data.polynomial.degree.lemmas | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

728baa2f

(last sync)

feat(archive/imo/imo2006_q5): IMO 2006 Q5 (#15613)

See module docstring for a thorough explanation of the proof.

Co-authored-by: Thomas Browning <tb65536@uw.edu>

Diff

@@ -327,6 +327,14 @@ begin
       ne_zero_of_nat_degree_gt (nat.pos_of_ne_zero q0), pow_ne_zero, ne.def, not_false_iff] }
 end
 
+@[simp] theorem nat_degree_iterate_comp (k : ℕ) :
+  (p.comp^[k] q).nat_degree = p.nat_degree ^ k * q.nat_degree :=
+begin
+  induction k with k IH,
+  { simp },
+  { rw [function.iterate_succ_apply', nat_degree_comp, IH, pow_succ, mul_assoc] }
+end
+
 lemma leading_coeff_comp (hq : nat_degree q ≠ 0) :
   leading_coeff (p.comp q) = leading_coeff p * leading_coeff q ^ nat_degree p :=
 by rw [← coeff_comp_degree_mul_degree hq, ← nat_degree_comp, coeff_nat_degree]

302eab4f

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

728baa2f

bump to nightly-2024-04-07-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

b03b8656

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2018 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
 -/
-import Data.Polynomial.Eval
+import Algebra.Polynomial.Eval
 
 #align_import data.polynomial.degree.lemmas from "leanprover-community/mathlib"@"728baa2f54e6062c5879a3e397ac6bac323e506f"

728baa2f

bump to nightly-2024-04-06-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

e34029c9

Diff

@@ -208,7 +208,7 @@ theorem coeff_pow_of_natDegree_le (pn : p.natDegree ≤ n) : (p ^ m).coeff (n *
   by
   induction' m with m hm
   · simp
-  · rw [pow_succ', pow_succ', ← hm, Nat.mul_succ, coeff_mul_of_nat_degree_le _ pn]
+  · rw [pow_succ, pow_succ, ← hm, Nat.mul_succ, coeff_mul_of_nat_degree_le _ pn]
     refine' nat_degree_pow_le.trans (le_trans _ (mul_comm _ _).le)
     exact mul_le_mul_of_nonneg_left pn m.zero_le
 #align polynomial.coeff_pow_of_nat_degree_le Polynomial.coeff_pow_of_natDegree_le
@@ -424,7 +424,7 @@ theorem natDegree_iterate_comp (k : ℕ) :
   by
   induction' k with k IH
   · simp
-  · rw [Function.iterate_succ_apply', nat_degree_comp, IH, pow_succ, mul_assoc]
+  · rw [Function.iterate_succ_apply', nat_degree_comp, IH, pow_succ', mul_assoc]
 #align polynomial.nat_degree_iterate_comp Polynomial.natDegree_iterate_comp
 -/

728baa2f

bump to nightly-2024-03-17-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

22f01ce4

Diff

@@ -69,8 +69,8 @@ theorem natDegree_comp_le : natDegree (p.comp q) ≤ natDegree p * natDegree q :
 theorem degree_pos_of_root {p : R[X]} (hp : p ≠ 0) (h : IsRoot p a) : 0 < degree p :=
   lt_of_not_ge fun hlt => by
     have := eq_C_of_degree_le_zero hlt
-    rw [is_root, this, eval_C] at h 
-    simp only [h, RingHom.map_zero] at this 
+    rw [is_root, this, eval_C] at h
+    simp only [h, RingHom.map_zero] at this
     exact hp this
 #align polynomial.degree_pos_of_root Polynomial.degree_pos_of_root
 -/
@@ -241,7 +241,7 @@ theorem degree_sum_eq_of_disjoint (f : S → R[X]) (s : Finset S)
     · rcases s.eq_empty_or_nonempty with (rfl | hs)
       · simp
       obtain ⟨y, hy, hy'⟩ := Finset.exists_mem_eq_sup s hs fun i => degree (f i)
-      rw [IH, hy'] at H 
+      rw [IH, hy'] at H
       by_cases hx0 : f x = 0
       · simp [hx0, IH]
       have hy0 : f y ≠ 0 := by
@@ -283,7 +283,7 @@ theorem natDegree_sum_eq_of_disjoint (f : S → R[X]) (s : Finset S)
           simpa [hb', degree_eq_bot] using hx'
         exact ⟨b, hb, (degree_eq_nat_degree hb').ge⟩
     · exact h.imp fun x y hxy hxy' => hxy (nat_degree_eq_of_degree_eq hxy')
-  · push_neg at H 
+  · push_neg at H
     rw [Finset.sum_eq_zero H, nat_degree_zero, eq_comm, show 0 = ⊥ from rfl, Finset.sup_eq_bot_iff]
     intro x hx
     simp [H x hx]
@@ -310,8 +310,8 @@ theorem natDegree_pos_of_eval₂_root {p : R[X]} (hp : p ≠ 0) (f : R →+* S)
   lt_of_not_ge fun hlt =>
     by
     have A : p = C (p.coeff 0) := eq_C_of_nat_degree_le_zero hlt
-    rw [A, eval₂_C] at hz 
-    simp only [inj (p.coeff 0) hz, RingHom.map_zero] at A 
+    rw [A, eval₂_C] at hz
+    simp only [inj (p.coeff 0) hz, RingHom.map_zero] at A
     exact hp A
 #align polynomial.nat_degree_pos_of_eval₂_root Polynomial.natDegree_pos_of_eval₂_root
 -/
@@ -350,7 +350,7 @@ theorem natDegree_sub : (p - q).natDegree = (q - p).natDegree := by rw [← nat_
 theorem natDegree_sub_le_iff_left (qn : q.natDegree ≤ n) :
     (p - q).natDegree ≤ n ↔ p.natDegree ≤ n :=
   by
-  rw [← nat_degree_neg] at qn 
+  rw [← nat_degree_neg] at qn
   rw [sub_eq_add_neg, nat_degree_add_le_iff_left _ _ qn]
 #align polynomial.nat_degree_sub_le_iff_left Polynomial.natDegree_sub_le_iff_left
 -/
@@ -364,7 +364,7 @@ theorem natDegree_sub_le_iff_right (pn : p.natDegree ≤ n) :
 #print Polynomial.coeff_sub_eq_left_of_lt /-
 theorem coeff_sub_eq_left_of_lt (dg : q.natDegree < n) : (p - q).coeff n = p.coeff n :=
   by
-  rw [← nat_degree_neg] at dg 
+  rw [← nat_degree_neg] at dg
   rw [sub_eq_add_neg, coeff_add_eq_left_of_lt dg]
 #align polynomial.coeff_sub_eq_left_of_lt Polynomial.coeff_sub_eq_left_of_lt
 -/

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bump to nightly-2023-12-20-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

058cd493

Diff

@@ -54,7 +54,7 @@ theorem natDegree_comp_le : natDegree (p.comp q) ≤ natDegree p * natDegree q :
               _ ≤ natDegree (C (coeff p n)) + n • degree q :=
                 (add_le_add degree_le_natDegree (degree_pow_le _ _))
               _ ≤ natDegree (C (coeff p n)) + n • natDegree q :=
-                (add_le_add_left (nsmul_le_nsmul_of_le_right (@degree_le_natDegree _ _ q) n) _)
+                (add_le_add_left (nsmul_le_nsmul_right (@degree_le_natDegree _ _ q) n) _)
               _ = (n * natDegree q : ℕ) := by
                 rw [nat_degree_C, WithBot.coe_zero, zero_add, ← WithBot.coe_nsmul, nsmul_eq_mul] <;>
                   simp

728baa2f

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2018 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
 -/
-import Mathbin.Data.Polynomial.Eval
+import Data.Polynomial.Eval
 
 #align_import data.polynomial.degree.lemmas from "leanprover-community/mathlib"@"728baa2f54e6062c5879a3e397ac6bac323e506f"

728baa2f

bump to nightly-2023-08-17-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

60285dcc

Diff

@@ -393,9 +393,9 @@ theorem degree_C_mul (a0 : a ≠ 0) : (C a * p).degree = p.degree := by
 #align polynomial.degree_C_mul Polynomial.degree_C_mul
 -/
 
-theorem natDegree_mul_c (a0 : a ≠ 0) : (p * C a).natDegree = p.natDegree := by
+theorem natDegree_hMul_c (a0 : a ≠ 0) : (p * C a).natDegree = p.natDegree := by
   simp only [nat_degree, degree_mul_C a0]
-#align polynomial.nat_degree_mul_C Polynomial.natDegree_mul_c
+#align polynomial.nat_degree_mul_C Polynomial.natDegree_hMul_c
 
 #print Polynomial.natDegree_C_mul /-
 theorem natDegree_C_mul (a0 : a ≠ 0) : (C a * p).natDegree = p.natDegree := by

728baa2f

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2018 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-
-! This file was ported from Lean 3 source module data.polynomial.degree.lemmas
-! leanprover-community/mathlib commit 728baa2f54e6062c5879a3e397ac6bac323e506f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Polynomial.Eval
 
+#align_import data.polynomial.degree.lemmas from "leanprover-community/mathlib"@"728baa2f54e6062c5879a3e397ac6bac323e506f"
+
 /-!
 # Theory of degrees of polynomials

728baa2f

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -78,9 +78,11 @@ theorem degree_pos_of_root {p : R[X]} (hp : p ≠ 0) (h : IsRoot p a) : 0 < degr
 #align polynomial.degree_pos_of_root Polynomial.degree_pos_of_root
 -/
 
+#print Polynomial.natDegree_le_iff_coeff_eq_zero /-
 theorem natDegree_le_iff_coeff_eq_zero : p.natDegree ≤ n ↔ ∀ N : ℕ, n < N → p.coeff N = 0 := by
   simp_rw [nat_degree_le_iff_degree_le, degree_le_iff_coeff_zero, WithBot.coe_lt_coe]
 #align polynomial.nat_degree_le_iff_coeff_eq_zero Polynomial.natDegree_le_iff_coeff_eq_zero
+-/
 
 #print Polynomial.natDegree_add_le_iff_left /-
 theorem natDegree_add_le_iff_left {n : ℕ} (p q : R[X]) (qn : q.natDegree ≤ n) :
@@ -102,19 +104,23 @@ theorem natDegree_add_le_iff_right {n : ℕ} (p q : R[X]) (pn : p.natDegree ≤
 #align polynomial.nat_degree_add_le_iff_right Polynomial.natDegree_add_le_iff_right
 -/
 
+#print Polynomial.natDegree_C_mul_le /-
 theorem natDegree_C_mul_le (a : R) (f : R[X]) : (C a * f).natDegree ≤ f.natDegree :=
   calc
     (C a * f).natDegree ≤ (C a).natDegree + f.natDegree := natDegree_mul_le
     _ = 0 + f.natDegree := by rw [nat_degree_C a]
     _ = f.natDegree := zero_add _
 #align polynomial.nat_degree_C_mul_le Polynomial.natDegree_C_mul_le
+-/
 
+#print Polynomial.natDegree_mul_C_le /-
 theorem natDegree_mul_C_le (f : R[X]) (a : R) : (f * C a).natDegree ≤ f.natDegree :=
   calc
     (f * C a).natDegree ≤ f.natDegree + (C a).natDegree := natDegree_mul_le
     _ = f.natDegree + 0 := by rw [nat_degree_C a]
     _ = f.natDegree := add_zero _
 #align polynomial.nat_degree_mul_C_le Polynomial.natDegree_mul_C_le
+-/
 
 #print Polynomial.eq_natDegree_of_le_mem_support /-
 theorem eq_natDegree_of_le_mem_support (pn : p.natDegree ≤ n) (ns : n ∈ p.support) :
@@ -123,6 +129,7 @@ theorem eq_natDegree_of_le_mem_support (pn : p.natDegree ≤ n) (ns : n ∈ p.su
 #align polynomial.eq_nat_degree_of_le_mem_support Polynomial.eq_natDegree_of_le_mem_support
 -/
 
+#print Polynomial.natDegree_C_mul_eq_of_mul_eq_one /-
 theorem natDegree_C_mul_eq_of_mul_eq_one {ai : R} (au : ai * a = 1) :
     (C a * p).natDegree = p.natDegree :=
   le_antisymm (natDegree_C_mul_le a p)
@@ -131,7 +138,9 @@ theorem natDegree_C_mul_eq_of_mul_eq_one {ai : R} (au : ai * a = 1) :
       _ = (C ai * (C a * p)).natDegree := by rw [← C_1, ← au, RingHom.map_mul, ← mul_assoc]
       _ ≤ (C a * p).natDegree := natDegree_C_mul_le ai (C a * p))
 #align polynomial.nat_degree_C_mul_eq_of_mul_eq_one Polynomial.natDegree_C_mul_eq_of_mul_eq_one
+-/
 
+#print Polynomial.natDegree_mul_C_eq_of_mul_eq_one /-
 theorem natDegree_mul_C_eq_of_mul_eq_one {ai : R} (au : a * ai = 1) :
     (p * C a).natDegree = p.natDegree :=
   le_antisymm (natDegree_mul_C_le p a)
@@ -140,7 +149,9 @@ theorem natDegree_mul_C_eq_of_mul_eq_one {ai : R} (au : a * ai = 1) :
       _ = (p * C a * C ai).natDegree := by rw [← C_1, ← au, RingHom.map_mul, ← mul_assoc]
       _ ≤ (p * C a).natDegree := natDegree_mul_C_le (p * C a) ai)
 #align polynomial.nat_degree_mul_C_eq_of_mul_eq_one Polynomial.natDegree_mul_C_eq_of_mul_eq_one
+-/
 
+#print Polynomial.natDegree_mul_C_eq_of_mul_ne_zero /-
 /-- Although not explicitly stated, the assumptions of lemma `nat_degree_mul_C_eq_of_mul_ne_zero`
 force the polynomial `p` to be non-zero, via `p.leading_coeff ≠ 0`.
 -/
@@ -151,7 +162,9 @@ theorem natDegree_mul_C_eq_of_mul_ne_zero (h : p.leadingCoeff * a ≠ 0) :
   refine' mem_support_iff.mpr _
   rwa [coeff_mul_C]
 #align polynomial.nat_degree_mul_C_eq_of_mul_ne_zero Polynomial.natDegree_mul_C_eq_of_mul_ne_zero
+-/
 
+#print Polynomial.natDegree_C_mul_eq_of_mul_ne_zero /-
 /-- Although not explicitly stated, the assumptions of lemma `nat_degree_C_mul_eq_of_mul_ne_zero`
 force the polynomial `p` to be non-zero, via `p.leading_coeff ≠ 0`.
 -/
@@ -162,17 +175,23 @@ theorem natDegree_C_mul_eq_of_mul_ne_zero (h : a * p.leadingCoeff ≠ 0) :
   refine' mem_support_iff.mpr _
   rwa [coeff_C_mul]
 #align polynomial.nat_degree_C_mul_eq_of_mul_ne_zero Polynomial.natDegree_C_mul_eq_of_mul_ne_zero
+-/
 
+#print Polynomial.natDegree_add_coeff_mul /-
 theorem natDegree_add_coeff_mul (f g : R[X]) :
     (f * g).coeff (f.natDegree + g.natDegree) = f.coeff f.natDegree * g.coeff g.natDegree := by
   simp only [coeff_nat_degree, coeff_mul_degree_add_degree]
 #align polynomial.nat_degree_add_coeff_mul Polynomial.natDegree_add_coeff_mul
+-/
 
+#print Polynomial.natDegree_lt_coeff_mul /-
 theorem natDegree_lt_coeff_mul (h : p.natDegree + q.natDegree < m + n) :
     (p * q).coeff (m + n) = 0 :=
   coeff_eq_zero_of_natDegree_lt (natDegree_mul_le.trans_lt h)
 #align polynomial.nat_degree_lt_coeff_mul Polynomial.natDegree_lt_coeff_mul
+-/
 
+#print Polynomial.coeff_mul_of_natDegree_le /-
 theorem coeff_mul_of_natDegree_le (pm : p.natDegree ≤ m) (qn : q.natDegree ≤ n) :
     (p * q).coeff (m + n) = p.coeff m * q.coeff n :=
   by
@@ -185,6 +204,7 @@ theorem coeff_mul_of_natDegree_le (pm : p.natDegree ≤ m) (qn : q.natDegree ≤
   · rw [coeff_eq_zero_of_nat_degree_lt hn, MulZeroClass.mul_zero]
     exact nat_degree_lt_coeff_mul (add_lt_add hm hn)
 #align polynomial.coeff_mul_of_nat_degree_le Polynomial.coeff_mul_of_natDegree_le
+-/
 
 #print Polynomial.coeff_pow_of_natDegree_le /-
 theorem coeff_pow_of_natDegree_le (pn : p.natDegree ≤ n) : (p ^ m).coeff (n * m) = p.coeff n ^ m :=
@@ -287,6 +307,7 @@ theorem natDegree_bit1 (a : R[X]) : (bit1 a).natDegree ≤ a.natDegree :=
 
 variable [Semiring S]
 
+#print Polynomial.natDegree_pos_of_eval₂_root /-
 theorem natDegree_pos_of_eval₂_root {p : R[X]} (hp : p ≠ 0) (f : R →+* S) {z : S}
     (hz : eval₂ f z p = 0) (inj : ∀ x : R, f x = 0 → x = 0) : 0 < natDegree p :=
   lt_of_not_ge fun hlt =>
@@ -296,11 +317,14 @@ theorem natDegree_pos_of_eval₂_root {p : R[X]} (hp : p ≠ 0) (f : R →+* S)
     simp only [inj (p.coeff 0) hz, RingHom.map_zero] at A 
     exact hp A
 #align polynomial.nat_degree_pos_of_eval₂_root Polynomial.natDegree_pos_of_eval₂_root
+-/
 
+#print Polynomial.degree_pos_of_eval₂_root /-
 theorem degree_pos_of_eval₂_root {p : R[X]} (hp : p ≠ 0) (f : R →+* S) {z : S}
     (hz : eval₂ f z p = 0) (inj : ∀ x : R, f x = 0 → x = 0) : 0 < degree p :=
   natDegree_pos_iff_degree_pos.mp (natDegree_pos_of_eval₂_root hp f hz inj)
 #align polynomial.degree_pos_of_eval₂_root Polynomial.degree_pos_of_eval₂_root
+-/
 
 #print Polynomial.coe_lt_degree /-
 @[simp]
@@ -348,9 +372,11 @@ theorem coeff_sub_eq_left_of_lt (dg : q.natDegree < n) : (p - q).coeff n = p.coe
 #align polynomial.coeff_sub_eq_left_of_lt Polynomial.coeff_sub_eq_left_of_lt
 -/
 
