data.polynomial.monic ⟷ Mathlib.Data.Polynomial.Monic

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

@@ -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.Reverse
+import Algebra.Polynomial.Reverse
 import Algebra.Regular.SMul
 
 #align_import data.polynomial.monic from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"

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

@@ -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
 -/
 import Data.Polynomial.Reverse
-import Algebra.Regular.Smul
+import Algebra.Regular.SMul
 
 #align_import data.polynomial.monic from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
 
@@ -142,7 +142,7 @@ theorem Monic.mul (hp : Monic p) (hq : Monic q) : Monic (p * q) :=
 #print Polynomial.Monic.pow /-
 theorem Monic.pow (hp : Monic p) : ∀ n : ℕ, Monic (p ^ n)
   | 0 => monic_one
-  | n + 1 => by rw [pow_succ]; exact hp.mul (monic.pow n)
+  | n + 1 => by rw [pow_succ']; exact hp.mul (monic.pow n)
 #align polynomial.monic.pow Polynomial.Monic.pow
 -/
 
@@ -285,7 +285,7 @@ theorem natDegree_pow (hp : p.Monic) (n : ℕ) : (p ^ n).natDegree = n * p.natDe
   by
   induction' n with n hn
   · simp
-  · rw [pow_succ, hp.nat_degree_mul (hp.pow n), hn]
+  · rw [pow_succ', hp.nat_degree_mul (hp.pow n), hn]
     ring
 #align polynomial.monic.nat_degree_pow Polynomial.Monic.natDegree_pow
 -/

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

@@ -68,8 +68,8 @@ theorem Monic.as_sum (hp : p.Monic) :
 theorem ne_zero_of_ne_zero_of_monic (hp : p ≠ 0) (hq : Monic q) : q ≠ 0 :=
   by
   rintro rfl
-  rw [monic.def, leading_coeff_zero] at hq 
-  rw [← mul_one p, ← C_1, ← hq, C_0, MulZeroClass.mul_zero] at hp 
+  rw [monic.def, leading_coeff_zero] at hq
+  rw [← mul_one p, ← C_1, ← hq, C_0, MulZeroClass.mul_zero] at hp
   exact hp rfl
 #align polynomial.ne_zero_of_ne_zero_of_monic Polynomial.ne_zero_of_ne_zero_of_monic
 -/
@@ -186,7 +186,7 @@ theorem natDegree_eq_zero_iff_eq_one (hp : p.Monic) : p.natDegree = 0 ↔ p = 1
   swap; · rw [h]; exact nat_degree_one
   have : p = C (p.coeff 0) := by
     rw [← Polynomial.degree_le_zero_iff]
-    rwa [Polynomial.natDegree_eq_zero_iff_degree_le_zero] at h 
+    rwa [Polynomial.natDegree_eq_zero_iff_degree_le_zero] at h
   rw [this]; convert C_1; rw [← h]; apply hp
 #align polynomial.monic.nat_degree_eq_zero_iff_eq_one Polynomial.Monic.natDegree_eq_zero_iff_eq_one
 -/
@@ -242,7 +242,7 @@ theorem natDegree_mul_comm (hp : p.Monic) (q : R[X]) : (p * q).natDegree = (q *
 theorem not_dvd_of_natDegree_lt (hp : Monic p) (h0 : q ≠ 0) (hl : natDegree q < natDegree p) :
     ¬p ∣ q := by
   rintro ⟨r, rfl⟩
-  rw [hp.nat_degree_mul' <| right_ne_zero_of_mul h0] at hl 
+  rw [hp.nat_degree_mul' <| right_ne_zero_of_mul h0] at hl
   exact hl.not_le (Nat.le_add_right _ _)
 #align polynomial.monic.not_dvd_of_nat_degree_lt Polynomial.Monic.not_dvd_of_natDegree_lt
 -/
@@ -305,7 +305,7 @@ theorem Monic.eq_one_of_isUnit (hm : Monic p) (hpu : IsUnit p) : p = 1 :=
   nontriviality R
   obtain ⟨q, h⟩ := hpu.exists_right_inv
   have := hm.nat_degree_mul' (right_ne_zero_of_mul_eq_one h)
-  rw [h, nat_degree_one, eq_comm, add_eq_zero_iff] at this 
+  rw [h, nat_degree_one, eq_comm, add_eq_zero_iff] at this
   exact hm.nat_degree_eq_zero_iff_eq_one.mp this.1
 #align polynomial.monic.eq_one_of_is_unit Polynomial.Monic.eq_one_of_isUnit
 -/
@@ -470,7 +470,7 @@ theorem monic_X_sub_C (x : R) : Monic (X - C x) := by
 
 #print Polynomial.monic_X_pow_sub /-
 theorem monic_X_pow_sub {n : ℕ} (H : degree p ≤ n) : Monic (X ^ (n + 1) - p) := by
-  simpa [sub_eq_add_neg] using monic_X_pow_add (show degree (-p) ≤ n by rwa [← degree_neg p] at H )
+  simpa [sub_eq_add_neg] using monic_X_pow_add (show degree (-p) ≤ n by rwa [← degree_neg p] at H)
 #align polynomial.monic_X_pow_sub Polynomial.monic_X_pow_sub
 -/
 
@@ -540,7 +540,7 @@ theorem Monic.mul_left_ne_zero (hp : Monic p) {q : R[X]} (hq : q ≠ 0) : q * p
   · simpa [h]
   rw [Ne.def, ← degree_eq_bot, hp.degree_mul, WithBot.add_eq_bot, not_or, degree_eq_bot]
   refine' ⟨hq, _⟩
-  rw [← hp.degree_le_zero_iff_eq_one, not_le] at h 
+  rw [← hp.degree_le_zero_iff_eq_one, not_le] at h
   refine' (lt_trans _ h).ne'
   simp
 #align polynomial.monic.mul_left_ne_zero Polynomial.Monic.mul_left_ne_zero
@@ -554,7 +554,7 @@ theorem Monic.mul_right_ne_zero (hp : Monic p) {q : R[X]} (hq : q ≠ 0) : p * q
   rw [Ne.def, ← degree_eq_bot, hp.degree_mul_comm, hp.degree_mul, WithBot.add_eq_bot, not_or,
     degree_eq_bot]
   refine' ⟨hq, _⟩
-  rw [← hp.degree_le_zero_iff_eq_one, not_le] at h 
+  rw [← hp.degree_le_zero_iff_eq_one, not_le] at h
   refine' (lt_trans _ h).ne'
   simp
 #align polynomial.monic.mul_right_ne_zero Polynomial.Monic.mul_right_ne_zero
@@ -590,7 +590,7 @@ theorem Monic.isRegular {R : Type _} [Ring R] {p : R[X]} (hp : Monic p) : IsRegu
   · intro q r h
     rw [← sub_eq_zero, ← hp.mul_right_eq_zero_iff, mul_sub, h, sub_self]
   · intro q r h
-    simp only at h 
+    simp only at h
     rw [← sub_eq_zero, ← hp.mul_left_eq_zero_iff, sub_mul, h, sub_self]
 #align polynomial.monic.is_regular Polynomial.Monic.isRegular
 -/
@@ -602,11 +602,11 @@ theorem degree_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction S
   refine' le_antisymm _ _
   · rw [degree_le_iff_coeff_zero]
     intro m hm
-    rw [degree_lt_iff_coeff_zero] at hm 
+    rw [degree_lt_iff_coeff_zero] at hm
     simp [hm m le_rfl]
   · rw [degree_le_iff_coeff_zero]
     intro m hm
-    rw [degree_lt_iff_coeff_zero] at hm 
+    rw [degree_lt_iff_coeff_zero] at hm
     refine' h _
     simpa using hm m le_rfl
 #align polynomial.degree_smul_of_smul_regular Polynomial.degree_smul_of_smul_regular
@@ -621,7 +621,7 @@ theorem natDegree_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction
   rw [← WithBot.coe_eq_coe, ← degree_eq_nat_degree hp, ← degree_eq_nat_degree,
     degree_smul_of_smul_regular p h]
   contrapose! hp
-  rw [← smul_zero k] at hp 
+  rw [← smul_zero k] at hp
   exact h.polynomial hp
 #align polynomial.nat_degree_smul_of_smul_regular Polynomial.natDegree_smul_of_smul_regular
 -/
@@ -648,14 +648,14 @@ theorem isUnit_leadingCoeff_mul_right_eq_zero_iff (h : IsUnit p.leadingCoeff) {q
     p * q = 0 ↔ q = 0 := by
   constructor
   · intro hp
-    rw [← smul_eq_zero_iff_eq h.unit⁻¹] at hp 
+    rw [← smul_eq_zero_iff_eq h.unit⁻¹] at hp
     have : h.unit⁻¹ • (p * q) = h.unit⁻¹ • p * q :=
       by
       ext
       simp only [Units.smul_def, coeff_smul, coeff_mul, smul_eq_mul, mul_sum]
       refine' sum_congr rfl fun x hx => _
       rw [← mul_assoc]
-    rwa [this, monic.mul_right_eq_zero_iff] at hp 
+    rwa [this, monic.mul_right_eq_zero_iff] at hp
     exact monic_of_is_unit_leading_coeff_inv_smul _
   · rintro rfl
     simp
@@ -668,8 +668,8 @@ theorem isUnit_leadingCoeff_mul_left_eq_zero_iff (h : IsUnit p.leadingCoeff) {q
   constructor
   · intro hp
     replace hp := congr_arg (· * C ↑h.unit⁻¹) hp
-    simp only [MulZeroClass.zero_mul] at hp 
-    rwa [mul_assoc, monic.mul_left_eq_zero_iff] at hp 
+    simp only [MulZeroClass.zero_mul] at hp
+    rwa [mul_assoc, monic.mul_left_eq_zero_iff] at hp
     refine' monic_mul_C_of_leading_coeff_mul_eq_one _
     simp [Units.mul_inv_eq_iff_eq_mul, IsUnit.unit_spec]
   · rintro rfl

