [TopologicalSpace Y]
     (φ : X ≃ₜ Y) : IsQuotientCoveringMap (φ ∘ f) G ↔ IsQuotientCoveringMap f G where
-  mp h := by convert h.homeomorph_comp φ.symm; ext; simp
+  mp h := by convert! h.homeomorph_comp φ.symm; ext; simp
   mpr h := h.homeomorph_comp φ
 
 end IsQuotientCoveringMap
@@ -105,7 +105,7 @@ noncomputable def trivializationOfSMulDisjoint [TopologicalSpace G] [DiscreteTop
       mul_inv_eq_one.mp (disjoint _ ⟨_, ⟨_, h₂, ?_⟩, h₁⟩)) preim_im.subset
   · rw [← hf.isOpen_preimage, preim_im]
     exact isOpen_iUnion fun g ↦ open_U.preimage (continuous_const_smul g)
-  · convert isOpen_iUnion fun g : G ↦ isOpen.preimage (continuous_const_smul g)
+  · convert! isOpen_iUnion fun g : G ↦ isOpen.preimage (continuous_const_smul g)
     ext e; refine ⟨fun hW ↦ ?_, ?_⟩
     · have ⟨e', he', hfe⟩ := hWU hW
       obtain ⟨g', rfl⟩ := hfG.mp hfe
@@ -214,7 +214,7 @@ namespace IsQuotientCoveringMap
     IsCoveringMap f :=
   isCoveringMap_iff_isCoveringMapOn_univ.mpr <| by
     have := h.toContinuousConstSMul
-    convert ← h.isCoveringMapOn_of_smul_disjoint h.apply_eq_iff_mem_orbit fun e ↦ ?_
+    convert! ← h.isCoveringMapOn_of_smul_disjoint h.apply_eq_iff_mem_orbit fun e ↦ ?_
     · refine Set.eq_univ_of_forall fun x ↦ ?_
       obtain ⟨e, rfl⟩ := h.surjective x
       have ⟨U, hU, hGU⟩ := h.disjoint e
diff --git a/Mathlib/Topology/DerivedSet.lean b/Mathlib/Topology/DerivedSet.lean
index 357a6aded0fa6f..d185432f3964d6 100644
--- a/Mathlib/Topology/DerivedSet.lean
+++ b/Mathlib/Topology/DerivedSet.lean
@@ -52,7 +52,7 @@ theorem Continuous.image_derivedSet {β : Type*} [TopologicalSpace β] {A : Set
   intro x hx
   simp only [Set.mem_image, mem_derivedSet] at hx
   obtain ⟨y, hy1, rfl⟩ := hx
-  convert hy1.map hf1.continuousAt hf2
+  convert! hy1.map hf1.continuousAt hf2
   simp
 
 lemma derivedSet_subset_closure (A : Set X) : derivedSet A ⊆ closure A :=
diff --git a/Mathlib/Topology/DiscreteQuotient.lean b/Mathlib/Topology/DiscreteQuotient.lean
index b3b5c8bb442f66..a690f782ef8391 100644
--- a/Mathlib/Topology/DiscreteQuotient.lean
+++ b/Mathlib/Topology/DiscreteQuotient.lean
@@ -229,7 +229,7 @@ instance [LocallyConnectedSpace X] : OrderBot (DiscreteQuotient X) where
   bot :=
     { toSetoid := connectedComponentSetoid X
       isOpen_setOf_rel := fun x => by
-        convert isOpen_connectedComponent (x := x)
+        convert! isOpen_connectedComponent (x := x)
         ext y
         simpa only [connectedComponentSetoid, ← connectedComponent_eq_iff_mem] using eq_comm }
   bot_le S := fun x y (h : connectedComponent x = connectedComponent y) =>
diff --git a/Mathlib/Topology/DiscreteSubset.lean b/Mathlib/Topology/DiscreteSubset.lean
index f3f647aa95548f..062352542e8720 100644
--- a/Mathlib/Topology/DiscreteSubset.lean
+++ b/Mathlib/Topology/DiscreteSubset.lean
@@ -164,7 +164,7 @@ lemma Continuous.discrete_of_tendsto_cofinite_cocompact [T1Space X] [WeaklyLocal
 lemma tendsto_cofinite_cocompact_of_discrete [DiscreteTopology X]
     (hf : Tendsto f (cocompact _) (cocompact _)) :
     Tendsto f cofinite (cocompact _) := by
-  convert hf
+  convert! hf
   rw [cocompact_eq_cofinite X]
 
 lemma IsClosed.tendsto_coe_cofinite_of_isDiscrete
diff --git a/Mathlib/Topology/EMetricSpace/BoundedVariation.lean b/Mathlib/Topology/EMetricSpace/BoundedVariation.lean
index 5f253e2f0386ef..ac16ca16607048 100644
--- a/Mathlib/Topology/EMetricSpace/BoundedVariation.lean
+++ b/Mathlib/Topology/EMetricSpace/BoundedVariation.lean
@@ -358,8 +358,9 @@ theorem add_le_union (f : α → E) {s t : Set α} (h : ∀ x ∈ s, ∀ y ∈ t
           ∑ i ∈ Finset.Ico (n + 1) (n + 1 + m), edist (f (w (i + 1))) (f (w i)) := by
       congr 1
       rw [Finset.range_eq_Ico]
-      convert Finset.sum_Ico_add (fun i : ℕ => edist (f (w (i + 1))) (f (w i))) 0 m (n + 1)
-        using 3 <;> abel
+      convert!
+          Finset.sum_Ico_add (fun i : ℕ => edist (f (w (i + 1))) (f (w i))) 0 m (n + 1) using 3 <;>
+        abel
     _ ≤ ∑ i ∈ Finset.range (n + 1 + m), edist (f (w (i + 1))) (f (w i)) := by
       rw [← Finset.sum_union]
       · gcongr; grind
@@ -406,8 +407,10 @@ theorem sum (f : α → E) {s : Set α} {E : ℕ → α} (hE : Monotone E) {n :
 theorem sum' (f : α → E) {I : ℕ → α} (hI : Monotone I) {n : ℕ} :
     ∑ i ∈ Finset.range n, eVariationOn f (Icc (I i) (I (i + 1)))
      = eVariationOn f (Icc (I 0) (I n)) := by
-  convert sum f hI (s := Icc (I 0) (I n)) (n := n)
-    (hn := by intros; rw [mem_Icc]; constructor <;> (apply hI; lia)) with i hi
+  convert!
+      sum f hI (s := Icc (I 0) (I n)) (n := n)
+        (hn := by intros; rw [mem_Icc]; constructor <;> (apply hI; lia))
+    with i hi
   · simp only [right_eq_inter]
     gcongr <;> (apply hI; rw [Finset.mem_range] at hi; lia)
   · simp
@@ -454,7 +457,7 @@ theorem comp_inter_Icc_eq_of_monotoneOn (f : α → E) {t : Set β} (φ : β →
     {x y : β} (hx : x ∈ t) (hy : y ∈ t) :
     eVariationOn (f ∘ φ) (t ∩ Icc x y) = eVariationOn f (φ '' t ∩ Icc (φ x) (φ y)) := by
   rcases le_total x y with (h | h)
-  · convert comp_eq_of_monotoneOn f φ (hφ.mono Set.inter_subset_left)
+  · convert! comp_eq_of_monotoneOn f φ (hφ.mono Set.inter_subset_left)
     apply le_antisymm
     · rintro _ ⟨⟨u, us, rfl⟩, vφx, vφy⟩
       rcases le_total x u with (xu | ux)
@@ -487,7 +490,7 @@ open OrderDual
 
 @[simp] theorem comp_ofDual (f : α → E) (s : Set α) :
     eVariationOn (f ∘ ofDual) (ofDual ⁻¹' s) = eVariationOn f s := by
-  convert comp_eq_of_antitoneOn f ofDual fun _ _ _ _ => id
+  convert! comp_eq_of_antitoneOn f ofDual fun _ _ _ _ => id
   simp only [Equiv.image_preimage]
 
 lemma _root_.BoundedVariationOn.ofDual {f : α → E} {s : Set α} (hf : BoundedVariationOn f s) :
@@ -699,7 +702,7 @@ theorem _root_.BoundedVariationOn.tendsto_eVariationOn_Icc_zero_left
       grind [Set.Subsingleton]
   have W := eVariationOn_inter_Iio_eq_inter_Iic_of_continuousWithinAt (f := f)
     (s := s ∩ Icc y x) (a := x) ?_ ?_
-  · convert W using 2 <;> grind
+  · convert! W using 2 <;> grind
   · rwa [show s ∩ Icc y x ∩ Iio x = (s ∩ Iio x) ∩ Ici y by grind, nhdsWithin_inter_of_mem']
     apply mem_nhdsWithin_of_mem_nhds
     exact Ici_mem_nhds hy
@@ -739,7 +742,7 @@ theorem _root_.BoundedVariationOn.tendsto_leftLim [CompleteSpace E] [Topological
     [OrderTopology α] {f : α → E} (hf : BoundedVariationOn f univ) (x : α) :
     Tendsto f (𝓝[<] x) (𝓝 (f.leftLim x)) := by
   apply tendsto_leftLim_of_tendsto
-  convert hf.exists_tendsto_left x
+  convert! hf.exists_tendsto_left x
   simp
 
 /-- A bounded variation function tends to its right-limit on its right. -/
diff --git a/Mathlib/Topology/EMetricSpace/Lipschitz.lean b/Mathlib/Topology/EMetricSpace/Lipschitz.lean
index 8e37ed75fa5d38..1dc507e1e1b54c 100644
--- a/Mathlib/Topology/EMetricSpace/Lipschitz.lean
+++ b/Mathlib/Topology/EMetricSpace/Lipschitz.lean
@@ -218,7 +218,7 @@ theorem subtype_mk (hf : LipschitzWith K f) {p : β → Prop} (hp : ∀ x, p (f
 
 protected theorem eval {α : ι → Type u} [∀ i, PseudoEMetricSpace (α i)] [Fintype ι] (i : ι) :
     LipschitzWith 1 (Function.eval i : (∀ i, α i) → α i) :=
-  LipschitzWith.of_edist_le fun f g => by convert edist_le_pi_edist f g i
+  LipschitzWith.of_edist_le fun f g => by convert! edist_le_pi_edist f g i
 
 /-- The restriction of a `K`-Lipschitz function is `K`-Lipschitz. -/
 protected theorem restrict (hf : LipschitzWith K f) (s : Set α) : LipschitzWith K (s.restrict f) :=
diff --git a/Mathlib/Topology/FiberBundle/Basic.lean b/Mathlib/Topology/FiberBundle/Basic.lean
index d5553f516df768..81c8a34b2ded66 100644
--- a/Mathlib/Topology/FiberBundle/Basic.lean
+++ b/Mathlib/Topology/FiberBundle/Basic.lean
@@ -597,7 +597,7 @@ def localTriv (i : ι) : Trivialization F Z.proj where
       rw [PartialEquiv.EqOnSource.source_inter_preimage_eq (Z.localTrivAsPartialEquiv_trans i j)]
       exact (continuousOn_open_iff (Z.trivChange i j).open_source).1
         (Z.trivChange i j).continuousOn _ s_open
-    convert this using 1
+    convert! this using 1
     dsimp [f, PartialEquiv.trans_source]
     rw [← preimage_comp, inter_assoc]
   toPartialEquiv := Z.localTrivAsPartialEquiv i
diff --git a/Mathlib/Topology/FiberBundle/Constructions.lean b/Mathlib/Topology/FiberBundle/Constructions.lean
index 554752cb6da4d5..cb6efb03ba94e4 100644
--- a/Mathlib/Topology/FiberBundle/Constructions.lean
+++ b/Mathlib/Topology/FiberBundle/Constructions.lean
@@ -201,7 +201,8 @@ noncomputable def prod : Trivialization (F₁ × F₂) (π (F₁ × F₂) (E₁
   left_inv' _ := Prod.left_inv
   right_inv' _ := Prod.right_inv
   open_source := by
-    convert (e₁.open_source.prod e₂.open_source).preimage
+    convert!
+      (e₁.open_source.prod e₂.open_source).preimage
         (FiberBundle.Prod.isInducing_diag F₁ E₁ F₂ E₂).continuous
     ext x
     simp only [Trivialization.source_eq, mfld_simps]
diff --git a/Mathlib/Topology/FiberBundle/Trivialization.lean b/Mathlib/Topology/FiberBundle/Trivialization.lean
index c7f8285dbe84bc..d4135d9f75bf2f 100644
--- a/Mathlib/Topology/FiberBundle/Trivialization.lean
+++ b/Mathlib/Topology/FiberBundle/Trivialization.lean
@@ -289,7 +289,7 @@ noncomputable def restrictPreimage' (e : Pretrivialization F proj) (s : Set B)
   right_inv' x hx := Subtype.val_injective.prodMap injective_id <| by
     simp only [mem_preimage, (Prod.map_apply), id_eq] at hx
     simp_rw [Prod.map_apply]; rw [dif_pos hx]
-    convert ← e.right_inv' hx; exact e.proj_toFun _ (e.map_target' hx)
+    convert! ← e.right_inv' hx; exact e.proj_toFun _ (e.map_target' hx)
   open_target := e.open_target.preimage <| by fun_prop
   baseSet := Subtype.val ⁻¹' e.baseSet
   open_baseSet := e.open_baseSet.preimage continuous_subtype_val
@@ -835,11 +835,11 @@ noncomputable def domExtend {s : Set B} (hps : IsOpen (proj ⁻¹' s))
   __ := e.toPretrivialization.domExtend
   open_source := hps.isOpenMap_subtype_val _ e.open_source
   continuousOn_toFun := Topology.IsInducing.subtypeVal.continuousOn_image_iff.mpr <| by
-    convert e.continuousOn_toFun
+    convert! e.continuousOn_toFun
     ext1 ⟨x, (hx : proj x ∈ s)⟩
     simpa [Pretrivialization.domExtend] using dif_pos hx
   continuousOn_invFun := continuous_subtype_val.comp_continuousOn <| by
-    convert e.continuousOn_invFun
+    convert! e.continuousOn_invFun
 
 /-- Extend the base of a trivialization from a set to the whole space. -/
 @[simps! apply source target baseSet]
@@ -850,7 +850,7 @@ noncomputable def codExtend' {s : Set B} (hs : IsOpen s) {proj : Z → s} (e : T
   continuousOn_toFun :=
     (continuous_subtype_val.prodMap continuous_id).comp_continuousOn e.continuousOn_toFun
   continuousOn_invFun := (Topology.IsInducing.subtypeVal.prodMap .id).continuousOn_image_iff.2 <| by
-    convert e.continuousOn_invFun; ext; simp [Pretrivialization.codExtend']; rfl
+    convert! e.continuousOn_invFun; ext; simp [Pretrivialization.codExtend']; rfl
 
 /-- Extend the base of a pretrivialization from a nonempty set to the whole space. -/
 @[simps! apply source target baseSet]
diff --git a/Mathlib/Topology/Germ.lean b/Mathlib/Topology/Germ.lean
index 3fb0da89414ea7..1d9a1d13eb4d42 100644
--- a/Mathlib/Topology/Germ.lean
+++ b/Mathlib/Topology/Germ.lean
@@ -107,7 +107,7 @@ theorem Filter.Eventually.germ_congr_set
   intro x hx
   apply ((hf x hx).and (h x hx).eventually_nhds).mono
   intro y hy
-  convert hy.1 using 1
+  convert! hy.1 using 1
   exact Germ.coe_eq.mpr hy.2
 
 theorem restrictGermPredicate_congr {P : ∀ x : X, Germ (𝓝 x) Y → Prop}
diff --git a/Mathlib/Topology/Gluing.lean b/Mathlib/Topology/Gluing.lean
index a7f51505bc0f98..7ef34eddab6686 100644
--- a/Mathlib/Topology/Gluing.lean
+++ b/Mathlib/Topology/Gluing.lean
@@ -245,7 +245,7 @@ theorem preimage_image_eq_image (i j : D.J) (U : Set (𝖣.U i)) :
 
 theorem preimage_image_eq_image' (i j : D.J) (U : Set (𝖣.U i)) :
     𝖣.ι j ⁻¹' 𝖣.ι i '' U = (D.t i j ≫ D.f _ _) '' D.f _ _ ⁻¹' U := by
-  convert D.preimage_image_eq_image i j U using 1
+  convert! D.preimage_image_eq_image i j U using 1
   rw [coe_comp, coe_comp, Set.image_comp]
   congr! 1
   rw [← Set.eq_preimage_iff_image_eq, Set.preimage_preimage]
@@ -299,7 +299,7 @@ structure MkCore where
 theorem MkCore.t_inv (h : MkCore) (i j : h.J) (x : h.V j i) : h.t i j ((h.t j i) x) = x := by
   have := h.cocycle j i j x ?_
   · rw [h.t_id] at this
-    · convert Subtype.ext this
+    · convert! Subtype.ext this
   rw [h.V_id]
   trivial
 