+#print Polynomial.coeff_sub_eq_neg_right_of_lt /-
 theorem coeff_sub_eq_neg_right_of_lt (df : p.natDegree < n) : (p - q).coeff n = -q.coeff n := by
   rwa [sub_eq_add_neg, coeff_add_eq_right_of_lt, coeff_neg]
 #align polynomial.coeff_sub_eq_neg_right_of_lt Polynomial.coeff_sub_eq_neg_right_of_lt
+-/
 
 end Ring
 
@@ -358,22 +384,29 @@ section NoZeroDivisors
 
 variable [Semiring R] [NoZeroDivisors R] {p q : R[X]}
 
+#print Polynomial.degree_mul_C /-
 theorem degree_mul_C (a0 : a ≠ 0) : (p * C a).degree = p.degree := by
   rw [degree_mul, degree_C a0, add_zero]
 #align polynomial.degree_mul_C Polynomial.degree_mul_C
+-/
 
+#print Polynomial.degree_C_mul /-
 theorem degree_C_mul (a0 : a ≠ 0) : (C a * p).degree = p.degree := by
   rw [degree_mul, degree_C a0, zero_add]
 #align polynomial.degree_C_mul Polynomial.degree_C_mul
+-/
 
 theorem natDegree_mul_c (a0 : a ≠ 0) : (p * C a).natDegree = p.natDegree := by
   simp only [nat_degree, degree_mul_C a0]
 #align polynomial.nat_degree_mul_C Polynomial.natDegree_mul_c
 
+#print Polynomial.natDegree_C_mul /-
 theorem natDegree_C_mul (a0 : a ≠ 0) : (C a * p).natDegree = p.natDegree := by
   simp only [nat_degree, degree_C_mul a0]
 #align polynomial.nat_degree_C_mul Polynomial.natDegree_C_mul
+-/
 
+#print Polynomial.natDegree_comp /-
 theorem natDegree_comp : natDegree (p.comp q) = natDegree p * natDegree q :=
   by
   by_cases q0 : q.nat_degree = 0
@@ -385,7 +418,9 @@ theorem natDegree_comp : natDegree (p.comp q) = natDegree p * natDegree q :=
     simp only [coeff_comp_degree_mul_degree q0, p0, mul_eq_zero, leading_coeff_eq_zero, or_self_iff,
       ne_zero_of_nat_degree_gt (Nat.pos_of_ne_zero q0), pow_ne_zero, Ne.def, not_false_iff]
 #align polynomial.nat_degree_comp Polynomial.natDegree_comp
+-/
 
+#print Polynomial.natDegree_iterate_comp /-
 @[simp]
 theorem natDegree_iterate_comp (k : ℕ) :
     ((p.comp^[k]) q).natDegree = p.natDegree ^ k * q.natDegree :=
@@ -394,11 +429,14 @@ theorem natDegree_iterate_comp (k : ℕ) :
   · simp
   · rw [Function.iterate_succ_apply', nat_degree_comp, IH, pow_succ, mul_assoc]
 #align polynomial.nat_degree_iterate_comp Polynomial.natDegree_iterate_comp
+-/
 
+#print Polynomial.leadingCoeff_comp /-
 theorem leadingCoeff_comp (hq : natDegree q ≠ 0) :
     leadingCoeff (p.comp q) = leadingCoeff p * leadingCoeff q ^ natDegree p := by
   rw [← coeff_comp_degree_mul_degree hq, ← nat_degree_comp, coeff_nat_degree]
 #align polynomial.leading_coeff_comp Polynomial.leadingCoeff_comp
+-/
 
 end NoZeroDivisors

728baa2f

bump to nightly-2023-06-09-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

16afdc39

Diff

@@ -65,8 +65,6 @@ theorem natDegree_comp_le : natDegree (p.comp q) ≤ natDegree p * natDegree q :
                 WithBot.coe_le_coe.2 <|
                   mul_le_mul_of_nonneg_right (le_natDegree_of_ne_zero (mem_support_iff.1 hn))
                     (Nat.zero_le _)
-              
-        
 #align polynomial.nat_degree_comp_le Polynomial.natDegree_comp_le
 -/
 
@@ -109,7 +107,6 @@ theorem natDegree_C_mul_le (a : R) (f : R[X]) : (C a * f).natDegree ≤ f.natDeg
     (C a * f).natDegree ≤ (C a).natDegree + f.natDegree := natDegree_mul_le
     _ = 0 + f.natDegree := by rw [nat_degree_C a]
     _ = f.natDegree := zero_add _
-    
 #align polynomial.nat_degree_C_mul_le Polynomial.natDegree_C_mul_le
 
 theorem natDegree_mul_C_le (f : R[X]) (a : R) : (f * C a).natDegree ≤ f.natDegree :=
@@ -117,7 +114,6 @@ theorem natDegree_mul_C_le (f : R[X]) (a : R) : (f * C a).natDegree ≤ f.natDeg
     (f * C a).natDegree ≤ f.natDegree + (C a).natDegree := natDegree_mul_le
     _ = f.natDegree + 0 := by rw [nat_degree_C a]
     _ = f.natDegree := add_zero _
-    
 #align polynomial.nat_degree_mul_C_le Polynomial.natDegree_mul_C_le
 
 #print Polynomial.eq_natDegree_of_le_mem_support /-
@@ -133,8 +129,7 @@ theorem natDegree_C_mul_eq_of_mul_eq_one {ai : R} (au : ai * a = 1) :
     (calc
       p.natDegree = (1 * p).natDegree := by nth_rw 1 [← one_mul p]
       _ = (C ai * (C a * p)).natDegree := by rw [← C_1, ← au, RingHom.map_mul, ← mul_assoc]
-      _ ≤ (C a * p).natDegree := natDegree_C_mul_le ai (C a * p)
-      )
+      _ ≤ (C a * p).natDegree := natDegree_C_mul_le ai (C a * p))
 #align polynomial.nat_degree_C_mul_eq_of_mul_eq_one Polynomial.natDegree_C_mul_eq_of_mul_eq_one
 
 theorem natDegree_mul_C_eq_of_mul_eq_one {ai : R} (au : a * ai = 1) :
@@ -143,8 +138,7 @@ theorem natDegree_mul_C_eq_of_mul_eq_one {ai : R} (au : a * ai = 1) :
     (calc
       p.natDegree = (p * 1).natDegree := by nth_rw 1 [← mul_one p]
       _ = (p * C a * C ai).natDegree := by rw [← C_1, ← au, RingHom.map_mul, ← mul_assoc]
-      _ ≤ (p * C a).natDegree := natDegree_mul_C_le (p * C a) ai
-      )
+      _ ≤ (p * C a).natDegree := natDegree_mul_C_le (p * C a) ai)
 #align polynomial.nat_degree_mul_C_eq_of_mul_eq_one Polynomial.natDegree_mul_C_eq_of_mul_eq_one
 
 /-- Although not explicitly stated, the assumptions of lemma `nat_degree_mul_C_eq_of_mul_ne_zero`

728baa2f

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -218,7 +218,7 @@ theorem coeff_add_eq_right_of_lt (pn : p.natDegree < n) : (p + q).coeff n = q.co
 
 #print Polynomial.degree_sum_eq_of_disjoint /-
 theorem degree_sum_eq_of_disjoint (f : S → R[X]) (s : Finset S)
-    (h : Set.Pairwise { i | i ∈ s ∧ f i ≠ 0 } (Ne on degree ∘ f)) :
+    (h : Set.Pairwise {i | i ∈ s ∧ f i ≠ 0} (Ne on degree ∘ f)) :
     degree (s.Sum f) = s.sup fun i => degree (f i) :=
   by
   induction' s using Finset.induction_on with x s hx IH
@@ -246,7 +246,7 @@ theorem degree_sum_eq_of_disjoint (f : S → R[X]) (s : Finset S)
 
 #print Polynomial.natDegree_sum_eq_of_disjoint /-
 theorem natDegree_sum_eq_of_disjoint (f : S → R[X]) (s : Finset S)
-    (h : Set.Pairwise { i | i ∈ s ∧ f i ≠ 0 } (Ne on natDegree ∘ f)) :
+    (h : Set.Pairwise {i | i ∈ s ∧ f i ≠ 0} (Ne on natDegree ∘ f)) :
     natDegree (s.Sum f) = s.sup fun i => natDegree (f i) :=
   by
   by_cases H : ∃ x ∈ s, f x ≠ 0
@@ -272,7 +272,7 @@ theorem natDegree_sum_eq_of_disjoint (f : S → R[X]) (s : Finset S)
           simpa [hb', degree_eq_bot] using hx'
         exact ⟨b, hb, (degree_eq_nat_degree hb').ge⟩
     · exact h.imp fun x y hxy hxy' => hxy (nat_degree_eq_of_degree_eq hxy')
-  · push_neg  at H 
+  · push_neg at H 
     rw [Finset.sum_eq_zero H, nat_degree_zero, eq_comm, show 0 = ⊥ from rfl, Finset.sup_eq_bot_iff]
     intro x hx
     simp [H x hx]

728baa2f

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -74,8 +74,8 @@ theorem natDegree_comp_le : natDegree (p.comp q) ≤ natDegree p * natDegree q :
 theorem degree_pos_of_root {p : R[X]} (hp : p ≠ 0) (h : IsRoot p a) : 0 < degree p :=
   lt_of_not_ge fun hlt => by
     have := eq_C_of_degree_le_zero hlt
-    rw [is_root, this, eval_C] at h
-    simp only [h, RingHom.map_zero] at this
+    rw [is_root, this, eval_C] at h 
+    simp only [h, RingHom.map_zero] at this 
     exact hp this
 #align polynomial.degree_pos_of_root Polynomial.degree_pos_of_root
 -/
@@ -230,7 +230,7 @@ theorem degree_sum_eq_of_disjoint (f : S → R[X]) (s : Finset S)
     · rcases s.eq_empty_or_nonempty with (rfl | hs)
       · simp
       obtain ⟨y, hy, hy'⟩ := Finset.exists_mem_eq_sup s hs fun i => degree (f i)
-      rw [IH, hy'] at H
+      rw [IH, hy'] at H 
       by_cases hx0 : f x = 0
       · simp [hx0, IH]
       have hy0 : f y ≠ 0 := by
@@ -272,7 +272,7 @@ theorem natDegree_sum_eq_of_disjoint (f : S → R[X]) (s : Finset S)
           simpa [hb', degree_eq_bot] using hx'
         exact ⟨b, hb, (degree_eq_nat_degree hb').ge⟩
     · exact h.imp fun x y hxy hxy' => hxy (nat_degree_eq_of_degree_eq hxy')
-  · push_neg  at H
+  · push_neg  at H 
     rw [Finset.sum_eq_zero H, nat_degree_zero, eq_comm, show 0 = ⊥ from rfl, Finset.sup_eq_bot_iff]
     intro x hx
     simp [H x hx]
@@ -298,8 +298,8 @@ theorem natDegree_pos_of_eval₂_root {p : R[X]} (hp : p ≠ 0) (f : R →+* S)
   lt_of_not_ge fun hlt =>
     by
     have A : p = C (p.coeff 0) := eq_C_of_nat_degree_le_zero hlt
-    rw [A, eval₂_C] at hz
-    simp only [inj (p.coeff 0) hz, RingHom.map_zero] at A
+    rw [A, eval₂_C] at hz 
+    simp only [inj (p.coeff 0) hz, RingHom.map_zero] at A 
     exact hp A
 #align polynomial.nat_degree_pos_of_eval₂_root Polynomial.natDegree_pos_of_eval₂_root
 
@@ -335,7 +335,7 @@ theorem natDegree_sub : (p - q).natDegree = (q - p).natDegree := by rw [← nat_
 theorem natDegree_sub_le_iff_left (qn : q.natDegree ≤ n) :
     (p - q).natDegree ≤ n ↔ p.natDegree ≤ n :=
   by
-  rw [← nat_degree_neg] at qn
+  rw [← nat_degree_neg] at qn 
   rw [sub_eq_add_neg, nat_degree_add_le_iff_left _ _ qn]
 #align polynomial.nat_degree_sub_le_iff_left Polynomial.natDegree_sub_le_iff_left
 -/
@@ -349,7 +349,7 @@ theorem natDegree_sub_le_iff_right (pn : p.natDegree ≤ n) :
 #print Polynomial.coeff_sub_eq_left_of_lt /-
 theorem coeff_sub_eq_left_of_lt (dg : q.natDegree < n) : (p - q).coeff n = p.coeff n :=
   by
-  rw [← nat_degree_neg] at dg
+  rw [← nat_degree_neg] at dg 
   rw [sub_eq_add_neg, coeff_add_eq_left_of_lt dg]
 #align polynomial.coeff_sub_eq_left_of_lt Polynomial.coeff_sub_eq_left_of_lt
 -/

728baa2f

bump to nightly-2023-05-28-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

8d353152

Diff

@@ -24,7 +24,7 @@ Some of the main results include
 
 noncomputable section
 
-open Classical Polynomial
+open scoped Classical Polynomial
 
 open Finsupp Finset
 
@@ -70,6 +70,7 @@ theorem natDegree_comp_le : natDegree (p.comp q) ≤ natDegree p * natDegree q :
 #align polynomial.nat_degree_comp_le Polynomial.natDegree_comp_le
 -/
 
+#print Polynomial.degree_pos_of_root /-
 theorem degree_pos_of_root {p : R[X]} (hp : p ≠ 0) (h : IsRoot p a) : 0 < degree p :=
   lt_of_not_ge fun hlt => by
     have := eq_C_of_degree_le_zero hlt
@@ -77,6 +78,7 @@ theorem degree_pos_of_root {p : R[X]} (hp : p ≠ 0) (h : IsRoot p a) : 0 < degr
     simp only [h, RingHom.map_zero] at this
     exact hp this
 #align polynomial.degree_pos_of_root Polynomial.degree_pos_of_root
+-/
 
 theorem natDegree_le_iff_coeff_eq_zero : p.natDegree ≤ n ↔ ∀ N : ℕ, n < N → p.coeff N = 0 := by
   simp_rw [nat_degree_le_iff_degree_le, degree_le_iff_coeff_zero, WithBot.coe_lt_coe]
@@ -306,6 +308,7 @@ theorem degree_pos_of_eval₂_root {p : R[X]} (hp : p ≠ 0) (f : R →+* S) {z
   natDegree_pos_iff_degree_pos.mp (natDegree_pos_of_eval₂_root hp f hz inj)
 #align polynomial.degree_pos_of_eval₂_root Polynomial.degree_pos_of_eval₂_root
 
+#print Polynomial.coe_lt_degree /-
 @[simp]
 theorem coe_lt_degree {p : R[X]} {n : ℕ} : (n : WithBot ℕ) < degree p ↔ n < natDegree p :=
   by
@@ -313,6 +316,7 @@ theorem coe_lt_degree {p : R[X]} {n : ℕ} : (n : WithBot ℕ) < degree p ↔ n
   · simp [h]
   rw [degree_eq_nat_degree h, WithBot.coe_lt_coe]
 #align polynomial.coe_lt_degree Polynomial.coe_lt_degree
+-/
 
 end Degree

728baa2f

bump to nightly-2023-05-28-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

ba5d8b97

Diff

@@ -70,12 +70,6 @@ theorem natDegree_comp_le : natDegree (p.comp q) ≤ natDegree p * natDegree q :
 #align polynomial.nat_degree_comp_le Polynomial.natDegree_comp_le
 -/
 
-/- warning: polynomial.degree_pos_of_root -> Polynomial.degree_pos_of_root is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align polynomial.degree_pos_of_root Polynomial.degree_pos_of_rootₓ'. -/
 theorem degree_pos_of_root {p : R[X]} (hp : p ≠ 0) (h : IsRoot p a) : 0 < degree p :=
   lt_of_not_ge fun hlt => by
     have := eq_C_of_degree_le_zero hlt
@@ -84,12 +78,6 @@ theorem degree_pos_of_root {p : R[X]} (hp : p ≠ 0) (h : IsRoot p a) : 0 < degr
     exact hp this
 #align polynomial.degree_pos_of_root Polynomial.degree_pos_of_root
 
-/- warning: polynomial.nat_degree_le_iff_coeff_eq_zero -> Polynomial.natDegree_le_iff_coeff_eq_zero is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_le_iff_coeff_eq_zero Polynomial.natDegree_le_iff_coeff_eq_zeroₓ'. -/
 theorem natDegree_le_iff_coeff_eq_zero : p.natDegree ≤ n ↔ ∀ N : ℕ, n < N → p.coeff N = 0 := by
   simp_rw [nat_degree_le_iff_degree_le, degree_le_iff_coeff_zero, WithBot.coe_lt_coe]
 #align polynomial.nat_degree_le_iff_coeff_eq_zero Polynomial.natDegree_le_iff_coeff_eq_zero
@@ -114,12 +102,6 @@ theorem natDegree_add_le_iff_right {n : ℕ} (p q : R[X]) (pn : p.natDegree ≤
 #align polynomial.nat_degree_add_le_iff_right Polynomial.natDegree_add_le_iff_right
 -/
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_C_mul_le Polynomial.natDegree_C_mul_leₓ'. -/
 theorem natDegree_C_mul_le (a : R) (f : R[X]) : (C a * f).natDegree ≤ f.natDegree :=
   calc
     (C a * f).natDegree ≤ (C a).natDegree + f.natDegree := natDegree_mul_le
@@ -128,12 +110,6 @@ theorem natDegree_C_mul_le (a : R) (f : R[X]) : (C a * f).natDegree ≤ f.natDeg
     
 #align polynomial.nat_degree_C_mul_le Polynomial.natDegree_C_mul_le
 
-/- warning: polynomial.nat_degree_mul_C_le -> Polynomial.natDegree_mul_C_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_mul_C_le Polynomial.natDegree_mul_C_leₓ'. -/
 theorem natDegree_mul_C_le (f : R[X]) (a : R) : (f * C a).natDegree ≤ f.natDegree :=
   calc
     (f * C a).natDegree ≤ f.natDegree + (C a).natDegree := natDegree_mul_le
@@ -149,12 +125,6 @@ theorem eq_natDegree_of_le_mem_support (pn : p.natDegree ≤ n) (ns : n ∈ p.su
 #align polynomial.eq_nat_degree_of_le_mem_support Polynomial.eq_natDegree_of_le_mem_support
 -/
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_C_mul_eq_of_mul_eq_one Polynomial.natDegree_C_mul_eq_of_mul_eq_oneₓ'. -/
 theorem natDegree_C_mul_eq_of_mul_eq_one {ai : R} (au : ai * a = 1) :
     (C a * p).natDegree = p.natDegree :=
   le_antisymm (natDegree_C_mul_le a p)
@@ -165,12 +135,6 @@ theorem natDegree_C_mul_eq_of_mul_eq_one {ai : R} (au : ai * a = 1) :
       )
 #align polynomial.nat_degree_C_mul_eq_of_mul_eq_one Polynomial.natDegree_C_mul_eq_of_mul_eq_one
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_mul_C_eq_of_mul_eq_one Polynomial.natDegree_mul_C_eq_of_mul_eq_oneₓ'. -/
 theorem natDegree_mul_C_eq_of_mul_eq_one {ai : R} (au : a * ai = 1) :
     (p * C a).natDegree = p.natDegree :=
   le_antisymm (natDegree_mul_C_le p a)
@@ -181,12 +145,6 @@ theorem natDegree_mul_C_eq_of_mul_eq_one {ai : R} (au : a * ai = 1) :
       )
 #align polynomial.nat_degree_mul_C_eq_of_mul_eq_one Polynomial.natDegree_mul_C_eq_of_mul_eq_one
 