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

@@ -3,8 +3,8 @@ 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.Reverse
-import Mathbin.Algebra.Regular.Smul
+import Data.Polynomial.Reverse
+import Algebra.Regular.Smul
 
 #align_import data.polynomial.monic from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
 

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

@@ -2,15 +2,12 @@
 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.monic
-! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Polynomial.Reverse
 import Mathbin.Algebra.Regular.Smul
 
+#align_import data.polynomial.monic from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
+
 /-!
 # Theory of monic polynomials
 

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

@@ -44,9 +44,11 @@ theorem monic_zero_iff_subsingleton : Monic (0 : R[X]) ↔ Subsingleton R :=
 #align polynomial.monic_zero_iff_subsingleton Polynomial.monic_zero_iff_subsingleton
 -/
 
+#print Polynomial.not_monic_zero_iff /-
 theorem not_monic_zero_iff : ¬Monic (0 : R[X]) ↔ (0 : R) ≠ 1 :=
   (monic_zero_iff_subsingleton.trans subsingleton_iff_zero_eq_one.symm).Not
 #align polynomial.not_monic_zero_iff Polynomial.not_monic_zero_iff
+-/
 
 #print Polynomial.monic_zero_iff_subsingleton' /-
 theorem monic_zero_iff_subsingleton' :
@@ -55,6 +57,7 @@ theorem monic_zero_iff_subsingleton' :
 #align polynomial.monic_zero_iff_subsingleton' Polynomial.monic_zero_iff_subsingleton'
 -/
 
+#print Polynomial.Monic.as_sum /-
 theorem Monic.as_sum (hp : p.Monic) :
     p = X ^ p.natDegree + ∑ i in range p.natDegree, C (p.coeff i) * X ^ i :=
   by
@@ -62,6 +65,7 @@ theorem Monic.as_sum (hp : p.Monic) :
   suffices C (p.coeff p.nat_degree) = 1 by rw [this, one_mul]
   exact congr_arg C hp
 #align polynomial.monic.as_sum Polynomial.Monic.as_sum
+-/
 
 #print Polynomial.ne_zero_of_ne_zero_of_monic /-
 theorem ne_zero_of_ne_zero_of_monic (hp : p ≠ 0) (hq : Monic q) : q ≠ 0 :=
@@ -87,15 +91,19 @@ theorem Monic.map [Semiring S] (f : R →+* S) (hp : Monic p) : Monic (p.map f)
 #align polynomial.monic.map Polynomial.Monic.map
 -/
 
+#print Polynomial.monic_C_mul_of_mul_leadingCoeff_eq_one /-
 theorem monic_C_mul_of_mul_leadingCoeff_eq_one {b : R} (hp : b * p.leadingCoeff = 1) :
     Monic (C b * p) := by nontriviality;
   rw [monic, leading_coeff_mul' _] <;> simp [leading_coeff_C b, hp]
 #align polynomial.monic_C_mul_of_mul_leading_coeff_eq_one Polynomial.monic_C_mul_of_mul_leadingCoeff_eq_one
+-/
 
+#print Polynomial.monic_mul_C_of_leadingCoeff_mul_eq_one /-
 theorem monic_mul_C_of_leadingCoeff_mul_eq_one {b : R} (hp : p.leadingCoeff * b = 1) :
     Monic (p * C b) := by nontriviality;
   rw [monic, leading_coeff_mul' _] <;> simp [leading_coeff_C b, hp]
 #align polynomial.monic_mul_C_of_leading_coeff_mul_eq_one Polynomial.monic_mul_C_of_leadingCoeff_mul_eq_one
+-/
 
 #print Polynomial.monic_of_degree_le /-
 theorem monic_of_degree_le (n : ℕ) (H1 : degree p ≤ n) (H2 : coeff p n = 1) : Monic p :=
@@ -115,9 +123,11 @@ theorem monic_X_pow_add {n : ℕ} (H : degree p ≤ n) : Monic (X ^ (n + 1) + p)
 #align polynomial.monic_X_pow_add Polynomial.monic_X_pow_add
 -/
 
+#print Polynomial.monic_X_add_C /-
 theorem monic_X_add_C (x : R) : Monic (X + C x) :=
   pow_one (X : R[X]) ▸ monic_X_pow_add degree_C_le
 #align polynomial.monic_X_add_C Polynomial.monic_X_add_C
+-/
 
 #print Polynomial.Monic.mul /-
 theorem Monic.mul (hp : Monic p) (hq : Monic q) : Monic (p * q) :=
@@ -246,6 +256,7 @@ theorem not_dvd_of_degree_lt (hp : Monic p) (h0 : q ≠ 0) (hl : degree q < degr
 #align polynomial.monic.not_dvd_of_degree_lt Polynomial.Monic.not_dvd_of_degree_lt
 -/
 
+#print Polynomial.Monic.nextCoeff_mul /-
 theorem nextCoeff_mul (hp : Monic p) (hq : Monic q) :
     nextCoeff (p * q) = nextCoeff p + nextCoeff q :=
   by
@@ -254,7 +265,9 @@ theorem nextCoeff_mul (hp : Monic p) (hq : Monic q) :
   rw [reverse_mul] <;>
     simp [coeff_mul, nat.antidiagonal, hp.leading_coeff, hq.leading_coeff, add_comm]
 #align polynomial.monic.next_coeff_mul Polynomial.Monic.nextCoeff_mul
+-/
 