@@ -347,7 +347,7 @@ def mk' (h : MkCore.{u}) : TopCat.GlueData where
     dsimp only [Opens.coe_inclusion', hom_comp, hom_ofHom, ContinuousMap.comp_assoc,
       ContinuousMap.comp_apply, ContinuousMap.coe_mk, hom_id, ContinuousMap.id_apply]
     rw [Subtype.mk_eq_mk, Prod.mk_inj, Subtype.mk_eq_mk, Subtype.ext_iff, and_self_iff]
-    convert congr_arg Subtype.val (h.t_inv k i ⟨x, hx'⟩) using 3
+    convert! congr_arg Subtype.val (h.t_inv k i ⟨x, hx'⟩) using 3
     refine Subtype.ext ?_
     exact h.cocycle i j k ⟨x, hx⟩ hx'
   f_mono _ _ := (TopCat.mono_iff_injective _).mpr fun _ _ h => Subtype.ext h
@@ -400,7 +400,7 @@ theorem fromOpenSubsetsGlue_isOpenMap : IsOpenMap (fromOpenSubsetsGlue U) := by
   constructor
   · rw [← Set.image_preimage_eq_inter_range]
     apply (Opens.isOpenEmbedding (X := TopCat.of α) (U i)).isOpenMap
-    convert hs i using 1
+    convert! hs i using 1
     rw [← ι_fromOpenSubsetsGlue, coe_comp, Set.preimage_comp]
     congr! 1
     exact Set.preimage_image_eq _ (fromOpenSubsetsGlue_injective U)
diff --git a/Mathlib/Topology/Homeomorph/Defs.lean b/Mathlib/Topology/Homeomorph/Defs.lean
index bc16027728b168..972277ef29035d 100644
--- a/Mathlib/Topology/Homeomorph/Defs.lean
+++ b/Mathlib/Topology/Homeomorph/Defs.lean
@@ -196,10 +196,10 @@ def changeInv (f : X ≃ₜ Y) (g : Y → X) (hg : Function.RightInverse g f) :
   haveI : g = f.symm := (f.left_inv.eq_rightInverse hg).symm
   { toFun := f
     invFun := g
-    left_inv := by convert f.left_inv
-    right_inv := by convert f.right_inv using 1
+    left_inv := by convert! f.left_inv
+    right_inv := by convert! f.right_inv using 1
     continuous_toFun := f.continuous
-    continuous_invFun := by convert f.symm.continuous }
+    continuous_invFun := by convert! f.symm.continuous }
 
 @[simp]
 theorem symm_comp_self (h : X ≃ₜ Y) : h.symm ∘ h = id :=
@@ -386,7 +386,7 @@ lemma toHomeomorph_apply (e : X ≃ Y) (he) (x : X) : e.toHomeomorph he x = e x
     (Equiv.refl X).toHomeomorph (fun _s ↦ Iff.rfl) = Homeomorph.refl _ := rfl
 
 @[simp] lemma symm_toHomeomorph (e : X ≃ Y) (he) :
-    (e.toHomeomorph he).symm = e.symm.toHomeomorph fun s ↦ by convert (he _).symm; simp := rfl
+    (e.toHomeomorph he).symm = e.symm.toHomeomorph fun s ↦ by convert! (he _).symm; simp := rfl
 
 lemma toHomeomorph_trans (e : X ≃ Y) (f : Y ≃ Z) (he hf) :
     (e.trans f).toHomeomorph (fun _s ↦ (he _).trans (hf _)) =
diff --git a/Mathlib/Topology/Homeomorph/Lemmas.lean b/Mathlib/Topology/Homeomorph/Lemmas.lean
index 163185ec7be34e..4e9b582d4d0f87 100644
--- a/Mathlib/Topology/Homeomorph/Lemmas.lean
+++ b/Mathlib/Topology/Homeomorph/Lemmas.lean
@@ -114,7 +114,7 @@ protected lemma totallyDisconnectedSpace (h : X ≃ₜ Y) [tdc : TotallyDisconne
 
 @[simp]
 theorem map_punctured_nhds_eq (h : X ≃ₜ Y) (x : X) : map h (𝓝[≠] x) = 𝓝[≠] (h x) := by
-  convert h.isEmbedding.map_nhdsWithin_eq ({x}ᶜ) x
+  convert! h.isEmbedding.map_nhdsWithin_eq ({ x }ᶜ) x
   rw [h.image_compl, Set.image_singleton]
 
 @[simp]
diff --git a/Mathlib/Topology/Homeomorph/TransferInstance.lean b/Mathlib/Topology/Homeomorph/TransferInstance.lean
index b0c85e9df29062..565e9c1044c042 100644
--- a/Mathlib/Topology/Homeomorph/TransferInstance.lean
+++ b/Mathlib/Topology/Homeomorph/TransferInstance.lean
@@ -36,7 +36,7 @@ def homeomorph [TopologicalSpace β] (e : α ≃ β) :
     continuous_toFun := continuous_induced_dom
     continuous_invFun := by
       simp only [Equiv.invFun_as_coe]
-      convert continuous_coinduced_rng
+      convert! continuous_coinduced_rng
       rw [e.coinduced_symm] }
 
 end Equiv
diff --git a/Mathlib/Topology/Homotopy/Contractible.lean b/Mathlib/Topology/Homotopy/Contractible.lean
index 2a6800f7c6a11d..6870928f9ab5ae 100644
--- a/Mathlib/Topology/Homotopy/Contractible.lean
+++ b/Mathlib/Topology/Homotopy/Contractible.lean
@@ -57,7 +57,7 @@ theorem id_nullhomotopic (X : Type*) [TopologicalSpace X] [ContractibleSpace X]
     (ContinuousMap.id X).Nullhomotopic := by
   obtain ⟨hv⟩ := ContractibleSpace.hequiv_unit X
   use hv.invFun ()
-  convert hv.left_inv.symm
+  convert! hv.left_inv.symm
 
 theorem contractible_iff_id_nullhomotopic (Y : Type*) [TopologicalSpace Y] :
     ContractibleSpace Y ↔ (ContinuousMap.id Y).Nullhomotopic := by
@@ -72,7 +72,7 @@ theorem contractible_iff_id_nullhomotopic (Y : Type*) [TopologicalSpace Y] :
             left_inv := ?_
             right_inv := ?_ }⟩ }
   · exact h.symm
-  · convert Homotopic.refl (ContinuousMap.id Unit)
+  · convert! Homotopic.refl (ContinuousMap.id Unit)
 
 variable {X Y : Type*} [TopologicalSpace X] [TopologicalSpace Y]
 
diff --git a/Mathlib/Topology/Homotopy/HomotopyGroup.lean b/Mathlib/Topology/Homotopy/HomotopyGroup.lean
index b79a0e8ef3b57e..c2ed2c6f3659f8 100644
--- a/Mathlib/Topology/Homotopy/HomotopyGroup.lean
+++ b/Mathlib/Topology/Homotopy/HomotopyGroup.lean
@@ -127,7 +127,7 @@ instance instContinuousEvalConst : ContinuousEvalConst (Ω^ N X x) (I^N) X := in
 /-- Copy of a `GenLoop` with a new map from the unit cube equal to the old one.
   Useful to fix definitional equalities. -/
 def copy (f : Ω^ N X x) (g : (I^N) → X) (h : g = f) : Ω^ N X x :=
-  ⟨⟨g, h.symm ▸ f.1.2⟩, by convert f.2⟩
+  ⟨⟨g, h.symm ▸ f.1.2⟩, by convert! f.2⟩
 
 theorem coe_copy (f : Ω^ N X x) {g : (I^N) → X} (h : g = f) : ⇑(copy f g h) = g :=
   rfl
diff --git a/Mathlib/Topology/Homotopy/Lifting.lean b/Mathlib/Topology/Homotopy/Lifting.lean
index d129476e075f9b..6af4b7979c1d54 100644
--- a/Mathlib/Topology/Homotopy/Lifting.lean
+++ b/Mathlib/Topology/Homotopy/Lifting.lean
@@ -64,7 +64,7 @@ theorem exists_lift_nhds {f : C(I × A, X)} {g : I × A → E} (g_lifts : p ∘
       p ∘ g' = f ∧ (∀ a, g' (0, a) = g (0, a)) ∧ ∀ t' ≤ t n, g' (t', a) = g (t', a) by
     obtain ⟨N, haN, N_open, hN⟩ := this n_max
     simp_rw [h_max _ le_rfl] at hN
-    refine ⟨N, N_open.mem_nhds haN, ?_⟩; convert hN
+    refine ⟨N, N_open.mem_nhds haN, ?_⟩; convert! hN
     · rw [eq_comm, Set.eq_univ_iff_forall]; exact fun t ↦ ⟨bot_le, le_top⟩
     · rw [imp_iff_right]; exact le_top
   refine Nat.rec ⟨_, Set.mem_univ a, isOpen_univ, g, ?_, g_lifts, fun a ↦ rfl, fun _ _ ↦ rfl⟩
@@ -224,7 +224,7 @@ theorem exists_path_lifts : ∃ Γ : C(I, E), p ∘ Γ = γ ∧ Γ 0 = e := by
     obtain ⟨Γ, cont, eqOn, Γ_0⟩ := this n_max
     rw [h_max _ le_rfl] at cont eqOn
     exact ⟨⟨Γ, continuousOn_univ.mp
-      (by convert cont; rw [eq_comm, Set.eq_univ_iff_forall]; exact fun t ↦ ⟨bot_le, le_top⟩)⟩,
+      (by convert! cont; rw [eq_comm, Set.eq_univ_iff_forall]; exact fun t ↦ ⟨bot_le, le_top⟩)⟩,
       funext fun _ ↦ eqOn ⟨bot_le, le_top⟩, Γ_0⟩
   intro n
   induction n with
@@ -299,7 +299,7 @@ variable (H : C(I × A, X)) (f : C(A, E)) (H_0 : ∀ a, H (0, a) = p (f a))
     (f ta.2) (H_0 ta.2) ta.1
   continuous_toFun := cov.isLocalHomeomorph.continuous_lift cov.isSeparatedMap H
     (by ext ⟨t, a⟩; exact congr_fun (cov.liftPath_lifts ..) t)
-    (by convert f.continuous with a; exact cov.liftPath_zero ..)
+    (by convert! f.continuous with a; exact cov.liftPath_zero ..)
     fun a ↦ by dsimp only; exact (cov.liftPath (γ_0 := by simp [*])).2
 
 lemma liftHomotopy_lifts : p ∘ cov.liftHomotopy H f H_0 = H :=
@@ -426,8 +426,11 @@ theorem existsUnique_continuousMap_lifts [SimplyConnectedSpace A] [LocPathConnec
   · simpa [and_comm] using cov.exists_path_lifts (f.comp γ) e₀ (by simp [γ_0, he])
   let pγ : Path a₀ (γ 1) := ⟨γ, γ_0, rfl⟩
   let pγ' : Path a₀ (γ 1) := ⟨γ', γ'_0, γγ'1.symm⟩
-  convert cov.liftPath_apply_one_eq_of_homotopicRel (ContinuousMap.HomotopicRel.comp_continuousMap
-    (SimplyConnectedSpace.paths_homotopic pγ pγ') f) e₀ (by simp [he]) (by simp [he]) <;>
+  convert!
+    cov.liftPath_apply_one_eq_of_homotopicRel
+      (ContinuousMap.HomotopicRel.comp_continuousMap (SimplyConnectedSpace.paths_homotopic pγ pγ')
+        f)
+      e₀ (by simp [he]) (by simp [he]) <;>
     rw [eq_liftPath_iff']
   exacts [⟨Γ_lifts, Γ_0⟩, ⟨Γ'_lifts, Γ'_0⟩]
 
diff --git a/Mathlib/Topology/Homotopy/LocallyContractible.lean b/Mathlib/Topology/Homotopy/LocallyContractible.lean
index dc6be96d51b7c8..746ef1a8a3ea24 100644
--- a/Mathlib/Topology/Homotopy/LocallyContractible.lean
+++ b/Mathlib/Topology/Homotopy/LocallyContractible.lean
@@ -179,7 +179,7 @@ theorem StronglyLocallyContractibleSpace.locallyContractible [StronglyLocallyCon
   obtain ⟨v₀, hid⟩ := id_nullhomotopic V
   -- The inclusion V ↪ U is homotopic to the constant map at (inclusion v₀)
   refine ⟨ContinuousMap.inclusion hVU v₀, ?_⟩
-  convert Homotopic.comp (.refl _) hid
+  convert! Homotopic.comp (.refl _) hid
   ext
   simp
 
diff --git a/Mathlib/Topology/Homotopy/Path.lean b/Mathlib/Topology/Homotopy/Path.lean
index b5ca7d3fa45b71..1055835b65e55b 100644
--- a/Mathlib/Topology/Homotopy/Path.lean
+++ b/Mathlib/Topology/Homotopy/Path.lean
@@ -404,8 +404,8 @@ end Quotient
 -- Porting note: we didn't previously need the `α := ...` and `β := ...` hints.
 theorem hpath_hext {p₁ : Path x₀ x₁} {p₂ : Path x₂ x₃} (hp : ∀ t, p₁ t = p₂ t) :
     HEq (α := Path.Homotopic.Quotient _ _) ⟦p₁⟧ (β := Path.Homotopic.Quotient _ _) ⟦p₂⟧ := by
-  obtain rfl : x₀ = x₂ := by convert hp 0 <;> simp
-  obtain rfl : x₁ = x₃ := by convert hp 1 <;> simp
+  obtain rfl : x₀ = x₂ := by convert! hp 0 <;> simp
+  obtain rfl : x₁ = x₃ := by convert! hp 1 <;> simp
   rw [heq_iff_eq]; congr; ext t; exact hp t
 
 end Homotopic
diff --git a/Mathlib/Topology/IndicatorConstPointwise.lean b/Mathlib/Topology/IndicatorConstPointwise.lean
index 867f40d4fdbc93..df11b94be10a5e 100644
--- a/Mathlib/Topology/IndicatorConstPointwise.lean
+++ b/Mathlib/Topology/IndicatorConstPointwise.lean
@@ -76,7 +76,7 @@ lemma tendsto_indicator_const_apply_iff_eventually' (b : β)
   classical
   have heart := @tendsto_ite ι L β (fun i ↦ x ∈ As i) _ (x ∈ A) _ b 0 (𝓝 b) (𝓝 (0 : β))
                 nhds_o nhds_b ?_ ?_
-  · convert heart
+  · convert! heart
     by_cases hxA : x ∈ A <;> simp [hxA]
   · simp only [principal_singleton, le_def, mem_pure]
     exact fun s s_nhds ↦ mem_of_mem_nhds s_nhds
diff --git a/Mathlib/Topology/Instances/AddCircle/Defs.lean b/Mathlib/Topology/Instances/AddCircle/Defs.lean
index 1bf98657de1de1..19d0f23e4a5ce7 100644
--- a/Mathlib/Topology/Instances/AddCircle/Defs.lean
+++ b/Mathlib/Topology/Instances/AddCircle/Defs.lean
@@ -137,7 +137,7 @@ theorem eventuallyEq_toIcoDiv_nhds (hx : ¬x ≡ a [PMOD p]) :
     toIcoDiv hp a =ᶠ[𝓝 x] fun _ ↦ toIcoDiv hp a x := by
   rw [← nhdsLT_sup_nhdsGE, Filter.EventuallyEq, Filter.eventually_sup]
   refine ⟨?_, eventuallyEq_toIcoDiv_nhdsGE hp a x⟩
-  convert (eventuallyEq_toIcoDiv_nhdsLT hp a x).eventually using 3
+  convert! (eventuallyEq_toIcoDiv_nhdsLT hp a x).eventually using 3
   rwa [← not_modEq_iff_toIcoDiv_eq_toIocDiv, AddCommGroup.modEq_comm]
 
 /-- If `x` is not congruent to `a` modulo `p`, then `toIcoDiv` is continuous at `x`.
@@ -156,7 +156,7 @@ theorem eventuallyEq_toIocDiv_nhds (hx : ¬x ≡ a [PMOD p]) :
     toIocDiv hp a =ᶠ[𝓝 x] fun _ ↦ toIocDiv hp a x := by
   rw [← nhdsLE_sup_nhdsGT, Filter.EventuallyEq, Filter.eventually_sup]
   refine ⟨eventuallyEq_toIocDiv_nhdsLE hp a x, ?_⟩
-  convert (eventuallyEq_toIocDiv_nhdsGT hp a x).eventually using 3
+  convert! (eventuallyEq_toIocDiv_nhdsGT hp a x).eventually using 3
   rwa [eq_comm, ← not_modEq_iff_toIcoDiv_eq_toIocDiv, AddCommGroup.modEq_comm]
 