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 /-- Although not explicitly stated, the assumptions of lemma `nat_degree_mul_C_eq_of_mul_ne_zero`
 force the polynomial `p` to be non-zero, via `p.leading_coeff ≠ 0`.
 -/
@@ -198,12 +156,6 @@ theorem natDegree_mul_C_eq_of_mul_ne_zero (h : p.leadingCoeff * a ≠ 0) :
   rwa [coeff_mul_C]
 #align polynomial.nat_degree_mul_C_eq_of_mul_ne_zero Polynomial.natDegree_mul_C_eq_of_mul_ne_zero
 
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 /-- Although not explicitly stated, the assumptions of lemma `nat_degree_C_mul_eq_of_mul_ne_zero`
 force the polynomial `p` to be non-zero, via `p.leading_coeff ≠ 0`.
 -/
@@ -215,34 +167,16 @@ theorem natDegree_C_mul_eq_of_mul_ne_zero (h : a * p.leadingCoeff ≠ 0) :
   rwa [coeff_C_mul]
 #align polynomial.nat_degree_C_mul_eq_of_mul_ne_zero Polynomial.natDegree_C_mul_eq_of_mul_ne_zero
 
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 theorem natDegree_add_coeff_mul (f g : R[X]) :
     (f * g).coeff (f.natDegree + g.natDegree) = f.coeff f.natDegree * g.coeff g.natDegree := by
   simp only [coeff_nat_degree, coeff_mul_degree_add_degree]
 #align polynomial.nat_degree_add_coeff_mul Polynomial.natDegree_add_coeff_mul
 
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 theorem natDegree_lt_coeff_mul (h : p.natDegree + q.natDegree < m + n) :
     (p * q).coeff (m + n) = 0 :=
   coeff_eq_zero_of_natDegree_lt (natDegree_mul_le.trans_lt h)
 #align polynomial.nat_degree_lt_coeff_mul Polynomial.natDegree_lt_coeff_mul
 
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 theorem coeff_mul_of_natDegree_le (pm : p.natDegree ≤ m) (qn : q.natDegree ≤ n) :
     (p * q).coeff (m + n) = p.coeff m * q.coeff n :=
   by
@@ -357,12 +291,6 @@ theorem natDegree_bit1 (a : R[X]) : (bit1 a).natDegree ≤ a.natDegree :=
 
 variable [Semiring S]
 
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 theorem natDegree_pos_of_eval₂_root {p : R[X]} (hp : p ≠ 0) (f : R →+* S) {z : S}
     (hz : eval₂ f z p = 0) (inj : ∀ x : R, f x = 0 → x = 0) : 0 < natDegree p :=
   lt_of_not_ge fun hlt =>
@@ -373,23 +301,11 @@ theorem natDegree_pos_of_eval₂_root {p : R[X]} (hp : p ≠ 0) (f : R →+* S)
     exact hp A
 #align polynomial.nat_degree_pos_of_eval₂_root Polynomial.natDegree_pos_of_eval₂_root
 
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 theorem degree_pos_of_eval₂_root {p : R[X]} (hp : p ≠ 0) (f : R →+* S) {z : S}
     (hz : eval₂ f z p = 0) (inj : ∀ x : R, f x = 0 → x = 0) : 0 < degree p :=
   natDegree_pos_iff_degree_pos.mp (natDegree_pos_of_eval₂_root hp f hz inj)
 #align polynomial.degree_pos_of_eval₂_root Polynomial.degree_pos_of_eval₂_root
 
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 @[simp]
 theorem coe_lt_degree {p : R[X]} {n : ℕ} : (n : WithBot ℕ) < degree p ↔ n < natDegree p :=
   by
@@ -434,12 +350,6 @@ theorem coeff_sub_eq_left_of_lt (dg : q.natDegree < n) : (p - q).coeff n = p.coe
 #align polynomial.coeff_sub_eq_left_of_lt Polynomial.coeff_sub_eq_left_of_lt
 -/
 
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 theorem coeff_sub_eq_neg_right_of_lt (df : p.natDegree < n) : (p - q).coeff n = -q.coeff n := by
   rwa [sub_eq_add_neg, coeff_add_eq_right_of_lt, coeff_neg]
 #align polynomial.coeff_sub_eq_neg_right_of_lt Polynomial.coeff_sub_eq_neg_right_of_lt
@@ -450,22 +360,10 @@ section NoZeroDivisors
 
 variable [Semiring R] [NoZeroDivisors R] {p q : R[X]}
 
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 theorem degree_mul_C (a0 : a ≠ 0) : (p * C a).degree = p.degree := by
   rw [degree_mul, degree_C a0, add_zero]
 #align polynomial.degree_mul_C Polynomial.degree_mul_C
 
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 theorem degree_C_mul (a0 : a ≠ 0) : (C a * p).degree = p.degree := by
   rw [degree_mul, degree_C a0, zero_add]
 #align polynomial.degree_C_mul Polynomial.degree_C_mul
@@ -474,22 +372,10 @@ theorem natDegree_mul_c (a0 : a ≠ 0) : (p * C a).natDegree = p.natDegree := by
   simp only [nat_degree, degree_mul_C a0]
 #align polynomial.nat_degree_mul_C Polynomial.natDegree_mul_c
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_C_mul Polynomial.natDegree_C_mulₓ'. -/
 theorem natDegree_C_mul (a0 : a ≠ 0) : (C a * p).natDegree = p.natDegree := by
   simp only [nat_degree, degree_C_mul a0]
 #align polynomial.nat_degree_C_mul Polynomial.natDegree_C_mul
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_comp Polynomial.natDegree_compₓ'. -/
 theorem natDegree_comp : natDegree (p.comp q) = natDegree p * natDegree q :=
   by
   by_cases q0 : q.nat_degree = 0
@@ -502,12 +388,6 @@ theorem natDegree_comp : natDegree (p.comp q) = natDegree p * natDegree q :=
       ne_zero_of_nat_degree_gt (Nat.pos_of_ne_zero q0), pow_ne_zero, Ne.def, not_false_iff]
 #align polynomial.nat_degree_comp Polynomial.natDegree_comp
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_iterate_comp Polynomial.natDegree_iterate_compₓ'. -/
 @[simp]
 theorem natDegree_iterate_comp (k : ℕ) :
     ((p.comp^[k]) q).natDegree = p.natDegree ^ k * q.natDegree :=
@@ -517,12 +397,6 @@ theorem natDegree_iterate_comp (k : ℕ) :
   · rw [Function.iterate_succ_apply', nat_degree_comp, IH, pow_succ, mul_assoc]
 #align polynomial.nat_degree_iterate_comp Polynomial.natDegree_iterate_comp
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_comp Polynomial.leadingCoeff_compₓ'. -/
 theorem leadingCoeff_comp (hq : natDegree q ≠ 0) :
     leadingCoeff (p.comp q) = leadingCoeff p * leadingCoeff q ^ natDegree p := by
   rw [← coeff_comp_degree_mul_degree hq, ← nat_degree_comp, coeff_nat_degree]

728baa2f

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -275,10 +275,8 @@ theorem coeff_add_eq_left_of_lt (qn : q.natDegree < n) : (p + q).coeff n = p.coe
 -/
 
 #print Polynomial.coeff_add_eq_right_of_lt /-
-theorem coeff_add_eq_right_of_lt (pn : p.natDegree < n) : (p + q).coeff n = q.coeff n :=
-  by
-  rw [add_comm]
-  exact coeff_add_eq_left_of_lt pn
+theorem coeff_add_eq_right_of_lt (pn : p.natDegree < n) : (p + q).coeff n = q.coeff n := by
+  rw [add_comm]; exact coeff_add_eq_left_of_lt pn
 #align polynomial.coeff_add_eq_right_of_lt Polynomial.coeff_add_eq_right_of_lt
 -/
 
@@ -498,8 +496,7 @@ theorem natDegree_comp : natDegree (p.comp q) = natDegree p * natDegree q :=
   ·
     rw [degree_le_zero_iff.mp (nat_degree_eq_zero_iff_degree_le_zero.mp q0), comp_C, nat_degree_C,
       nat_degree_C, MulZeroClass.mul_zero]
-  · by_cases p0 : p = 0
-    · simp only [p0, zero_comp, nat_degree_zero, MulZeroClass.zero_mul]
+  · by_cases p0 : p = 0; · simp only [p0, zero_comp, nat_degree_zero, MulZeroClass.zero_mul]
     refine' le_antisymm nat_degree_comp_le (le_nat_degree_of_ne_zero _)
     simp only [coeff_comp_degree_mul_degree q0, p0, mul_eq_zero, leading_coeff_eq_zero, or_self_iff,
       ne_zero_of_nat_degree_gt (Nat.pos_of_ne_zero q0), pow_ne_zero, Ne.def, not_false_iff]

728baa2f

bump to nightly-2023-05-19-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

a31df521

Diff

@@ -118,7 +118,7 @@ theorem natDegree_add_le_iff_right {n : ℕ} (p q : R[X]) (pn : p.natDegree ≤
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   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R) (f : Polynomial.{u1} R _inst_1), LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) f)) (Polynomial.natDegree.{u1} R _inst_1 f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R) (f : Polynomial.{u1} R _inst_1), LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) f)) (Polynomial.natDegree.{u1} R _inst_1 f)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R) (f : Polynomial.{u1} R _inst_1), LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) f)) (Polynomial.natDegree.{u1} R _inst_1 f)
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_C_mul_le Polynomial.natDegree_C_mul_leₓ'. -/
 theorem natDegree_C_mul_le (a : R) (f : R[X]) : (C a * f).natDegree ≤ f.natDegree :=
   calc
@@ -132,7 +132,7 @@ theorem natDegree_C_mul_le (a : R) (f : R[X]) : (C a * f).natDegree ≤ f.natDeg
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1) (a : R), LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.natDegree.{u1} R _inst_1 f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1) (a : R), LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.natDegree.{u1} R _inst_1 f)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1) (a : R), LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.natDegree.{u1} R _inst_1 f)
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_mul_C_le Polynomial.natDegree_mul_C_leₓ'. -/
 theorem natDegree_mul_C_le (f : R[X]) (a : R) : (f * C a).natDegree ≤ f.natDegree :=
   calc
@@ -153,7 +153,7 @@ theorem eq_natDegree_of_le_mem_support (pn : p.natDegree ≤ n) (ns : n ∈ p.su
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {ai : R}, (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) ai a) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {ai : R}, (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) ai a) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {ai : R}, (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) ai a) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_C_mul_eq_of_mul_eq_one Polynomial.natDegree_C_mul_eq_of_mul_eq_oneₓ'. -/
 theorem natDegree_C_mul_eq_of_mul_eq_one {ai : R} (au : ai * a = 1) :
     (C a * p).natDegree = p.natDegree :=
@@ -169,7 +169,7 @@ theorem natDegree_C_mul_eq_of_mul_eq_one {ai : R} (au : ai * a = 1) :
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {ai : R}, (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a ai) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.natDegree.{u1} R _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {ai : R}, (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a ai) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.natDegree.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {ai : R}, (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a ai) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.natDegree.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_mul_C_eq_of_mul_eq_one Polynomial.natDegree_mul_C_eq_of_mul_eq_oneₓ'. -/
 theorem natDegree_mul_C_eq_of_mul_eq_one {ai : R} (au : a * ai = 1) :
     (p * C a).natDegree = p.natDegree :=
@@ -185,7 +185,7 @@ theorem natDegree_mul_C_eq_of_mul_eq_one {ai : R} (au : a * ai = 1) :
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Polynomial.leadingCoeff.{u1} R _inst_1 p) a) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.natDegree.{u1} R _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Polynomial.leadingCoeff.{u1} R _inst_1 p) a) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.natDegree.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Polynomial.leadingCoeff.{u1} R _inst_1 p) a) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.natDegree.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_mul_C_eq_of_mul_ne_zero Polynomial.natDegree_mul_C_eq_of_mul_ne_zeroₓ'. -/
 /-- Although not explicitly stated, the assumptions of lemma `nat_degree_mul_C_eq_of_mul_ne_zero`
 force the polynomial `p` to be non-zero, via `p.leading_coeff ≠ 0`.
@@ -202,7 +202,7 @@ theorem natDegree_mul_C_eq_of_mul_ne_zero (h : p.leadingCoeff * a ≠ 0) :
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_C_mul_eq_of_mul_ne_zero Polynomial.natDegree_C_mul_eq_of_mul_ne_zeroₓ'. -/
 /-- Although not explicitly stated, the assumptions of lemma `nat_degree_C_mul_eq_of_mul_ne_zero`
 force the polynomial `p` to be non-zero, via `p.leading_coeff ≠ 0`.
@@ -363,7 +363,7 @@ variable [Semiring S]
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) -> (forall (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) {z : S}, (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f z p) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (forall (x : R), (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f x) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) -> (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (Polynomial.natDegree.{u1} R _inst_1 p)))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) -> (forall (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) {z : S}, (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f z p) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) -> (forall (x : R), (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2))))) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) -> (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (Polynomial.natDegree.{u1} R _inst_1 p)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) -> (forall (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) {z : S}, (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f z p) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) -> (forall (x : R), (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) _inst_2))))) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) -> (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (Polynomial.natDegree.{u1} R _inst_1 p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_pos_of_eval₂_root Polynomial.natDegree_pos_of_eval₂_rootₓ'. -/
 theorem natDegree_pos_of_eval₂_root {p : R[X]} (hp : p ≠ 0) (f : R →+* S) {z : S}
     (hz : eval₂ f z p = 0) (inj : ∀ x : R, f x = 0 → x = 0) : 0 < natDegree p :=
@@ -379,7 +379,7 @@ theorem natDegree_pos_of_eval₂_root {p : R[X]} (hp : p ≠ 0) (f : R →+* S)
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) -> (forall (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) {z : S}, (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f z p) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (forall (x : R), (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f x) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R _inst_1 p)))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) -> (forall (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) {z : S}, (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f z p) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) -> (forall (x : R), (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2))))) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u1} R _inst_1 p)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) -> (forall (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) {z : S}, (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f z p) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) -> (forall (x : R), (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) _inst_2))))) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u1} R _inst_1 p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_pos_of_eval₂_root Polynomial.degree_pos_of_eval₂_rootₓ'. -/
 theorem degree_pos_of_eval₂_root {p : R[X]} (hp : p ≠ 0) (f : R →+* S) {z : S}
     (hz : eval₂ f z p = 0) (inj : ∀ x : R, f x = 0 → x = 0) : 0 < degree p :=
@@ -456,7 +456,7 @@ variable [Semiring R] [NoZeroDivisors R] {p q : R[X]}
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.degree.{u1} R _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.degree.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.degree.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_mul_C Polynomial.degree_mul_Cₓ'. -/
 theorem degree_mul_C (a0 : a ≠ 0) : (p * C a).degree = p.degree := by
   rw [degree_mul, degree_C a0, add_zero]
@@ -466,7 +466,7 @@ theorem degree_mul_C (a0 : a ≠ 0) : (p * C a).degree = p.degree := by
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.degree.{u1} R _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.degree.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.degree.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_C_mul Polynomial.degree_C_mulₓ'. -/
 theorem degree_C_mul (a0 : a ≠ 0) : (C a * p).degree = p.degree := by
   rw [degree_mul, degree_C a0, zero_add]
@@ -480,7 +480,7 @@ theorem natDegree_mul_c (a0 : a ≠ 0) : (p * C a).natDegree = p.natDegree := by
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_C_mul Polynomial.natDegree_C_mulₓ'. -/
 theorem natDegree_C_mul (a0 : a ≠ 0) : (C a * p).natDegree = p.natDegree := by
   simp only [nat_degree, degree_C_mul a0]

728baa2f

bump to nightly-2023-05-16-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

9cb92e8c

Diff

@@ -70,7 +70,12 @@ theorem natDegree_comp_le : natDegree (p.comp q) ≤ natDegree p * natDegree q :
 #align polynomial.nat_degree_comp_le Polynomial.natDegree_comp_le
 -/
 
-#print Polynomial.degree_pos_of_root /-
+/- warning: polynomial.degree_pos_of_root -> Polynomial.degree_pos_of_root is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) -> (Polynomial.IsRoot.{u1} R _inst_1 p a) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R _inst_1 p))
+but is expected to have type
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) -> (Polynomial.IsRoot.{u1} R _inst_1 p a) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u1} R _inst_1 p))
+Case conversion may be inaccurate. Consider using '#align polynomial.degree_pos_of_root Polynomial.degree_pos_of_rootₓ'. -/
 theorem degree_pos_of_root {p : R[X]} (hp : p ≠ 0) (h : IsRoot p a) : 0 < degree p :=
   lt_of_not_ge fun hlt => by
     have := eq_C_of_degree_le_zero hlt
@@ -78,7 +83,6 @@ theorem degree_pos_of_root {p : R[X]} (hp : p ≠ 0) (h : IsRoot p a) : 0 < degr
     simp only [h, RingHom.map_zero] at this
     exact hp this
 #align polynomial.degree_pos_of_root Polynomial.degree_pos_of_root
--/
 
 /- warning: polynomial.nat_degree_le_iff_coeff_eq_zero -> Polynomial.natDegree_le_iff_coeff_eq_zero is a dubious translation:
 lean 3 declaration is
@@ -373,7 +377,7 @@ theorem natDegree_pos_of_eval₂_root {p : R[X]} (hp : p ≠ 0) (f : R →+* S)
 
 /- warning: polynomial.degree_pos_of_eval₂_root -> Polynomial.degree_pos_of_eval₂_root is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) -> (forall (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) {z : S}, (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f z p) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (forall (x : R), (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f x) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R _inst_1 p)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) -> (forall (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) {z : S}, (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f z p) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (forall (x : R), (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f x) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R _inst_1 p)))
 but is expected to have type
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) -> (forall (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) {z : S}, (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f z p) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) -> (forall (x : R), (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2))))) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u1} R _inst_1 p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_pos_of_eval₂_root Polynomial.degree_pos_of_eval₂_rootₓ'. -/
@@ -382,7 +386,12 @@ theorem degree_pos_of_eval₂_root {p : R[X]} (hp : p ≠ 0) (f : R →+* S) {z
   natDegree_pos_iff_degree_pos.mp (natDegree_pos_of_eval₂_root hp f hz inj)
 #align polynomial.degree_pos_of_eval₂_root Polynomial.degree_pos_of_eval₂_root
 