+#print Polynomial.Monic.eq_one_of_map_eq_one /-
 theorem eq_one_of_map_eq_one {S : Type _} [Semiring S] [Nontrivial S] (f : R →+* S) (hp : p.Monic)
     (map_eq : p.map f = 1) : p = 1 := by
   nontriviality R
@@ -268,6 +281,7 @@ theorem eq_one_of_map_eq_one {S : Type _} [Semiring S] [Nontrivial S] (f : R →
   convert eq_C_of_degree_eq_zero hdeg
   rw [← hndeg, ← Polynomial.leadingCoeff, hp.leading_coeff, C.map_one]
 #align polynomial.monic.eq_one_of_map_eq_one Polynomial.Monic.eq_one_of_map_eq_one
+-/
 
 #print Polynomial.Monic.natDegree_pow /-
 theorem natDegree_pow (hp : p.Monic) (n : ℕ) : (p ^ n).natDegree = n * p.natDegree :=
@@ -281,10 +295,12 @@ theorem natDegree_pow (hp : p.Monic) (n : ℕ) : (p ^ n).natDegree = n * p.natDe
 
 end Monic
 
+#print Polynomial.natDegree_pow_X_add_C /-
 @[simp]
 theorem natDegree_pow_X_add_C [Nontrivial R] (n : ℕ) (r : R) : ((X + C r) ^ n).natDegree = n := by
   rw [(monic_X_add_C r).natDegree_pow, nat_degree_X_add_C, mul_one]
 #align polynomial.nat_degree_pow_X_add_C Polynomial.natDegree_pow_X_add_C
+-/
 
 #print Polynomial.Monic.eq_one_of_isUnit /-
 theorem Monic.eq_one_of_isUnit (hm : Monic p) (hpu : IsUnit p) : p = 1 :=
@@ -387,47 +403,59 @@ open Function
 
 variable [Semiring S] {f : R →+* S} (hf : Injective f)
 
-include hf
-
+#print Polynomial.degree_map_eq_of_injective /-
 theorem degree_map_eq_of_injective (p : R[X]) : degree (p.map f) = degree p :=
   if h : p = 0 then by simp [h]
   else
     degree_map_eq_of_leadingCoeff_ne_zero _
       (by rw [← f.map_zero] <;> exact mt hf.eq_iff.1 (mt leading_coeff_eq_zero.1 h))
 #align polynomial.degree_map_eq_of_injective Polynomial.degree_map_eq_of_injective
+-/
 
+#print Polynomial.natDegree_map_eq_of_injective /-
 theorem natDegree_map_eq_of_injective (p : R[X]) : natDegree (p.map f) = natDegree p :=
   natDegree_eq_of_degree_eq (degree_map_eq_of_injective hf p)
 #align polynomial.nat_degree_map_eq_of_injective Polynomial.natDegree_map_eq_of_injective
+-/
 
+#print Polynomial.leadingCoeff_map' /-
 theorem leadingCoeff_map' (p : R[X]) : leadingCoeff (p.map f) = f (leadingCoeff p) :=
   by
   unfold leading_coeff
   rw [coeff_map, nat_degree_map_eq_of_injective hf p]
 #align polynomial.leading_coeff_map' Polynomial.leadingCoeff_map'
+-/
 
+#print Polynomial.nextCoeff_map /-
 theorem nextCoeff_map (p : R[X]) : (p.map f).nextCoeff = f p.nextCoeff :=
   by
   unfold next_coeff
   rw [nat_degree_map_eq_of_injective hf]
   split_ifs <;> simp
 #align polynomial.next_coeff_map Polynomial.nextCoeff_map
+-/
 
+#print Polynomial.leadingCoeff_of_injective /-
 theorem leadingCoeff_of_injective (p : R[X]) : leadingCoeff (p.map f) = f (leadingCoeff p) :=
   by
   delta leading_coeff
   rw [coeff_map f, nat_degree_map_eq_of_injective hf p]
 #align polynomial.leading_coeff_of_injective Polynomial.leadingCoeff_of_injective
+-/
 
+#print Polynomial.monic_of_injective /-
 theorem monic_of_injective {p : R[X]} (hp : (p.map f).Monic) : p.Monic :=
   by
   apply hf
   rw [← leading_coeff_of_injective hf, hp.leading_coeff, f.map_one]
 #align polynomial.monic_of_injective Polynomial.monic_of_injective
+-/
 
+#print Function.Injective.monic_map_iff /-
 theorem Function.Injective.monic_map_iff {p : R[X]} : p.Monic ↔ (p.map f).Monic :=
   ⟨Monic.map _, Polynomial.monic_of_injective hf⟩
 #align function.injective.monic_map_iff Function.Injective.monic_map_iff
+-/
 
 end Injective
 
@@ -437,14 +465,19 @@ section Ring
 
 variable [Ring R] {p : R[X]}
 
+#print Polynomial.monic_X_sub_C /-
 theorem monic_X_sub_C (x : R) : Monic (X - C x) := by
   simpa only [sub_eq_add_neg, C_neg] using monic_X_add_C (-x)
 #align polynomial.monic_X_sub_C Polynomial.monic_X_sub_C
+-/
 
+#print Polynomial.monic_X_pow_sub /-
 theorem monic_X_pow_sub {n : ℕ} (H : degree p ≤ n) : Monic (X ^ (n + 1) - p) := by
   simpa [sub_eq_add_neg] using monic_X_pow_add (show degree (-p) ≤ n by rwa [← degree_neg p] at H )
 #align polynomial.monic_X_pow_sub Polynomial.monic_X_pow_sub
+-/
 
+#print Polynomial.monic_X_pow_sub_C /-
 /-- `X ^ n - a` is monic. -/
 theorem monic_X_pow_sub_C {R : Type u} [Ring R] (a : R) {n : ℕ} (h : n ≠ 0) : (X ^ n - C a).Monic :=
   by
@@ -452,7 +485,9 @@ theorem monic_X_pow_sub_C {R : Type u} [Ring R] (a : R) {n : ℕ} (h : n ≠ 0)
   convert monic_X_pow_sub _
   exact le_trans degree_C_le Nat.WithBot.coe_nonneg
 #align polynomial.monic_X_pow_sub_C Polynomial.monic_X_pow_sub_C
+-/
 
+#print Polynomial.not_isUnit_X_pow_sub_one /-
 theorem not_isUnit_X_pow_sub_one (R : Type _) [CommRing R] [Nontrivial R] (n : ℕ) :
     ¬IsUnit (X ^ n - 1 : R[X]) := by
   intro h
@@ -461,6 +496,7 @@ theorem not_isUnit_X_pow_sub_one (R : Type _) [CommRing R] [Nontrivial R] (n : 
   apply hn
   rw [← @nat_degree_one R, ← (monic_X_pow_sub_C _ hn).eq_one_of_isUnit h, nat_degree_X_pow_sub_C]
 #align polynomial.not_is_unit_X_pow_sub_one Polynomial.not_isUnit_X_pow_sub_one
+-/
 
 #print Polynomial.Monic.sub_of_left /-
 theorem Monic.sub_of_left {p q : R[X]} (hp : Monic p) (hpq : degree q < degree p) : Monic (p - q) :=
@@ -468,6 +504,7 @@ theorem Monic.sub_of_left {p q : R[X]} (hp : Monic p) (hpq : degree q < degree p
 #align polynomial.monic.sub_of_left Polynomial.Monic.sub_of_left
 -/
 