 /-- If `x` is not congruent to `a` modulo `p`, then `toIocDiv` is continuous at `x`.
@@ -266,8 +266,9 @@ theorem finite_torsion_of_isSMulRegular (n : ℕ) (hn : IsSMulRegular 𝕜 n) :
 
 theorem card_torsion_le_of_isSMulRegular_int (n : ℤ) (h0 : n ≠ 0) (hn : IsSMulRegular 𝕜 n) :
     {x : AddCircle p | n • x = 0}.encard ≤ n.natAbs := by
-  convert card_torsion_le_of_isSMulRegular p _
-    (Int.natAbs_ne_zero.mpr h0) (IsSMulRegular.natAbs_iff.mpr hn) using 1
+  convert!
+    card_torsion_le_of_isSMulRegular p _ (Int.natAbs_ne_zero.mpr h0)
+      (IsSMulRegular.natAbs_iff.mpr hn) using 1
   simp
 
 theorem finite_torsion_of_isSMulRegular_int (n : ℤ) (hn : IsSMulRegular 𝕜 n) :
@@ -590,7 +591,7 @@ theorem gcd_mul_addOrderOf_div_eq {n : ℕ} (m : ℕ) (hn : 0 < n) :
 
 theorem addOrderOf_div_of_gcd_eq_one {m n : ℕ} (hn : 0 < n) (h : m.gcd n = 1) :
     addOrderOf (↑(↑m / ↑n * p) : AddCircle p) = n := by
-  convert gcd_mul_addOrderOf_div_eq p m hn
+  convert! gcd_mul_addOrderOf_div_eq p m hn
   rw [h, one_mul]
 
 theorem addOrderOf_div_of_gcd_eq_one' {m : ℤ} {n : ℕ} (hn : 0 < n) (h : m.natAbs.gcd n = 1) :
@@ -635,7 +636,7 @@ theorem addOrderOf_eq_pos_iff {u : AddCircle p} {n : ℕ} (h : 0 < n) :
   obtain ⟨m, hm, hk⟩ := (AddCircle.nsmul_eq_zero_iff h).mp
     (addOrderOf_nsmul_eq_zero (k : AddCircle p))
   refine ⟨m, hm, mul_right_cancel₀ h.ne' ?_, hk⟩
-  convert gcd_mul_addOrderOf_div_eq p m h using 1
+  convert! gcd_mul_addOrderOf_div_eq p m h using 1
   · rw [hk]
   · apply one_mul
 
diff --git a/Mathlib/Topology/Instances/Complex.lean b/Mathlib/Topology/Instances/Complex.lean
index ae025ce2d675d0..ca6270fc0f245a 100644
--- a/Mathlib/Topology/Instances/Complex.lean
+++ b/Mathlib/Topology/Instances/Complex.lean
@@ -83,7 +83,7 @@ theorem Complex.uniformContinuous_ringHom_eq_id_or_conj (K : Subfield ℂ) {ψ :
         -- We could add a `@[simp]` lemma fixing this, but it breaks later steps of the proof.
         erw [hr] at this
         rw [RingEquiv.toRingHom_eq_coe] at this
-        convert this using 1
+        convert! this using 1
         · exact (IsDenseInducing.extend_eq di hc.continuous _).symm
         · rw [← ofRealHom.coe_rangeRestrict, hr]
           rfl
@@ -101,24 +101,25 @@ theorem Complex.uniformContinuous_ringHom_eq_id_or_conj (K : Subfield ℂ) {ψ :
       rcases ringHom_eq_id_or_conj_of_continuous hψ₁ with h | h
       · left
         ext1 z
-        convert RingHom.congr_fun h z using 1
+        convert! RingHom.congr_fun h z using 1
         exact (IsDenseInducing.extend_eq di hc.continuous z).symm
       · right
         ext1 z
-        convert RingHom.congr_fun h z using 1
+        convert! RingHom.congr_fun h z using 1
         exact (IsDenseInducing.extend_eq di hc.continuous z).symm
   · let j : { x // x ∈ closure (id '' K) } → (K.topologicalClosure : Set ℂ) :=
       fun x =>
       ⟨x, by
-        convert x.prop
+        convert! x.prop
         simp only [id, Set.image_id']
         rfl ⟩
-    convert DenseRange.comp (Function.Surjective.denseRange _)
-      (IsDenseEmbedding.id.subtype (· ∈ K)).dense (by fun_prop : Continuous j)
+    convert!
+      DenseRange.comp (Function.Surjective.denseRange _) (IsDenseEmbedding.id.subtype (· ∈ K)).dense
+        (by fun_prop : Continuous j)
     rintro ⟨y, hy⟩
     use
       ⟨y, by
-        convert hy
+        convert! hy
         simp only [id, Set.image_id']
         rfl ⟩
 
diff --git a/Mathlib/Topology/Instances/EReal/Lemmas.lean b/Mathlib/Topology/Instances/EReal/Lemmas.lean
index 1ca43ae39c84e5..2fae51424907ce 100644
--- a/Mathlib/Topology/Instances/EReal/Lemmas.lean
+++ b/Mathlib/Topology/Instances/EReal/Lemmas.lean
@@ -460,7 +460,7 @@ much as possible the symmetries of the multiplication. -/
 private lemma continuousAt_mul_swap {a b : EReal}
     (h : ContinuousAt (fun p : EReal × EReal ↦ p.1 * p.2) (a, b)) :
     ContinuousAt (fun p : EReal × EReal ↦ p.1 * p.2) (b, a) := by
-  convert h.comp continuous_swap.continuousAt (x := (b, a))
+  convert! h.comp continuous_swap.continuousAt (x := (b, a))
   simp [mul_comm]
 
 private lemma continuousAt_mul_symm1 {a b : EReal}
diff --git a/Mathlib/Topology/Instances/Real/Lemmas.lean b/Mathlib/Topology/Instances/Real/Lemmas.lean
index c1947cdd896f7d..1603147677df83 100644
--- a/Mathlib/Topology/Instances/Real/Lemmas.lean
+++ b/Mathlib/Topology/Instances/Real/Lemmas.lean
@@ -110,7 +110,7 @@ theorem closure_ordConnected_inter_rat {s : Set ℝ} (conn : s.OrdConnected) (nt
 
 theorem closure_of_rat_image_lt {q : ℚ} :
     closure (((↑) : ℚ → ℝ) '' { x | q < x }) = { r | ↑q ≤ r } := by
-  convert closure_ordConnected_inter_rat (ordConnected_Ioi (a := (q : ℝ))) _ using 1
+  convert! closure_ordConnected_inter_rat (ordConnected_Ioi (a := (q : ℝ))) _ using 1
   · congr!; aesop
   · exact (closure_Ioi _).symm
   · exact ⟨q + 1, show (q : ℝ) < _ by linarith, q + 2, show (q : ℝ) < _ by linarith, by simp⟩
diff --git a/Mathlib/Topology/JacobsonSpace.lean b/Mathlib/Topology/JacobsonSpace.lean
index 582242e789be61..9723f4d810ef80 100644
--- a/Mathlib/Topology/JacobsonSpace.lean
+++ b/Mathlib/Topology/JacobsonSpace.lean
@@ -46,7 +46,7 @@ lemma preimage_closedPoints_subset (hf : Function.Injective f) (hf' : Continuous
     f ⁻¹' closedPoints Y ⊆ closedPoints X := by
   intro x hx
   rw [mem_closedPoints_iff]
-  convert continuous_iff_isClosed.mp hf' _ hx
+  convert! continuous_iff_isClosed.mp hf' _ hx
   rw [← Set.image_singleton, Set.preimage_image_eq _ hf]
 
 lemma Topology.IsClosedEmbedding.preimage_closedPoints (hf : IsClosedEmbedding f) :
@@ -60,7 +60,7 @@ lemma closedPoints_eq_univ [T1Space X] :
 
 lemma Set.Finite.isDiscrete_of_subset_closedPoints
     {s : Set X} (hs : s.Finite) (hs' : s ⊆ closedPoints X) : IsDiscrete s := by
-  have : T1Space s := ⟨fun x ↦ by convert (hs' x.2).preimage continuous_subtype_val; aesop⟩
+  have : T1Space s := ⟨fun x ↦ by convert! (hs' x.2).preimage continuous_subtype_val; aesop⟩
   have : Finite s := hs
   exact ⟨inferInstance⟩
 
@@ -182,12 +182,13 @@ lemma TopologicalSpace.IsOpenCover.jacobsonSpace_iff {ι : Type*} {U : ι → Op
   · convert_to IsClosed {(⟨y, h⟩ : U j)}
     · ext; simp [← Subtype.coe_inj]
     apply isClosed_singleton_of_isLocallyClosed_singleton
-    convert (hy'.isLocallyClosed.image IsEmbedding.subtypeVal.isInducing
-      (U i).2.isOpenEmbedding_subtypeVal.isOpen_range.isLocallyClosed).preimage
-      continuous_subtype_val
+    convert!
+      (hy'.isLocallyClosed.image IsEmbedding.subtypeVal.isInducing
+            (U i).2.isOpenEmbedding_subtypeVal.isOpen_range.isLocallyClosed).preimage
+        continuous_subtype_val
     ext
     simp [← Subtype.coe_inj]
-  · convert isClosed_empty
+  · convert! isClosed_empty
     rw [Set.eq_empty_iff_forall_notMem]
     intro z (hz : z.1 = y.1)
     exact h (hz ▸ z.2)
diff --git a/Mathlib/Topology/LocalAtTarget.lean b/Mathlib/Topology/LocalAtTarget.lean
index adba5129b27f71..6bb1eb268b78e7 100644
--- a/Mathlib/Topology/LocalAtTarget.lean
+++ b/Mathlib/Topology/LocalAtTarget.lean
@@ -132,7 +132,7 @@ theorem isOpenMap_iff_restrictPreimage :
   refine ⟨fun h i ↦ h.restrictPreimage _, fun H s hs ↦ ?_⟩
   rw [hU.isOpen_iff_coe_preimage]
   intro i
-  convert H i _ (hs.preimage continuous_subtype_val)
+  convert! H i _ (hs.preimage continuous_subtype_val)
   ext ⟨x, hx⟩
   suffices (∃ y, y ∈ s ∧ f y = x) ↔ ∃ y, y ∈ s ∧ f y ∈ U i ∧ f y = x by simpa [← Subtype.coe_inj]
   exact ⟨fun ⟨a, b, c⟩ ↦ ⟨a, b, c.symm ▸ hx, c⟩, by tauto⟩
@@ -142,7 +142,7 @@ theorem isClosedMap_iff_restrictPreimage :
   refine ⟨fun h i => h.restrictPreimage _, fun H s hs ↦ ?_⟩
   rw [hU.isClosed_iff_coe_preimage]
   intro i
-  convert H i _ ⟨⟨_, hs.1, eq_compl_comm.mpr rfl⟩⟩
+  convert! H i _ ⟨⟨_, hs.1, eq_compl_comm.mpr rfl⟩⟩
   ext ⟨x, hx⟩
   suffices (∃ y, y ∈ s ∧ f y = x) ↔ ∃ y, y ∈ s ∧ f y ∈ U i ∧ f y = x by simpa [← Subtype.coe_inj]
   exact ⟨fun ⟨a, b, c⟩ => ⟨a, b, c.symm ▸ hx, c⟩, by tauto⟩
@@ -218,7 +218,7 @@ include hU
 lemma isOpenMap_iff_comp : IsOpenMap f ↔ ∀ i, IsOpenMap (f ∘ ((↑) : U i → α)) := by
   refine ⟨fun hf ↦ fun i ↦ hf.comp (U i).isOpenEmbedding'.isOpenMap, fun hf ↦ ?_⟩
   intro V hV
-  convert isOpen_iUnion (fun i ↦ hf i _ <| isOpen_induced hV)
+  convert! isOpen_iUnion (fun i ↦ hf i _ <| isOpen_induced hV)
   simp_rw [Set.image_comp, Set.image_preimage_eq_inter_range, ← Set.image_iUnion,
     Subtype.range_coe_subtype, SetLike.setOf_mem_eq, hU.iUnion_inter]
 
@@ -274,7 +274,7 @@ theorem isEmbedding_of_iSup_eq_top_of_preimage_subset_range
     simpa [f', Set.range_comp, Set.range_restrictPreimage] using hV i
   let e := this.toHomeomorph.trans (Homeomorph.setCongr hf')
   refine IsEmbedding.of_comp (by fun_prop) continuous_subtype_val ?_
-  convert ((hV' i).comp IsEmbedding.subtypeVal).comp e.symm.isEmbedding
+  convert! ((hV' i).comp IsEmbedding.subtypeVal).comp e.symm.isEmbedding
   ext x
   obtain ⟨x, rfl⟩ := e.surjective x
   simp
diff --git a/Mathlib/Topology/LocallyClosed.lean b/Mathlib/Topology/LocallyClosed.lean
index 79e32cd48efdc5..7869c01614701d 100644
--- a/Mathlib/Topology/LocallyClosed.lean
+++ b/Mathlib/Topology/LocallyClosed.lean
@@ -180,8 +180,9 @@ lemma isLocallyClosed_tfae (s : Set X) :
     · exact (subset_iUnion₂ _ _ <| hxU x ·)
   tfae_have 5 → 1
   | H => by
-    convert H.isLocallyClosed.image IsInducing.subtypeVal
-      (by simpa using isClosed_closure.isLocallyClosed)
+    convert!
+      H.isLocallyClosed.image IsInducing.subtypeVal
+        (by simpa using isClosed_closure.isLocallyClosed)
     simpa using subset_closure
   tfae_finish
 
diff --git a/Mathlib/Topology/LocallyConstant/Basic.lean b/Mathlib/Topology/LocallyConstant/Basic.lean
index 3ed81a9bfdb292..6d585bf8b7e870 100644
--- a/Mathlib/Topology/LocallyConstant/Basic.lean
+++ b/Mathlib/Topology/LocallyConstant/Basic.lean
@@ -289,13 +289,13 @@ def ofIsClopen {X : Type*} [TopologicalSpace X] {U : Set X} [∀ x, Decidable (x
   toFun x := if x ∈ U then 0 else 1
   isLocallyConstant := by
     refine IsLocallyConstant.iff_isOpen_fiber.2 <| Fin.forall_fin_two.2 ⟨?_, ?_⟩
-    · convert hU.2 using 1
+    · convert! hU.2 using 1
       ext
       simp only [mem_singleton_iff, Fin.one_eq_zero_iff, mem_preimage, ite_eq_left_iff,
         Nat.succ_succ_ne_one]
       tauto
     · rw [← isClosed_compl_iff]
-      convert hU.1
+      convert! hU.1
       ext
       simp
 
@@ -534,7 +534,7 @@ def piecewise {C₁ C₂ : Set X} (h₁ : IsClosed C₁) (h₂ : IsClosed C₂)
     refine (locallyFinite_of_finite _).continuous h (fun i ↦ ?_) (fun i ↦ ?_)
     · cases i <;> [exact h₂; exact h₁]
     · cases i <;> rw [continuousOn_iff_continuous_restrict]
-      · convert hg
+      · convert! hg
         ext x
         simp only [cond_false, restrict_apply, Subtype.coe_eta, dite_eq_right_iff]
         exact fun hx ↦ hfg x ⟨hx, x.prop⟩
diff --git a/Mathlib/Topology/LocallyFinsupp.lean b/Mathlib/Topology/LocallyFinsupp.lean
index 80612fc9ca39a6..c3eac2f6669606 100644
--- a/Mathlib/Topology/LocallyFinsupp.lean
+++ b/Mathlib/Topology/LocallyFinsupp.lean
@@ -229,8 +229,11 @@ support within `U` is also closed.
 theorem closedSupport [T1Space X] [Zero Y] (D : locallyFinsuppWithin U Y)
     (hU : IsClosed U) :
     IsClosed D.support := by
-  convert isClosed_sdiff_of_codiscreteWithin ((supportDiscreteWithin_iff_locallyFiniteWithin
-    D.supportWithinDomain).2 D.supportLocallyFiniteWithinDomain) hU
+  convert!
+    isClosed_sdiff_of_codiscreteWithin
+      ((supportDiscreteWithin_iff_locallyFiniteWithin D.supportWithinDomain).2
+        D.supportLocallyFiniteWithinDomain)
+      hU
   ext x
   constructor <;> intro hx
   · simp_all [D.supportWithinDomain hx]
diff --git a/Mathlib/Topology/Maps/Basic.lean b/Mathlib/Topology/Maps/Basic.lean
index afbe2e24db61b9..95ca6b0a625fdb 100644
--- a/Mathlib/Topology/Maps/Basic.lean
+++ b/Mathlib/Topology/Maps/Basic.lean
@@ -706,7 +706,9 @@ theorem IsOpenEmbedding.map_nhds_eq (hf : IsOpenEmbedding f) (x : X) :
 lemma IsOpenEmbedding.isOpen_iff_image_isOpen (hf : IsOpenEmbedding f) {s : Set X} :
     IsOpen s ↔ IsOpen (f '' s) where
   mp := hf.isOpenMap s
-  mpr h := by convert ← h.preimage hf.isEmbedding.continuous; apply preimage_image_eq _ hf.injective
+  mpr h := by
+    convert! ← h.preimage hf.isEmbedding.continuous
+    apply preimage_image_eq _ hf.injective
 
 theorem IsOpenEmbedding.tendsto_nhds_iff [TopologicalSpace Z] {f : ι → Y} {l : Filter ι} {y : Y}
     (hg : IsOpenEmbedding g) : Tendsto f l (𝓝 y) ↔ Tendsto (g ∘ f) l (𝓝 (g y)) :=
@@ -857,7 +859,7 @@ protected lemma of_comp (hg : IsEmbedding g) (hgf : IsClosedEmbedding (g ∘ f))
     IsClosedEmbedding f where
   __ := hg.of_comp_iff.mp hgf.isEmbedding
   isClosed_range := by
-    convert hg.isClosed_preimage _ hgf.isClosed_range
+    convert! hg.isClosed_preimage _ hgf.isClosed_range
     rw [range_comp, hg.injective.preimage_image]
 
 theorem closure_image_eq (hf : IsClosedEmbedding f) (s : Set X) :
diff --git a/Mathlib/Topology/Maps/Proper/CompactlyGenerated.lean b/Mathlib/Topology/Maps/Proper/CompactlyGenerated.lean
index 1d8957bc71ffdc..e822be9ffaacd4 100644
--- a/Mathlib/Topology/Maps/Proper/CompactlyGenerated.lean
+++ b/Mathlib/Topology/Maps/Proper/CompactlyGenerated.lean
@@ -34,7 +34,7 @@ theorem isProperMap_iff_isCompact_preimage :
   mp hf := ⟨hf.continuous, fun _ ↦ hf.isCompact_preimage⟩
   mpr := fun ⟨hf, h⟩ ↦ isProperMap_iff_isClosedMap_and_compact_fibers.2
     ⟨hf, fun s hs ↦ (CompactlyCoherentSpace.isClosed_iff _).mpr fun K hK ↦ by
-        convert (((h hK).inter_left hs).image hf).isClosed.preimage continuous_subtype_val using 1
+        convert! (((h hK).inter_left hs).image hf).isClosed.preimage continuous_subtype_val using 1
         aesop, fun _ ↦ h isCompact_singleton⟩
 
 /-- Version of `isProperMap_iff_isCompact_preimage` in terms of `cocompact`.
diff --git a/Mathlib/Topology/MetricSpace/Algebra.lean b/Mathlib/Topology/MetricSpace/Algebra.lean
index dae2966c7fed05..d308dc570b83eb 100644
--- a/Mathlib/Topology/MetricSpace/Algebra.lean
+++ b/Mathlib/Topology/MetricSpace/Algebra.lean
@@ -79,7 +79,7 @@ instance (priority := 100) LipschitzMul.continuousMul : ContinuousMul β :=
 instance Submonoid.lipschitzMul (s : Submonoid β) : LipschitzMul s where
   lipschitz_mul := ⟨LipschitzMul.C β, by
     rintro ⟨x₁, x₂⟩ ⟨y₁, y₂⟩
-    convert lipschitzWith_lipschitz_const_mul_edist ⟨(x₁ : β), x₂⟩ ⟨y₁, y₂⟩ using 1⟩
+    convert! lipschitzWith_lipschitz_const_mul_edist ⟨(x₁ : β), x₂⟩ ⟨y₁, y₂⟩ using 1⟩
 