-#print Polynomial.coe_lt_degree /-
+/- warning: polynomial.coe_lt_degree -> Polynomial.coe_lt_degree is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {n : Nat}, Iff (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) n) (Polynomial.degree.{u1} R _inst_1 p)) (LT.lt.{0} Nat Nat.hasLt n (Polynomial.natDegree.{u1} R _inst_1 p))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {n : Nat}, Iff (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) n) (Polynomial.degree.{u1} R _inst_1 p)) (LT.lt.{0} Nat instLTNat n (Polynomial.natDegree.{u1} R _inst_1 p))
+Case conversion may be inaccurate. Consider using '#align polynomial.coe_lt_degree Polynomial.coe_lt_degreeₓ'. -/
 @[simp]
 theorem coe_lt_degree {p : R[X]} {n : ℕ} : (n : WithBot ℕ) < degree p ↔ n < natDegree p :=
   by
@@ -390,7 +399,6 @@ theorem coe_lt_degree {p : R[X]} {n : ℕ} : (n : WithBot ℕ) < degree p ↔ n
   · simp [h]
   rw [degree_eq_nat_degree h, WithBot.coe_lt_coe]
 #align polynomial.coe_lt_degree Polynomial.coe_lt_degree
--/
 
 end Degree

728baa2f

bump to nightly-2023-04-01-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/172bf2812857f5e56938cc148b7a539f52f84ca9

bfc4190c

Diff

@@ -177,39 +177,39 @@ theorem natDegree_mul_C_eq_of_mul_eq_one {ai : R} (au : a * ai = 1) :
       )
 #align polynomial.nat_degree_mul_C_eq_of_mul_eq_one Polynomial.natDegree_mul_C_eq_of_mul_eq_one
 
-/- warning: polynomial.nat_degree_mul_C_eq_of_mul_ne_zero -> Polynomial.natDegree_mul_c_eq_of_mul_ne_zero is a dubious translation:
+/- warning: polynomial.nat_degree_mul_C_eq_of_mul_ne_zero -> Polynomial.natDegree_mul_C_eq_of_mul_ne_zero is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Polynomial.leadingCoeff.{u1} R _inst_1 p) a) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.natDegree.{u1} R _inst_1 p))
 but is expected to have type
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Polynomial.leadingCoeff.{u1} R _inst_1 p) a) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.natDegree.{u1} R _inst_1 p))
-Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_mul_C_eq_of_mul_ne_zero Polynomial.natDegree_mul_c_eq_of_mul_ne_zeroₓ'. -/
+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_mul_C_eq_of_mul_ne_zero Polynomial.natDegree_mul_C_eq_of_mul_ne_zeroₓ'. -/
 /-- Although not explicitly stated, the assumptions of lemma `nat_degree_mul_C_eq_of_mul_ne_zero`
 force the polynomial `p` to be non-zero, via `p.leading_coeff ≠ 0`.
 -/
-theorem natDegree_mul_c_eq_of_mul_ne_zero (h : p.leadingCoeff * a ≠ 0) :
+theorem natDegree_mul_C_eq_of_mul_ne_zero (h : p.leadingCoeff * a ≠ 0) :
     (p * C a).natDegree = p.natDegree :=
   by
   refine' eq_nat_degree_of_le_mem_support (nat_degree_mul_C_le p a) _
   refine' mem_support_iff.mpr _
   rwa [coeff_mul_C]
-#align polynomial.nat_degree_mul_C_eq_of_mul_ne_zero Polynomial.natDegree_mul_c_eq_of_mul_ne_zero
+#align polynomial.nat_degree_mul_C_eq_of_mul_ne_zero Polynomial.natDegree_mul_C_eq_of_mul_ne_zero
 
-/- warning: polynomial.nat_degree_C_mul_eq_of_mul_ne_zero -> Polynomial.natDegree_c_mul_eq_of_mul_ne_zero is a dubious translation:
+/- warning: polynomial.nat_degree_C_mul_eq_of_mul_ne_zero -> Polynomial.natDegree_C_mul_eq_of_mul_ne_zero is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
 but is expected to have type
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
-Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_C_mul_eq_of_mul_ne_zero Polynomial.natDegree_c_mul_eq_of_mul_ne_zeroₓ'. -/
+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_C_mul_eq_of_mul_ne_zero Polynomial.natDegree_C_mul_eq_of_mul_ne_zeroₓ'. -/
 /-- Although not explicitly stated, the assumptions of lemma `nat_degree_C_mul_eq_of_mul_ne_zero`
 force the polynomial `p` to be non-zero, via `p.leading_coeff ≠ 0`.
 -/
-theorem natDegree_c_mul_eq_of_mul_ne_zero (h : a * p.leadingCoeff ≠ 0) :
+theorem natDegree_C_mul_eq_of_mul_ne_zero (h : a * p.leadingCoeff ≠ 0) :
     (C a * p).natDegree = p.natDegree :=
   by
   refine' eq_nat_degree_of_le_mem_support (nat_degree_C_mul_le a p) _
   refine' mem_support_iff.mpr _
   rwa [coeff_C_mul]
-#align polynomial.nat_degree_C_mul_eq_of_mul_ne_zero Polynomial.natDegree_c_mul_eq_of_mul_ne_zero
+#align polynomial.nat_degree_C_mul_eq_of_mul_ne_zero Polynomial.natDegree_C_mul_eq_of_mul_ne_zero
 
 /- warning: polynomial.nat_degree_add_coeff_mul -> Polynomial.natDegree_add_coeff_mul is a dubious translation:
 lean 3 declaration is

728baa2f

bump to nightly-2023-03-29-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/0148d455199ed64bf8eb2f493a1e7eb9211ce170

335439ff

Diff

@@ -497,6 +497,12 @@ theorem natDegree_comp : natDegree (p.comp q) = natDegree p * natDegree q :=
       ne_zero_of_nat_degree_gt (Nat.pos_of_ne_zero q0), pow_ne_zero, Ne.def, not_false_iff]
 #align polynomial.nat_degree_comp Polynomial.natDegree_comp
 
+/- warning: polynomial.nat_degree_iterate_comp -> Polynomial.natDegree_iterate_comp is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1} (k : Nat), Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (Nat.iterate.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p) k q)) (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat Nat.hasMul) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (Polynomial.natDegree.{u1} R _inst_1 p) k) (Polynomial.natDegree.{u1} R _inst_1 q))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1} (k : Nat), Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (Nat.iterate.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p) k q)) (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat instMulNat) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (Polynomial.natDegree.{u1} R _inst_1 p) k) (Polynomial.natDegree.{u1} R _inst_1 q))
+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_iterate_comp Polynomial.natDegree_iterate_compₓ'. -/
 @[simp]
 theorem natDegree_iterate_comp (k : ℕ) :
     ((p.comp^[k]) q).natDegree = p.natDegree ^ k * q.natDegree :=

728baa2f

bump to nightly-2023-03-28-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/728baa2f54e6062c5879a3e397ac6bac323e506f

869495ce

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
 
 ! This file was ported from Lean 3 source module data.polynomial.degree.lemmas
-! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
+! leanprover-community/mathlib commit 728baa2f54e6062c5879a3e397ac6bac323e506f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -497,6 +497,15 @@ theorem natDegree_comp : natDegree (p.comp q) = natDegree p * natDegree q :=
       ne_zero_of_nat_degree_gt (Nat.pos_of_ne_zero q0), pow_ne_zero, Ne.def, not_false_iff]
 #align polynomial.nat_degree_comp Polynomial.natDegree_comp
 
+@[simp]
+theorem natDegree_iterate_comp (k : ℕ) :
+    ((p.comp^[k]) q).natDegree = p.natDegree ^ k * q.natDegree :=
+  by
+  induction' k with k IH
+  · simp
+  · rw [Function.iterate_succ_apply', nat_degree_comp, IH, pow_succ, mul_assoc]
+#align polynomial.nat_degree_iterate_comp Polynomial.natDegree_iterate_comp
+
 /- warning: polynomial.leading_coeff_comp -> Polynomial.leadingCoeff_comp is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Ne.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 q) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R _inst_1 (Polynomial.comp.{u1} R _inst_1 p q)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Polynomial.leadingCoeff.{u1} R _inst_1 p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (Polynomial.leadingCoeff.{u1} R _inst_1 q) (Polynomial.natDegree.{u1} R _inst_1 p))))

69c6a5a1

bump to nightly-2023-03-27-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1

0e4ebd8c

Diff

@@ -430,7 +430,7 @@ theorem coeff_sub_eq_left_of_lt (dg : q.natDegree < n) : (p - q).coeff n = p.coe
 
 /- warning: polynomial.coeff_sub_eq_neg_right_of_lt -> Polynomial.coeff_sub_eq_neg_right_of_lt is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {n : Nat} [_inst_1 : Ring.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, (LT.lt.{0} Nat Nat.hasLt (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p) n) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.sub.{u1} R _inst_1)) p q) n) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) q n)))
+  forall {R : Type.{u1}} {n : Nat} [_inst_1 : Ring.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, (LT.lt.{0} Nat Nat.hasLt (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p) n) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.sub.{u1} R _inst_1)) p q) n) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) q n)))
 but is expected to have type
   forall {R : Type.{u1}} {n : Nat} [_inst_1 : Ring.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p) n) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.sub.{u1} R _inst_1)) p q) n) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) q n)))
 Case conversion may be inaccurate. Consider using '#align polynomial.coeff_sub_eq_neg_right_of_lt Polynomial.coeff_sub_eq_neg_right_of_ltₓ'. -/

69c6a5a1

bump to nightly-2023-03-14-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2

d4b38a42

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
 
 ! This file was ported from Lean 3 source module data.polynomial.degree.lemmas
-! leanprover-community/mathlib commit 302eab4f46abb63de520828de78c04cb0f9b5836
+! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Data.Polynomial.Eval
 /-!
 # Theory of degrees of polynomials
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Some of the main results include
 - `nat_degree_comp_le` : The degree of the composition is at most the product of degrees

302eab4f

bump to nightly-2023-03-11-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

a8ee822f

Diff

@@ -111,7 +111,7 @@ theorem natDegree_add_le_iff_right {n : ℕ} (p q : R[X]) (pn : p.natDegree ≤
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R) (f : Polynomial.{u1} R _inst_1), LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) f)) (Polynomial.natDegree.{u1} R _inst_1 f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R) (f : Polynomial.{u1} R _inst_1), LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) f)) (Polynomial.natDegree.{u1} R _inst_1 f)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R) (f : Polynomial.{u1} R _inst_1), LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) f)) (Polynomial.natDegree.{u1} R _inst_1 f)
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_C_mul_le Polynomial.natDegree_C_mul_leₓ'. -/
 theorem natDegree_C_mul_le (a : R) (f : R[X]) : (C a * f).natDegree ≤ f.natDegree :=
   calc
@@ -125,7 +125,7 @@ theorem natDegree_C_mul_le (a : R) (f : R[X]) : (C a * f).natDegree ≤ f.natDeg
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1) (a : R), LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.natDegree.{u1} R _inst_1 f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1) (a : R), LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.natDegree.{u1} R _inst_1 f)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1) (a : R), LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.natDegree.{u1} R _inst_1 f)
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_mul_C_le Polynomial.natDegree_mul_C_leₓ'. -/
 theorem natDegree_mul_C_le (f : R[X]) (a : R) : (f * C a).natDegree ≤ f.natDegree :=
   calc
@@ -146,7 +146,7 @@ theorem eq_natDegree_of_le_mem_support (pn : p.natDegree ≤ n) (ns : n ∈ p.su
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {ai : R}, (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) ai a) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {ai : R}, (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) ai a) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {ai : R}, (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) ai a) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_C_mul_eq_of_mul_eq_one Polynomial.natDegree_C_mul_eq_of_mul_eq_oneₓ'. -/
 theorem natDegree_C_mul_eq_of_mul_eq_one {ai : R} (au : ai * a = 1) :
     (C a * p).natDegree = p.natDegree :=
@@ -162,7 +162,7 @@ theorem natDegree_C_mul_eq_of_mul_eq_one {ai : R} (au : ai * a = 1) :
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {ai : R}, (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a ai) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.natDegree.{u1} R _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {ai : R}, (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a ai) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.natDegree.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {ai : R}, (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a ai) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.natDegree.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_mul_C_eq_of_mul_eq_one Polynomial.natDegree_mul_C_eq_of_mul_eq_oneₓ'. -/
 theorem natDegree_mul_C_eq_of_mul_eq_one {ai : R} (au : a * ai = 1) :
     (p * C a).natDegree = p.natDegree :=
@@ -178,7 +178,7 @@ theorem natDegree_mul_C_eq_of_mul_eq_one {ai : R} (au : a * ai = 1) :
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Polynomial.leadingCoeff.{u1} R _inst_1 p) a) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.natDegree.{u1} R _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Polynomial.leadingCoeff.{u1} R _inst_1 p) a) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.natDegree.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Polynomial.leadingCoeff.{u1} R _inst_1 p) a) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.natDegree.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_mul_C_eq_of_mul_ne_zero Polynomial.natDegree_mul_c_eq_of_mul_ne_zeroₓ'. -/
 /-- Although not explicitly stated, the assumptions of lemma `nat_degree_mul_C_eq_of_mul_ne_zero`
 force the polynomial `p` to be non-zero, via `p.leading_coeff ≠ 0`.
@@ -195,7 +195,7 @@ theorem natDegree_mul_c_eq_of_mul_ne_zero (h : p.leadingCoeff * a ≠ 0) :
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_C_mul_eq_of_mul_ne_zero Polynomial.natDegree_c_mul_eq_of_mul_ne_zeroₓ'. -/
 /-- Although not explicitly stated, the assumptions of lemma `nat_degree_C_mul_eq_of_mul_ne_zero`
 force the polynomial `p` to be non-zero, via `p.leading_coeff ≠ 0`.
@@ -356,7 +356,7 @@ variable [Semiring S]
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) -> (forall (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) {z : S}, (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f z p) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (forall (x : R), (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f x) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) -> (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (Polynomial.natDegree.{u1} R _inst_1 p)))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) -> (forall (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) {z : S}, (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f z p) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) -> (forall (x : R), (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2))))) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) -> (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (Polynomial.natDegree.{u1} R _inst_1 p)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) -> (forall (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) {z : S}, (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f z p) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) -> (forall (x : R), (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2))))) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) -> (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (Polynomial.natDegree.{u1} R _inst_1 p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_pos_of_eval₂_root Polynomial.natDegree_pos_of_eval₂_rootₓ'. -/
 theorem natDegree_pos_of_eval₂_root {p : R[X]} (hp : p ≠ 0) (f : R →+* S) {z : S}
     (hz : eval₂ f z p = 0) (inj : ∀ x : R, f x = 0 → x = 0) : 0 < natDegree p :=
@@ -372,7 +372,7 @@ theorem natDegree_pos_of_eval₂_root {p : R[X]} (hp : p ≠ 0) (f : R →+* S)
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) -> (forall (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) {z : S}, (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f z p) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (forall (x : R), (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f x) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R _inst_1 p)))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) -> (forall (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) {z : S}, (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f z p) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) -> (forall (x : R), (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2))))) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u1} R _inst_1 p)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) -> (forall (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) {z : S}, (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f z p) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) -> (forall (x : R), (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2))))) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u1} R _inst_1 p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_pos_of_eval₂_root Polynomial.degree_pos_of_eval₂_rootₓ'. -/
 theorem degree_pos_of_eval₂_root {p : R[X]} (hp : p ≠ 0) (f : R →+* S) {z : S}
     (hz : eval₂ f z p = 0) (inj : ∀ x : R, f x = 0 → x = 0) : 0 < degree p :=
@@ -445,7 +445,7 @@ variable [Semiring R] [NoZeroDivisors R] {p q : R[X]}
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.degree.{u1} R _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.degree.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a))) (Polynomial.degree.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_mul_C Polynomial.degree_mul_Cₓ'. -/
 theorem degree_mul_C (a0 : a ≠ 0) : (p * C a).degree = p.degree := by
   rw [degree_mul, degree_C a0, add_zero]
@@ -455,7 +455,7 @@ theorem degree_mul_C (a0 : a ≠ 0) : (p * C a).degree = p.degree := by
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.degree.{u1} R _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.degree.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.degree.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_C_mul Polynomial.degree_C_mulₓ'. -/
 theorem degree_C_mul (a0 : a ≠ 0) : (C a * p).degree = p.degree := by
   rw [degree_mul, degree_C a0, zero_add]
@@ -469,7 +469,7 @@ theorem natDegree_mul_c (a0 : a ≠ 0) : (p * C a).natDegree = p.natDegree := by
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_C_mul Polynomial.natDegree_C_mulₓ'. -/
 theorem natDegree_C_mul (a0 : a ≠ 0) : (C a * p).natDegree = p.natDegree := by
   simp only [nat_degree, degree_C_mul a0]

302eab4f

bump to nightly-2023-03-11-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

cd44fb92

Diff

@@ -241,11 +241,11 @@ theorem coeff_mul_of_natDegree_le (pm : p.natDegree ≤ m) (qn : q.natDegree ≤
   by
   rcases eq_or_lt_of_le pm with (rfl | hm) <;> rcases eq_or_lt_of_le qn with (rfl | hn)
   · exact nat_degree_add_coeff_mul _ _
-  · rw [coeff_eq_zero_of_nat_degree_lt hn, mul_zero]
+  · rw [coeff_eq_zero_of_nat_degree_lt hn, MulZeroClass.mul_zero]
     exact nat_degree_lt_coeff_mul (add_lt_add_left hn _)
-  · rw [coeff_eq_zero_of_nat_degree_lt hm, zero_mul]
+  · rw [coeff_eq_zero_of_nat_degree_lt hm, MulZeroClass.zero_mul]
     exact nat_degree_lt_coeff_mul (add_lt_add_right hm _)
-  · rw [coeff_eq_zero_of_nat_degree_lt hn, mul_zero]
+  · rw [coeff_eq_zero_of_nat_degree_lt hn, MulZeroClass.mul_zero]
     exact nat_degree_lt_coeff_mul (add_lt_add hm hn)
 #align polynomial.coeff_mul_of_nat_degree_le Polynomial.coeff_mul_of_natDegree_le
 