+#print Polynomial.Monic.sub_of_right /-
 theorem Monic.sub_of_right {p q : R[X]} (hq : q.leadingCoeff = -1) (hpq : degree p < degree q) :
     Monic (p - q) :=
   by
@@ -477,6 +514,7 @@ theorem Monic.sub_of_right {p q : R[X]} (hq : q.leadingCoeff = -1) (hpq : degree
   apply monic.add_of_right this
   rwa [degree_neg]
 #align polynomial.monic.sub_of_right Polynomial.Monic.sub_of_right
+-/
 
 end Ring
 
@@ -560,6 +598,7 @@ theorem Monic.isRegular {R : Type _} [Ring R] {p : R[X]} (hp : Monic p) : IsRegu
 #align polynomial.monic.is_regular Polynomial.Monic.isRegular
 -/
 
+#print Polynomial.degree_smul_of_smul_regular /-
 theorem degree_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction S R] {k : S}
     (p : R[X]) (h : IsSMulRegular R k) : (k • p).degree = p.degree :=
   by
@@ -574,7 +613,9 @@ theorem degree_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction S
     refine' h _
     simpa using hm m le_rfl
 #align polynomial.degree_smul_of_smul_regular Polynomial.degree_smul_of_smul_regular
+-/
 
+#print Polynomial.natDegree_smul_of_smul_regular /-
 theorem natDegree_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction S R] {k : S}
     (p : R[X]) (h : IsSMulRegular R k) : (k • p).natDegree = p.natDegree :=
   by
@@ -586,11 +627,14 @@ theorem natDegree_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction
   rw [← smul_zero k] at hp 
   exact h.polynomial hp
 #align polynomial.nat_degree_smul_of_smul_regular Polynomial.natDegree_smul_of_smul_regular
+-/
 
+#print Polynomial.leadingCoeff_smul_of_smul_regular /-
 theorem leadingCoeff_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction S R] {k : S}
     (p : R[X]) (h : IsSMulRegular R k) : (k • p).leadingCoeff = k • p.leadingCoeff := by
   rw [leading_coeff, leading_coeff, coeff_smul, nat_degree_smul_of_smul_regular p h]
 #align polynomial.leading_coeff_smul_of_smul_regular Polynomial.leadingCoeff_smul_of_smul_regular
+-/
 
 #print Polynomial.monic_of_isUnit_leadingCoeff_inv_smul /-
 theorem monic_of_isUnit_leadingCoeff_inv_smul (h : IsUnit p.leadingCoeff) : Monic (h.Unit⁻¹ • p) :=

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

@@ -51,7 +51,7 @@ theorem not_monic_zero_iff : ¬Monic (0 : R[X]) ↔ (0 : R) ≠ 1 :=
 #print Polynomial.monic_zero_iff_subsingleton' /-
 theorem monic_zero_iff_subsingleton' :
     Monic (0 : R[X]) ↔ (∀ f g : R[X], f = g) ∧ ∀ a b : R, a = b :=
-  Polynomial.monic_zero_iff_subsingleton.trans ⟨by intro ; simp, fun h => subsingleton_iff.mpr h.2⟩
+  Polynomial.monic_zero_iff_subsingleton.trans ⟨by intro; simp, fun h => subsingleton_iff.mpr h.2⟩
 #align polynomial.monic_zero_iff_subsingleton' Polynomial.monic_zero_iff_subsingleton'
 -/
 
@@ -67,8 +67,8 @@ theorem Monic.as_sum (hp : p.Monic) :
 theorem ne_zero_of_ne_zero_of_monic (hp : p ≠ 0) (hq : Monic q) : q ≠ 0 :=
   by
   rintro rfl
-  rw [monic.def, leading_coeff_zero] at hq
-  rw [← mul_one p, ← C_1, ← hq, C_0, MulZeroClass.mul_zero] at hp
+  rw [monic.def, leading_coeff_zero] at hq 
+  rw [← mul_one p, ← C_1, ← hq, C_0, MulZeroClass.mul_zero] at hp 
   exact hp rfl
 #align polynomial.ne_zero_of_ne_zero_of_monic Polynomial.ne_zero_of_ne_zero_of_monic
 -/
@@ -155,7 +155,7 @@ theorem Monic.add_of_right (hq : Monic q) (hpq : degree p < degree q) : Monic (p
 theorem Monic.of_mul_monic_left (hp : p.Monic) (hpq : (p * q).Monic) : q.Monic :=
   by
   contrapose! hpq
-  rw [monic.def] at hpq⊢
+  rw [monic.def] at hpq ⊢
   rwa [leading_coeff_monic_mul hp]
 #align polynomial.monic.of_mul_monic_left Polynomial.Monic.of_mul_monic_left
 -/
@@ -164,7 +164,7 @@ theorem Monic.of_mul_monic_left (hp : p.Monic) (hpq : (p * q).Monic) : q.Monic :
 theorem Monic.of_mul_monic_right (hq : q.Monic) (hpq : (p * q).Monic) : p.Monic :=
   by
   contrapose! hpq
-  rw [monic.def] at hpq⊢
+  rw [monic.def] at hpq ⊢
   rwa [leading_coeff_mul_monic hq]
 #align polynomial.monic.of_mul_monic_right Polynomial.Monic.of_mul_monic_right
 -/
@@ -179,7 +179,7 @@ theorem natDegree_eq_zero_iff_eq_one (hp : p.Monic) : p.natDegree = 0 ↔ p = 1
   swap; · rw [h]; exact nat_degree_one
   have : p = C (p.coeff 0) := by
     rw [← Polynomial.degree_le_zero_iff]
-    rwa [Polynomial.natDegree_eq_zero_iff_degree_le_zero] at h
+    rwa [Polynomial.natDegree_eq_zero_iff_degree_le_zero] at h 
   rw [this]; convert C_1; rw [← h]; apply hp
 #align polynomial.monic.nat_degree_eq_zero_iff_eq_one Polynomial.Monic.natDegree_eq_zero_iff_eq_one
 -/
@@ -235,7 +235,7 @@ theorem natDegree_mul_comm (hp : p.Monic) (q : R[X]) : (p * q).natDegree = (q *
 theorem not_dvd_of_natDegree_lt (hp : Monic p) (h0 : q ≠ 0) (hl : natDegree q < natDegree p) :
     ¬p ∣ q := by
   rintro ⟨r, rfl⟩
-  rw [hp.nat_degree_mul' <| right_ne_zero_of_mul h0] at hl
+  rw [hp.nat_degree_mul' <| right_ne_zero_of_mul h0] at hl 
   exact hl.not_le (Nat.le_add_right _ _)
 #align polynomial.monic.not_dvd_of_nat_degree_lt Polynomial.Monic.not_dvd_of_natDegree_lt
 -/
@@ -292,7 +292,7 @@ theorem Monic.eq_one_of_isUnit (hm : Monic p) (hpu : IsUnit p) : p = 1 :=
   nontriviality R
   obtain ⟨q, h⟩ := hpu.exists_right_inv
   have := hm.nat_degree_mul' (right_ne_zero_of_mul_eq_one h)
-  rw [h, nat_degree_one, eq_comm, add_eq_zero_iff] at this
+  rw [h, nat_degree_one, eq_comm, add_eq_zero_iff] at this 
   exact hm.nat_degree_eq_zero_iff_eq_one.mp this.1
 #align polynomial.monic.eq_one_of_is_unit Polynomial.Monic.eq_one_of_isUnit
 -/
@@ -338,7 +338,7 @@ theorem Monic.nextCoeff_multiset_prod (t : Multiset ι) (f : ι → R[X]) (h : 
     rw [← C_1]; rw [next_coeff_C_eq_zero]
   · rw [Multiset.map_cons, Multiset.prod_cons, Multiset.map_cons, Multiset.sum_cons,
       monic.next_coeff_mul, ih]
-    exacts[fun i hi => ht i (Multiset.mem_cons_of_mem hi), ht a (Multiset.mem_cons_self _ _),
+    exacts [fun i hi => ht i (Multiset.mem_cons_of_mem hi), ht a (Multiset.mem_cons_self _ _),
       monic_multiset_prod_of_monic _ _ fun b bs => ht _ (Multiset.mem_cons_of_mem bs)]
 #align polynomial.monic.next_coeff_multiset_prod Polynomial.Monic.nextCoeff_multiset_prod
 -/
@@ -442,7 +442,7 @@ theorem monic_X_sub_C (x : R) : Monic (X - C x) := by
 #align polynomial.monic_X_sub_C Polynomial.monic_X_sub_C
 
 theorem monic_X_pow_sub {n : ℕ} (H : degree p ≤ n) : Monic (X ^ (n + 1) - p) := by
-  simpa [sub_eq_add_neg] using monic_X_pow_add (show degree (-p) ≤ n by rwa [← degree_neg p] at H)
+  simpa [sub_eq_add_neg] using monic_X_pow_add (show degree (-p) ≤ n by rwa [← degree_neg p] at H )
 #align polynomial.monic_X_pow_sub Polynomial.monic_X_pow_sub
 