 @[to_additive]
 instance MulOpposite.lipschitzMul : LipschitzMul βᵐᵒᵖ where
@@ -256,8 +256,8 @@ instance Real.isBoundedSMul : IsBoundedSMul ℝ ℝ where
   dist_pair_smul' x₁ x₂ y := by simpa [Real.dist_eq, sub_mul] using (abs_mul (x₁ - x₂) y).le
 
 instance NNReal.isBoundedSMul : IsBoundedSMul ℝ≥0 ℝ≥0 where
-  dist_smul_pair' x y₁ y₂ := by convert dist_smul_pair (x : ℝ) (y₁ : ℝ) y₂ using 1
-  dist_pair_smul' x₁ x₂ y := by convert dist_pair_smul (x₁ : ℝ) x₂ (y : ℝ) using 1
+  dist_smul_pair' x y₁ y₂ := by convert! dist_smul_pair (x : ℝ) (y₁ : ℝ) y₂ using 1
+  dist_pair_smul' x₁ x₂ y := by convert! dist_pair_smul (x₁ : ℝ) x₂ (y : ℝ) using 1
 
 /-- If a scalar is central, then its right action is bounded when its left action is. -/
 instance IsBoundedSMul.op [SMul αᵐᵒᵖ β] [IsCentralScalar α β] : IsBoundedSMul αᵐᵒᵖ β where
diff --git a/Mathlib/Topology/MetricSpace/Antilipschitz.lean b/Mathlib/Topology/MetricSpace/Antilipschitz.lean
index e140ce8310d24e..58c0a94a57fa0d 100644
--- a/Mathlib/Topology/MetricSpace/Antilipschitz.lean
+++ b/Mathlib/Topology/MetricSpace/Antilipschitz.lean
@@ -227,7 +227,7 @@ protected theorem properSpace {α : Type*} [MetricSpace α] {K : ℝ≥0} {f : 
   have A : IsClosed K := isClosed_closedBall.preimage f_cont
   have B : IsBounded K := hK.isBounded_preimage isBounded_closedBall
   have : IsCompact K := isCompact_iff_isClosed_bounded.2 ⟨A, B⟩
-  convert this.image f_cont
+  convert! this.image f_cont
   exact (hf.image_preimage _).symm
 
 theorem isBounded_of_image2_left (f : α → β → γ) {K₁ : ℝ≥0}
diff --git a/Mathlib/Topology/MetricSpace/Bounded.lean b/Mathlib/Topology/MetricSpace/Bounded.lean
index 0872efa8d57104..26419b89790cfd 100644
--- a/Mathlib/Topology/MetricSpace/Bounded.lean
+++ b/Mathlib/Topology/MetricSpace/Bounded.lean
@@ -382,12 +382,12 @@ variable {α : Type*} [AddCommGroup α] [LinearOrder α] [IsOrderedAddMonoid α]
   [CompactIccSpace α]
 
 lemma isBounded_of_abs_le (C : α) : Bornology.IsBounded {x : α | |x| ≤ C} := by
-  convert Metric.isBounded_Icc (-C) C
+  convert! Metric.isBounded_Icc (-C) C
   ext1 x
   simp [abs_le]
 
 lemma isBounded_of_abs_lt (C : α) : Bornology.IsBounded {x : α | |x| < C} := by
-  convert Metric.isBounded_Ioo (-C) C
+  convert! Metric.isBounded_Ioo (-C) C
   ext1 x
   simp [abs_lt]
 
diff --git a/Mathlib/Topology/MetricSpace/Contracting.lean b/Mathlib/Topology/MetricSpace/Contracting.lean
index 280fe0b089915f..89c82e3676563f 100644
--- a/Mathlib/Topology/MetricSpace/Contracting.lean
+++ b/Mathlib/Topology/MetricSpace/Contracting.lean
@@ -125,7 +125,7 @@ theorem apriori_edist_iterate_efixedPoint_le (hf : ContractingWith K f) {x : α}
 
 theorem edist_efixedPoint_le (hf : ContractingWith K f) {x : α} (hx : edist x (f x) ≠ ∞) :
     edist x (efixedPoint f hf x hx) ≤ edist x (f x) / (1 - K) := by
-  convert hf.apriori_edist_iterate_efixedPoint_le hx 0
+  convert! hf.apriori_edist_iterate_efixedPoint_le hx 0
   simp only [pow_zero, mul_one]
 
 theorem edist_efixedPoint_lt_top (hf : ContractingWith K f) {x : α} (hx : edist x (f x) ≠ ∞) :
@@ -155,9 +155,9 @@ theorem exists_fixedPoint' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s
   haveI := hsc.completeSpace_coe
   rcases hf.exists_fixedPoint ⟨x, hxs⟩ hx with ⟨y, hfy, h_tendsto, hle⟩
   refine ⟨y, y.2, Subtype.ext_iff.1 hfy, ?_, fun n ↦ ?_⟩
-  · convert (continuous_subtype_val.tendsto _).comp h_tendsto
+  · convert! (continuous_subtype_val.tendsto _).comp h_tendsto
     simp only [(· ∘ ·), MapsTo.iterate_restrict, MapsTo.val_restrict_apply]
-  · convert hle n
+  · convert! hle n
     rw [MapsTo.iterate_restrict]
     rfl
 
@@ -196,7 +196,7 @@ theorem apriori_edist_iterate_efixedPoint_le' {s : Set α} (hsc : IsComplete s)
 theorem edist_efixedPoint_le' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
     edist x (efixedPoint' f hsc hsf hf x hxs hx) ≤ edist x (f x) / (1 - K) := by
-  convert hf.apriori_edist_iterate_efixedPoint_le' hsc hsf hxs hx 0
+  convert! hf.apriori_edist_iterate_efixedPoint_le' hsc hsf hxs hx 0
   rw [pow_zero, mul_one]
 
 theorem edist_efixedPoint_lt_top' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
@@ -298,7 +298,7 @@ theorem apriori_dist_iterate_fixedPoint_le (x n) :
 
 theorem tendsto_iterate_fixedPoint (x) :
     Tendsto (fun n ↦ f^[n] x) atTop (𝓝 <| fixedPoint f hf) := by
-  convert tendsto_iterate_efixedPoint hf (edist_ne_top x _)
+  convert! tendsto_iterate_efixedPoint hf (edist_ne_top x _)
   refine (fixedPoint_unique _ ?_).symm
   apply efixedPoint_isFixedPt
 
diff --git a/Mathlib/Topology/MetricSpace/Gluing.lean b/Mathlib/Topology/MetricSpace/Gluing.lean
index 843aeb1d0dc9ef..26c5c470426f76 100644
--- a/Mathlib/Topology/MetricSpace/Gluing.lean
+++ b/Mathlib/Topology/MetricSpace/Gluing.lean
@@ -452,7 +452,7 @@ protected theorem completeSpace [∀ i, CompleteSpace (E i)] : CompleteSpace (Σ
   have hd : ∀ (i j), ∀ x ∈ s i, ∀ y ∈ s j, (x, y) ∈ U → i = j := fun i j x hx y hy hxy =>
     (Eq.symm hx).trans ((fst_eq_of_dist_lt_one _ _ hxy).trans hy)
   refine completeSpace_of_isComplete_univ ?_
-  convert isComplete_iUnion_separated hc (dist_mem_uniformity zero_lt_one) hd
+  convert! isComplete_iUnion_separated hc (dist_mem_uniformity zero_lt_one) hd
   simp only [s, ← preimage_iUnion, iUnion_of_singleton, preimage_univ]
 
 end Sigma
diff --git a/Mathlib/Topology/MetricSpace/GromovHausdorff.lean b/Mathlib/Topology/MetricSpace/GromovHausdorff.lean
index aae27911017575..70934af7912b61 100644
--- a/Mathlib/Topology/MetricSpace/GromovHausdorff.lean
+++ b/Mathlib/Topology/MetricSpace/GromovHausdorff.lean
@@ -1007,7 +1007,7 @@ instance : CompleteSpace GHSpace := by
     rw [Function.comp_apply, NonemptyCompacts.toGHSpace, ← (u n).toGHSpace_rep,
       toGHSpace_eq_toGHSpace_iff_isometryEquiv]
     constructor
-    convert (isom n).isometryEquivOnRange.symm
+    convert! (isom n).isometryEquivOnRange.symm
   -- the images of `X3 n` in the Gromov-Hausdorff space converge to the image of `L`
   -- so the images of `u n` converge to the image of `L` as well
   use L.toGHSpace
diff --git a/Mathlib/Topology/MetricSpace/HausdorffDistance.lean b/Mathlib/Topology/MetricSpace/HausdorffDistance.lean
index 8e76472a7aa26c..bc5626fe15264c 100644
--- a/Mathlib/Topology/MetricSpace/HausdorffDistance.lean
+++ b/Mathlib/Topology/MetricSpace/HausdorffDistance.lean
@@ -431,7 +431,7 @@ theorem hausdorffEDist_iUnion_le {ι : Sort*} {s t : ι → Set α} :
 theorem hausdorffEDist_union_le {s₁ s₂ t₁ t₂ : Set α} :
     hausdorffEDist (s₁ ∪ s₂) (t₁ ∪ t₂) ≤ max (hausdorffEDist s₁ t₁) (hausdorffEDist s₂ t₂) := by
   simp_rw [union_eq_iUnion, sup_eq_iSup]
-  convert hausdorffEDist_iUnion_le with (_ | _)
+  convert! hausdorffEDist_iUnion_le with (_ | _)
 
 theorem hausdorffEDist_prod_le {s₁ t₁ : Set α} {s₂ t₂ : Set β} :
     hausdorffEDist (s₁ ×ˢ s₂) (t₁ ×ˢ t₂) ≤ max (hausdorffEDist s₁ t₁) (hausdorffEDist s₂ t₂) := by
diff --git a/Mathlib/Topology/MetricSpace/Holder.lean b/Mathlib/Topology/MetricSpace/Holder.lean
index 48f17d61e15830..11d9e8bf780056 100644
--- a/Mathlib/Topology/MetricSpace/Holder.lean
+++ b/Mathlib/Topology/MetricSpace/Holder.lean
@@ -217,7 +217,7 @@ then it is `(C, r * t₁ + s * t₂)`-Hölder for all `t₁ t₂ : ℝ≥0` such
 lemma interpolate_const {C s t₁ t₂ : ℝ≥0} {A : Set X}
     (hf₁ : HolderOnWith C r f A) (hf₂ : HolderOnWith C s f A) (ht : t₁ + t₂ = 1) :
     HolderOnWith C (r * t₁ + s * t₂) f A := by
-  convert hf₁.interpolate hf₂ ht
+  convert! hf₁.interpolate hf₂ ht
   simp [← NNReal.rpow_add_of_nonneg, ← NNReal.coe_add, ht]
 
 variable (f) in
diff --git a/Mathlib/Topology/MetricSpace/Infsep.lean b/Mathlib/Topology/MetricSpace/Infsep.lean
index 83692fb4366851..1432be6a0ca356 100644
--- a/Mathlib/Topology/MetricSpace/Infsep.lean
+++ b/Mathlib/Topology/MetricSpace/Infsep.lean
@@ -178,7 +178,7 @@ variable [PseudoEMetricSpace α] {x y z : α} {s : Set α}
 
 theorem einfsep_pair (hxy : x ≠ y) : ({x, y} : Set α).einfsep = edist x y := by
   nth_rw 1 [← min_self (edist x y)]
-  convert einfsep_pair_eq_inf hxy using 2
+  convert! einfsep_pair_eq_inf hxy using 2
   rw [edist_comm]
 
 theorem einfsep_insert : einfsep (insert x s) =
diff --git a/Mathlib/Topology/MetricSpace/Kuratowski.lean b/Mathlib/Topology/MetricSpace/Kuratowski.lean
index 5a4d750043a78a..b09bddacde1d24 100644
--- a/Mathlib/Topology/MetricSpace/Kuratowski.lean
+++ b/Mathlib/Topology/MetricSpace/Kuratowski.lean
@@ -53,7 +53,7 @@ theorem embeddingOfSubset_dist_le (a b : α) :
   rw [dist_eq_norm]
   refine lp.norm_le_of_forall_le dist_nonneg fun n => ?_
   simp only [lp.coeFn_sub, Pi.sub_apply, embeddingOfSubset_coe]
-  convert abs_dist_sub_le a b (x n) using 2
+  convert! abs_dist_sub_le a b (x n) using 2
   ring
 
 /-- When the reference set is dense, the embedding map is an isometry on its image. -/
diff --git a/Mathlib/Topology/MetricSpace/Perfect.lean b/Mathlib/Topology/MetricSpace/Perfect.lean
index 676fdf3eda2b24..b128c20a2c79d9 100644
--- a/Mathlib/Topology/MetricSpace/Perfect.lean
+++ b/Mathlib/Topology/MetricSpace/Perfect.lean
@@ -52,7 +52,7 @@ private theorem Perfect.small_diam_aux (hC : Perfect C) (ε_pos : 0 < ε) {x : 
     apply inter_subset_right
   rw [Metric.ediam_closure]
   apply le_trans (Metric.ediam_mono inter_subset_left)
-  convert Metric.ediam_eball_le (x := x)
+  convert! Metric.ediam_eball_le (x := x)
   rw [mul_comm, ENNReal.div_mul_cancel] <;> norm_num
 
 /-- A refinement of `Perfect.splitting` for metric spaces, where we also control
@@ -109,9 +109,9 @@ theorem Perfect.exists_nat_bool_injection
     rcases Nat.exists_eq_succ_of_ne_zero hm with ⟨n, rfl⟩
     dsimp
     cases x n
-    · convert (h0 _ _ _).2.2.2
+    · convert! (h0 _ _ _).2.2.2
       rw [PiNat.res_length]
-    convert (h1 _ _ _).2.2.2
+    convert! (h1 _ _ _).2.2.2
     rw [PiNat.res_length]
   have hdisj' : CantorScheme.Disjoint D := by
     rintro l (a | a) (b | b) hab <;> try contradiction
diff --git a/Mathlib/Topology/MetricSpace/PiNat.lean b/Mathlib/Topology/MetricSpace/PiNat.lean
index 4d4ee1dd17ef55..b5a8e220cd71af 100644
--- a/Mathlib/Topology/MetricSpace/PiNat.lean
+++ b/Mathlib/Topology/MetricSpace/PiNat.lean
@@ -1121,7 +1121,7 @@ lemma continuous_distDenseSeq (n : ℕ) : Continuous (distDenseSeq X n) := by
   cases isEmpty_or_nonempty X
   · exact continuous_of_discreteTopology
   refine continuous_projIcc.comp <| Continuous.dist continuous_id' ?_
-  convert continuous_const (y := denseSeq X n)
+  convert! continuous_const (y := denseSeq X n)
 
 lemma separation {x : X} {C : Set X} (hxC : C ∈ 𝓝 x) :
     ∃ (n : ℕ), C ∈ (𝓝 (distDenseSeq X n x)).comap (distDenseSeq X n) := by
diff --git a/Mathlib/Topology/MetricSpace/ProperSpace/Lemmas.lean b/Mathlib/Topology/MetricSpace/ProperSpace/Lemmas.lean
index c9fe60566ad5d4..ecac5545dbd00e 100644
--- a/Mathlib/Topology/MetricSpace/ProperSpace/Lemmas.lean
+++ b/Mathlib/Topology/MetricSpace/ProperSpace/Lemmas.lean
@@ -68,7 +68,7 @@ lemma isProperMap_dist (x : α) : IsProperMap (dist x) :=
 omit [ProperSpace α] in
 lemma properSpace_iff_isProperMap_dist : ProperSpace α ↔ ∀ x : α, IsProperMap (dist x) := by
   refine ⟨fun _ ↦ isProperMap_dist, fun H ↦ ⟨fun x r ↦ ?_⟩⟩
-  convert (H x).isCompact_preimage (isCompact_closedBall 0 r)
+  convert! (H x).isCompact_preimage (isCompact_closedBall 0 r)
   ext
   simp [dist_comm, Real.dist_eq]
 
diff --git a/Mathlib/Topology/MetricSpace/Pseudo/Constructions.lean b/Mathlib/Topology/MetricSpace/Pseudo/Constructions.lean
index 5e3283018fd154..b8c6b9bf74083b 100644
--- a/Mathlib/Topology/MetricSpace/Pseudo/Constructions.lean
+++ b/Mathlib/Topology/MetricSpace/Pseudo/Constructions.lean
@@ -139,7 +139,7 @@ lemma NNReal.ball_zero_eq_Ico' (c : ℝ≥0) :
 lemma NNReal.ball_zero_eq_Ico (c : ℝ) :
     Metric.ball (0 : ℝ≥0) c = Set.Ico 0 c.toNNReal := by
   by_cases! c_pos : 0 < c
-  · convert NNReal.ball_zero_eq_Ico' (NNReal.mk c c_pos.le)
+  · convert! NNReal.ball_zero_eq_Ico' (NNReal.mk c c_pos.le)
     simp [Real.toNNReal, c_pos.le]
   simp [c_pos]
 