@@ -486,9 +486,9 @@ theorem natDegree_comp : natDegree (p.comp q) = natDegree p * natDegree q :=
   by_cases q0 : q.nat_degree = 0
   ·
     rw [degree_le_zero_iff.mp (nat_degree_eq_zero_iff_degree_le_zero.mp q0), comp_C, nat_degree_C,
-      nat_degree_C, mul_zero]
+      nat_degree_C, MulZeroClass.mul_zero]
   · by_cases p0 : p = 0
-    · simp only [p0, zero_comp, nat_degree_zero, zero_mul]
+    · simp only [p0, zero_comp, nat_degree_zero, MulZeroClass.zero_mul]
     refine' le_antisymm nat_degree_comp_le (le_nat_degree_of_ne_zero _)
     simp only [coeff_comp_degree_mul_degree q0, p0, mul_eq_zero, leading_coeff_eq_zero, or_self_iff,
       ne_zero_of_nat_degree_gt (Nat.pos_of_ne_zero q0), pow_ne_zero, Ne.def, not_false_iff]

302eab4f

bump to nightly-2023-03-08-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

b313bdac

Diff

@@ -37,6 +37,7 @@ variable [Semiring R] {p q r : R[X]}
 
 section Degree
 
+#print Polynomial.natDegree_comp_le /-
 theorem natDegree_comp_le : natDegree (p.comp q) ≤ natDegree p * natDegree q :=
   if h0 : p.comp q = 0 then by rw [h0, nat_degree_zero] <;> exact Nat.zero_le _
   else
@@ -64,7 +65,9 @@ theorem natDegree_comp_le : natDegree (p.comp q) ≤ natDegree p * natDegree q :
               
         
 #align polynomial.nat_degree_comp_le Polynomial.natDegree_comp_le
+-/
 
+#print Polynomial.degree_pos_of_root /-
 theorem degree_pos_of_root {p : R[X]} (hp : p ≠ 0) (h : IsRoot p a) : 0 < degree p :=
   lt_of_not_ge fun hlt => by
     have := eq_C_of_degree_le_zero hlt
@@ -72,11 +75,19 @@ theorem degree_pos_of_root {p : R[X]} (hp : p ≠ 0) (h : IsRoot p a) : 0 < degr
     simp only [h, RingHom.map_zero] at this
     exact hp this
 #align polynomial.degree_pos_of_root Polynomial.degree_pos_of_root
+-/
 
+/- warning: polynomial.nat_degree_le_iff_coeff_eq_zero -> Polynomial.natDegree_le_iff_coeff_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {n : Nat} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Iff (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_1 p) n) (forall (N : Nat), (LT.lt.{0} Nat Nat.hasLt n N) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R _inst_1 p N) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))))
+but is expected to have type
+  forall {R : Type.{u1}} {n : Nat} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Iff (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 p) n) (forall (N : Nat), (LT.lt.{0} Nat instLTNat n N) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R _inst_1 p N) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_le_iff_coeff_eq_zero Polynomial.natDegree_le_iff_coeff_eq_zeroₓ'. -/
 theorem natDegree_le_iff_coeff_eq_zero : p.natDegree ≤ n ↔ ∀ N : ℕ, n < N → p.coeff N = 0 := by
   simp_rw [nat_degree_le_iff_degree_le, degree_le_iff_coeff_zero, WithBot.coe_lt_coe]
 #align polynomial.nat_degree_le_iff_coeff_eq_zero Polynomial.natDegree_le_iff_coeff_eq_zero
 
+#print Polynomial.natDegree_add_le_iff_left /-
 theorem natDegree_add_le_iff_left {n : ℕ} (p q : R[X]) (qn : q.natDegree ≤ n) :
     (p + q).natDegree ≤ n ↔ p.natDegree ≤ n :=
   by
@@ -85,55 +96,90 @@ theorem natDegree_add_le_iff_left {n : ℕ} (p q : R[X]) (qn : q.natDegree ≤ n
   convert nat_degree_le_iff_coeff_eq_zero.mp h m hm using 1
   rw [coeff_add, nat_degree_le_iff_coeff_eq_zero.mp qn _ hm, add_zero]
 #align polynomial.nat_degree_add_le_iff_left Polynomial.natDegree_add_le_iff_left
+-/
 
+#print Polynomial.natDegree_add_le_iff_right /-
 theorem natDegree_add_le_iff_right {n : ℕ} (p q : R[X]) (pn : p.natDegree ≤ n) :
     (p + q).natDegree ≤ n ↔ q.natDegree ≤ n :=
   by
   rw [add_comm]
   exact nat_degree_add_le_iff_left _ _ pn
 #align polynomial.nat_degree_add_le_iff_right Polynomial.natDegree_add_le_iff_right
+-/
 
-theorem natDegree_c_mul_le (a : R) (f : R[X]) : (C a * f).natDegree ≤ f.natDegree :=
+/- warning: polynomial.nat_degree_C_mul_le -> Polynomial.natDegree_C_mul_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R) (f : Polynomial.{u1} R _inst_1), LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) f)) (Polynomial.natDegree.{u1} R _inst_1 f)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_C_mul_le Polynomial.natDegree_C_mul_leₓ'. -/
+theorem natDegree_C_mul_le (a : R) (f : R[X]) : (C a * f).natDegree ≤ f.natDegree :=
   calc
     (C a * f).natDegree ≤ (C a).natDegree + f.natDegree := natDegree_mul_le
     _ = 0 + f.natDegree := by rw [nat_degree_C a]
     _ = f.natDegree := zero_add _
     
-#align polynomial.nat_degree_C_mul_le Polynomial.natDegree_c_mul_le
-
-theorem natDegree_mul_c_le (f : R[X]) (a : R) : (f * C a).natDegree ≤ f.natDegree :=
+#align polynomial.nat_degree_C_mul_le Polynomial.natDegree_C_mul_le
+
+/- warning: polynomial.nat_degree_mul_C_le -> Polynomial.natDegree_mul_C_le is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_mul_C_le Polynomial.natDegree_mul_C_leₓ'. -/
+theorem natDegree_mul_C_le (f : R[X]) (a : R) : (f * C a).natDegree ≤ f.natDegree :=
   calc
     (f * C a).natDegree ≤ f.natDegree + (C a).natDegree := natDegree_mul_le
     _ = f.natDegree + 0 := by rw [nat_degree_C a]
     _ = f.natDegree := add_zero _
     
-#align polynomial.nat_degree_mul_C_le Polynomial.natDegree_mul_c_le
+#align polynomial.nat_degree_mul_C_le Polynomial.natDegree_mul_C_le
 
+#print Polynomial.eq_natDegree_of_le_mem_support /-
 theorem eq_natDegree_of_le_mem_support (pn : p.natDegree ≤ n) (ns : n ∈ p.support) :
     p.natDegree = n :=
   le_antisymm pn (le_natDegree_of_mem_supp _ ns)
 #align polynomial.eq_nat_degree_of_le_mem_support Polynomial.eq_natDegree_of_le_mem_support
+-/
 
-theorem natDegree_c_mul_eq_of_mul_eq_one {ai : R} (au : ai * a = 1) :
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+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_C_mul_eq_of_mul_eq_one Polynomial.natDegree_C_mul_eq_of_mul_eq_oneₓ'. -/
+theorem natDegree_C_mul_eq_of_mul_eq_one {ai : R} (au : ai * a = 1) :
     (C a * p).natDegree = p.natDegree :=
-  le_antisymm (natDegree_c_mul_le a p)
+  le_antisymm (natDegree_C_mul_le a p)
     (calc
       p.natDegree = (1 * p).natDegree := by nth_rw 1 [← one_mul p]
       _ = (C ai * (C a * p)).natDegree := by rw [← C_1, ← au, RingHom.map_mul, ← mul_assoc]
-      _ ≤ (C a * p).natDegree := natDegree_c_mul_le ai (C a * p)
+      _ ≤ (C a * p).natDegree := natDegree_C_mul_le ai (C a * p)
       )
-#align polynomial.nat_degree_C_mul_eq_of_mul_eq_one Polynomial.natDegree_c_mul_eq_of_mul_eq_one
-
-theorem natDegree_mul_c_eq_of_mul_eq_one {ai : R} (au : a * ai = 1) :
+#align polynomial.nat_degree_C_mul_eq_of_mul_eq_one Polynomial.natDegree_C_mul_eq_of_mul_eq_one
+
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+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_mul_C_eq_of_mul_eq_one Polynomial.natDegree_mul_C_eq_of_mul_eq_oneₓ'. -/
+theorem natDegree_mul_C_eq_of_mul_eq_one {ai : R} (au : a * ai = 1) :
     (p * C a).natDegree = p.natDegree :=
-  le_antisymm (natDegree_mul_c_le p a)
+  le_antisymm (natDegree_mul_C_le p a)
     (calc
       p.natDegree = (p * 1).natDegree := by nth_rw 1 [← mul_one p]
       _ = (p * C a * C ai).natDegree := by rw [← C_1, ← au, RingHom.map_mul, ← mul_assoc]
-      _ ≤ (p * C a).natDegree := natDegree_mul_c_le (p * C a) ai
+      _ ≤ (p * C a).natDegree := natDegree_mul_C_le (p * C a) ai
       )
-#align polynomial.nat_degree_mul_C_eq_of_mul_eq_one Polynomial.natDegree_mul_c_eq_of_mul_eq_one
-
+#align polynomial.nat_degree_mul_C_eq_of_mul_eq_one Polynomial.natDegree_mul_C_eq_of_mul_eq_one
+
+/- warning: polynomial.nat_degree_mul_C_eq_of_mul_ne_zero -> Polynomial.natDegree_mul_c_eq_of_mul_ne_zero is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_mul_C_eq_of_mul_ne_zero Polynomial.natDegree_mul_c_eq_of_mul_ne_zeroₓ'. -/
 /-- Although not explicitly stated, the assumptions of lemma `nat_degree_mul_C_eq_of_mul_ne_zero`
 force the polynomial `p` to be non-zero, via `p.leading_coeff ≠ 0`.
 -/
@@ -145,6 +191,12 @@ theorem natDegree_mul_c_eq_of_mul_ne_zero (h : p.leadingCoeff * a ≠ 0) :
   rwa [coeff_mul_C]
 #align polynomial.nat_degree_mul_C_eq_of_mul_ne_zero Polynomial.natDegree_mul_c_eq_of_mul_ne_zero
 
+/- warning: polynomial.nat_degree_C_mul_eq_of_mul_ne_zero -> Polynomial.natDegree_c_mul_eq_of_mul_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
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+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_C_mul_eq_of_mul_ne_zero Polynomial.natDegree_c_mul_eq_of_mul_ne_zeroₓ'. -/
 /-- Although not explicitly stated, the assumptions of lemma `nat_degree_C_mul_eq_of_mul_ne_zero`
 force the polynomial `p` to be non-zero, via `p.leading_coeff ≠ 0`.
 -/
@@ -156,16 +208,34 @@ theorem natDegree_c_mul_eq_of_mul_ne_zero (h : a * p.leadingCoeff ≠ 0) :
   rwa [coeff_C_mul]
 #align polynomial.nat_degree_C_mul_eq_of_mul_ne_zero Polynomial.natDegree_c_mul_eq_of_mul_ne_zero
 
+/- warning: polynomial.nat_degree_add_coeff_mul -> Polynomial.natDegree_add_coeff_mul is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_add_coeff_mul Polynomial.natDegree_add_coeff_mulₓ'. -/
 theorem natDegree_add_coeff_mul (f g : R[X]) :
     (f * g).coeff (f.natDegree + g.natDegree) = f.coeff f.natDegree * g.coeff g.natDegree := by
   simp only [coeff_nat_degree, coeff_mul_degree_add_degree]
 #align polynomial.nat_degree_add_coeff_mul Polynomial.natDegree_add_coeff_mul
 
+/- warning: polynomial.nat_degree_lt_coeff_mul -> Polynomial.natDegree_lt_coeff_mul is a dubious translation:
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+  forall {R : Type.{u1}} {m : Nat} {n : Nat} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (LT.lt.{0} Nat Nat.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Polynomial.natDegree.{u1} R _inst_1 p) (Polynomial.natDegree.{u1} R _inst_1 q)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p q) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_lt_coeff_mul Polynomial.natDegree_lt_coeff_mulₓ'. -/
 theorem natDegree_lt_coeff_mul (h : p.natDegree + q.natDegree < m + n) :
     (p * q).coeff (m + n) = 0 :=
   coeff_eq_zero_of_natDegree_lt (natDegree_mul_le.trans_lt h)
 #align polynomial.nat_degree_lt_coeff_mul Polynomial.natDegree_lt_coeff_mul
 
+/- warning: polynomial.coeff_mul_of_nat_degree_le -> Polynomial.coeff_mul_of_natDegree_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {m : Nat} {n : Nat} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_1 p) m) -> (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_1 q) n) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p q) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Polynomial.coeff.{u1} R _inst_1 p m) (Polynomial.coeff.{u1} R _inst_1 q n)))
+but is expected to have type
+  forall {R : Type.{u1}} {m : Nat} {n : Nat} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 p) m) -> (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 q) n) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p q) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Polynomial.coeff.{u1} R _inst_1 p m) (Polynomial.coeff.{u1} R _inst_1 q n)))
+Case conversion may be inaccurate. Consider using '#align polynomial.coeff_mul_of_nat_degree_le Polynomial.coeff_mul_of_natDegree_leₓ'. -/
 theorem coeff_mul_of_natDegree_le (pm : p.natDegree ≤ m) (qn : q.natDegree ≤ n) :
     (p * q).coeff (m + n) = p.coeff m * q.coeff n :=
   by
@@ -179,6 +249,7 @@ theorem coeff_mul_of_natDegree_le (pm : p.natDegree ≤ m) (qn : q.natDegree ≤
     exact nat_degree_lt_coeff_mul (add_lt_add hm hn)
 #align polynomial.coeff_mul_of_nat_degree_le Polynomial.coeff_mul_of_natDegree_le
 
+#print Polynomial.coeff_pow_of_natDegree_le /-
 theorem coeff_pow_of_natDegree_le (pn : p.natDegree ≤ n) : (p ^ m).coeff (n * m) = p.coeff n ^ m :=
   by
   induction' m with m hm
@@ -187,18 +258,24 @@ theorem coeff_pow_of_natDegree_le (pn : p.natDegree ≤ n) : (p ^ m).coeff (n *
     refine' nat_degree_pow_le.trans (le_trans _ (mul_comm _ _).le)
     exact mul_le_mul_of_nonneg_left pn m.zero_le
 #align polynomial.coeff_pow_of_nat_degree_le Polynomial.coeff_pow_of_natDegree_le
+-/
 
+#print Polynomial.coeff_add_eq_left_of_lt /-
 theorem coeff_add_eq_left_of_lt (qn : q.natDegree < n) : (p + q).coeff n = p.coeff n :=
   (coeff_add _ _ _).trans <|
     (congr_arg _ <| coeff_eq_zero_of_natDegree_lt <| qn).trans <| add_zero _
 #align polynomial.coeff_add_eq_left_of_lt Polynomial.coeff_add_eq_left_of_lt
+-/
 
+#print Polynomial.coeff_add_eq_right_of_lt /-
 theorem coeff_add_eq_right_of_lt (pn : p.natDegree < n) : (p + q).coeff n = q.coeff n :=
   by
   rw [add_comm]
   exact coeff_add_eq_left_of_lt pn
 #align polynomial.coeff_add_eq_right_of_lt Polynomial.coeff_add_eq_right_of_lt
+-/
 
+#print Polynomial.degree_sum_eq_of_disjoint /-
 theorem degree_sum_eq_of_disjoint (f : S → R[X]) (s : Finset S)
     (h : Set.Pairwise { i | i ∈ s ∧ f i ≠ 0 } (Ne on degree ∘ f)) :
     degree (s.Sum f) = s.sup fun i => degree (f i) :=
@@ -224,7 +301,9 @@ theorem degree_sum_eq_of_disjoint (f : S → R[X]) (s : Finset S)
       · exact H.symm ▸ hy
     · rw [← IH, sup_eq_left.mpr H.le, degree_add_eq_left_of_degree_lt H]
 #align polynomial.degree_sum_eq_of_disjoint Polynomial.degree_sum_eq_of_disjoint
+-/
 
+#print Polynomial.natDegree_sum_eq_of_disjoint /-
 theorem natDegree_sum_eq_of_disjoint (f : S → R[X]) (s : Finset S)
     (h : Set.Pairwise { i | i ∈ s ∧ f i ≠ 0 } (Ne on natDegree ∘ f)) :
     natDegree (s.Sum f) = s.sup fun i => natDegree (f i) :=
@@ -257,17 +336,28 @@ theorem natDegree_sum_eq_of_disjoint (f : S → R[X]) (s : Finset S)
     intro x hx
     simp [H x hx]
 #align polynomial.nat_degree_sum_eq_of_disjoint Polynomial.natDegree_sum_eq_of_disjoint
+-/
 
+#print Polynomial.natDegree_bit0 /-
 theorem natDegree_bit0 (a : R[X]) : (bit0 a).natDegree ≤ a.natDegree :=
   (natDegree_add_le _ _).trans (max_self _).le
 #align polynomial.nat_degree_bit0 Polynomial.natDegree_bit0
+-/
 
+#print Polynomial.natDegree_bit1 /-
 theorem natDegree_bit1 (a : R[X]) : (bit1 a).natDegree ≤ a.natDegree :=
   (natDegree_add_le _ _).trans (by simp [nat_degree_bit0])
 #align polynomial.nat_degree_bit1 Polynomial.natDegree_bit1
+-/
 
 variable [Semiring S]
 
+/- warning: polynomial.nat_degree_pos_of_eval₂_root -> Polynomial.natDegree_pos_of_eval₂_root is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_pos_of_eval₂_root Polynomial.natDegree_pos_of_eval₂_rootₓ'. -/
 theorem natDegree_pos_of_eval₂_root {p : R[X]} (hp : p ≠ 0) (f : R →+* S) {z : S}
     (hz : eval₂ f z p = 0) (inj : ∀ x : R, f x = 0 → x = 0) : 0 < natDegree p :=
   lt_of_not_ge fun hlt =>
@@ -278,11 +368,18 @@ theorem natDegree_pos_of_eval₂_root {p : R[X]} (hp : p ≠ 0) (f : R →+* S)
     exact hp A
 #align polynomial.nat_degree_pos_of_eval₂_root Polynomial.natDegree_pos_of_eval₂_root
 
