chore: kill some erws

Mathlib/Algebra/Category/ModuleCat/Presheaf/Limits.lean

@@ -79,8 +79,7 @@ noncomputable def limitPresheafOfModules : PresheafOfModules R where
     dsimp
     simp only [limMap_π, Functor.comp_obj, evaluation_obj, Functor.whiskerLeft_app,
       restriction_app, assoc]
-    -- Here we should rewrite using `Functor.assoc` but that gives a "motive is type-incorrect"
-    erw [preservesLimitIso_hom_π]
+    simp only [← Functor.assoc, preservesLimitIso_hom_π]
     rw [← ModuleCat.restrictScalarsId'App_inv_naturality, map_id,
       ModuleCat.restrictScalarsId'_inv_app]
     dsimp
@@ -92,18 +91,15 @@ noncomputable def limitPresheafOfModules : PresheafOfModules R where
     intro j
     simp only [Functor.comp_obj, evaluation_obj, limMap_π, Functor.whiskerLeft_app, restriction_app,
       map_comp, ModuleCat.restrictScalarsComp'_inv_app, Functor.map_comp, assoc]
-    -- Here we should rewrite using `Functor.assoc` but that gives a "motive is type-incorrect"
-    erw [preservesLimitIso_hom_π]
+    simp only [← Functor.assoc, preservesLimitIso_hom_π]
     rw [← ModuleCat.restrictScalarsComp'App_inv_naturality]
     dsimp
     rw [← Functor.map_comp_assoc, ← Functor.map_comp_assoc, assoc,
       preservesLimitIso_inv_π]
-    -- Here we should rewrite using `Functor.assoc` but that gives a "motive is type-incorrect"
-    erw [limMap_π]
+    rw [limMap_π]
     dsimp
     simp only [Functor.map_comp, assoc, preservesLimitIso_inv_π_assoc]
-    -- Here we should rewrite using `Functor.assoc` but that gives a "motive is type-incorrect"
-    erw [limMap_π_assoc]
+    rw [limMap_π_assoc]
     dsimp
 
 set_option backward.isDefEq.respectTransparency false in

Mathlib/Algebra/Homology/ShortComplex/SnakeLemma.lean

@@ -307,15 +307,11 @@ lemma L₀X₂ToP_comp_φ₁ : S.L₀X₂ToP ≫ S.φ₁ = 0 := by
 
 set_option backward.isDefEq.respectTransparency false in
 lemma L₀_g_δ : S.L₀.g ≫ S.δ = 0 := by
-  rw [← L₀X₂ToP_comp_pullback_snd, assoc]
-  erw [S.L₀'_exact.g_desc]
-  rw [L₀X₂ToP_comp_φ₁_assoc, zero_comp]
+  rw [← L₀X₂ToP_comp_pullback_snd, assoc, S.snd_δ, L₀X₂ToP_comp_φ₁_assoc, zero_comp]
 
 set_option backward.isDefEq.respectTransparency false in
 lemma δ_L₃_f : S.δ ≫ S.L₃.f = 0 := by
-  rw [← cancel_epi S.L₀'.g]
-  erw [S.L₀'_exact.g_desc_assoc]
-  simp [S.v₂₃.comm₁₂, φ₂]
+  simp [← cancel_epi S.L₀'.g, δ, S.v₂₃.comm₁₂, φ₂]
 
 /-- The short complex `L₀.X₂ ⟶ L₀.X₃ ⟶ L₃.X₁`. -/
 @[simps]

Mathlib/Algebra/Lie/Classical.lean

@@ -232,7 +232,8 @@ theorem soIndefiniteEquiv_apply {i : R} (hi : i * i = -1) (A : so' p q R) :
     (soIndefiniteEquiv p q R hi A : Matrix (p ⊕ q) (p ⊕ q) R) =
       (Pso p q R i)⁻¹ * (A : Matrix (p ⊕ q) (p ⊕ q) R) * Pso p q R i := by
   rw [soIndefiniteEquiv, LieEquiv.trans_apply, LieEquiv.ofEq_apply]
-  erw [skewAdjointMatricesLieSubalgebraEquiv_apply]
+  simp only [so']
+  rw [skewAdjointMatricesLieSubalgebraEquiv_apply]
 
 /-- A matrix defining a canonical even-rank symmetric bilinear form.
 

Mathlib/Analysis/InnerProductSpace/Projection/Basic.lean

@@ -71,7 +71,7 @@ instance HasOrthogonalProjection.map_linearIsometryEquiv [K.HasOrthogonalProject
   exists_orthogonal v := by
     rcases HasOrthogonalProjection.exists_orthogonal (K := K) (f.symm v) with ⟨w, hwK, hw⟩
     refine ⟨f w, Submodule.mem_map_of_mem hwK, Set.forall_mem_image.2 fun u hu ↦ ?_⟩
-    erw [← f.symm.inner_map_map, f.symm_apply_apply, map_sub, f.symm_apply_apply, hw u hu]
+    simp [← f.symm.inner_map_map, map_sub, hw u hu]
 
 instance HasOrthogonalProjection.map_linearIsometryEquiv' [K.HasOrthogonalProjection]
     {E' : Type*} [NormedAddCommGroup E'] [InnerProductSpace 𝕜 E'] (f : E ≃ₗᵢ[𝕜] E') :

Mathlib/LinearAlgebra/CliffordAlgebra/SpinGroup.lean

@@ -136,7 +136,7 @@ theorem conjAct_smul_range_ι {x : (CliffordAlgebra Q)ˣ} (hx : x ∈ lipschitzG
       refine Eq.trans_le ?_ this
       simp only [map_inv, smul_inv_smul]
   intro x hx
-  erw [Submodule.map_le_iff_le_comap]
+  rw [Submodule.pointwise_smul_def, Submodule.map_le_iff_le_comap]
   rintro _ ⟨m, rfl⟩
   exact conjAct_smul_ι_mem_range_ι hx _
 

Mathlib/Topology/Sheaves/SheafCondition/PairwiseIntersections.lean

@@ -371,7 +371,7 @@ def interUnionPullbackConeLift : s.pt ⟶ F.1.obj (op (U ⊔ V)) := by
 set_option backward.isDefEq.respectTransparency false in
 theorem interUnionPullbackConeLift_left :
     interUnionPullbackConeLift F U V s ≫ F.1.map (homOfLE le_sup_left).op = s.fst := by
-  erw [Category.assoc]
+  rw [interUnionPullbackConeLift, Category.assoc]
   simp_rw [← F.1.map_comp]
   exact
     (F.presheaf.isSheaf_iff_isSheafPairwiseIntersections.mp F.2 _).some.fac _ <|
@@ -380,7 +380,7 @@ theorem interUnionPullbackConeLift_left :
 set_option backward.isDefEq.respectTransparency false in
 theorem interUnionPullbackConeLift_right :
     interUnionPullbackConeLift F U V s ≫ F.1.map (homOfLE le_sup_right).op = s.snd := by
-  erw [Category.assoc]
+  rw [interUnionPullbackConeLift, Category.assoc]
   simp_rw [← F.1.map_comp]
   exact
     (F.presheaf.isSheaf_iff_isSheafPairwiseIntersections.mp F.2 _).some.fac _ <|
@@ -409,10 +409,10 @@ 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]
-    · erw [← F.1.map_comp]
+    · rw [Functor.mapCone_π_app, ← F.1.map_comp]
       convert h₁
       apply interUnionPullbackConeLift_left
-    · erw [← F.1.map_comp]
+    · rw [Functor.mapCone_π_app, ← F.1.map_comp]
       convert h₂
       apply interUnionPullbackConeLift_right
     all_goals