@@ -148,7 +148,7 @@ lemma NNReal.closedBall_zero_eq_Icc' (c : ℝ≥0) :
 
 lemma NNReal.closedBall_zero_eq_Icc {c : ℝ} (c_nn : 0 ≤ c) :
     Metric.closedBall (0 : ℝ≥0) c = Set.Icc 0 c.toNNReal := by
-  convert NNReal.closedBall_zero_eq_Icc' (NNReal.mk c c_nn)
+  convert! NNReal.closedBall_zero_eq_Icc' (NNReal.mk c c_nn)
   simp [Real.toNNReal, c_nn]
 
 end NNReal
diff --git a/Mathlib/Topology/MetricSpace/UniformConvergence.lean b/Mathlib/Topology/MetricSpace/UniformConvergence.lean
index 24b4a7b5548da0..c63df0f2087219 100644
--- a/Mathlib/Topology/MetricSpace/UniformConvergence.lean
+++ b/Mathlib/Topology/MetricSpace/UniformConvergence.lean
@@ -303,7 +303,7 @@ noncomputable instance [BoundedSpace β] : PseudoMetricSpace (α →ᵤ[𝔖] β
 
 noncomputable instance [BoundedSpace β] : BoundedSpace (α →ᵤ[𝔖] β) where
   bounded_univ := by
-    convert lipschitzWith_one_ofFun_toFun (𝔖 := 𝔖) (β := β) |>.isBounded_image (.all Set.univ)
+    convert! lipschitzWith_one_ofFun_toFun (𝔖 := 𝔖) (β := β) |>.isBounded_image (.all Set.univ)
     ext f
     simp only [Set.mem_univ, Function.comp_apply, Set.image_univ, Set.mem_range, true_iff]
     exact ⟨UniformFun.ofFun (toFun 𝔖 f), by simp⟩
diff --git a/Mathlib/Topology/Metrizable/CompletelyMetrizable.lean b/Mathlib/Topology/Metrizable/CompletelyMetrizable.lean
index 2cd4cbb2d45069..e03365274cc588 100644
--- a/Mathlib/Topology/Metrizable/CompletelyMetrizable.lean
+++ b/Mathlib/Topology/Metrizable/CompletelyMetrizable.lean
@@ -82,7 +82,7 @@ noncomputable def completelyPseudoMetrizableMetric (X : Type*) [TopologicalSpace
 theorem complete_completelyPseudoMetrizableMetric (X : Type*) [ht : TopologicalSpace X]
     [h : IsCompletelyPseudoMetrizableSpace X] :
     @CompleteSpace X (completelyPseudoMetrizableMetric X).toUniformSpace := by
-  convert h.complete.choose_spec.2
+  convert! h.complete.choose_spec.2
   exact PseudoMetricSpace.replaceTopology_eq _ _
 
 /-- This definition endows a completely pseudometrizable space with a complete pseudometric.
@@ -195,7 +195,7 @@ noncomputable def completelyMetrizableMetric (X : Type*) [TopologicalSpace X]
 theorem complete_completelyMetrizableMetric (X : Type*) [ht : TopologicalSpace X]
     [h : IsCompletelyMetrizableSpace X] :
     @CompleteSpace X (completelyMetrizableMetric X).toUniformSpace := by
-  convert h.complete.choose_spec.2
+  convert! h.complete.choose_spec.2
   exact MetricSpace.replaceTopology_eq _ _
 
 /-- This definition endows a completely metrizable space with a complete metric. Use it as:
@@ -273,7 +273,7 @@ instance (priority := 50) discrete [TopologicalSpace X] [DiscreteTopology X] :
   refine ⟨m, ?_, ?_⟩
   · rw [DiscreteTopology.eq_bot (α := X)]
     refine eq_bot_of_singletons_open fun x ↦ ?_
-    convert @Metric.isOpen_ball _ _ x 1
+    convert! @Metric.isOpen_ball _ _ x 1
     refine subset_antisymm (singleton_subset_iff.2 (Metric.mem_ball_self (by simp)))
       fun y hy ↦ ?_
     simp only [Metric.mem_ball, mem_singleton_iff] at *
diff --git a/Mathlib/Topology/Metrizable/Uniformity.lean b/Mathlib/Topology/Metrizable/Uniformity.lean
index 7f668fb099985d..be1e4a773f8837 100644
--- a/Mathlib/Topology/Metrizable/Uniformity.lean
+++ b/Mathlib/Topology/Metrizable/Uniformity.lean
@@ -156,7 +156,7 @@ theorem le_two_mul_dist_ofPreNNDist (d : X → X → ℝ≥0) (dist_self : ∀ x
       rw [Nat.succ_le_iff] at hMl
       have hMl' : length (take M l) = M := length_take.trans (min_eq_left hMl.le)
       refine (ihn _ hMl _ _ _ hMl').trans ?_
-      convert hMs.1.out
+      convert! hMs.1.out
       rw [take_zipWith, take, take_add_one, getElem?_append_left hMl, getElem?_eq_getElem hMl,
         ← Option.coe_def, Option.toList_some, take_append_of_le_length hMl.le, getElem_cons_succ]
   · exact single_le_sum (fun x _ => zero_le) _ (mem_iff_get.2 ⟨⟨M, hM_lt⟩, getElem_zipWith⟩)
@@ -171,7 +171,7 @@ theorem le_two_mul_dist_ofPreNNDist (d : X → X → ℝ≥0) (dist_self : ∀ x
       not_lt.1 fun h => (hMs.2 h.le).not_gt M.lt_succ_self
     rw [← sum_take_add_sum_drop L (M + 1), two_mul, add_le_add_iff_left, ← add_le_add_iff_right,
       sum_take_add_sum_drop, ← two_mul] at hMs'
-    convert hMs'
+    convert! hMs'
     rwa [drop_zipWith, drop, drop_append_of_le_length]
 
 end PseudoMetricSpace
diff --git a/Mathlib/Topology/Neighborhoods.lean b/Mathlib/Topology/Neighborhoods.lean
index ce567742a17afb..67f7e7387f7058 100644
--- a/Mathlib/Topology/Neighborhoods.lean
+++ b/Mathlib/Topology/Neighborhoods.lean
@@ -104,7 +104,7 @@ theorem IsOpen.eventually_mem (hs : IsOpen s) (hx : x ∈ s) :
 for a variant using open sets around `x` instead. -/
 theorem nhds_basis_opens' (x : X) :
     (𝓝 x).HasBasis (fun s : Set X => s ∈ 𝓝 x ∧ IsOpen s) fun x => x := by
-  convert nhds_basis_opens x using 2
+  convert! nhds_basis_opens x using 2
   exact and_congr_left_iff.2 IsOpen.mem_nhds_iff
 
 /-- If `U` is a neighborhood of each point of a set `s` then it is a neighborhood of `s`:
diff --git a/Mathlib/Topology/OmegaCompletePartialOrder.lean b/Mathlib/Topology/OmegaCompletePartialOrder.lean
index b05a8c57b1ca27..009eb1cfc0a39f 100644
--- a/Mathlib/Topology/OmegaCompletePartialOrder.lean
+++ b/Mathlib/Topology/OmegaCompletePartialOrder.lean
@@ -58,7 +58,7 @@ theorem IsOpen.inter (s t : Set α) : IsOpen α s → IsOpen α t → IsOpen α
 
 theorem isOpen_sUnion (s : Set (Set α)) (hs : ∀ t ∈ s, IsOpen α t) : IsOpen α (⋃₀ s) := by
   simp only [IsOpen] at hs ⊢
-  convert CompleteLattice.ωScottContinuous.sSup hs
+  convert! CompleteLattice.ωScottContinuous.sSup hs
   aesop
 
 theorem IsOpen.isUpperSet {s : Set α} (hs : IsOpen α s) : IsUpperSet s := hs.monotone
diff --git a/Mathlib/Topology/Order/Compact.lean b/Mathlib/Topology/Order/Compact.lean
index 19efa166d31f8a..8f328aaa190157 100644
--- a/Mathlib/Topology/Order/Compact.lean
+++ b/Mathlib/Topology/Order/Compact.lean
@@ -70,7 +70,7 @@ lemma CompactIccSpace.mk'' [TopologicalSpace α] [PartialOrder α]
 instance [TopologicalSpace α] [Preorder α] [CompactIccSpace α] : CompactIccSpace (αᵒᵈ) where
   isCompact_Icc := by
     intro a b
-    convert isCompact_Icc (α := α) (a := b) (b := a) using 1
+    convert! isCompact_Icc (α := α) (a := b) (b := a) using 1
     exact Icc_toDual (α := α)
 
 /-- A closed interval in a conditionally complete linear order is compact. -/
@@ -194,7 +194,7 @@ theorem atBot_le_cocompact [NoMinOrder α] [ClosedIicTopology α] :
   obtain ⟨t, ht, hts⟩ := mem_cocompact.mp hs
   refine (Set.eq_empty_or_nonempty t).casesOn (fun h_empty ↦ ?_) (fun h_nonempty ↦ ?_)
   · rewrite [compl_univ_iff.mpr h_empty, univ_subset_iff] at hts
-    convert univ_mem
+    convert! univ_mem
   · haveI := h_nonempty.nonempty
     obtain ⟨a, ha⟩ := ht.exists_isLeast h_nonempty
     obtain ⟨b, hb⟩ := exists_lt a
diff --git a/Mathlib/Topology/Order/HullKernel.lean b/Mathlib/Topology/Order/HullKernel.lean
index 6212b91015284c..9929a2596d6b7d 100644
--- a/Mathlib/Topology/Order/HullKernel.lean
+++ b/Mathlib/Topology/Order/HullKernel.lean
@@ -111,7 +111,7 @@ Lower topology.
 -/
 lemma isTopologicalBasis_relativeLower (hT : ∀ p ∈ T, InfPrime p) :
     IsTopologicalBasis { S : Set T | ∃ (a : α), (hull T a)ᶜ = S } := by
-  convert isTopologicalBasis_subtype Topology.IsLower.isTopologicalBasis (· ∈ T)
+  convert! isTopologicalBasis_subtype Topology.IsLower.isTopologicalBasis (· ∈ T)
   ext R
   simp only [preimage_compl, mem_setOf_eq, IsLower.lowerBasis, mem_image, exists_exists_and_eq_and]
   constructor <;> intro ha
diff --git a/Mathlib/Topology/Order/LawsonTopology.lean b/Mathlib/Topology/Order/LawsonTopology.lean
index d932803400d32a..778406eacc043c 100644
--- a/Mathlib/Topology/Order/LawsonTopology.lean
+++ b/Mathlib/Topology/Order/LawsonTopology.lean
@@ -95,9 +95,9 @@ protected theorem isTopologicalBasis : TopologicalSpace.IsTopologicalBasis (laws
     simp_rw [diff_eq_compl_inter]
     aesop
   rw [lawsonBasis_image2]
-  convert IsTopologicalBasis.inf_induced IsLower.isTopologicalBasis
-    (isTopologicalBasis_opens (α := WithScott α))
-    WithLower.toLower WithScott.toScott
+  convert!
+    IsTopologicalBasis.inf_induced IsLower.isTopologicalBasis
+      (isTopologicalBasis_opens (α := WithScott α)) WithLower.toLower WithScott.toScott
   rw [@topology_eq_lawson α _ _ _, lawson]
   apply (congrArg₂ min _) _
   · letI _ := lower α
diff --git a/Mathlib/Topology/Order/LeftRightNhds.lean b/Mathlib/Topology/Order/LeftRightNhds.lean
index 6fbcd3ffa6b139..042bfe6bb0fe20 100644
--- a/Mathlib/Topology/Order/LeftRightNhds.lean
+++ b/Mathlib/Topology/Order/LeftRightNhds.lean
@@ -211,8 +211,8 @@ theorem nhdsLT_basis [NoMinOrder α] (a : α) : (𝓝[<] a).HasBasis (· < a) (I
   nhdsLT_basis_of_exists_lt <| exists_lt a
 
 theorem nhdsLT_eq_bot_iff {a : α} : 𝓝[<] a = ⊥ ↔ IsBot a ∨ ∃ b, b ⋖ a := by
-  convert (config := { preTransparency := .default }) nhdsGT_eq_bot_iff (a := OrderDual.toDual a)
-    using 4
+  convert! (config := { preTransparency := .default })
+    nhdsGT_eq_bot_iff (a := OrderDual.toDual a) using 4
   exact ofDual_covBy_ofDual_iff
 
 open List in
@@ -405,7 +405,7 @@ theorem nhds_basis_mabs_div_lt [NoMaxOrder α] (a : α) :
 @[to_additive]
 theorem nhds_basis_Ioo_one_lt [NoMaxOrder α] (a : α) :
     (𝓝 a).HasBasis (fun ε : α => (1 : α) < ε) fun ε => Ioo (a / ε) (a * ε) := by
-  convert nhds_basis_mabs_div_lt a
+  convert! nhds_basis_mabs_div_lt a
   simp only [Ioo, mabs_lt, ← div_lt_iff_lt_mul, inv_lt_div_iff_lt_mul, div_lt_comm]
 
 @[to_additive]
diff --git a/Mathlib/Topology/Order/LowerUpperTopology.lean b/Mathlib/Topology/Order/LowerUpperTopology.lean
index 9865873195a3d2..dea040dc9c0ff3 100644
--- a/Mathlib/Topology/Order/LowerUpperTopology.lean
+++ b/Mathlib/Topology/Order/LowerUpperTopology.lean
@@ -279,7 +279,7 @@ theorem closure_singleton (a : α) : closure {a} = Ici a :=
     (isUpperSet_of_isClosed isClosed_closure).Ici_subset <| subset_closure rfl
 
 protected theorem isTopologicalBasis : IsTopologicalBasis (lowerBasis α) := by
-  convert isTopologicalBasis_of_subbasis (topology_eq α)
+  convert! isTopologicalBasis_of_subbasis (topology_eq α)
   simp_rw [lowerBasis, coe_upperClosure, compl_iUnion]
   ext s
   constructor
@@ -341,7 +341,7 @@ lemma isTopologicalSpace_basis (U : Set α) : IsOpen U ↔ U = univ ∨ ∃ a, (
   refine ⟨?_, isTopologicalBasis_insert_univ_subbasis.isOpen⟩
   intro hO
   apply Or.inr
-  convert IsTopologicalBasis.open_eq_sUnion isTopologicalBasis_insert_univ_subbasis hO
+  convert! IsTopologicalBasis.open_eq_sUnion isTopologicalBasis_insert_univ_subbasis hO
   constructor
   · intro ⟨a, ha⟩
     use {U}
@@ -511,7 +511,7 @@ variable [CompleteLattice α] [CompleteLattice β] [TopologicalSpace α] [IsLowe
 
 protected lemma _root_.sInfHom.continuous (f : sInfHom α β) : Continuous f := by
   refine IsLower.continuous_iff_Ici.2 fun b => ?_
-  convert isClosed_Ici (a := sInf <| f ⁻¹' Ici b)
+  convert! isClosed_Ici (a := sInf <| f ⁻¹' Ici b)
   refine Subset.antisymm (fun a => sInf_le) fun a ha => le_trans ?_ <|
     OrderHomClass.mono (f : α →o β) ha
   refine LE.le.trans ?_ (map_sInf f _).ge
diff --git a/Mathlib/Topology/Order/MonotoneConvergence.lean b/Mathlib/Topology/Order/MonotoneConvergence.lean
index ba8a0274862b43..525b8006cece8f 100644
--- a/Mathlib/Topology/Order/MonotoneConvergence.lean
+++ b/Mathlib/Topology/Order/MonotoneConvergence.lean
@@ -93,7 +93,7 @@ theorem tendsto_atTop_isLUB (h_mono : Monotone f) (ha : IsLUB (Set.range f) a) :
   exact h_mono.rangeFactorization.tendsto_atTop_atTop fun b => b.2.imp fun a ha => ha.ge
 
 theorem tendsto_atBot_isLUB (h_anti : Antitone f) (ha : IsLUB (Set.range f) a) :
-    Tendsto f atBot (𝓝 a) := by convert tendsto_atTop_isLUB h_anti.dual_left ha using 1
+    Tendsto f atBot (𝓝 a) := by convert! tendsto_atTop_isLUB h_anti.dual_left ha using 1
 
 end IsLUB
 
@@ -102,10 +102,10 @@ section IsGLB
 variable [Preorder α] [InfConvergenceClass α] {f : ι → α} {a : α}
 
 theorem tendsto_atBot_isGLB (h_mono : Monotone f) (ha : IsGLB (Set.range f) a) :
-    Tendsto f atBot (𝓝 a) := by convert tendsto_atTop_isLUB h_mono.dual ha.dual using 1
+    Tendsto f atBot (𝓝 a) := by convert! tendsto_atTop_isLUB h_mono.dual ha.dual using 1
 
 theorem tendsto_atTop_isGLB (h_anti : Antitone f) (ha : IsGLB (Set.range f) a) :
-    Tendsto f atTop (𝓝 a) := by convert tendsto_atBot_isLUB h_anti.dual ha.dual using 1
+    Tendsto f atTop (𝓝 a) := by convert! tendsto_atBot_isLUB h_anti.dual ha.dual using 1
 
 end IsGLB
 
@@ -122,7 +122,7 @@ theorem tendsto_atTop_ciSup (h_mono : Monotone f) (hbdd : BddAbove <| range f) :
       h_mono.directed_le.directedOn_range.isLUB_csSup (Set.range_nonempty f) hbdd
 
 theorem tendsto_atBot_ciSup (h_anti : Antitone f) (hbdd : BddAbove <| range f) :
-    Tendsto f atBot (𝓝 (⨆ i, f i)) := by convert tendsto_atTop_ciSup h_anti.dual hbdd.dual using 1
+    Tendsto f atBot (𝓝 (⨆ i, f i)) := by convert! tendsto_atTop_ciSup h_anti.dual hbdd.dual using 1
 
 end CiSup
 
@@ -131,10 +131,10 @@ section CiInf
 variable [ConditionallyCompletePartialOrderInf α] [InfConvergenceClass α] {f : ι → α}
 
 theorem tendsto_atBot_ciInf (h_mono : Monotone f) (hbdd : BddBelow <| range f) :
-    Tendsto f atBot (𝓝 (⨅ i, f i)) := by convert tendsto_atTop_ciSup h_mono.dual hbdd.dual using 1
+    Tendsto f atBot (𝓝 (⨅ i, f i)) := by convert! tendsto_atTop_ciSup h_mono.dual hbdd.dual using 1
 
 theorem tendsto_atTop_ciInf (h_anti : Antitone f) (hbdd : BddBelow <| range f) :
-    Tendsto f atTop (𝓝 (⨅ i, f i)) := by convert tendsto_atBot_ciSup h_anti.dual hbdd.dual using 1
+    Tendsto f atTop (𝓝 (⨅ i, f i)) := by convert! tendsto_atBot_ciSup h_anti.dual hbdd.dual using 1
 
 end CiInf
 
diff --git a/Mathlib/Topology/Order/OrderClosed.lean b/Mathlib/Topology/Order/OrderClosed.lean
index 9fb4490dc6837e..4ebda2231a68ca 100644
--- a/Mathlib/Topology/Order/OrderClosed.lean
+++ b/Mathlib/Topology/Order/OrderClosed.lean
@@ -621,7 +621,7 @@ theorem frontier_le_subset_eq (hf : Continuous f) (hg : Continuous g) :
   rw [frontier_eq_closure_inter_closure, closure_le_eq hf hg]
   rintro b ⟨hb₁, hb₂⟩
   refine le_antisymm hb₁ (closure_lt_subset_le hg hf ?_)
-  convert hb₂ using 2; simp only [not_le.symm]; rfl
+  convert! hb₂ using 2; simp only [not_le.symm]; rfl
 