+/- warning: polynomial.degree_pos_of_eval₂_root -> Polynomial.degree_pos_of_eval₂_root is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) -> (forall (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) {z : S}, (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f z p) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (forall (x : R), (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f x) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R _inst_1 p)))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.degree_pos_of_eval₂_root Polynomial.degree_pos_of_eval₂_rootₓ'. -/
 theorem degree_pos_of_eval₂_root {p : R[X]} (hp : p ≠ 0) (f : R →+* S) {z : S}
     (hz : eval₂ f z p = 0) (inj : ∀ x : R, f x = 0 → x = 0) : 0 < degree p :=
   natDegree_pos_iff_degree_pos.mp (natDegree_pos_of_eval₂_root hp f hz inj)
 #align polynomial.degree_pos_of_eval₂_root Polynomial.degree_pos_of_eval₂_root
 
+#print Polynomial.coe_lt_degree /-
 @[simp]
 theorem coe_lt_degree {p : R[X]} {n : ℕ} : (n : WithBot ℕ) < degree p ↔ n < natDegree p :=
   by
@@ -290,6 +387,7 @@ theorem coe_lt_degree {p : R[X]} {n : ℕ} : (n : WithBot ℕ) < degree p ↔ n
   · simp [h]
   rw [degree_eq_nat_degree h, WithBot.coe_lt_coe]
 #align polynomial.coe_lt_degree Polynomial.coe_lt_degree
+-/
 
 end Degree
 
@@ -299,26 +397,40 @@ section Ring
 
 variable [Ring R] {p q : R[X]}
 
+#print Polynomial.natDegree_sub /-
 theorem natDegree_sub : (p - q).natDegree = (q - p).natDegree := by rw [← nat_degree_neg, neg_sub]
 #align polynomial.nat_degree_sub Polynomial.natDegree_sub
+-/
 
+#print Polynomial.natDegree_sub_le_iff_left /-
 theorem natDegree_sub_le_iff_left (qn : q.natDegree ≤ n) :
     (p - q).natDegree ≤ n ↔ p.natDegree ≤ n :=
   by
   rw [← nat_degree_neg] at qn
   rw [sub_eq_add_neg, nat_degree_add_le_iff_left _ _ qn]
 #align polynomial.nat_degree_sub_le_iff_left Polynomial.natDegree_sub_le_iff_left
+-/
 
+#print Polynomial.natDegree_sub_le_iff_right /-
 theorem natDegree_sub_le_iff_right (pn : p.natDegree ≤ n) :
     (p - q).natDegree ≤ n ↔ q.natDegree ≤ n := by rwa [nat_degree_sub, nat_degree_sub_le_iff_left]
 #align polynomial.nat_degree_sub_le_iff_right Polynomial.natDegree_sub_le_iff_right
+-/
 
+#print Polynomial.coeff_sub_eq_left_of_lt /-
 theorem coeff_sub_eq_left_of_lt (dg : q.natDegree < n) : (p - q).coeff n = p.coeff n :=
   by
   rw [← nat_degree_neg] at dg
   rw [sub_eq_add_neg, coeff_add_eq_left_of_lt dg]
 #align polynomial.coeff_sub_eq_left_of_lt Polynomial.coeff_sub_eq_left_of_lt
+-/
 
+/- warning: polynomial.coeff_sub_eq_neg_right_of_lt -> Polynomial.coeff_sub_eq_neg_right_of_lt is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {n : Nat} [_inst_1 : Ring.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, (LT.lt.{0} Nat Nat.hasLt (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p) n) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.sub.{u1} R _inst_1)) p q) n) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) q n)))
+but is expected to have type
+  forall {R : Type.{u1}} {n : Nat} [_inst_1 : Ring.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p) n) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.sub.{u1} R _inst_1)) p q) n) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) q n)))
+Case conversion may be inaccurate. Consider using '#align polynomial.coeff_sub_eq_neg_right_of_lt Polynomial.coeff_sub_eq_neg_right_of_ltₓ'. -/
 theorem coeff_sub_eq_neg_right_of_lt (df : p.natDegree < n) : (p - q).coeff n = -q.coeff n := by
   rwa [sub_eq_add_neg, coeff_add_eq_right_of_lt, coeff_neg]
 #align polynomial.coeff_sub_eq_neg_right_of_lt Polynomial.coeff_sub_eq_neg_right_of_lt
@@ -329,22 +441,46 @@ section NoZeroDivisors
 
 variable [Semiring R] [NoZeroDivisors R] {p q : R[X]}
 
-theorem degree_mul_c (a0 : a ≠ 0) : (p * C a).degree = p.degree := by
+/- warning: polynomial.degree_mul_C -> Polynomial.degree_mul_C is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.degree_mul_C Polynomial.degree_mul_Cₓ'. -/
+theorem degree_mul_C (a0 : a ≠ 0) : (p * C a).degree = p.degree := by
   rw [degree_mul, degree_C a0, add_zero]
-#align polynomial.degree_mul_C Polynomial.degree_mul_c
-
-theorem degree_c_mul (a0 : a ≠ 0) : (C a * p).degree = p.degree := by
+#align polynomial.degree_mul_C Polynomial.degree_mul_C
+
+/- warning: polynomial.degree_C_mul -> Polynomial.degree_C_mul is a dubious translation:
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+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.degree.{u1} R _inst_1 p))
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+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.degree.{u1} R _inst_1 p))
+Case conversion may be inaccurate. Consider using '#align polynomial.degree_C_mul Polynomial.degree_C_mulₓ'. -/
+theorem degree_C_mul (a0 : a ≠ 0) : (C a * p).degree = p.degree := by
   rw [degree_mul, degree_C a0, zero_add]
-#align polynomial.degree_C_mul Polynomial.degree_c_mul
+#align polynomial.degree_C_mul Polynomial.degree_C_mul
 
 theorem natDegree_mul_c (a0 : a ≠ 0) : (p * C a).natDegree = p.natDegree := by
   simp only [nat_degree, degree_mul_C a0]
 #align polynomial.nat_degree_mul_C Polynomial.natDegree_mul_c
 
-theorem natDegree_c_mul (a0 : a ≠ 0) : (C a * p).natDegree = p.natDegree := by
+/- warning: polynomial.nat_degree_C_mul -> Polynomial.natDegree_C_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
+but is expected to have type
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (Polynomial.natDegree.{u1} R _inst_1 p))
+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_C_mul Polynomial.natDegree_C_mulₓ'. -/
+theorem natDegree_C_mul (a0 : a ≠ 0) : (C a * p).natDegree = p.natDegree := by
   simp only [nat_degree, degree_C_mul a0]
-#align polynomial.nat_degree_C_mul Polynomial.natDegree_c_mul
-
+#align polynomial.nat_degree_C_mul Polynomial.natDegree_C_mul
+
+/- warning: polynomial.nat_degree_comp -> Polynomial.natDegree_comp is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (Polynomial.comp.{u1} R _inst_1 p q)) (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat Nat.hasMul) (Polynomial.natDegree.{u1} R _inst_1 p) (Polynomial.natDegree.{u1} R _inst_1 q))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (Polynomial.comp.{u1} R _inst_1 p q)) (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat instMulNat) (Polynomial.natDegree.{u1} R _inst_1 p) (Polynomial.natDegree.{u1} R _inst_1 q))
+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_comp Polynomial.natDegree_compₓ'. -/
 theorem natDegree_comp : natDegree (p.comp q) = natDegree p * natDegree q :=
   by
   by_cases q0 : q.nat_degree = 0
@@ -358,6 +494,12 @@ theorem natDegree_comp : natDegree (p.comp q) = natDegree p * natDegree q :=
       ne_zero_of_nat_degree_gt (Nat.pos_of_ne_zero q0), pow_ne_zero, Ne.def, not_false_iff]
 #align polynomial.nat_degree_comp Polynomial.natDegree_comp
 
+/- warning: polynomial.leading_coeff_comp -> Polynomial.leadingCoeff_comp is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Ne.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 q) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R _inst_1 (Polynomial.comp.{u1} R _inst_1 p q)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Polynomial.leadingCoeff.{u1} R _inst_1 p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (Polynomial.leadingCoeff.{u1} R _inst_1 q) (Polynomial.natDegree.{u1} R _inst_1 p))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Ne.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 q) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R _inst_1 (Polynomial.comp.{u1} R _inst_1 p q)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Polynomial.leadingCoeff.{u1} R _inst_1 p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (Polynomial.leadingCoeff.{u1} R _inst_1 q) (Polynomial.natDegree.{u1} R _inst_1 p))))
+Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_comp Polynomial.leadingCoeff_compₓ'. -/
 theorem leadingCoeff_comp (hq : natDegree q ≠ 0) :
     leadingCoeff (p.comp q) = leadingCoeff p * leadingCoeff q ^ natDegree p := by
   rw [← coeff_comp_degree_mul_degree hq, ← nat_degree_comp, coeff_nat_degree]

302eab4f

bump to nightly-2023-03-08-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

422cc012

Diff

@@ -48,11 +48,11 @@ theorem natDegree_comp_le : natDegree (p.comp q) ≤ natDegree p * natDegree q :
         _ ≤ _ :=
           Finset.sup_le fun n hn =>
             calc
-              degree (c (coeff p n) * q ^ n) ≤ degree (c (coeff p n)) + degree (q ^ n) :=
+              degree (C (coeff p n) * q ^ n) ≤ degree (C (coeff p n)) + degree (q ^ n) :=
                 degree_mul_le _ _
-              _ ≤ natDegree (c (coeff p n)) + n • degree q :=
+              _ ≤ natDegree (C (coeff p n)) + n • degree q :=
                 (add_le_add degree_le_natDegree (degree_pow_le _ _))
-              _ ≤ natDegree (c (coeff p n)) + n • natDegree q :=
+              _ ≤ natDegree (C (coeff p n)) + n • natDegree q :=
                 (add_le_add_left (nsmul_le_nsmul_of_le_right (@degree_le_natDegree _ _ q) n) _)
               _ = (n * natDegree q : ℕ) := by
                 rw [nat_degree_C, WithBot.coe_zero, zero_add, ← WithBot.coe_nsmul, nsmul_eq_mul] <;>
@@ -93,17 +93,17 @@ theorem natDegree_add_le_iff_right {n : ℕ} (p q : R[X]) (pn : p.natDegree ≤
   exact nat_degree_add_le_iff_left _ _ pn
 #align polynomial.nat_degree_add_le_iff_right Polynomial.natDegree_add_le_iff_right
 
-theorem natDegree_c_mul_le (a : R) (f : R[X]) : (c a * f).natDegree ≤ f.natDegree :=
+theorem natDegree_c_mul_le (a : R) (f : R[X]) : (C a * f).natDegree ≤ f.natDegree :=
   calc
-    (c a * f).natDegree ≤ (c a).natDegree + f.natDegree := natDegree_mul_le
+    (C a * f).natDegree ≤ (C a).natDegree + f.natDegree := natDegree_mul_le
     _ = 0 + f.natDegree := by rw [nat_degree_C a]
     _ = f.natDegree := zero_add _
     
 #align polynomial.nat_degree_C_mul_le Polynomial.natDegree_c_mul_le
 
-theorem natDegree_mul_c_le (f : R[X]) (a : R) : (f * c a).natDegree ≤ f.natDegree :=
+theorem natDegree_mul_c_le (f : R[X]) (a : R) : (f * C a).natDegree ≤ f.natDegree :=
   calc
-    (f * c a).natDegree ≤ f.natDegree + (c a).natDegree := natDegree_mul_le
+    (f * C a).natDegree ≤ f.natDegree + (C a).natDegree := natDegree_mul_le
     _ = f.natDegree + 0 := by rw [nat_degree_C a]
     _ = f.natDegree := add_zero _
     
@@ -115,22 +115,22 @@ theorem eq_natDegree_of_le_mem_support (pn : p.natDegree ≤ n) (ns : n ∈ p.su
 #align polynomial.eq_nat_degree_of_le_mem_support Polynomial.eq_natDegree_of_le_mem_support
 
 theorem natDegree_c_mul_eq_of_mul_eq_one {ai : R} (au : ai * a = 1) :
-    (c a * p).natDegree = p.natDegree :=
+    (C a * p).natDegree = p.natDegree :=
   le_antisymm (natDegree_c_mul_le a p)
     (calc
       p.natDegree = (1 * p).natDegree := by nth_rw 1 [← one_mul p]
-      _ = (c ai * (c a * p)).natDegree := by rw [← C_1, ← au, RingHom.map_mul, ← mul_assoc]
-      _ ≤ (c a * p).natDegree := natDegree_c_mul_le ai (c a * p)
+      _ = (C ai * (C a * p)).natDegree := by rw [← C_1, ← au, RingHom.map_mul, ← mul_assoc]
+      _ ≤ (C a * p).natDegree := natDegree_c_mul_le ai (C a * p)
       )
 #align polynomial.nat_degree_C_mul_eq_of_mul_eq_one Polynomial.natDegree_c_mul_eq_of_mul_eq_one
 
 theorem natDegree_mul_c_eq_of_mul_eq_one {ai : R} (au : a * ai = 1) :
-    (p * c a).natDegree = p.natDegree :=
+    (p * C a).natDegree = p.natDegree :=
   le_antisymm (natDegree_mul_c_le p a)
     (calc
       p.natDegree = (p * 1).natDegree := by nth_rw 1 [← mul_one p]
-      _ = (p * c a * c ai).natDegree := by rw [← C_1, ← au, RingHom.map_mul, ← mul_assoc]
-      _ ≤ (p * c a).natDegree := natDegree_mul_c_le (p * c a) ai
+      _ = (p * C a * C ai).natDegree := by rw [← C_1, ← au, RingHom.map_mul, ← mul_assoc]
+      _ ≤ (p * C a).natDegree := natDegree_mul_c_le (p * C a) ai
       )
 #align polynomial.nat_degree_mul_C_eq_of_mul_eq_one Polynomial.natDegree_mul_c_eq_of_mul_eq_one
 
@@ -138,7 +138,7 @@ theorem natDegree_mul_c_eq_of_mul_eq_one {ai : R} (au : a * ai = 1) :
 force the polynomial `p` to be non-zero, via `p.leading_coeff ≠ 0`.
 -/
 theorem natDegree_mul_c_eq_of_mul_ne_zero (h : p.leadingCoeff * a ≠ 0) :
-    (p * c a).natDegree = p.natDegree :=
+    (p * C a).natDegree = p.natDegree :=
   by
   refine' eq_nat_degree_of_le_mem_support (nat_degree_mul_C_le p a) _
   refine' mem_support_iff.mpr _
@@ -149,7 +149,7 @@ theorem natDegree_mul_c_eq_of_mul_ne_zero (h : p.leadingCoeff * a ≠ 0) :
 force the polynomial `p` to be non-zero, via `p.leading_coeff ≠ 0`.
 -/
 theorem natDegree_c_mul_eq_of_mul_ne_zero (h : a * p.leadingCoeff ≠ 0) :
-    (c a * p).natDegree = p.natDegree :=
+    (C a * p).natDegree = p.natDegree :=
   by
   refine' eq_nat_degree_of_le_mem_support (nat_degree_C_mul_le a p) _
   refine' mem_support_iff.mpr _
@@ -329,19 +329,19 @@ section NoZeroDivisors
 
 variable [Semiring R] [NoZeroDivisors R] {p q : R[X]}
 
-theorem degree_mul_c (a0 : a ≠ 0) : (p * c a).degree = p.degree := by
+theorem degree_mul_c (a0 : a ≠ 0) : (p * C a).degree = p.degree := by
   rw [degree_mul, degree_C a0, add_zero]
 #align polynomial.degree_mul_C Polynomial.degree_mul_c
 
-theorem degree_c_mul (a0 : a ≠ 0) : (c a * p).degree = p.degree := by
+theorem degree_c_mul (a0 : a ≠ 0) : (C a * p).degree = p.degree := by
   rw [degree_mul, degree_C a0, zero_add]
 #align polynomial.degree_C_mul Polynomial.degree_c_mul
 
-theorem natDegree_mul_c (a0 : a ≠ 0) : (p * c a).natDegree = p.natDegree := by
+theorem natDegree_mul_c (a0 : a ≠ 0) : (p * C a).natDegree = p.natDegree := by
   simp only [nat_degree, degree_mul_C a0]
 #align polynomial.nat_degree_mul_C Polynomial.natDegree_mul_c
 
-theorem natDegree_c_mul (a0 : a ≠ 0) : (c a * p).natDegree = p.natDegree := by
+theorem natDegree_c_mul (a0 : a ≠ 0) : (C a * p).natDegree = p.natDegree := by
   simp only [nat_degree, degree_C_mul a0]
 #align polynomial.nat_degree_C_mul Polynomial.natDegree_c_mul

302eab4f

bump to nightly-2023-03-01-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

20cadee0

Diff

@@ -43,17 +43,17 @@ theorem natDegree_comp_le : natDegree (p.comp q) ≤ natDegree p * natDegree q :
     WithBot.coe_le_coe.1 <|
       calc
         ↑(natDegree (p.comp q)) = degree (p.comp q) := (degree_eq_natDegree h0).symm
-        _ = _ := congr_arg degree comp_eq_sum_left
-        _ ≤ _ := degree_sum_le _ _
+        _ = _ := (congr_arg degree comp_eq_sum_left)
+        _ ≤ _ := (degree_sum_le _ _)
         _ ≤ _ :=
           Finset.sup_le fun n hn =>
             calc
               degree (c (coeff p n) * q ^ n) ≤ degree (c (coeff p n)) + degree (q ^ n) :=
                 degree_mul_le _ _
               _ ≤ natDegree (c (coeff p n)) + n • degree q :=
-                add_le_add degree_le_natDegree (degree_pow_le _ _)
+                (add_le_add degree_le_natDegree (degree_pow_le _ _))
               _ ≤ natDegree (c (coeff p n)) + n • natDegree q :=
-                add_le_add_left (nsmul_le_nsmul_of_le_right (@degree_le_natDegree _ _ q) n) _
+                (add_le_add_left (nsmul_le_nsmul_of_le_right (@degree_le_natDegree _ _ q) n) _)
               _ = (n * natDegree q : ℕ) := by
                 rw [nat_degree_C, WithBot.coe_zero, zero_add, ← WithBot.coe_nsmul, nsmul_eq_mul] <;>
                   simp

302eab4f

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

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chore: superfluous parentheses part 2 (#12131)

Co-authored-by: Moritz Firsching <firsching@google.com>

d48d30ac

Diff

@@ -41,8 +41,8 @@ theorem natDegree_comp_le : natDegree (p.comp q) ≤ natDegree p * natDegree q :
     WithBot.coe_le_coe.1 <|
       calc
         ↑(natDegree (p.comp q)) = degree (p.comp q) := (degree_eq_natDegree h0).symm
-        _ = _ := (congr_arg degree comp_eq_sum_left)
-        _ ≤ _ := (degree_sum_le _ _)
+        _ = _ := congr_arg degree comp_eq_sum_left
+        _ ≤ _ := degree_sum_le _ _
         _ ≤ _ :=
           Finset.sup_le fun n hn =>
             calc