 /-- `X ^ n - a` is monic. -/
@@ -505,7 +505,7 @@ theorem Monic.mul_left_ne_zero (hp : Monic p) {q : R[X]} (hq : q ≠ 0) : q * p
   · simpa [h]
   rw [Ne.def, ← degree_eq_bot, hp.degree_mul, WithBot.add_eq_bot, not_or, degree_eq_bot]
   refine' ⟨hq, _⟩
-  rw [← hp.degree_le_zero_iff_eq_one, not_le] at h
+  rw [← hp.degree_le_zero_iff_eq_one, not_le] at h 
   refine' (lt_trans _ h).ne'
   simp
 #align polynomial.monic.mul_left_ne_zero Polynomial.Monic.mul_left_ne_zero
@@ -519,7 +519,7 @@ theorem Monic.mul_right_ne_zero (hp : Monic p) {q : R[X]} (hq : q ≠ 0) : p * q
   rw [Ne.def, ← degree_eq_bot, hp.degree_mul_comm, hp.degree_mul, WithBot.add_eq_bot, not_or,
     degree_eq_bot]
   refine' ⟨hq, _⟩
-  rw [← hp.degree_le_zero_iff_eq_one, not_le] at h
+  rw [← hp.degree_le_zero_iff_eq_one, not_le] at h 
   refine' (lt_trans _ h).ne'
   simp
 #align polynomial.monic.mul_right_ne_zero Polynomial.Monic.mul_right_ne_zero
@@ -555,7 +555,7 @@ theorem Monic.isRegular {R : Type _} [Ring R] {p : R[X]} (hp : Monic p) : IsRegu
   · intro q r h
     rw [← sub_eq_zero, ← hp.mul_right_eq_zero_iff, mul_sub, h, sub_self]
   · intro q r h
-    simp only at h
+    simp only at h 
     rw [← sub_eq_zero, ← hp.mul_left_eq_zero_iff, sub_mul, h, sub_self]
 #align polynomial.monic.is_regular Polynomial.Monic.isRegular
 -/
@@ -566,11 +566,11 @@ theorem degree_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction S
   refine' le_antisymm _ _
   · rw [degree_le_iff_coeff_zero]
     intro m hm
-    rw [degree_lt_iff_coeff_zero] at hm
+    rw [degree_lt_iff_coeff_zero] at hm 
     simp [hm m le_rfl]
   · rw [degree_le_iff_coeff_zero]
     intro m hm
-    rw [degree_lt_iff_coeff_zero] at hm
+    rw [degree_lt_iff_coeff_zero] at hm 
     refine' h _
     simpa using hm m le_rfl
 #align polynomial.degree_smul_of_smul_regular Polynomial.degree_smul_of_smul_regular
@@ -583,7 +583,7 @@ theorem natDegree_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction
   rw [← WithBot.coe_eq_coe, ← degree_eq_nat_degree hp, ← degree_eq_nat_degree,
     degree_smul_of_smul_regular p h]
   contrapose! hp
-  rw [← smul_zero k] at hp
+  rw [← smul_zero k] at hp 
   exact h.polynomial hp
 #align polynomial.nat_degree_smul_of_smul_regular Polynomial.natDegree_smul_of_smul_regular
 
@@ -607,14 +607,14 @@ theorem isUnit_leadingCoeff_mul_right_eq_zero_iff (h : IsUnit p.leadingCoeff) {q
     p * q = 0 ↔ q = 0 := by
   constructor
   · intro hp
-    rw [← smul_eq_zero_iff_eq h.unit⁻¹] at hp
+    rw [← smul_eq_zero_iff_eq h.unit⁻¹] at hp 
     have : h.unit⁻¹ • (p * q) = h.unit⁻¹ • p * q :=
       by
       ext
       simp only [Units.smul_def, coeff_smul, coeff_mul, smul_eq_mul, mul_sum]
       refine' sum_congr rfl fun x hx => _
       rw [← mul_assoc]
-    rwa [this, monic.mul_right_eq_zero_iff] at hp
+    rwa [this, monic.mul_right_eq_zero_iff] at hp 
     exact monic_of_is_unit_leading_coeff_inv_smul _
   · rintro rfl
     simp
@@ -627,8 +627,8 @@ theorem isUnit_leadingCoeff_mul_left_eq_zero_iff (h : IsUnit p.leadingCoeff) {q
   constructor
   · intro hp
     replace hp := congr_arg (· * C ↑h.unit⁻¹) hp
-    simp only [MulZeroClass.zero_mul] at hp
-    rwa [mul_assoc, monic.mul_left_eq_zero_iff] at hp
+    simp only [MulZeroClass.zero_mul] at hp 
+    rwa [mul_assoc, monic.mul_left_eq_zero_iff] at hp 
     refine' monic_mul_C_of_leading_coeff_mul_eq_one _
     simp [Units.mul_inv_eq_iff_eq_mul, IsUnit.unit_spec]
   · rintro rfl

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

@@ -26,7 +26,7 @@ noncomputable section
 
 open Finset
 
-open BigOperators Classical Polynomial
+open scoped BigOperators Classical Polynomial
 
 namespace Polynomial
 
@@ -97,19 +97,23 @@ theorem monic_mul_C_of_leadingCoeff_mul_eq_one {b : R} (hp : p.leadingCoeff * b
   rw [monic, leading_coeff_mul' _] <;> simp [leading_coeff_C b, hp]
 #align polynomial.monic_mul_C_of_leading_coeff_mul_eq_one Polynomial.monic_mul_C_of_leadingCoeff_mul_eq_one
 
+#print Polynomial.monic_of_degree_le /-
 theorem monic_of_degree_le (n : ℕ) (H1 : degree p ≤ n) (H2 : coeff p n = 1) : Monic p :=
   Decidable.byCases
     (fun H : degree p < n => eq_of_zero_eq_one (H2 ▸ (coeff_eq_zero_of_degree_lt H).symm) _ _)
     fun H : ¬degree p < n => by
     rwa [monic, leading_coeff, nat_degree, (lt_or_eq_of_le H1).resolve_left H]
 #align polynomial.monic_of_degree_le Polynomial.monic_of_degree_le
+-/
 
+#print Polynomial.monic_X_pow_add /-
 theorem monic_X_pow_add {n : ℕ} (H : degree p ≤ n) : Monic (X ^ (n + 1) + p) :=
   have H1 : degree p < n + 1 := lt_of_le_of_lt H (WithBot.coe_lt_coe.2 (Nat.lt_succ_self n))
   monic_of_degree_le (n + 1)
     (le_trans (degree_add_le _ _) (max_le (degree_X_pow_le _) (le_of_lt H1)))
     (by rw [coeff_add, coeff_X_pow, if_pos rfl, coeff_eq_zero_of_degree_lt H1, add_zero])
 #align polynomial.monic_X_pow_add Polynomial.monic_X_pow_add
+-/
 
 theorem monic_X_add_C (x : R) : Monic (X + C x) :=
   pow_one (X : R[X]) ▸ monic_X_pow_add degree_C_le
@@ -135,13 +139,17 @@ theorem Monic.pow (hp : Monic p) : ∀ n : ℕ, Monic (p ^ n)
 #align polynomial.monic.pow Polynomial.Monic.pow
 -/
 
