@@ -408,10 +408,11 @@ private theorem coeff_taylor_sub_eq (g : R[X])
408408 simp only [zero_add, Nat.choose_self, Nat.cast_one, one_mul,
409409 show 1 + (g.natDegree - 1 ) = g.natDegree from by omega,
410410 add_sub_cancel_left, leadingCoeff]
411- congr 1 ; push_cast; congr 1
411+ congr 1 ; congr 1
412412 rw [show g.natDegree = g.natDegree - 1 + 1 from by omega]
413413 simp [Nat.choose_succ_self_right]
414414
415+ set_option linter.unusedSectionVars false in
415416/-- `Q` applied to a polynomial of degree `< N` gives degree `≤ N - 2`. -/
416417private theorem natDegree_Q_of_bounded
417418 {Q : R[X] →ₗ[R] R[X]} {p : R[X]} {N : ℕ}
@@ -457,7 +458,7 @@ private theorem natDegree_delta_op_pow
457458 | n + 2 , _ =>
458459 set m := n + 2
459460 set g := Q (X ^ m)
460- by_contra hbig; push_neg at hbig
461+ by_contra hbig; push Not at hbig
461462 have hg_ne : g ≠ 0 :=
462463 ne_zero_of_natDegree_gt (by omega)
463464 have htf : IsAddTorsionFree R := instTorsionFree
@@ -528,11 +529,12 @@ private theorem natDegree_delta_op_pow
528529 omega
529530 rw [diff_eq] at hnd_lb; omega
530531
532+ set_option linter.unusedSectionVars false in
531533/-- Over a ℚ-algebra, `natDegree (taylor a p - p) ≤ natDegree p - 1`. -/
532534private theorem natDegree_taylor_sub_le (a : R) (p : R[X])
533535 (hp : 1 ≤ p.natDegree) :
534536 (taylor a p - p).natDegree ≤ p.natDegree - 1 := by
535- by_contra h; push_neg at h
537+ by_contra h; push Not at h
536538 have hbound : (taylor a p - p).natDegree ≤ p.natDegree :=
537539 (natDegree_sub_le _ _).trans
538540 (by rw [natDegree_taylor, max_self])
@@ -584,14 +586,13 @@ private theorem eval_determines (p : R[X])
584586private theorem sum_hasseDeriv_eq_zero
585587 {Q : R[X] →ₗ[R] R[X]}
586588 (hse : ∀ a : R, Q.comp (taylor a) = (taylor a).comp Q)
587- (hkc : ∀ r : R, Q (C r) = 0 )
589+ (_hkc : ∀ r : R, Q (C r) = 0 )
588590 {f : R[X]} (hQf : Q f = 0 ) :
589591 (range (f.natDegree + 1 )).sum
590592 (fun k => (Q (X ^ k)).eval 0 • hasseDeriv k f) =
591593 0 := by
592594 apply eval_determines; intro a
593- simp only [eval_finset_sum, eval_smul, smul_eq_mul,
594- eval_zero]
595+ simp only [eval_finsetSum, eval_smul, smul_eq_mul]
595596 have hQta : Q (taylor a f) = 0 := by
596597 have := congr_arg (· f) (hse a)
597598 simp only [LinearMap.comp_apply] at this
@@ -611,7 +612,7 @@ private theorem sum_hasseDeriv_eq_zero
611612 exact Q.map_smul _ _
612613 have h0 :=
613614 congr_arg (Polynomial.eval 0 ) (hdecomp ▸ hQta)
614- simp only [eval_finset_sum , eval_smul, smul_eq_mul,
615+ simp only [eval_finsetSum , eval_smul, smul_eq_mul,
615616 eval_zero] at h0
616617 convert h0 using 1 ; apply Finset.sum_congr rfl
617618 intro k _
@@ -744,13 +745,14 @@ private theorem taylor_basic_eq
744745 rw [hQ_lhs, hQ_rhs, ih]
745746 · -- D.eval 0 = 0
746747 rw [eval_sub, taylor_eval, zero_add,
747- sub_eq_zero, eval_finset_sum ]
748+ sub_eq_zero, eval_finsetSum ]
748749 rw [Finset.sum_eq_single_of_mem 0
749750 (Finset.mem_range.mpr (by omega))]
750751 · simp [hp.zero_one, Nat.choose_zero_right]
751752 · intro k _ hk
752753 simp [hp.normalized k (by omega : 0 < k)]
753754
755+ set_option linter.unusedSectionVars false in
754756/-- The composition `lmul' ∘ (id ⊗ aeval(C a)) ∘ Δ` equals `taylor a`
755757as algebra homs. -/
756758private theorem comul_taylor_bridge (a : R) :
@@ -766,6 +768,7 @@ private theorem comul_taylor_bridge (a : R) :
766768 Algebra.TensorProduct.lmul'_apply_tmul,
767769 taylor_X]
768770
771+ set_option linter.unusedSectionVars false in
769772/-- `aeval (C a) g = C (g.eval a)`. -/
770773private theorem aeval_C_eq_C_eval (a : R)
771774 (g : R[X]) :
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