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move(Polynomial): Move out of Data (#11751)

Polynomial and MvPolynomial are algebraic objects, hence should be under Algebra (or at least not under Data)

56e439ec

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2018 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
 -/
-import Mathlib.Data.Polynomial.Eval
+import Mathlib.Algebra.Polynomial.Eval
 
 #align_import data.polynomial.degree.lemmas from "leanprover-community/mathlib"@"728baa2f54e6062c5879a3e397ac6bac323e506f"

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chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11801)

1b40c7bc

Diff

@@ -399,7 +399,7 @@ theorem natDegree_comp : natDegree (p.comp q) = natDegree p * natDegree q := by
     · simp only [p0, zero_comp, natDegree_zero, zero_mul]
     refine' le_antisymm natDegree_comp_le (le_natDegree_of_ne_zero _)
     simp only [coeff_comp_degree_mul_degree q0, p0, mul_eq_zero, leadingCoeff_eq_zero, or_self_iff,
-      ne_zero_of_natDegree_gt (Nat.pos_of_ne_zero q0), pow_ne_zero, Ne.def, not_false_iff]
+      ne_zero_of_natDegree_gt (Nat.pos_of_ne_zero q0), pow_ne_zero, Ne, not_false_iff]
 #align polynomial.nat_degree_comp Polynomial.natDegree_comp
 
 @[simp]

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change the order of operation in zsmulRec and nsmulRec (#11451)

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

pow_succ and pow_succ' have switched their meanings.
Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

9a3feeae

Diff

@@ -173,7 +173,7 @@ theorem coeff_pow_of_natDegree_le (pn : p.natDegree ≤ n) :
     (p ^ m).coeff (m * n) = p.coeff n ^ m := by
   induction' m with m hm
   · simp
-  · rw [pow_succ', pow_succ', ← hm, Nat.succ_mul, coeff_mul_of_natDegree_le _ pn]
+  · rw [pow_succ, pow_succ, ← hm, Nat.succ_mul, coeff_mul_of_natDegree_le _ pn]
     refine' natDegree_pow_le.trans (le_trans _ (le_refl _))
     exact mul_le_mul_of_nonneg_left pn m.zero_le
 #align polynomial.coeff_pow_of_nat_degree_le Polynomial.coeff_pow_of_natDegree_le
@@ -407,7 +407,7 @@ theorem natDegree_iterate_comp (k : ℕ) :
     (p.comp^[k] q).natDegree = p.natDegree ^ k * q.natDegree := by
   induction' k with k IH
   · simp
-  · rw [Function.iterate_succ_apply', natDegree_comp, IH, pow_succ, mul_assoc]
+  · rw [Function.iterate_succ_apply', natDegree_comp, IH, pow_succ', mul_assoc]
 #align polynomial.nat_degree_iterate_comp Polynomial.natDegree_iterate_comp
 
 theorem leadingCoeff_comp (hq : natDegree q ≠ 0) :

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chore: remove stream-of-consciousness uses of have, replace and suffices (#10640)

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

a13e8040

Diff

@@ -295,10 +295,9 @@ theorem degree_map_eq_iff {f : R →+* S} {p : Polynomial R} :
   · simp [h]
   simp only [h, or_false]
   refine ⟨fun h2 ↦ ?_, degree_map_eq_of_leadingCoeff_ne_zero f⟩
-  have h3 : natDegree (map f p) = natDegree p
-  · simp_rw [natDegree, h2]
-  have h4 : map f p ≠ 0
-  · rwa [ne_eq, ← degree_eq_bot, h2, degree_eq_bot]
+  have h3 : natDegree (map f p) = natDegree p := by simp_rw [natDegree, h2]
+  have h4 : map f p ≠ 0 := by
+    rwa [ne_eq, ← degree_eq_bot, h2, degree_eq_bot]
   rwa [← coeff_natDegree, ← coeff_map, ← h3, coeff_natDegree, ne_eq, leadingCoeff_eq_zero]
 
 @[simp]

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feat: connect AddMonoidAlgebra.supDegree and Polynomial.natDegree/degree (#10518)

f0a799f7

Diff

@@ -162,14 +162,11 @@ theorem natDegree_lt_coeff_mul (h : p.natDegree + q.natDegree < m + n) :
 
 theorem coeff_mul_of_natDegree_le (pm : p.natDegree ≤ m) (qn : q.natDegree ≤ n) :
     (p * q).coeff (m + n) = p.coeff m * q.coeff n := by
-  rcases eq_or_lt_of_le pm with (rfl | hm) <;> rcases eq_or_lt_of_le qn with (rfl | hn)
-  · exact natDegree_add_coeff_mul _ _
-  · rw [coeff_eq_zero_of_natDegree_lt hn, mul_zero]
-    exact natDegree_lt_coeff_mul (add_lt_add_left hn _)
-  · rw [coeff_eq_zero_of_natDegree_lt hm, zero_mul]
-    exact natDegree_lt_coeff_mul (add_lt_add_right hm _)
-  · rw [coeff_eq_zero_of_natDegree_lt hn, mul_zero]
-    exact natDegree_lt_coeff_mul (add_lt_add hm hn)
+  simp_rw [← Polynomial.toFinsupp_apply, toFinsupp_mul]
+  refine AddMonoidAlgebra.apply_add_of_supDegree_le ?_ Function.injective_id ?_ ?_
+  · simp
+  · rwa [supDegree_eq_natDegree, id_eq]
+  · rwa [supDegree_eq_natDegree, id_eq]
 #align polynomial.coeff_mul_of_nat_degree_le Polynomial.coeff_mul_of_natDegree_le
 
 theorem coeff_pow_of_natDegree_le (pn : p.natDegree ≤ n) :

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feat(Data/Polynomial): irreducibility of degree-{2,3} polynomials (#9697)

The goal is to show that a degree 2 or 3 polynomial is irreducible iff it doesn't have roots. We already have Polynomial.Monic.irreducible_iff_natDegree' and some existing results in Lean 3: https://github.com/lean-forward/class-group-and-mordell-equation/blob/main/src/number_theory/assorted_lemmas.lean#L254 and the main work is to connect these bits together.

I added a few helper lemmas about the "monicization" of a polynomial p, p * C (leadingCoeff p)⁻¹. Then I used these to show the Polynomial.Monic.irreducible_iff ... statements could be translated to (not necessarily monic) polynomials over a field, then I specialized these results to the degree-{2,3} case.

I created a new file because I couldn't find an obvious place that imported both Polynomial.FieldDivision and Tactic.IntervalCases.

Zulip discussion: https://leanprover.zulipchat.com/#narrow/stream/113489-new-members/topic/Polynomial.20irreducible

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

1799b8c3

Diff

@@ -421,4 +421,59 @@ theorem leadingCoeff_comp (hq : natDegree q ≠ 0) :
 
 end NoZeroDivisors
 
+section DivisionRing
+
+variable {K : Type*} [DivisionRing K]
+
+/-! Useful lemmas for the "monicization" of a nonzero polynomial `p`. -/
+@[simp]
+theorem irreducible_mul_leadingCoeff_inv {p : K[X]} :
+    Irreducible (p * C (leadingCoeff p)⁻¹) ↔ Irreducible p := by
+  by_cases hp0 : p = 0
+  · simp [hp0]
+  exact irreducible_mul_isUnit
+    (isUnit_C.mpr (IsUnit.mk0 _ (inv_ne_zero (leadingCoeff_ne_zero.mpr hp0))))
+
+@[simp] lemma dvd_mul_leadingCoeff_inv {p q : K[X]} (hp0 : p ≠ 0) :
+    q ∣ p * C (leadingCoeff p)⁻¹ ↔ q ∣ p :=
+  IsUnit.dvd_mul_right <| isUnit_C.mpr <| IsUnit.mk0 _ <|
+    inv_ne_zero <| leadingCoeff_ne_zero.mpr hp0
+
+theorem monic_mul_leadingCoeff_inv {p : K[X]} (h : p ≠ 0) : Monic (p * C (leadingCoeff p)⁻¹) := by
+  rw [Monic, leadingCoeff_mul, leadingCoeff_C,
+    mul_inv_cancel (show leadingCoeff p ≠ 0 from mt leadingCoeff_eq_zero.1 h)]
+#align polynomial.monic_mul_leading_coeff_inv Polynomial.monic_mul_leadingCoeff_inv
+
+-- `simp` normal form of `degree_mul_leadingCoeff_inv`
+@[simp] lemma degree_leadingCoeff_inv {p : K[X]} (hp0 : p ≠ 0) :
+    degree (C (leadingCoeff p)⁻¹) = 0 :=
+  degree_C (inv_ne_zero <| leadingCoeff_ne_zero.mpr hp0)
+
+theorem degree_mul_leadingCoeff_inv (p : K[X]) {q : K[X]} (h : q ≠ 0) :
+    degree (p * C (leadingCoeff q)⁻¹) = degree p := by
+  have h₁ : (leadingCoeff q)⁻¹ ≠ 0 := inv_ne_zero (mt leadingCoeff_eq_zero.1 h)
+  rw [degree_mul_C h₁]
+#align polynomial.degree_mul_leading_coeff_inv Polynomial.degree_mul_leadingCoeff_inv
+
+theorem natDegree_mul_leadingCoeff_inv (p : K[X]) {q : K[X]} (h : q ≠ 0) :
+    natDegree (p * C (leadingCoeff q)⁻¹) = natDegree p :=
+  natDegree_eq_of_degree_eq (degree_mul_leadingCoeff_inv _ h)
+
+theorem degree_mul_leadingCoeff_self_inv (p : K[X]) :
+    degree (p * C (leadingCoeff p)⁻¹) = degree p := by
+  by_cases hp : p = 0
+  · simp [hp]
+  exact degree_mul_leadingCoeff_inv _ hp
+
+theorem natDegree_mul_leadingCoeff_self_inv (p : K[X]) :
+    natDegree (p * C (leadingCoeff p)⁻¹) = natDegree p :=
+  natDegree_eq_of_degree_eq (degree_mul_leadingCoeff_self_inv _)
+
+-- `simp` normal form of `degree_mul_leadingCoeff_self_inv`
+@[simp] lemma degree_add_degree_leadingCoeff_inv (p : K[X]) :
+    degree p + degree (C (leadingCoeff p)⁻¹) = degree p := by
+  rw [← degree_mul, degree_mul_leadingCoeff_self_inv]
+
+end DivisionRing
+
 end Polynomial

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feat: Lemmas relating Polynomial.eraseLead and nextCoeff. (#9083)

Some little theorems relating eraseLead and nextCoeff to each other. Also includes monomial_sub and card_support_mul which could be of independent interest.

Co-authored-by: Alex Meiburg <timeroot.alex@gmail.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

716dfd4a

Diff

@@ -315,6 +315,12 @@ theorem natDegree_map_eq_iff {f : R →+* S} {p : Polynomial R} :
   simp [h, h2, h3] -- simp doesn't rewrite in the hypothesis for some reason
   tauto
 
+theorem natDegree_pos_of_nextCoeff_ne_zero (h : p.nextCoeff ≠ 0) : 0 < p.natDegree := by
+  rw [nextCoeff] at h
+  by_cases hpz : p.natDegree = 0
+  · simp_all only [ne_eq, zero_le, ite_true, not_true_eq_false]
+  · apply Nat.zero_lt_of_ne_zero hpz
+
 end Degree
 
 end Semiring
@@ -349,7 +355,7 @@ end Ring
 
 section NoZeroDivisors
 
-variable [Semiring R] [NoZeroDivisors R] {p q : R[X]}
+variable [Semiring R] [NoZeroDivisors R] {p q : R[X]} {a : R}
 
 theorem degree_mul_C (a0 : a ≠ 0) : (p * C a).degree = p.degree := by
   rw [degree_mul, degree_C a0, add_zero]
@@ -371,6 +377,24 @@ theorem natDegree_C_mul (a0 : a ≠ 0) : (C a * p).natDegree = p.natDegree := by
 set_option linter.uppercaseLean3 false in
 #align polynomial.nat_degree_C_mul Polynomial.natDegree_C_mul
 
+@[simp]
+lemma nextCoeff_C_mul_X_add_C (ha : a ≠ 0) (c : R) : nextCoeff (C a * X + C c) = c := by
+  rw [nextCoeff_of_natDegree_pos] <;> simp [ha]
+
+lemma natDegree_eq_one : p.natDegree = 1 ↔ ∃ a ≠ 0, ∃ b, C a * X + C b = p := by
+  refine ⟨fun hp ↦ ⟨p.coeff 1, fun h ↦ ?_, p.coeff 0, ?_⟩, ?_⟩
+  · rw [← hp, coeff_natDegree, leadingCoeff_eq_zero] at h
+    aesop
+  · ext n
+    obtain _ | _ | n := n
+    · simp
+    · simp
+    · simp only [coeff_add, coeff_mul_X, coeff_C_succ, add_zero]
+      rw [coeff_eq_zero_of_natDegree_lt]
+      simp [hp]
+  · rintro ⟨a, ha, b, rfl⟩
+    simp [ha]
+
 theorem natDegree_comp : natDegree (p.comp q) = natDegree p * natDegree q := by
   by_cases q0 : q.natDegree = 0
   · rw [degree_le_zero_iff.mp (natDegree_eq_zero_iff_degree_le_zero.mp q0), comp_C, natDegree_C,

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chore(*): replace $ with <| (#9319)

See Zulip thread for the discussion.

9f6d3388

Diff

@@ -186,7 +186,7 @@ theorem coeff_pow_eq_ite_of_natDegree_le_of_le {o : ℕ}
     coeff (p ^ m) o = if o = m * n then (coeff p n) ^ m else 0 := by
   rcases eq_or_ne o (m * n) with rfl | h
   · simpa only [ite_true] using coeff_pow_of_natDegree_le pn
-  · simpa only [h, ite_false] using coeff_eq_zero_of_natDegree_lt $
+  · simpa only [h, ite_false] using coeff_eq_zero_of_natDegree_lt <|
       lt_of_le_of_lt (natDegree_pow_le_of_le m pn) (lt_of_le_of_ne mno h.symm)
 
 theorem coeff_add_eq_left_of_lt (qn : q.natDegree < n) : (p + q).coeff n = p.coeff n :=

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chore: Rename pow monotonicity lemmas (#9095)

The names for lemmas about monotonicity of (a ^ ·) and (· ^ n) were a mess. This PR tidies up everything related by following the naming convention for (a * ·) and (· * b). Namely, (a ^ ·) is pow_right and (· ^ n) is pow_left in lemma names. All lemma renames follow the corresponding multiplication lemma names closely.

Renames

`Algebra.GroupPower.Order`

pow_mono → pow_right_mono
pow_le_pow → pow_le_pow_right
pow_le_pow_of_le_left → pow_le_pow_left
pow_lt_pow_of_lt_left → pow_lt_pow_left
strictMonoOn_pow → pow_left_strictMonoOn
pow_strictMono_right → pow_right_strictMono
pow_lt_pow → pow_lt_pow_right
pow_lt_pow_iff → pow_lt_pow_iff_right
pow_le_pow_iff → pow_le_pow_iff_right
self_lt_pow → lt_self_pow
strictAnti_pow → pow_right_strictAnti
pow_lt_pow_iff_of_lt_one → pow_lt_pow_iff_right_of_lt_one
pow_lt_pow_of_lt_one → pow_lt_pow_right_of_lt_one
lt_of_pow_lt_pow → lt_of_pow_lt_pow_left
le_of_pow_le_pow → le_of_pow_le_pow_left
pow_lt_pow₀ → pow_lt_pow_right₀

`Algebra.GroupPower.CovariantClass`

pow_le_pow_of_le_left' → pow_le_pow_left'
nsmul_le_nsmul_of_le_right → nsmul_le_nsmul_right
pow_lt_pow' → pow_lt_pow_right'
nsmul_lt_nsmul → nsmul_lt_nsmul_left
pow_strictMono_left → pow_right_strictMono'
nsmul_strictMono_right → nsmul_left_strictMono
StrictMono.pow_right' → StrictMono.pow_const
StrictMono.nsmul_left → StrictMono.const_nsmul
pow_strictMono_right' → pow_left_strictMono
nsmul_strictMono_left → nsmul_right_strictMono
Monotone.pow_right → Monotone.pow_const
Monotone.nsmul_left → Monotone.const_nsmul
lt_of_pow_lt_pow' → lt_of_pow_lt_pow_left'
lt_of_nsmul_lt_nsmul → lt_of_nsmul_lt_nsmul_right
pow_le_pow' → pow_le_pow_right'
nsmul_le_nsmul → nsmul_le_nsmul_left
pow_le_pow_of_le_one' → pow_le_pow_right_of_le_one'
nsmul_le_nsmul_of_nonpos → nsmul_le_nsmul_left_of_nonpos
le_of_pow_le_pow' → le_of_pow_le_pow_left'
le_of_nsmul_le_nsmul' → le_of_nsmul_le_nsmul_right'
pow_le_pow_iff' → pow_le_pow_iff_right'
nsmul_le_nsmul_iff → nsmul_le_nsmul_iff_left
pow_lt_pow_iff' → pow_lt_pow_iff_right'
nsmul_lt_nsmul_iff → nsmul_lt_nsmul_iff_left

`Data.Nat.Pow`

Nat.pow_lt_pow_of_lt_left → Nat.pow_lt_pow_left
Nat.pow_le_iff_le_left → Nat.pow_le_pow_iff_left
Nat.pow_lt_iff_lt_left → Nat.pow_lt_pow_iff_left

Lemmas added

pow_le_pow_iff_left
pow_lt_pow_iff_left
pow_right_injective
pow_right_inj
Nat.pow_le_pow_left to have the correct name since Nat.pow_le_pow_of_le_left is in Std.
Nat.pow_le_pow_right to have the correct name since Nat.pow_le_pow_of_le_right is in Std.

Lemmas removed

self_le_pow was a duplicate of le_self_pow.
Nat.pow_lt_pow_of_lt_right is defeq to pow_lt_pow_right.
Nat.pow_right_strictMono is defeq to pow_right_strictMono.
Nat.pow_le_iff_le_right is defeq to pow_le_pow_iff_right.
Nat.pow_lt_iff_lt_right is defeq to pow_lt_pow_iff_right.