 @[to_dual]
 theorem frontier_Iic_subset (a : α) : frontier (Iic a) ⊆ {a} :=
diff --git a/Mathlib/Topology/Order/ScottTopology.lean b/Mathlib/Topology/Order/ScottTopology.lean
index 8e996159cb0c82..8896519e0aa8e9 100644
--- a/Mathlib/Topology/Order/ScottTopology.lean
+++ b/Mathlib/Topology/Order/ScottTopology.lean
@@ -216,7 +216,7 @@ lemma dirSupClosed_of_isClosed [IsScott α univ] : IsClosed s → DirSupClosed s
   (isClosed_iff_isLowerSet_and_dirSupClosed.mp h).right
 
 lemma lowerClosure_subset_closure [IsScott α univ] : ↑(lowerClosure s) ⊆ closure s := by
-  convert closure.mono (@upperSet_le_scott α _)
+  convert! closure.mono (@upperSet_le_scott α _)
   · rw [@IsUpperSet.closure_eq_lowerClosure α _ (upperSet α) ?_ s]
     infer_instance
   · exact topology_eq α univ
diff --git a/Mathlib/Topology/Order/SuccPred.lean b/Mathlib/Topology/Order/SuccPred.lean
index e029b17eb4f49b..7428499593dcb1 100644
--- a/Mathlib/Topology/Order/SuccPred.lean
+++ b/Mathlib/Topology/Order/SuccPred.lean
@@ -29,10 +29,10 @@ variable [SuccOrder α]
 theorem isOpen_singleton_of_not_isSuccPrelimit (ha : ¬ IsSuccPrelimit a) : IsOpen {a} := by
   obtain ⟨b, hb⟩ := not_isSuccPrelimit_iff.1 ha
   by_cases ha' : IsMax a
-  · convert isOpen_Ioi (a := b) using 1
+  · convert! isOpen_Ioi (a := b) using 1
     rw [hb.Ioi_eq]
     grind [IsMax]
-  · convert isOpen_Ioo (a := b) (b := Order.succ a) using 1
+  · convert! isOpen_Ioo (a := b) (b := Order.succ a) using 1
     simp [(covBy_succ_of_not_isMax ha').Ioo_eq_Ioc, hb.Ioc_eq]
 
 variable [NoMaxOrder α]
@@ -48,7 +48,7 @@ theorem isOpen_singleton_iff : IsOpen {a} ↔ ¬ IsSuccLimit a := by
     simp only [Set.mem_Ioo, Set.subset_singleton_iff] at h₁ h₂
     exact h₂ _ ⟨lt_succ l, h₁.1.succ_le.trans_lt h₁.2⟩
   · obtain (ha | ha) := not_isSuccLimit_iff.mp ha
-    · convert isOpen_Iio (a := Order.succ a) using 1
+    · convert! isOpen_Iio (a := Order.succ a) using 1
       simp [ha.Iic_eq]
     · exact isOpen_singleton_of_not_isSuccPrelimit ha
 
diff --git a/Mathlib/Topology/PartitionOfUnity.lean b/Mathlib/Topology/PartitionOfUnity.lean
index cc9187a2d979f3..3fee10d94b7a40 100644
--- a/Mathlib/Topology/PartitionOfUnity.lean
+++ b/Mathlib/Topology/PartitionOfUnity.lean
@@ -526,7 +526,7 @@ theorem sum_toPOUFun_eq (x : X) : ∑ᶠ i, f.toPOUFun i x = 1 - ∏ᶠ i, (1 -
   rw [finsum_eq_sum_of_support_subset _ A, finprod_eq_prod_of_mulSupport_subset _ B,
     Finset.prod_one_sub_ordered, sub_sub_cancel]
   refine Finset.sum_congr rfl fun i _ => ?_
-  convert f.toPOUFun_eq_mul_prod _ _ _ fun j _ hj => _
+  convert! f.toPOUFun_eq_mul_prod _ _ _ fun j _ hj => _
   rwa [Finite.mem_toFinset]
 
 open Classical in
diff --git a/Mathlib/Topology/Path.lean b/Mathlib/Topology/Path.lean
index 9a457721244ada..13bbc3699273fe 100644
--- a/Mathlib/Topology/Path.lean
+++ b/Mathlib/Topology/Path.lean
@@ -585,11 +585,11 @@ theorem truncate_self {a b : X} (γ : Path a b) (t : ℝ) :
 
 theorem truncate_zero_zero {a b : X} (γ : Path a b) :
     γ.truncate 0 0 = (Path.refl a).cast (by rw [min_self, γ.extend_zero]) γ.extend_zero := by
-  convert γ.truncate_self 0
+  convert! γ.truncate_self 0
 
 theorem truncate_one_one {a b : X} (γ : Path a b) :
     γ.truncate 1 1 = (Path.refl b).cast (by rw [min_self, γ.extend_one]) γ.extend_one := by
-  convert γ.truncate_self 1
+  convert! γ.truncate_self 1
 
 @[simp]
 theorem truncate_zero_one {a b : X} (γ : Path a b) :
diff --git a/Mathlib/Topology/Piecewise.lean b/Mathlib/Topology/Piecewise.lean
index ff26e0bd9b815d..240b950c285f02 100644
--- a/Mathlib/Topology/Piecewise.lean
+++ b/Mathlib/Topology/Piecewise.lean
@@ -134,7 +134,7 @@ theorem IsOpen.ite' (hs : IsOpen s) (hs' : IsOpen s')
     (ht : ∀ x ∈ frontier t, x ∈ s ↔ x ∈ s') : IsOpen (t.ite s s') := by
   classical
     simp only [isOpen_iff_continuous_mem, Set.ite] at *
-    convert
+    convert!
       continuous_piecewise (fun x hx => propext (ht x hx)) hs.continuousOn hs'.continuousOn using 2
     rename_i x
     by_cases hx : x ∈ t <;> simp [hx]
diff --git a/Mathlib/Topology/QuasiSeparated.lean b/Mathlib/Topology/QuasiSeparated.lean
index 31975c6d0330cf..40bdc80392322c 100644
--- a/Mathlib/Topology/QuasiSeparated.lean
+++ b/Mathlib/Topology/QuasiSeparated.lean
@@ -61,9 +61,9 @@ theorem isQuasiSeparated_univ {α : Type*} [TopologicalSpace α] [QuasiSeparated
 theorem IsQuasiSeparated.image_of_isEmbedding {s : Set α} (H : IsQuasiSeparated s)
     (h : IsEmbedding f) : IsQuasiSeparated (f '' s) := by
   intro U V hU hU' hU'' hV hV' hV''
-  convert
-    (H (f ⁻¹' U) (f ⁻¹' V)
-      ?_ (h.continuous.1 _ hU') ?_ ?_ (h.continuous.1 _ hV') ?_).image h.continuous
+  convert!
+    (H (f ⁻¹' U) (f ⁻¹' V) ?_ (h.continuous.1 _ hU') ?_ ?_ (h.continuous.1 _ hV') ?_).image
+      h.continuous
   · symm
     rw [← Set.preimage_inter, Set.image_preimage_eq_inter_range, Set.inter_eq_left]
     exact Set.inter_subset_left.trans (hU.trans (Set.image_subset_range _ _))
@@ -71,14 +71,14 @@ theorem IsQuasiSeparated.image_of_isEmbedding {s : Set α} (H : IsQuasiSeparated
     rw [← h.injective.injOn.mem_image_iff (Set.subset_univ _) trivial]
     exact hU hx
   · rw [h.isCompact_iff]
-    convert hU''
+    convert! hU''
     rw [Set.image_preimage_eq_inter_range, Set.inter_eq_left]
     exact hU.trans (Set.image_subset_range _ _)
   · intro x hx
     rw [← h.injective.injOn.mem_image_iff (Set.subset_univ _) trivial]
     exact hV hx
   · rw [h.isCompact_iff]
-    convert hV''
+    convert! hV''
     rw [Set.image_preimage_eq_inter_range, Set.inter_eq_left]
     exact hV.trans (Set.image_subset_range _ _)
 
@@ -104,7 +104,7 @@ lemma Topology.IsOpenEmbedding.quasiSeparatedSpace [QuasiSeparatedSpace β] (h :
 theorem isQuasiSeparated_iff_quasiSeparatedSpace (s : Set α) (hs : IsOpen s) :
     IsQuasiSeparated s ↔ QuasiSeparatedSpace s := by
   rw [← isQuasiSeparated_univ_iff]
-  convert (hs.isOpenEmbedding_subtypeVal.isQuasiSeparated_iff (s := Set.univ)).symm
+  convert! (hs.isOpenEmbedding_subtypeVal.isQuasiSeparated_iff (s := Set.univ)).symm
   simp
 
 instance (priority := 100) T2Space.to_quasiSeparatedSpace [T2Space α] : QuasiSeparatedSpace α :=
diff --git a/Mathlib/Topology/SeparatedMap.lean b/Mathlib/Topology/SeparatedMap.lean
index 76a3040390a779..fa21f476ac921a 100644
--- a/Mathlib/Topology/SeparatedMap.lean
+++ b/Mathlib/Topology/SeparatedMap.lean
@@ -161,7 +161,7 @@ theorem discreteTopology_iff_locallyInjective (y : Y) :
     DiscreteTopology X ↔ IsLocallyInjective fun _ : X ↦ y := by
   rw [discreteTopology_iff_singleton_mem_nhds, isLocallyInjective_iff_nhds]
   refine forall_congr' fun x ↦ ⟨fun h ↦ ⟨{x}, h, Set.injOn_singleton _ _⟩, fun ⟨U, hU, inj⟩ ↦ ?_⟩
-  convert hU; ext x'; refine ⟨?_, fun h ↦ inj h (mem_of_mem_nhds hU) rfl⟩
+  convert! hU; ext x'; refine ⟨?_, fun h ↦ inj h (mem_of_mem_nhds hU) rfl⟩
   rintro rfl; exact mem_of_mem_nhds hU
 
 theorem IsLocallyInjective.comp_left {A} {f : X → Y} (hf : IsLocallyInjective f) {g : Y → A}
diff --git a/Mathlib/Topology/Separation/Basic.lean b/Mathlib/Topology/Separation/Basic.lean
index e7938a01e7c8d0..83376d6bad82c8 100644
--- a/Mathlib/Topology/Separation/Basic.lean
+++ b/Mathlib/Topology/Separation/Basic.lean
@@ -125,7 +125,7 @@ theorem TopologicalSpace.IsTopologicalBasis.inseparable_iff {b : Set (Set X)}
     (hb : IsTopologicalBasis b) {x y : X} : Inseparable x y ↔ ∀ s ∈ b, (x ∈ s ↔ y ∈ s) :=
   ⟨fun h _ hs ↦ inseparable_iff_forall_isOpen.1 h _ (hb.isOpen hs),
     fun h ↦ hb.nhds_hasBasis.eq_of_same_basis <| by
-      convert hb.nhds_hasBasis using 2
+      convert! hb.nhds_hasBasis using 2
       exact and_congr_right (h _)⟩
 
 theorem TopologicalSpace.IsTopologicalBasis.eq_iff [T0Space X] {b : Set (Set X)}
@@ -670,7 +670,7 @@ theorem Dense.diff_finset [T1Space X] [∀ x : X, NeBot (𝓝[≠] x)] {s : Set
 obtains a dense set. -/
 theorem Dense.diff_finite [T1Space X] [∀ x : X, NeBot (𝓝[≠] x)] {s : Set X} (hs : Dense s)
     {t : Set X} (ht : t.Finite) : Dense (s \ t) := by
-  convert hs.diff_finset ht.toFinset
+  convert! hs.diff_finset ht.toFinset
   exact (Finite.coe_toFinset _).symm
 
 /-- If a function to a `T1Space` tends to some limit `y` at some point `x`, then necessarily
diff --git a/Mathlib/Topology/Separation/DisjointCover.lean b/Mathlib/Topology/Separation/DisjointCover.lean
index 04ab4742a8d1d7..447423c54ab6be 100644
--- a/Mathlib/Topology/Separation/DisjointCover.lean
+++ b/Mathlib/Topology/Separation/DisjointCover.lean
@@ -150,7 +150,7 @@ lemma exists_finite_approximation_of_mem_nhds_diagonal (hS : S ∈ nhdsSet (diag
     simpa [← SetLike.coe_set_eq, ← nonempty_iff_ne_empty] using hEne i
   choose r hr using h_ex -- for each `i`, choose an `r i ∈ E i`
   refine ⟨n, g, f ∘ r, continuous_discrete_rng.mpr fun j ↦ ?_, fun x ↦ (hES _) _ (hg _) _ (hr _)⟩
-  convert (E j).isOpen
+  convert! (E j).isOpen
   exact Set.ext fun x ↦ ⟨fun hj ↦ hj ▸ hg x, fun hx ↦ (hg' _ _ hx).symm⟩
 
 /--
@@ -170,7 +170,7 @@ lemma exists_finite_sum_const_mulIndicator_approximation_of_mem_nhds_diagonal [C
     ∀ x, (f x, ∏ n, mulIndicator (U n) (fun _ ↦ v n) x) ∈ S := by
   obtain ⟨n, g, h, hg, hgh⟩ := exists_finite_approximation_of_mem_nhds_diagonal f hS
   refine ⟨n, fun i ↦ ⟨_, (isClopen_discrete {i}).preimage hg⟩, h, fun x ↦ ?_⟩
-  convert hgh x
+  convert! hgh x
   exact (Fintype.prod_eq_single _ fun i hi ↦ mulIndicator_of_notMem hi.symm _).trans
     (mulIndicator_of_mem rfl _)
 
diff --git a/Mathlib/Topology/Separation/Hausdorff.lean b/Mathlib/Topology/Separation/Hausdorff.lean
index 0b3c1cd2be2717..03e84f278b8fa2 100644
--- a/Mathlib/Topology/Separation/Hausdorff.lean
+++ b/Mathlib/Topology/Separation/Hausdorff.lean
@@ -173,7 +173,7 @@ theorem t2Space_iff_of_isOpenQuotientMap [TopologicalSpace Y] {π : X → Y}
   replace h := IsOpenQuotientMap.prodMap h h
   refine ⟨fun H ↦ H.preimage h.continuous, fun H ↦ ?_⟩
   simp_rw [← isOpen_compl_iff] at H ⊢
-  convert h.isOpenMap _ H
+  convert! h.isOpenMap _ H
   exact (h.surjective.image_preimage _).symm
 
 theorem tendsto_nhds_unique [T2Space X] {f : Y → X} {l : Filter Y} {a b : X} [NeBot l]
diff --git a/Mathlib/Topology/Sets/CompactOpenCovered.lean b/Mathlib/Topology/Sets/CompactOpenCovered.lean
index 047f37915ffcfc..9fde3074afc7f4 100644
--- a/Mathlib/Topology/Sets/CompactOpenCovered.lean
+++ b/Mathlib/Topology/Sets/CompactOpenCovered.lean
@@ -85,7 +85,7 @@ lemma of_iUnion_eq_of_finite {κ : Type*} [Finite κ] (s : κ → Set S) (hs : 
     (H : ∀ i, IsCompactOpenCovered f (s i)) : IsCompactOpenCovered f U := by
   rw [iff_isCompactOpenCovered_sigmaMk, iff_of_unique]
   have (i : κ) : ∃ (V : Opens (Σ i, X i)), IsCompact V.1 ∧ (f _ ·.snd) '' V.1 = s i := by
-    convert H i; rw [iff_isCompactOpenCovered_sigmaMk, iff_of_unique]
+    convert! H i; rw [iff_isCompactOpenCovered_sigmaMk, iff_of_unique]
   choose V hVeq hVc using this
   exact ⟨⨆ i, V i, by simpa using isCompact_iUnion hVeq, by simp_all [Set.image_iUnion, ← hs]⟩
 
diff --git a/Mathlib/Topology/Sets/Opens.lean b/Mathlib/Topology/Sets/Opens.lean
index 019b93e6be6b43..6111c84201394f 100644
--- a/Mathlib/Topology/Sets/Opens.lean
+++ b/Mathlib/Topology/Sets/Opens.lean
@@ -329,7 +329,7 @@ theorem IsBasis.isCompact_open_iff_eq_finite_iUnion {ι : Type*} (b : ι → Ope
     (hb : IsBasis (Set.range b)) (hb' : ∀ i, IsCompact (b i : Set α)) (U : Set α) :
     IsCompact U ∧ IsOpen U ↔ ∃ s : Set ι, s.Finite ∧ U = ⋃ i ∈ s, b i := by
   apply isCompact_open_iff_eq_finite_iUnion_of_isTopologicalBasis fun i : ι => (b i).1
-  · convert (config := { transparency := .default }) hb
+  · convert! (config := { transparency := .default }) hb
     ext
     simp
   · exact hb'
@@ -351,14 +351,14 @@ lemma IsBasis.le_iff {α} {t₁ t₂ : TopologicalSpace α}
 lemma isBasis_sigma {ι : Type*} {α : ι → Type*} [∀ i, TopologicalSpace (α i)]
     {B : ∀ i, Set (Opens (α i))} (hB : ∀ i, IsBasis (B i)) :
     IsBasis (⋃ i : ι, (fun U ↦ ⟨Sigma.mk i '' U.1, isOpenMap_sigmaMk _ U.2⟩) '' B i) := by
-  convert TopologicalSpace.IsTopologicalBasis.sigma hB
+  convert! TopologicalSpace.IsTopologicalBasis.sigma hB
   simp only [IsBasis, Set.image_iUnion, ← Set.image_comp]
   simp
 
 lemma IsBasis.of_isInducing {B : Set (Opens β)} (H : IsBasis B) {f : α → β} (h : IsInducing f) :
     IsBasis { ⟨f ⁻¹' U, U.2.preimage h.continuous⟩ | U ∈ B } := by
   simp only [IsBasis] at H ⊢
-  convert H.isInducing h
+  convert! H.isInducing h
   ext; simp
 