+#print Polynomial.Monic.add_of_left /-
 theorem Monic.add_of_left (hp : Monic p) (hpq : degree q < degree p) : Monic (p + q) := by
   rwa [monic, add_comm, leading_coeff_add_of_degree_lt hpq]
 #align polynomial.monic.add_of_left Polynomial.Monic.add_of_left
+-/
 
+#print Polynomial.Monic.add_of_right /-
 theorem Monic.add_of_right (hq : Monic q) (hpq : degree p < degree q) : Monic (p + q) := by
   rwa [monic, leading_coeff_add_of_degree_lt hpq]
 #align polynomial.monic.add_of_right Polynomial.Monic.add_of_right
+-/
 
 #print Polynomial.Monic.of_mul_monic_left /-
 theorem Monic.of_mul_monic_left (hp : p.Monic) (hpq : (p * q).Monic) : q.Monic :=
@@ -176,10 +184,12 @@ theorem natDegree_eq_zero_iff_eq_one (hp : p.Monic) : p.natDegree = 0 ↔ p = 1
 #align polynomial.monic.nat_degree_eq_zero_iff_eq_one Polynomial.Monic.natDegree_eq_zero_iff_eq_one
 -/
 
+#print Polynomial.Monic.degree_le_zero_iff_eq_one /-
 @[simp]
 theorem degree_le_zero_iff_eq_one (hp : p.Monic) : p.degree ≤ 0 ↔ p = 1 := by
   rw [← hp.nat_degree_eq_zero_iff_eq_one, nat_degree_eq_zero_iff_degree_le_zero]
 #align polynomial.monic.degree_le_zero_iff_eq_one Polynomial.Monic.degree_le_zero_iff_eq_one
+-/
 
 #print Polynomial.Monic.natDegree_mul /-
 theorem natDegree_mul (hp : p.Monic) (hq : q.Monic) :
@@ -230,9 +240,11 @@ theorem not_dvd_of_natDegree_lt (hp : Monic p) (h0 : q ≠ 0) (hl : natDegree q
 #align polynomial.monic.not_dvd_of_nat_degree_lt Polynomial.Monic.not_dvd_of_natDegree_lt
 -/
 
+#print Polynomial.Monic.not_dvd_of_degree_lt /-
 theorem not_dvd_of_degree_lt (hp : Monic p) (h0 : q ≠ 0) (hl : degree q < degree p) : ¬p ∣ q :=
   Monic.not_dvd_of_natDegree_lt hp h0 <| natDegree_lt_natDegree h0 hl
 #align polynomial.monic.not_dvd_of_degree_lt Polynomial.Monic.not_dvd_of_degree_lt
+-/
 
 theorem nextCoeff_mul (hp : Monic p) (hq : Monic q) :
     nextCoeff (p * q) = nextCoeff p + nextCoeff q :=
@@ -450,9 +462,11 @@ theorem not_isUnit_X_pow_sub_one (R : Type _) [CommRing R] [Nontrivial R] (n : 
   rw [← @nat_degree_one R, ← (monic_X_pow_sub_C _ hn).eq_one_of_isUnit h, nat_degree_X_pow_sub_C]
 #align polynomial.not_is_unit_X_pow_sub_one Polynomial.not_isUnit_X_pow_sub_one
 
+#print Polynomial.Monic.sub_of_left /-
 theorem Monic.sub_of_left {p q : R[X]} (hp : Monic p) (hpq : degree q < degree p) : Monic (p - q) :=
   by rw [sub_eq_add_neg]; apply hp.add_of_left; rwa [degree_neg]
 #align polynomial.monic.sub_of_left Polynomial.Monic.sub_of_left
+-/
 
 theorem Monic.sub_of_right {p q : R[X]} (hq : q.leadingCoeff = -1) (hpq : degree p < degree q) :
     Monic (p - q) :=

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

@@ -44,12 +44,6 @@ theorem monic_zero_iff_subsingleton : Monic (0 : R[X]) ↔ Subsingleton R :=
 #align polynomial.monic_zero_iff_subsingleton Polynomial.monic_zero_iff_subsingleton
 -/
 
-/- warning: polynomial.not_monic_zero_iff -> Polynomial.not_monic_zero_iff is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Iff (Not (Polynomial.Monic.{u1} R _inst_1 (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)))))) (Ne.{succ u1} R (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))))))) (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))))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Iff (Not (Polynomial.Monic.{u1} R _inst_1 (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) (Ne.{succ u1} R (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))
-Case conversion may be inaccurate. Consider using '#align polynomial.not_monic_zero_iff Polynomial.not_monic_zero_iffₓ'. -/
 theorem not_monic_zero_iff : ¬Monic (0 : R[X]) ↔ (0 : R) ≠ 1 :=
   (monic_zero_iff_subsingleton.trans subsingleton_iff_zero_eq_one.symm).Not
 #align polynomial.not_monic_zero_iff Polynomial.not_monic_zero_iff
@@ -61,12 +55,6 @@ theorem monic_zero_iff_subsingleton' :
 #align polynomial.monic_zero_iff_subsingleton' Polynomial.monic_zero_iff_subsingleton'
 -/
 
-/- warning: polynomial.monic.as_sum -> Polynomial.Monic.as_sum is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align polynomial.monic.as_sum Polynomial.Monic.as_sumₓ'. -/
 theorem Monic.as_sum (hp : p.Monic) :
     p = X ^ p.natDegree + ∑ i in range p.natDegree, C (p.coeff i) * X ^ i :=
   by
@@ -99,34 +87,16 @@ theorem Monic.map [Semiring S] (f : R →+* S) (hp : Monic p) : Monic (p.map f)
 #align polynomial.monic.map Polynomial.Monic.map
 -/
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.monic_C_mul_of_mul_leading_coeff_eq_one Polynomial.monic_C_mul_of_mul_leadingCoeff_eq_oneₓ'. -/
 theorem monic_C_mul_of_mul_leadingCoeff_eq_one {b : R} (hp : b * p.leadingCoeff = 1) :
     Monic (C b * p) := by nontriviality;
   rw [monic, leading_coeff_mul' _] <;> simp [leading_coeff_C b, hp]
 #align polynomial.monic_C_mul_of_mul_leading_coeff_eq_one Polynomial.monic_C_mul_of_mul_leadingCoeff_eq_one
 
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 theorem monic_mul_C_of_leadingCoeff_mul_eq_one {b : R} (hp : p.leadingCoeff * b = 1) :
     Monic (p * C b) := by nontriviality;
   rw [monic, leading_coeff_mul' _] <;> simp [leading_coeff_C b, hp]
 #align polynomial.monic_mul_C_of_leading_coeff_mul_eq_one Polynomial.monic_mul_C_of_leadingCoeff_mul_eq_one
 
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 theorem monic_of_degree_le (n : ℕ) (H1 : degree p ≤ n) (H2 : coeff p n = 1) : Monic p :=
   Decidable.byCases
     (fun H : degree p < n => eq_of_zero_eq_one (H2 ▸ (coeff_eq_zero_of_degree_lt H).symm) _ _)
@@ -134,12 +104,6 @@ theorem monic_of_degree_le (n : ℕ) (H1 : degree p ≤ n) (H2 : coeff p n = 1)
     rwa [monic, leading_coeff, nat_degree, (lt_or_eq_of_le H1).resolve_left H]
 #align polynomial.monic_of_degree_le Polynomial.monic_of_degree_le
 