Other changes

A bunch of proofs have been golfed.
Some lemma assumptions have been turned from 0 < n or 1 ≤ n to n ≠ 0.
A few Nat lemmas have been protected.
One docstring has been fixed.

d61c95e1

Diff

@@ -51,7 +51,7 @@ theorem natDegree_comp_le : natDegree (p.comp q) ≤ natDegree p * natDegree q :
               _ ≤ natDegree (C (coeff p n)) + n • degree q :=
                 (add_le_add degree_le_natDegree (degree_pow_le _ _))
               _ ≤ natDegree (C (coeff p n)) + n • ↑(natDegree q) :=
-                (add_le_add_left (nsmul_le_nsmul_of_le_right (@degree_le_natDegree _ _ q) n) _)
+                (add_le_add_left (nsmul_le_nsmul_right (@degree_le_natDegree _ _ q) n) _)
               _ = (n * natDegree q : ℕ) := by
                 rw [natDegree_C, Nat.cast_zero, zero_add, nsmul_eq_mul];
                   simp

728baa2f

refactor(Data/Polynomial): remove open Classical (#7706)

This doesn't change any polynomial operations, but:

Makes some Decidable values computable (otherwise, they're pointless!)
Add a few missing arguments to lemmas here and there to make them more general

This is exhaustive, within the directories it touches.

Once again, the use of letI := Classical.decEq R instead of classical here is because of the weird style of proofs in these files, where if is preferred to by_cases.

4a7ff0e3

Diff

@@ -18,7 +18,7 @@ Some of the main results include
 
 noncomputable section
 
-open Classical Polynomial
+open Polynomial
 
 open Finsupp Finset
 
@@ -35,6 +35,7 @@ variable [Semiring R] {p q r : R[X]}
 section Degree
 
 theorem natDegree_comp_le : natDegree (p.comp q) ≤ natDegree p * natDegree q :=
+  letI := Classical.decEq R
   if h0 : p.comp q = 0 then by rw [h0, natDegree_zero]; exact Nat.zero_le _
   else
     WithBot.coe_le_coe.1 <|
@@ -201,6 +202,7 @@ theorem coeff_add_eq_right_of_lt (pn : p.natDegree < n) : (p + q).coeff n = q.co
 theorem degree_sum_eq_of_disjoint (f : S → R[X]) (s : Finset S)
     (h : Set.Pairwise { i | i ∈ s ∧ f i ≠ 0 } (Ne on degree ∘ f)) :
     degree (s.sum f) = s.sup fun i => degree (f i) := by
+  classical
   induction' s using Finset.induction_on with x s hx IH
   · simp
   · simp only [hx, Finset.sum_insert, not_false_iff, Finset.sup_insert]

728baa2f

feat: add degree_map_eq_iff (#7170)

Stub lemma for degree_map_eq_iff. Feel free to try proving it!

Co-authored-by: Floris van Doorn

Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>

374447aa

Diff

@@ -289,6 +289,30 @@ theorem coe_lt_degree {p : R[X]} {n : ℕ} : (n : WithBot ℕ) < degree p ↔ n
   simp [degree_eq_natDegree h, Nat.cast_lt]
 #align polynomial.coe_lt_degree Polynomial.coe_lt_degree
 
+@[simp]
+theorem degree_map_eq_iff {f : R →+* S} {p : Polynomial R} :
+    degree (map f p) = degree p ↔ f (leadingCoeff p) ≠ 0 ∨ p = 0 := by
+  rcases eq_or_ne p 0 with h|h
+  · simp [h]
+  simp only [h, or_false]
+  refine ⟨fun h2 ↦ ?_, degree_map_eq_of_leadingCoeff_ne_zero f⟩
+  have h3 : natDegree (map f p) = natDegree p
+  · simp_rw [natDegree, h2]
+  have h4 : map f p ≠ 0
+  · rwa [ne_eq, ← degree_eq_bot, h2, degree_eq_bot]
+  rwa [← coeff_natDegree, ← coeff_map, ← h3, coeff_natDegree, ne_eq, leadingCoeff_eq_zero]
+
+@[simp]
+theorem natDegree_map_eq_iff {f : R →+* S} {p : Polynomial R} :
+    natDegree (map f p) = natDegree p ↔ f (p.leadingCoeff) ≠ 0 ∨ natDegree p = 0 := by
+  rcases eq_or_ne (natDegree p) 0 with h|h
+  · simp_rw [h, ne_eq, or_true, iff_true, ← Nat.le_zero, ← h, natDegree_map_le f p]
+  have h2 : p ≠ 0 := by rintro rfl; simp at h
+  have h3 : degree p ≠ (0 : ℕ)  := degree_ne_of_natDegree_ne h
+  simp_rw [h, or_false, natDegree, WithBot.unbot'_eq_unbot'_iff, degree_map_eq_iff]
+  simp [h, h2, h3] -- simp doesn't rewrite in the hypothesis for some reason
+  tauto
+
 end Degree
 
 end Semiring

728baa2f

feat: WithTop.charZero (#6992)

Also WithBot.charZero

844436b8

Diff

@@ -69,8 +69,7 @@ theorem degree_pos_of_root {p : R[X]} (hp : p ≠ 0) (h : IsRoot p a) : 0 < degr
 #align polynomial.degree_pos_of_root Polynomial.degree_pos_of_root
 
 theorem natDegree_le_iff_coeff_eq_zero : p.natDegree ≤ n ↔ ∀ N : ℕ, n < N → p.coeff N = 0 := by
-  simp_rw [natDegree_le_iff_degree_le, degree_le_iff_coeff_zero, Nat.cast_withBot,
-    WithBot.coe_lt_coe]
+  simp_rw [natDegree_le_iff_degree_le, degree_le_iff_coeff_zero, Nat.cast_lt]
 #align polynomial.nat_degree_le_iff_coeff_eq_zero Polynomial.natDegree_le_iff_coeff_eq_zero
 
 theorem natDegree_add_le_iff_left {n : ℕ} (p q : R[X]) (qn : q.natDegree ≤ n) :
@@ -287,7 +286,7 @@ theorem degree_pos_of_eval₂_root {p : R[X]} (hp : p ≠ 0) (f : R →+* S) {z
 theorem coe_lt_degree {p : R[X]} {n : ℕ} : (n : WithBot ℕ) < degree p ↔ n < natDegree p := by
   by_cases h : p = 0
   · simp [h]
-  simp [degree_eq_natDegree h, Nat.cast_withBot, WithBot.coe_lt_coe]
+  simp [degree_eq_natDegree h, Nat.cast_lt]
 #align polynomial.coe_lt_degree Polynomial.coe_lt_degree
 
 end Degree

728baa2f

chore: remove unused simps (#6632)

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

916c75c1

Diff

@@ -232,8 +232,7 @@ theorem natDegree_sum_eq_of_disjoint (f : S → R[X]) (s : Finset S)
     have hs : s.Nonempty := ⟨x, hx⟩
     refine' natDegree_eq_of_degree_eq_some _
     rw [degree_sum_eq_of_disjoint]
-    · dsimp
-      rw [← Finset.sup'_eq_sup hs, ← Finset.sup'_eq_sup hs,
+    · rw [← Finset.sup'_eq_sup hs, ← Finset.sup'_eq_sup hs,
         Nat.cast_withBot, Finset.coe_sup' hs, ←
         Finset.sup'_eq_sup hs]
       refine' le_antisymm _ _

728baa2f

feat: simple lemmas about polynomials and their degrees (#6220)

This PR extracts some lemmas about polynomials that are helpful for the tactic compute_degree (#6221).

The signature of a theorem changed:

theorem coeff_pow_of_natDegree_le (pn : p.natDegree ≤ n) :
    (p ^ m).coeff (n * m) = p.coeff n ^ m  -- <-- the order of the product was `n * m`
    (p ^ m).coeff (m * n) = p.coeff n ^ m  -- <-- and it became `m * n`

Modified files:

Data/Polynomial/Basic.lean
Data/Polynomial/Degree/Lemmas.lean
Data/Polynomial/Degree/Definitions.lean
Data/Polynomial/Coeff.lean  -- for a "`simp` can prove this" golf

8c698a52

Diff

@@ -173,14 +173,22 @@ theorem coeff_mul_of_natDegree_le (pm : p.natDegree ≤ m) (qn : q.natDegree ≤
 #align polynomial.coeff_mul_of_nat_degree_le Polynomial.coeff_mul_of_natDegree_le
 
 theorem coeff_pow_of_natDegree_le (pn : p.natDegree ≤ n) :
-    (p ^ m).coeff (n * m) = p.coeff n ^ m := by
+    (p ^ m).coeff (m * n) = p.coeff n ^ m := by
   induction' m with m hm
   · simp
-  · rw [pow_succ', pow_succ', ← hm, Nat.mul_succ, coeff_mul_of_natDegree_le _ pn]
-    refine' natDegree_pow_le.trans (le_trans _ (mul_comm _ _).le)
+  · rw [pow_succ', pow_succ', ← hm, Nat.succ_mul, coeff_mul_of_natDegree_le _ pn]
+    refine' natDegree_pow_le.trans (le_trans _ (le_refl _))
     exact mul_le_mul_of_nonneg_left pn m.zero_le
 #align polynomial.coeff_pow_of_nat_degree_le Polynomial.coeff_pow_of_natDegree_le
 
+theorem coeff_pow_eq_ite_of_natDegree_le_of_le {o : ℕ}
+    (pn : natDegree p ≤ n) (mno : m * n ≤ o) :
+    coeff (p ^ m) o = if o = m * n then (coeff p n) ^ m else 0 := by
+  rcases eq_or_ne o (m * n) with rfl | h
+  · simpa only [ite_true] using coeff_pow_of_natDegree_le pn
+  · simpa only [h, ite_false] using coeff_eq_zero_of_natDegree_lt $
+      lt_of_le_of_lt (natDegree_pow_le_of_le m pn) (lt_of_le_of_ne mno h.symm)
+
 theorem coeff_add_eq_left_of_lt (qn : q.natDegree < n) : (p + q).coeff n = p.coeff n :=
   (coeff_add _ _ _).trans <|
     (congr_arg _ <| coeff_eq_zero_of_natDegree_lt <| qn).trans <| add_zero _

728baa2f

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2018 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-
-! This file was ported from Lean 3 source module data.polynomial.degree.lemmas
-! leanprover-community/mathlib commit 728baa2f54e6062c5879a3e397ac6bac323e506f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Polynomial.Eval
 
+#align_import data.polynomial.degree.lemmas from "leanprover-community/mathlib"@"728baa2f54e6062c5879a3e397ac6bac323e506f"
+
 /-!
 # Theory of degrees of polynomials

728baa2f

fix precedence of Nat.iterate (#5589)

bd2fff86

Diff

@@ -355,7 +355,7 @@ theorem natDegree_comp : natDegree (p.comp q) = natDegree p * natDegree q := by
 
 @[simp]
 theorem natDegree_iterate_comp (k : ℕ) :
-    ((p.comp^[k]) q).natDegree = p.natDegree ^ k * q.natDegree := by
+    (p.comp^[k] q).natDegree = p.natDegree ^ k * q.natDegree := by
   induction' k with k IH
   · simp
   · rw [Function.iterate_succ_apply', natDegree_comp, IH, pow_succ, mul_assoc]

728baa2f

chore: clean up spacing around at and goals (#5387)

Changes are of the form

some_tactic at h⊢ -> some_tactic at h ⊢
some_tactic at h -> some_tactic at h

2a870323

Diff

@@ -247,7 +247,7 @@ theorem natDegree_sum_eq_of_disjoint (f : S → R[X]) (s : Finset S)
           simpa [← Nat.cast_withBot, hb', degree_eq_bot] using hx'
         exact ⟨b, hb, (degree_eq_natDegree hb').ge⟩
     · exact h.imp fun x y hxy hxy' => hxy (natDegree_eq_of_degree_eq hxy')
-  · push_neg  at H
+  · push_neg at H
     rw [Finset.sum_eq_zero H, natDegree_zero, eq_comm, show 0 = ⊥ from rfl, Finset.sup_eq_bot_iff]
     intro x hx
     simp [H x hx]

728baa2f

chore: bye-bye, solo bys! (#3825)

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

14167e48

Diff

@@ -175,8 +175,8 @@ theorem coeff_mul_of_natDegree_le (pm : p.natDegree ≤ m) (qn : q.natDegree ≤
     exact natDegree_lt_coeff_mul (add_lt_add hm hn)
 #align polynomial.coeff_mul_of_nat_degree_le Polynomial.coeff_mul_of_natDegree_le
 
-theorem coeff_pow_of_natDegree_le (pn : p.natDegree ≤ n) : (p ^ m).coeff (n * m) = p.coeff n ^ m :=
-  by
+theorem coeff_pow_of_natDegree_le (pn : p.natDegree ≤ n) :
+    (p ^ m).coeff (n * m) = p.coeff n ^ m := by
   induction' m with m hm
   · simp
   · rw [pow_succ', pow_succ', ← hm, Nat.mul_succ, coeff_mul_of_natDegree_le _ pn]
@@ -267,8 +267,7 @@ variable [Semiring S]
 
 theorem natDegree_pos_of_eval₂_root {p : R[X]} (hp : p ≠ 0) (f : R →+* S) {z : S}
     (hz : eval₂ f z p = 0) (inj : ∀ x : R, f x = 0 → x = 0) : 0 < natDegree p :=
-  lt_of_not_ge fun hlt =>
-    by
+  lt_of_not_ge fun hlt => by
     have A : p = C (p.coeff 0) := eq_C_of_natDegree_le_zero hlt
     rw [A, eval₂_C] at hz
     simp only [inj (p.coeff 0) hz, RingHom.map_zero] at A

728baa2f

chore: tidy various files (#3124)

55209140

Diff

@@ -134,24 +134,24 @@ set_option linter.uppercaseLean3 false in
 /-- Although not explicitly stated, the assumptions of lemma `nat_degree_mul_C_eq_of_mul_ne_zero`
 force the polynomial `p` to be non-zero, via `p.leading_coeff ≠ 0`.
 -/
-theorem natDegree_mul_c_eq_of_mul_ne_zero (h : p.leadingCoeff * a ≠ 0) :
+theorem natDegree_mul_C_eq_of_mul_ne_zero (h : p.leadingCoeff * a ≠ 0) :
     (p * C a).natDegree = p.natDegree := by
   refine' eq_natDegree_of_le_mem_support (natDegree_mul_C_le p a) _
   refine' mem_support_iff.mpr _
   rwa [coeff_mul_C]
 set_option linter.uppercaseLean3 false in
-#align polynomial.nat_degree_mul_C_eq_of_mul_ne_zero Polynomial.natDegree_mul_c_eq_of_mul_ne_zero
+#align polynomial.nat_degree_mul_C_eq_of_mul_ne_zero Polynomial.natDegree_mul_C_eq_of_mul_ne_zero
 
 /-- Although not explicitly stated, the assumptions of lemma `nat_degree_C_mul_eq_of_mul_ne_zero`
 force the polynomial `p` to be non-zero, via `p.leading_coeff ≠ 0`.
 -/
-theorem natDegree_c_mul_eq_of_mul_ne_zero (h : a * p.leadingCoeff ≠ 0) :
+theorem natDegree_C_mul_eq_of_mul_ne_zero (h : a * p.leadingCoeff ≠ 0) :
     (C a * p).natDegree = p.natDegree := by
   refine' eq_natDegree_of_le_mem_support (natDegree_C_mul_le a p) _
   refine' mem_support_iff.mpr _
   rwa [coeff_C_mul]
 set_option linter.uppercaseLean3 false in
-#align polynomial.nat_degree_C_mul_eq_of_mul_ne_zero Polynomial.natDegree_c_mul_eq_of_mul_ne_zero
+#align polynomial.nat_degree_C_mul_eq_of_mul_ne_zero Polynomial.natDegree_C_mul_eq_of_mul_ne_zero
 
 theorem natDegree_add_coeff_mul (f g : R[X]) :
     (f * g).coeff (f.natDegree + g.natDegree) = f.coeff f.natDegree * g.coeff g.natDegree := by
@@ -345,8 +345,7 @@ set_option linter.uppercaseLean3 false in
 
 theorem natDegree_comp : natDegree (p.comp q) = natDegree p * natDegree q := by
   by_cases q0 : q.natDegree = 0
-  ·
-    rw [degree_le_zero_iff.mp (natDegree_eq_zero_iff_degree_le_zero.mp q0), comp_C, natDegree_C,
+  · rw [degree_le_zero_iff.mp (natDegree_eq_zero_iff_degree_le_zero.mp q0), comp_C, natDegree_C,
       natDegree_C, mul_zero]
   · by_cases p0 : p = 0
     · simp only [p0, zero_comp, natDegree_zero, zero_mul]

728baa2f

feat: port IMO 2006 Q5 helper results (#3136)

We don't port the IMO proof itself since it seems there's no archive in Mathlib4.

Mathlib 3: https://github.com/leanprover-community/mathlib/pull/15613

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

074dad72

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
 
 ! This file was ported from Lean 3 source module data.polynomial.degree.lemmas
-! leanprover-community/mathlib commit 302eab4f46abb63de520828de78c04cb0f9b5836
+! leanprover-community/mathlib commit 728baa2f54e6062c5879a3e397ac6bac323e506f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -355,6 +355,14 @@ theorem natDegree_comp : natDegree (p.comp q) = natDegree p * natDegree q := by
       ne_zero_of_natDegree_gt (Nat.pos_of_ne_zero q0), pow_ne_zero, Ne.def, not_false_iff]
 #align polynomial.nat_degree_comp Polynomial.natDegree_comp
 
+@[simp]
+theorem natDegree_iterate_comp (k : ℕ) :
+    ((p.comp^[k]) q).natDegree = p.natDegree ^ k * q.natDegree := by
+  induction' k with k IH
+  · simp
+  · rw [Function.iterate_succ_apply', natDegree_comp, IH, pow_succ, mul_assoc]
+#align polynomial.nat_degree_iterate_comp Polynomial.natDegree_iterate_comp
+
 theorem leadingCoeff_comp (hq : natDegree q ≠ 0) :
     leadingCoeff (p.comp q) = leadingCoeff p * leadingCoeff q ^ natDegree p := by
   rw [← coeff_comp_degree_mul_degree hq, ← natDegree_comp, coeff_natDegree]

302eab4f

feat: port Data.Polynomial.Degree.Lemmas (#2723)

13b68bd9

`data.polynomial.degree.lemmas` ⟷ `Mathlib.Data.Polynomial.Degree.Lemmas`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

`Algebra.GroupPower.Order`

`Algebra.GroupPower.CovariantClass`

`Data.Nat.Pow`

Lemmas added

Lemmas removed

Other changes

Dependencies 8 + 395

data.polynomial.degree.lemmas ⟷ Mathlib.Data.Polynomial.Degree.Lemmas

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Algebra.GroupPower.Order

Algebra.GroupPower.CovariantClass

Data.Nat.Pow

Lemmas added

Lemmas removed

Other changes

Dependencies 8 + 395

`data.polynomial.degree.lemmas` ⟷ `Mathlib.Data.Polynomial.Degree.Lemmas`

`Algebra.GroupPower.Order`

`Algebra.GroupPower.CovariantClass`

`Data.Nat.Pow`