 @[simp]
diff --git a/Mathlib/Topology/Sets/VietorisTopology.lean b/Mathlib/Topology/Sets/VietorisTopology.lean
index 5f6df6e1a31ecb..0eaa904aa1b3e1 100644
--- a/Mathlib/Topology/Sets/VietorisTopology.lean
+++ b/Mathlib/Topology/Sets/VietorisTopology.lean
@@ -351,7 +351,7 @@ theorem isClosed_inter_nonempty_of_isClosed {F : Set α} (h : IsClosed F) :
   exact (isOpen_subsets_of_isOpen h.isOpen_compl).isClosed_compl
 
 theorem isClopen_singleton_bot : IsClopen {(⊥ : Compacts α)} := by
-  convert vietoris.isClopen_singleton_empty.preimage continuous_coe
+  convert! vietoris.isClopen_singleton_empty.preimage continuous_coe
   rw [← coe_bot, ← image_singleton (f := SetLike.coe), SetLike.coe_injective.preimage_image]
 
 /-- Given a basis `B` on a topological space `α`, the topology of `Compacts α` has a basis
@@ -468,9 +468,10 @@ theorem _root_.Topology.IsClosedEmbedding.compacts_map (hf : IsClosedEmbedding f
 instance [DiscreteTopology α] : DiscreteTopology (Compacts α) := by
   rw [discreteTopology_iff_isOpen_singleton]
   intro K
-  convert (isOpen_subsets_of_isOpen (isOpen_discrete (K : Set α))).inter
-    (K.isCompact.finite_of_discrete.isOpen_biInter fun x hx =>
-      isOpen_inter_nonempty_of_isOpen (isOpen_discrete {x}))
+  convert!
+    (isOpen_subsets_of_isOpen (isOpen_discrete (K : Set α))).inter
+      (K.isCompact.finite_of_discrete.isOpen_biInter fun x hx =>
+        isOpen_inter_nonempty_of_isOpen (isOpen_discrete { x }))
   simp_rw [← setOf_forall, inter_singleton_nonempty, ← Set.subset_def, ← setOf_and,
     ← subset_antisymm_iff, SetLike.coe_set_eq, setOf_eq_eq_singleton]
 
@@ -554,7 +555,7 @@ theorem isCompact_biUnion_coe_of_isCompact {S : Set (Compacts α)} (hS : IsCompa
 @[simp]
 theorem compactSpace_iff : CompactSpace (Compacts α) ↔ CompactSpace α := by
   refine ⟨fun h => ⟨?_⟩, fun _ => inferInstance⟩
-  convert isCompact_biUnion_coe_of_isCompact (α := α) isCompact_univ
+  convert! isCompact_biUnion_coe_of_isCompact (α := α) isCompact_univ
   symm
   simp_rw [biUnion_univ, eq_univ_iff_forall, mem_iUnion]
   exact fun x => ⟨{x}, Set.mem_singleton x⟩
@@ -779,13 +780,13 @@ theorem isCompact_subsets_of_isCompact {K : Set α} (hK : IsCompact K) :
 
 theorem isCompact_biUnion_coe_of_isCompact {S : Set (NonemptyCompacts α)} (hs : IsCompact S) :
     IsCompact (⋃ K ∈ S, (K : Set α)) := by
-  convert Compacts.isCompact_biUnion_coe_of_isCompact (hs.image continuous_toCompacts)
+  convert! Compacts.isCompact_biUnion_coe_of_isCompact (hs.image continuous_toCompacts)
   simp_rw [biUnion_image, coe_toCompacts]
 
 @[simp]
 theorem compactSpace_iff : CompactSpace (NonemptyCompacts α) ↔ CompactSpace α := by
   refine ⟨fun h => ⟨?_⟩, fun _ => inferInstance⟩
-  convert isCompact_biUnion_coe_of_isCompact (α := α) isCompact_univ
+  convert! isCompact_biUnion_coe_of_isCompact (α := α) isCompact_univ
   symm
   simp_rw [biUnion_univ, eq_univ_iff_forall, mem_iUnion]
   exact fun x => ⟨{x}, Set.mem_singleton x⟩
diff --git a/Mathlib/Topology/Sheaves/LocalPredicate.lean b/Mathlib/Topology/Sheaves/LocalPredicate.lean
index 3b5f28bb6a914b..4e30ef071016f1 100644
--- a/Mathlib/Topology/Sheaves/LocalPredicate.lean
+++ b/Mathlib/Topology/Sheaves/LocalPredicate.lean
@@ -160,7 +160,7 @@ namespace PrelocalPredicate
 
 theorem sheafifyOf {T : X → Type*} {P : PrelocalPredicate T} {U : Opens X}
     {f : ∀ x : U, T x} (h : P.pred f) : P.sheafify.pred f := fun x ↦
-  ⟨U, x.2, 𝟙 _, by convert h⟩
+  ⟨U, x.2, 𝟙 _, by convert! h⟩
 
 /-- For a unary operation (e.g. `x ↦ -x`) defined at each stalk, if a prelocal predicate is closed
 under the operation on each open set (possibly by refinement), then the sheafified predicate is
@@ -264,7 +264,7 @@ theorem isSheaf (P : LocalPredicate T) : (subpresheafToTypes P.toPrelocalPredica
       -- We claim that the predicate holds in `U i`
       use U i, hi, Opens.leSupr U i
       -- This follows, since our original family `sf` satisfies the predicate
-      convert (sf i).property using 1
+      convert! (sf i).property using 1
       exact gl_spec i
     -- It remains to show that the chosen lift is really a gluing for the subsheaf and
     -- that it is unique. Both of which follow immediately from the corresponding facts
diff --git a/Mathlib/Topology/Sheaves/LocallySurjective.lean b/Mathlib/Topology/Sheaves/LocallySurjective.lean
index bf7b87fee2acee..691f46d117301d 100644
--- a/Mathlib/Topology/Sheaves/LocallySurjective.lean
+++ b/Mathlib/Topology/Sheaves/LocallySurjective.lean
@@ -108,12 +108,12 @@ theorem locally_surjective_iff_surjective_on_stalks (T : ℱ ⟶ 𝒢) :
     obtain ⟨V, hxV, s, rfl⟩ := ℱ.exists_germ_eq s_x
     -- rfl : ℱ.germ x s = s_x
     have key_W := 𝒢.germ_eq x hxV hxU (T.app _ s) t <| by
-      convert hs_x using 1
+      convert! hs_x using 1
       symm
-      convert stalkFunctor_map_germ_apply _ _ _ _ s
+      convert! stalkFunctor_map_germ_apply _ _ _ _ s
     obtain ⟨W, hxW, hWV, hWU, h_eq⟩ := key_W
     refine ⟨W, hWU, ⟨ℱ.map hWV.op s, ?_⟩, hxW⟩
-    convert h_eq using 1
+    convert! h_eq using 1
     simp only [← ConcreteCategory.comp_apply, T.naturality]
 
 end SurjectiveOnStalks
diff --git a/Mathlib/Topology/Sheaves/PUnit.lean b/Mathlib/Topology/Sheaves/PUnit.lean
index 38c225801bf182..7b181a0b513cb2 100644
--- a/Mathlib/Topology/Sheaves/PUnit.lean
+++ b/Mathlib/Topology/Sheaves/PUnit.lean
@@ -33,7 +33,7 @@ theorem isSheaf_of_isTerminal_of_indiscrete {X : TopCat.{w}} (hind : X.str = ⊤
     · refine ⟨it.from _, fun U hU hs => IsTerminal.hom_ext ?_ _ _⟩
       rwa [le_bot_iff.1 hU.le]
     · apply it.hom_ext
-  · convert Presieve.isSheafFor_top (F ⋙ coyoneda.obj (@op C c))
+  · convert! Presieve.isSheafFor_top (F ⋙ coyoneda.obj (@op C c))
     rw [Sieve.arrows_eq_top_iff, ← Sieve.id_mem_iff_eq_top]
     have := U.eq_bot_or_top.resolve_left hne
     subst this
@@ -42,7 +42,7 @@ theorem isSheaf_of_isTerminal_of_indiscrete {X : TopCat.{w}} (hind : X.str = ⊤
     obtain ⟨U, f, hf, hm⟩ := hs x _root_.trivial
     obtain rfl | rfl := U.eq_bot_or_top
     · cases hm
-    · convert hf
+    · convert! hf
 
 theorem isSheaf_iff_isTerminal_of_indiscrete {X : TopCat.{w}} (hind : X.str = ⊤)
     (F : Presheaf C X) : F.IsSheaf ↔ Nonempty (IsTerminal <| F.obj <| op ⊥) :=
diff --git a/Mathlib/Topology/Sheaves/SheafCondition/OpensLeCover.lean b/Mathlib/Topology/Sheaves/SheafCondition/OpensLeCover.lean
index e3a169dcbfdd42..629aa8690e6946 100644
--- a/Mathlib/Topology/Sheaves/SheafCondition/OpensLeCover.lean
+++ b/Mathlib/Topology/Sheaves/SheafCondition/OpensLeCover.lean
@@ -196,7 +196,8 @@ def isLimitOpensLeEquivGenerate₂ (R : Presieve Y)
     (hR : Sieve.generate R ∈ Opens.grothendieckTopology X Y) :
     IsLimit (F.mapCone (opensLeCoverCocone (coveringOfPresieve Y R)).op) ≃
       IsLimit (F.mapCone (Sieve.generate R).arrows.cocone.op) := by
-  convert isLimitOpensLeEquivGenerate₁ F (coveringOfPresieve Y R)
+  convert!
+    isLimitOpensLeEquivGenerate₁ F (coveringOfPresieve Y R)
       (coveringOfPresieve.iSup_eq_of_mem_grothendieck Y R hR).symm using 1
   rw [covering_presieve_eq_self R]
 
diff --git a/Mathlib/Topology/Sheaves/SheafCondition/PairwiseIntersections.lean b/Mathlib/Topology/Sheaves/SheafCondition/PairwiseIntersections.lean
index ca6c8e5d071c37..8d953d3657996d 100644
--- a/Mathlib/Topology/Sheaves/SheafCondition/PairwiseIntersections.lean
+++ b/Mathlib/Topology/Sheaves/SheafCondition/PairwiseIntersections.lean
@@ -407,9 +407,9 @@ def isLimitPullbackCone : IsLimit (interUnionPullbackCone F U V) := by
     apply (F.presheaf.isSheaf_iff_isSheafPairwiseIntersections.mp F.2 ι).some.hom_ext
     rintro ((_ | _) | (_ | _)) <;>
     rw [Category.assoc, Category.assoc, Functor.mapCone_π_app, ← F.1.map_comp]
-    · convert h₁
+    · convert! h₁
       apply interUnionPullbackConeLift_left
-    · convert h₂
+    · convert! h₂
       apply interUnionPullbackConeLift_right
     all_goals
       dsimp only [Functor.op, Pairwise.cocone_ι_app, Functor.mapCone_π_app, Cocone.op,
@@ -417,9 +417,9 @@ def isLimitPullbackCone : IsLimit (interUnionPullbackCone F U V) := by
       simp_rw [F.1.map_comp, ← Category.assoc]
       congr 1
       simp_rw [Category.assoc, ← F.1.map_comp]
-    · convert h₁
+    · convert! h₁
       apply interUnionPullbackConeLift_left
-    · convert h₂
+    · convert! h₂
       apply interUnionPullbackConeLift_right
 
 /-- If `U, V` are disjoint, then `F(U ⊔ V) = F(U) × F(V)`. -/
diff --git a/Mathlib/Topology/Sheaves/SheafCondition/Sites.lean b/Mathlib/Topology/Sheaves/SheafCondition/Sites.lean
index 1c6c808733c1ff..d7528b2f93fbcd 100644
--- a/Mathlib/Topology/Sheaves/SheafCondition/Sites.lean
+++ b/Mathlib/Topology/Sheaves/SheafCondition/Sites.lean
@@ -222,7 +222,7 @@ def isTerminalOfEmpty (F : Sheaf C X) : Limits.IsTerminal (F.obj.obj (op ⊥)) :
 /-- A variant of `isTerminalOfEmpty` that is easier to `apply`. -/
 def isTerminalOfEqEmpty (F : X.Sheaf C) {U : Opens X} (h : U = ⊥) :
     Limits.IsTerminal (F.obj.obj (op U)) := by
-  convert F.isTerminalOfEmpty
+  convert! F.isTerminalOfEmpty
 
 /-- If a family `B` of open sets forms a basis of the topology on `X`, and if `F'`
 is a sheaf on `X`, then a homomorphism between a presheaf `F` on `X` and `F'`
diff --git a/Mathlib/Topology/Sheaves/SheafCondition/UniqueGluing.lean b/Mathlib/Topology/Sheaves/SheafCondition/UniqueGluing.lean
index 5f3595c54a0fad..351db260af4098 100644
--- a/Mathlib/Topology/Sheaves/SheafCondition/UniqueGluing.lean
+++ b/Mathlib/Topology/Sheaves/SheafCondition/UniqueGluing.lean
@@ -129,7 +129,7 @@ theorem isSheaf_iff_isSheafUniqueGluing_types : F.IsSheaf ↔ F.IsSheafUniqueGlu
   · exact h _ cpt.sectionPairwise.prop
   · specialize h (fun i ↦ s <| op <| Pairwise.single i) fun i j ↦
       (hs <| op <| Pairwise.Hom.left i j).trans (hs <| op <| Pairwise.Hom.right i j).symm
-    convert h; ext (i | ⟨i, j⟩)
+    convert! h; ext (i | ⟨i, j⟩)
     · rfl
     · exact (hs <| op <| Pairwise.Hom.left i j).symm
 
@@ -195,7 +195,7 @@ theorem existsUnique_gluing' (V : Opens X) (iUV : ∀ i : ι, U i ⟶ V) (hcover
     rw [← ConcreteCategory.comp_apply, ← F.1.map_comp]
     exact gl_spec i
   · intro gl' gl'_spec
-    convert congr_arg _ (gl_uniq (F.1.map (eqToHom V_eq_supr_U.symm).op gl') fun i => _) <;>
+    convert! congr_arg _ (gl_uniq (F.1.map (eqToHom V_eq_supr_U.symm).op gl') fun i => _) <;>
       rw [← ConcreteCategory.comp_apply, ← F.1.map_comp]
     · simp
     · exact gl'_spec i
@@ -226,7 +226,7 @@ theorem eq_of_locally_eq' (V : Opens X) (iUV : ∀ i : ι, U i ⟶ V) (hcover :
     s = t := by
   have V_eq_supr_U : V = iSup U := le_antisymm hcover (iSup_le fun i => (iUV i).le)
   suffices F.1.map (eqToHom V_eq_supr_U.symm).op s = F.1.map (eqToHom V_eq_supr_U.symm).op t by
-    convert congr_arg (F.1.map (eqToHom V_eq_supr_U).op) this <;>
+    convert! congr_arg (F.1.map (eqToHom V_eq_supr_U).op) this <;>
     rw [← ConcreteCategory.comp_apply, ← F.1.map_comp, eqToHom_op, eqToHom_op, eqToHom_trans,
       eqToHom_refl, F.1.map_id, ConcreteCategory.id_apply]
   apply eq_of_locally_eq
diff --git a/Mathlib/Topology/Sheaves/Stalks.lean b/Mathlib/Topology/Sheaves/Stalks.lean
index c9ee0dee12bb3b..41cf82dd8e08df 100644
--- a/Mathlib/Topology/Sheaves/Stalks.lean
+++ b/Mathlib/Topology/Sheaves/Stalks.lean
@@ -216,7 +216,8 @@ theorem comp (ℱ : X.Presheaf C) (f : X ⟶ Y) (g : Y ⟶ Z) (x : X) :
 theorem stalkPushforward_iso_of_isInducing {f : X ⟶ Y} (hf : IsInducing f)
     (F : X.Presheaf C) (x : X) : IsIso (F.stalkPushforward _ f x) := by
   haveI := Functor.initial_of_adjunction (hf.adjunctionNhds x)
-  convert (Functor.Final.colimitIso (OpenNhds.map f x).op ((OpenNhds.inclusion x).op ⋙ F)).isIso_hom
+  convert!
+    (Functor.Final.colimitIso (OpenNhds.map f x).op ((OpenNhds.inclusion x).op ⋙ F)).isIso_hom
   refine stalk_hom_ext _ fun U hU ↦ (stalkPushforward_germ _ f F _ x hU).trans ?_
   symm
   exact colimit.ι_pre ((OpenNhds.inclusion x).op ⋙ F) (OpenNhds.map f x).op _
@@ -452,7 +453,7 @@ theorem stalkFunctor_map_injective_of_app_injective {F G : Presheaf C X} {f : F
   rw [← ConcreteCategory.comp_apply, ← ConcreteCategory.comp_apply, ← f.naturality, ← f.naturality,
     ConcreteCategory.comp_apply, ConcreteCategory.comp_apply] at heq
   replace heq := h W heq
-  convert congr_arg (F.germ _ x hxW) heq using 1
+  convert! congr_arg (F.germ _ x hxW) heq using 1
   exacts [(F.germ_res_apply iWU₁ x hxW s).symm, (F.germ_res_apply iWU₂ x hxW t).symm]
 
 section IsBasis
diff --git a/Mathlib/Topology/Sion.lean b/Mathlib/Topology/Sion.lean
index d9abac39346f70..7357c61de05382 100644
--- a/Mathlib/Topology/Sion.lean
+++ b/Mathlib/Topology/Sion.lean
@@ -503,13 +503,13 @@ public theorem DMCompletion.exists_isSaddlePointOn :
   let φ : E → F → γ := fun x y ↦ ι (f x y)
   -- suffices : ∃ a ∈ X, ∃ b ∈ Y, IsSaddlePointOn X Y φ a b
   have hφx (x) (hx : x ∈ X) : UpperSemicontinuousOn (fun y ↦ φ x y) Y := by
-    convert Continuous.comp_upperSemicontinuousOn hι (hfx x hx) ι.monotone
+    convert! Continuous.comp_upperSemicontinuousOn hι (hfx x hx) ι.monotone
   have hφx' (x) (hx : x ∈ X) : QuasiconcaveOn ℝ Y fun y ↦ φ x y := by
-    convert (hfx' x hx).monotone_comp ι.monotone
+    convert! (hfx' x hx).monotone_comp ι.monotone
   have hφy (y) (hy : y ∈ Y) : LowerSemicontinuousOn (fun x ↦ φ x y) X := by
-    convert Continuous.comp_lowerSemicontinuousOn hι (hfy y hy) ι.monotone
+    convert! Continuous.comp_lowerSemicontinuousOn hι (hfy y hy) ι.monotone
   have hφy' (y) (hy : y ∈ Y) : QuasiconvexOn ℝ X fun x ↦ φ x y := by
-    convert (hfy' y hy).monotone_comp ι.monotone
+    convert! (hfy' y hy).monotone_comp ι.monotone
   obtain ⟨a, ha, b, hb, hab⟩ :=
     exists_isSaddlePointOn' ne_X kX hφy hφy' cY kY hφx hφx' cX ne_Y
   use a, ha, b, hb
diff --git a/Mathlib/Topology/Sober.lean b/Mathlib/Topology/Sober.lean
index 06321a5d6a8df4..ce6450b5990f04 100644
--- a/Mathlib/Topology/Sober.lean
+++ b/Mathlib/Topology/Sober.lean
@@ -122,7 +122,7 @@ theorem IsIrreducible.isGenericPoint_genericPoint_closure
 theorem IsIrreducible.isGenericPoint_genericPoint [QuasiSober α] {S : Set α}
     (hS : IsIrreducible S) (hS' : IsClosed S) :
     IsGenericPoint hS.genericPoint S := by
-  convert hS.isGenericPoint_genericPoint_closure; exact hS'.closure_eq.symm
+  convert! hS.isGenericPoint_genericPoint_closure; exact hS'.closure_eq.symm
 