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 theorem monic_X_pow_add {n : ℕ} (H : degree p ≤ n) : Monic (X ^ (n + 1) + p) :=
   have H1 : degree p < n + 1 := lt_of_le_of_lt H (WithBot.coe_lt_coe.2 (Nat.lt_succ_self n))
   monic_of_degree_le (n + 1)
@@ -147,12 +111,6 @@ theorem monic_X_pow_add {n : ℕ} (H : degree p ≤ n) : Monic (X ^ (n + 1) + p)
     (by rw [coeff_add, coeff_X_pow, if_pos rfl, coeff_eq_zero_of_degree_lt H1, add_zero])
 #align polynomial.monic_X_pow_add Polynomial.monic_X_pow_add
 
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 theorem monic_X_add_C (x : R) : Monic (X + C x) :=
   pow_one (X : R[X]) ▸ monic_X_pow_add degree_C_le
 #align polynomial.monic_X_add_C Polynomial.monic_X_add_C
@@ -177,22 +135,10 @@ theorem Monic.pow (hp : Monic p) : ∀ n : ℕ, Monic (p ^ n)
 #align polynomial.monic.pow Polynomial.Monic.pow
 -/
 
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 theorem Monic.add_of_left (hp : Monic p) (hpq : degree q < degree p) : Monic (p + q) := by
   rwa [monic, add_comm, leading_coeff_add_of_degree_lt hpq]
 #align polynomial.monic.add_of_left Polynomial.Monic.add_of_left
 
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 theorem Monic.add_of_right (hq : Monic q) (hpq : degree p < degree q) : Monic (p + q) := by
   rwa [monic, leading_coeff_add_of_degree_lt hpq]
 #align polynomial.monic.add_of_right Polynomial.Monic.add_of_right
@@ -230,12 +176,6 @@ theorem natDegree_eq_zero_iff_eq_one (hp : p.Monic) : p.natDegree = 0 ↔ p = 1
 #align polynomial.monic.nat_degree_eq_zero_iff_eq_one Polynomial.Monic.natDegree_eq_zero_iff_eq_one
 -/
 
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 @[simp]
 theorem degree_le_zero_iff_eq_one (hp : p.Monic) : p.degree ≤ 0 ↔ p = 1 := by
   rw [← hp.nat_degree_eq_zero_iff_eq_one, nat_degree_eq_zero_iff_degree_le_zero]
@@ -290,22 +230,10 @@ theorem not_dvd_of_natDegree_lt (hp : Monic p) (h0 : q ≠ 0) (hl : natDegree q
 #align polynomial.monic.not_dvd_of_nat_degree_lt Polynomial.Monic.not_dvd_of_natDegree_lt
 -/
 
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 theorem not_dvd_of_degree_lt (hp : Monic p) (h0 : q ≠ 0) (hl : degree q < degree p) : ¬p ∣ q :=
   Monic.not_dvd_of_natDegree_lt hp h0 <| natDegree_lt_natDegree h0 hl
 #align polynomial.monic.not_dvd_of_degree_lt Polynomial.Monic.not_dvd_of_degree_lt
 
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 theorem nextCoeff_mul (hp : Monic p) (hq : Monic q) :
     nextCoeff (p * q) = nextCoeff p + nextCoeff q :=
   by
@@ -315,12 +243,6 @@ theorem nextCoeff_mul (hp : Monic p) (hq : Monic q) :
     simp [coeff_mul, nat.antidiagonal, hp.leading_coeff, hq.leading_coeff, add_comm]
 #align polynomial.monic.next_coeff_mul Polynomial.Monic.nextCoeff_mul
 
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 theorem eq_one_of_map_eq_one {S : Type _} [Semiring S] [Nontrivial S] (f : R →+* S) (hp : p.Monic)
     (map_eq : p.map f = 1) : p = 1 := by
   nontriviality R
@@ -347,12 +269,6 @@ theorem natDegree_pow (hp : p.Monic) (n : ℕ) : (p ^ n).natDegree = n * p.natDe
 
 end Monic
 
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 @[simp]
 theorem natDegree_pow_X_add_C [Nontrivial R] (n : ℕ) (r : R) : ((X + C r) ^ n).natDegree = n := by
   rw [(monic_X_add_C r).natDegree_pow, nat_degree_X_add_C, mul_one]
@@ -461,12 +377,6 @@ variable [Semiring S] {f : R →+* S} (hf : Injective f)
 
 include hf
 
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 theorem degree_map_eq_of_injective (p : R[X]) : degree (p.map f) = degree p :=
   if h : p = 0 then by simp [h]
   else
@@ -474,34 +384,16 @@ theorem degree_map_eq_of_injective (p : R[X]) : degree (p.map f) = degree p :=
       (by rw [← f.map_zero] <;> exact mt hf.eq_iff.1 (mt leading_coeff_eq_zero.1 h))
 #align polynomial.degree_map_eq_of_injective Polynomial.degree_map_eq_of_injective
 
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 theorem natDegree_map_eq_of_injective (p : R[X]) : natDegree (p.map f) = natDegree p :=
   natDegree_eq_of_degree_eq (degree_map_eq_of_injective hf p)
 #align polynomial.nat_degree_map_eq_of_injective Polynomial.natDegree_map_eq_of_injective
 
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 theorem leadingCoeff_map' (p : R[X]) : leadingCoeff (p.map f) = f (leadingCoeff p) :=
   by
   unfold leading_coeff
   rw [coeff_map, nat_degree_map_eq_of_injective hf p]
 #align polynomial.leading_coeff_map' Polynomial.leadingCoeff_map'
 
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 theorem nextCoeff_map (p : R[X]) : (p.map f).nextCoeff = f p.nextCoeff :=
   by
   unfold next_coeff
@@ -509,36 +401,18 @@ theorem nextCoeff_map (p : R[X]) : (p.map f).nextCoeff = f p.nextCoeff :=
   split_ifs <;> simp
 #align polynomial.next_coeff_map Polynomial.nextCoeff_map
 
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 theorem leadingCoeff_of_injective (p : R[X]) : leadingCoeff (p.map f) = f (leadingCoeff p) :=
   by
   delta leading_coeff
   rw [coeff_map f, nat_degree_map_eq_of_injective hf p]
 #align polynomial.leading_coeff_of_injective Polynomial.leadingCoeff_of_injective
 
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 theorem monic_of_injective {p : R[X]} (hp : (p.map f).Monic) : p.Monic :=
   by
   apply hf
   rw [← leading_coeff_of_injective hf, hp.leading_coeff, f.map_one]
 #align polynomial.monic_of_injective Polynomial.monic_of_injective
 
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 theorem Function.Injective.monic_map_iff {p : R[X]} : p.Monic ↔ (p.map f).Monic :=
   ⟨Monic.map _, Polynomial.monic_of_injective hf⟩
 #align function.injective.monic_map_iff Function.Injective.monic_map_iff
@@ -551,32 +425,14 @@ section Ring
 
 variable [Ring R] {p : R[X]}
 
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 theorem monic_X_sub_C (x : R) : Monic (X - C x) := by
   simpa only [sub_eq_add_neg, C_neg] using monic_X_add_C (-x)
 #align polynomial.monic_X_sub_C Polynomial.monic_X_sub_C
 
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 theorem monic_X_pow_sub {n : ℕ} (H : degree p ≤ n) : Monic (X ^ (n + 1) - p) := by
   simpa [sub_eq_add_neg] using monic_X_pow_add (show degree (-p) ≤ n by rwa [← degree_neg p] at H)
 #align polynomial.monic_X_pow_sub Polynomial.monic_X_pow_sub
 