 @[simp]
 theorem IsIrreducible.genericPoint_closure_eq [QuasiSober α] {S : Set α} (hS : IsIrreducible S) :
diff --git a/Mathlib/Topology/Spectral/Prespectral.lean b/Mathlib/Topology/Spectral/Prespectral.lean
index ae29626e43db41..c259887f6e8c49 100644
--- a/Mathlib/Topology/Spectral/Prespectral.lean
+++ b/Mathlib/Topology/Spectral/Prespectral.lean
@@ -103,7 +103,7 @@ variable (X) in
 lemma PrespectralSpace.isBasis_opens [PrespectralSpace X] :
     TopologicalSpace.Opens.IsBasis { U : Opens X | IsCompact (U : Set X) } := by
   dsimp only [TopologicalSpace.Opens.IsBasis]
-  convert isTopologicalBasis (X := X)
+  convert! isTopologicalBasis (X := X)
   ext s
   exact ⟨fun ⟨V, hV, heq⟩ ↦ heq ▸ ⟨V.2, hV⟩, fun h ↦ ⟨⟨s, h.1⟩, h.2, rfl⟩⟩
 
diff --git a/Mathlib/Topology/Subpath.lean b/Mathlib/Topology/Subpath.lean
index 2c48773ad40568..00687690175054 100644
--- a/Mathlib/Topology/Subpath.lean
+++ b/Mathlib/Topology/Subpath.lean
@@ -166,7 +166,7 @@ theorem concat_refl (n : ℕ) (x : X) :
   | zero => rw [concat_zero]
   | succ _ _ =>
     rw [concat_succ]
-    convert refl_trans_refl
+    convert! refl_trans_refl
 
 namespace Homotopy
 
diff --git a/Mathlib/Topology/TietzeExtension.lean b/Mathlib/Topology/TietzeExtension.lean
index 9de9a7a007a2e1..d2af841d53e837 100644
--- a/Mathlib/Topology/TietzeExtension.lean
+++ b/Mathlib/Topology/TietzeExtension.lean
@@ -485,7 +485,7 @@ theorem exists_extension_forall_mem_of_isClosedEmbedding (f : C(X, ℝ)) {t : Se
     h.toEquiv.symm_apply_eq.trans Subtype.ext_iff
   refine ⟨g, fun y => ?_, ?_⟩
   · rcases hG y with ⟨a, ha, hay⟩
-    convert ha
+    convert! ha
     exact hgG.2 hay.symm
   · ext x
     exact hgG.2 (congr_fun hGF _)
diff --git a/Mathlib/Topology/UniformSpace/Cauchy.lean b/Mathlib/Topology/UniformSpace/Cauchy.lean
index 78e14554c036cd..b9ac8cec007ce9 100644
--- a/Mathlib/Topology/UniformSpace/Cauchy.lean
+++ b/Mathlib/Topology/UniformSpace/Cauchy.lean
@@ -287,7 +287,7 @@ theorem cauchySeq_shift {u : ℕ → α} (k : ℕ) : CauchySeq (fun n ↦ u (n +
     obtain ⟨N, h⟩ := h V mV
     use N + k
     intro a ha b hb
-    convert h (a - k) (Nat.le_sub_of_add_le ha) (b - k) (Nat.le_sub_of_add_le hb) <;> lia
+    convert! h (a - k) (Nat.le_sub_of_add_le ha) (b - k) (Nat.le_sub_of_add_le hb) <;> lia
   · exact h.comp_tendsto (tendsto_add_atTop_nat k)
 
 theorem Filter.HasBasis.cauchySeq_iff {γ} [Nonempty β] [SemilatticeSup β] {u : β → α} {p : γ → Prop}
diff --git a/Mathlib/Topology/UniformSpace/Closeds.lean b/Mathlib/Topology/UniformSpace/Closeds.lean
index 7f1289b7ac8bbc..9306374ea70f17 100644
--- a/Mathlib/Topology/UniformSpace/Closeds.lean
+++ b/Mathlib/Topology/UniformSpace/Closeds.lean
@@ -247,7 +247,7 @@ theorem isClosed_setOf_totallyBounded : IsClosed {s : Set α | TotallyBounded s}
 
 instance [DiscreteUniformity α] : DiscreteUniformity (Set α) := by
   rw [discreteUniformity_iff_setRelId_mem_uniformity]
-  convert Filter.mem_lift' (DiscreteUniformity.relId_mem_uniformity α)
+  convert! Filter.mem_lift' (DiscreteUniformity.relId_mem_uniformity α)
   rw [hausdorffEntourage_id]
 
 end UniformSpace.hausdorff
@@ -372,8 +372,7 @@ theorem isClosed_subsets_of_isClosed {s : Set α} (hs : IsClosed s) :
   isClosed_induced hs.powerset_hausdorff
 
 theorem isClopen_singleton_bot : IsClopen {(⊥ : Closeds α)} := by
-  convert UniformSpace.hausdorff.isClopen_singleton_empty.preimage
-    uniformContinuous_coe.continuous
+  convert! UniformSpace.hausdorff.isClopen_singleton_empty.preimage uniformContinuous_coe.continuous
   ext; simp
 
 theorem totallyBounded_subsets_of_totallyBounded {t : Set α} (ht : TotallyBounded t) :
@@ -536,7 +535,7 @@ theorem isClosedEmbedding_toCloseds [T2Space α] [CompleteSpace α] :
     IsClosedEmbedding (toCloseds (α := α)) where
   __ := isEmbedding_toCloseds
   isClosed_range := by
-    convert Closeds.isClosed_setOf_totallyBounded
+    convert! Closeds.isClosed_setOf_totallyBounded
     exact subset_antisymm
       (Set.range_subset_iff.mpr fun K => K.isCompact.totallyBounded)
       (fun K hK => ⟨⟨K, hK.isCompact_of_isClosed K.isClosed⟩, rfl⟩)
diff --git a/Mathlib/Topology/UniformSpace/Defs.lean b/Mathlib/Topology/UniformSpace/Defs.lean
index 44edfa0e02df9f..f23cfccc9011c6 100644
--- a/Mathlib/Topology/UniformSpace/Defs.lean
+++ b/Mathlib/Topology/UniformSpace/Defs.lean
@@ -233,7 +233,7 @@ abbrev UniformSpace.toCore (u : UniformSpace α) : UniformSpace.Core α where
     have : Prod.mk x ⁻¹' U ∈ 𝓝 x := by
       rw [UniformSpace.nhds_eq_comap_uniformity]
       exact preimage_mem_comap hU
-    convert mem_of_mem_nhds this
+    convert! mem_of_mem_nhds this
 
 theorem UniformSpace.toCore_toTopologicalSpace (u : UniformSpace α) :
     u.toCore.toTopologicalSpace = u.toTopologicalSpace :=
diff --git a/Mathlib/Topology/UniformSpace/Equiv.lean b/Mathlib/Topology/UniformSpace/Equiv.lean
index 0ae62e96c881eb..a9ebab6a8e1bae 100644
--- a/Mathlib/Topology/UniformSpace/Equiv.lean
+++ b/Mathlib/Topology/UniformSpace/Equiv.lean
@@ -167,10 +167,10 @@ def changeInv (f : α ≃ᵤ β) (g : β → α) (hg : Function.RightInverse g f
       _ = f.symm x := by rw [hg x]
   { toFun := f
     invFun := g
-    left_inv := by convert f.left_inv
-    right_inv := by convert f.right_inv using 1
+    left_inv := by convert! f.left_inv
+    right_inv := by convert! f.right_inv using 1
     uniformContinuous_toFun := f.uniformContinuous
-    uniformContinuous_invFun := by convert f.symm.uniformContinuous }
+    uniformContinuous_invFun := by convert! f.symm.uniformContinuous }
 
 @[simp]
 theorem symm_comp_self (h : α ≃ᵤ β) : (h.symm : β → α) ∘ h = id :=
diff --git a/Mathlib/Topology/UniformSpace/ProdApproximation.lean b/Mathlib/Topology/UniformSpace/ProdApproximation.lean
index b347bae7450eac..9975b76d1389d5 100644
--- a/Mathlib/Topology/UniformSpace/ProdApproximation.lean
+++ b/Mathlib/Topology/UniformSpace/ProdApproximation.lean
@@ -47,7 +47,7 @@ lemma exists_finite_sum_smul_approximation_of_mem_uniformity [TopologicalSpace R
     f.curry (nhdsSet_diagonal_le_uniformity hS')
   refine ⟨n, fun i ↦ ⟨_, (U i).isClopen.continuous_indicator <| continuous_const (y := 1)⟩,
     v, fun x y ↦ ?_⟩
-  convert hv x y using 2
+  convert! hv x y using 2
   simp only [sum_apply]
   congr 1 with i
   by_cases hi : x ∈ U i <;> simp [hi]
diff --git a/Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean b/Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean
index dc707f93247aa6..3ed0b24930d838 100644
--- a/Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean
+++ b/Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean
@@ -1062,7 +1062,7 @@ protected def uniformEquivProdArrow [UniformSpace γ] :
       have H := @UniformOnFun.inf_eq α (β × γ) 𝔖
         (UniformSpace.comap Prod.fst ‹_›) (UniformSpace.comap Prod.snd ‹_›)
       apply_fun (fun u ↦ @uniformity (α →ᵤ[𝔖] β × γ) u) at H
-      convert H.symm using 1
+      convert! H.symm using 1
       rw [UniformOnFun.comap_eq, UniformOnFun.comap_eq]
       erw [inf_uniformity]
       rw [uniformity_comap, uniformity_comap]
diff --git a/Mathlib/Topology/VectorBundle/ContinuousAlternatingMap.lean b/Mathlib/Topology/VectorBundle/ContinuousAlternatingMap.lean
index f627a7ac332e8e..8a1fb98ff57e10 100644
--- a/Mathlib/Topology/VectorBundle/ContinuousAlternatingMap.lean
+++ b/Mathlib/Topology/VectorBundle/ContinuousAlternatingMap.lean
@@ -275,7 +275,7 @@ def vectorPrebundle :
     let L₂ : E₂ b ≃L[𝕜] F₂ :=
       (trivializationAt F₂ E₂ b).continuousLinearEquivAt 𝕜 b
         (mem_baseSet_trivializationAt _ _ _)
-    convert (L₁.continuousAlternatingMapCongr L₂).toHomeomorph.isInducing
+    convert! (L₁.continuousAlternatingMapCongr L₂).toHomeomorph.isInducing
     ext f
     simp [Trivialization.linearMapAt_def_of_mem _ (mem_baseSet_trivializationAt _ _ _), L₁, L₂]
 
diff --git a/Mathlib/Topology/VectorBundle/Hom.lean b/Mathlib/Topology/VectorBundle/Hom.lean
index 6ece0639b5037c..7daddac92db7b0 100644
--- a/Mathlib/Topology/VectorBundle/Hom.lean
+++ b/Mathlib/Topology/VectorBundle/Hom.lean
@@ -203,7 +203,7 @@ def Bundle.ContinuousLinearMap.vectorPrebundle :
         (mem_baseSet_trivializationAt _ _ _)
     let φ : (E₁ b →SL[σ] E₂ b) ≃L[𝕜₂] F₁ →SL[σ] F₂ := L₁.arrowCongrSL L₂
     have : IsInducing fun x ↦ (b, φ x) := isInducing_const_prod.mpr φ.toHomeomorph.isInducing
-    convert this
+    convert! this
     ext f
     dsimp [Pretrivialization.continuousLinearMap_apply]
     rw [Trivialization.linearMapAt_def_of_mem _ (mem_baseSet_trivializationAt _ _ _)]
diff --git a/Mathlib/Topology/VectorBundle/Riemannian.lean b/Mathlib/Topology/VectorBundle/Riemannian.lean
index ce32b6145ac055..084a49871a5ddc 100644
--- a/Mathlib/Topology/VectorBundle/Riemannian.lean
+++ b/Mathlib/Topology/VectorBundle/Riemannian.lean
@@ -78,7 +78,7 @@ instance : IsContinuousRiemannianBundle F₁ (Bundle.Trivial B F₁) := by
   intro x
   rw [FiberBundle.continuousAt_totalSpace]
   refine ⟨continuousAt_id, ?_⟩
-  convert continuousAt_const (y := innerSL ℝ)
+  convert! continuousAt_const (y := innerSL ℝ)
   ext v w
   simp [hom_trivializationAt_apply, inCoordinates]
 
@@ -188,7 +188,7 @@ lemma eventually_norm_symmL_trivializationAt_self_comp_lt (x : B) {r : ℝ} (hr
     rw [inCoordinates_apply_eq₂ h'y h'y (Set.mem_univ _)]
     have A : ((trivializationAt F E x).symm y)
        ((trivializationAt F E x).linearMapAt ℝ y v) = v := by
-      convert ((trivializationAt F E x).continuousLinearEquivAt ℝ _ h'y).symm_apply_apply v
+      convert! ((trivializationAt F E x).continuousLinearEquivAt ℝ _ h'y).symm_apply_apply v
       simp [Trivialization.coe_continuousLinearEquivAt_eq _ h'y]
     simp [A, w]
   have hgx : g x ((trivializationAt F E x).symm x w) ((trivializationAt F E x).symm x w) =
@@ -230,7 +230,7 @@ lemma eventually_norm_trivializationAt_lt (x : B) :
     have h'x : x ∈ (trivializationAt F E x).baseSet := FiberBundle.mem_baseSet_trivializationAt' x
     simp only [coe_comp', Trivialization.continuousLinearMapAt_apply, Trivialization.symmL_apply,
       Function.comp_apply, coe_id', id_eq]
-    convert ((trivializationAt F E x).continuousLinearEquivAt ℝ _ h'x).apply_symm_apply v
+    convert! ((trivializationAt F E x).continuousLinearEquivAt ℝ _ h'x).apply_symm_apply v
     simp [Trivialization.coe_continuousLinearEquivAt_eq _ h'x]
   have : (trivializationAt F E x).continuousLinearMapAt ℝ y =
     (ContinuousLinearMap.id _ _) ∘L ((trivializationAt F E x).continuousLinearMapAt ℝ y) := by simp
@@ -291,7 +291,7 @@ lemma eventually_norm_symmL_trivializationAt_comp_self_lt (x : B) {r : ℝ} (hr
     rw [inCoordinates_apply_eq₂ h'x h'x (Set.mem_univ _)]
     have A : ((trivializationAt F E x).symm x)
        ((trivializationAt F E x).linearMapAt ℝ x v) = v := by
-      convert ((trivializationAt F E x).continuousLinearEquivAt ℝ _ h'x).symm_apply_apply v
+      convert! ((trivializationAt F E x).continuousLinearEquivAt ℝ _ h'x).symm_apply_apply v
       simp [Trivialization.coe_continuousLinearEquivAt_eq _ h'x]
     simp [A, w]
   have hgy : g y ((trivializationAt F E x).symm y w) ((trivializationAt F E x).symm y w)
@@ -335,7 +335,7 @@ lemma eventually_norm_symmL_trivializationAt_lt (x : B) :
     have h'x : x ∈ (trivializationAt F E x).baseSet := FiberBundle.mem_baseSet_trivializationAt' x
     simp only [coe_comp', Trivialization.continuousLinearMapAt_apply, Trivialization.symmL_apply,
       Function.comp_apply, coe_id', id_eq]
-    convert ((trivializationAt F E x).continuousLinearEquivAt ℝ _ h'x).apply_symm_apply v
+    convert! ((trivializationAt F E x).continuousLinearEquivAt ℝ _ h'x).apply_symm_apply v
     simp [Trivialization.coe_continuousLinearEquivAt_eq _ h'x]
   have : (trivializationAt F E x).symmL ℝ y =
      ((trivializationAt F E x).symmL ℝ y) ∘L (ContinuousLinearMap.id _ _) := by simp