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 /-- `X ^ n - a` is monic. -/
 theorem monic_X_pow_sub_C {R : Type u} [Ring R] (a : R) {n : ℕ} (h : n ≠ 0) : (X ^ n - C a).Monic :=
   by
@@ -585,12 +441,6 @@ theorem monic_X_pow_sub_C {R : Type u} [Ring R] (a : R) {n : ℕ} (h : n ≠ 0)
   exact le_trans degree_C_le Nat.WithBot.coe_nonneg
 #align polynomial.monic_X_pow_sub_C Polynomial.monic_X_pow_sub_C
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.not_is_unit_X_pow_sub_one Polynomial.not_isUnit_X_pow_sub_oneₓ'. -/
 theorem not_isUnit_X_pow_sub_one (R : Type _) [CommRing R] [Nontrivial R] (n : ℕ) :
     ¬IsUnit (X ^ n - 1 : R[X]) := by
   intro h
@@ -600,22 +450,10 @@ theorem not_isUnit_X_pow_sub_one (R : Type _) [CommRing R] [Nontrivial R] (n : 
   rw [← @nat_degree_one R, ← (monic_X_pow_sub_C _ hn).eq_one_of_isUnit h, nat_degree_X_pow_sub_C]
 #align polynomial.not_is_unit_X_pow_sub_one Polynomial.not_isUnit_X_pow_sub_one
 
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 theorem Monic.sub_of_left {p q : R[X]} (hp : Monic p) (hpq : degree q < degree p) : Monic (p - q) :=
   by rw [sub_eq_add_neg]; apply hp.add_of_left; rwa [degree_neg]
 #align polynomial.monic.sub_of_left Polynomial.Monic.sub_of_left
 
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 theorem Monic.sub_of_right {p q : R[X]} (hq : q.leadingCoeff = -1) (hpq : degree p < degree q) :
     Monic (p - q) :=
   by
@@ -708,12 +546,6 @@ theorem Monic.isRegular {R : Type _} [Ring R] {p : R[X]} (hp : Monic p) : IsRegu
 #align polynomial.monic.is_regular Polynomial.Monic.isRegular
 -/
 
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 theorem degree_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction S R] {k : S}
     (p : R[X]) (h : IsSMulRegular R k) : (k • p).degree = p.degree :=
   by
@@ -729,12 +561,6 @@ theorem degree_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction S
     simpa using hm m le_rfl
 #align polynomial.degree_smul_of_smul_regular Polynomial.degree_smul_of_smul_regular
 
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 theorem natDegree_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction S R] {k : S}
     (p : R[X]) (h : IsSMulRegular R k) : (k • p).natDegree = p.natDegree :=
   by
@@ -747,12 +573,6 @@ theorem natDegree_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction
   exact h.polynomial hp
 #align polynomial.nat_degree_smul_of_smul_regular Polynomial.natDegree_smul_of_smul_regular
 
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-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Monoid.{u2} S] [_inst_3 : DistribMulAction.{u2, u1} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {k : S} (p : Polynomial.{u1} R _inst_1), (IsSMulRegular.{u2, u1} S R (SMulZeroClass.toHasSmul.{u2, u1} S R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribSMul.toSmulZeroClass.{u2, u1} S R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (DistribMulAction.toDistribSMul.{u2, u1} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3))) k) -> (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R _inst_1 (SMul.smul.{u2, u1} S (Polynomial.{u1} R _inst_1) (SMulZeroClass.toHasSmul.{u2, u1} S (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1) (Polynomial.smulZeroClass.{u1, u2} R _inst_1 S (DistribSMul.toSmulZeroClass.{u2, u1} S R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (DistribMulAction.toDistribSMul.{u2, u1} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3)))) k p)) (SMul.smul.{u2, u1} S R (SMulZeroClass.toHasSmul.{u2, u1} S R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribSMul.toSmulZeroClass.{u2, u1} S R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (DistribMulAction.toDistribSMul.{u2, u1} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3))) k (Polynomial.leadingCoeff.{u1} R _inst_1 p)))
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-  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {S : Type.{u1}} [_inst_2 : Monoid.{u1} S] [_inst_3 : DistribMulAction.{u1, u2} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))] {k : S} (p : Polynomial.{u2} R _inst_1), (IsSMulRegular.{u1, u2} S R (SMulZeroClass.toSMul.{u1, u2} S R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (DistribSMul.toSMulZeroClass.{u1, u2} S R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, u2} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3))) k) -> (Eq.{succ u2} R (Polynomial.leadingCoeff.{u2} R _inst_1 (HSMul.hSMul.{u1, u2, u2} S (Polynomial.{u2} R _inst_1) (Polynomial.{u2} R _inst_1) (instHSMul.{u1, u2} S (Polynomial.{u2} R _inst_1) (SMulZeroClass.toSMul.{u1, u2} S (Polynomial.{u2} R _inst_1) (Polynomial.zero.{u2} R _inst_1) (Polynomial.smulZeroClass.{u2, u1} R _inst_1 S (DistribSMul.toSMulZeroClass.{u1, u2} S R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, u2} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3))))) k p)) (HSMul.hSMul.{u1, u2, u2} S R R (instHSMul.{u1, u2} S R (SMulZeroClass.toSMul.{u1, u2} S R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (DistribSMul.toSMulZeroClass.{u1, u2} S R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, u2} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3)))) k (Polynomial.leadingCoeff.{u2} R _inst_1 p)))
-Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_smul_of_smul_regular Polynomial.leadingCoeff_smul_of_smul_regularₓ'. -/
 theorem leadingCoeff_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction S R] {k : S}
     (p : R[X]) (h : IsSMulRegular R k) : (k • p).leadingCoeff = k • p.leadingCoeff := by
   rw [leading_coeff, leading_coeff, coeff_smul, nat_degree_smul_of_smul_regular p h]

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

@@ -57,10 +57,7 @@ theorem not_monic_zero_iff : ¬Monic (0 : R[X]) ↔ (0 : R) ≠ 1 :=
 #print Polynomial.monic_zero_iff_subsingleton' /-
 theorem monic_zero_iff_subsingleton' :
     Monic (0 : R[X]) ↔ (∀ f g : R[X], f = g) ∧ ∀ a b : R, a = b :=
-  Polynomial.monic_zero_iff_subsingleton.trans
-    ⟨by
-      intro
-      simp, fun h => subsingleton_iff.mpr h.2⟩
+  Polynomial.monic_zero_iff_subsingleton.trans ⟨by intro ; simp, fun h => subsingleton_iff.mpr h.2⟩
 #align polynomial.monic_zero_iff_subsingleton' Polynomial.monic_zero_iff_subsingleton'
 -/
 
@@ -109,8 +106,7 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {b : 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)))) b (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Polynomial.Monic.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) b) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) b) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) b) (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) b) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_C_mul_of_mul_leading_coeff_eq_one Polynomial.monic_C_mul_of_mul_leadingCoeff_eq_oneₓ'. -/
 theorem monic_C_mul_of_mul_leadingCoeff_eq_one {b : R} (hp : b * p.leadingCoeff = 1) :
-    Monic (C b * p) := by
-  nontriviality
+    Monic (C b * p) := by nontriviality;
   rw [monic, leading_coeff_mul' _] <;> simp [leading_coeff_C b, hp]
 #align polynomial.monic_C_mul_of_mul_leading_coeff_eq_one Polynomial.monic_C_mul_of_mul_leadingCoeff_eq_one
 
@@ -121,8 +117,7 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {b : 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)))) (Polynomial.leadingCoeff.{u1} R _inst_1 p) b) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Polynomial.Monic.{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) b) (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) b)))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_mul_C_of_leading_coeff_mul_eq_one Polynomial.monic_mul_C_of_leadingCoeff_mul_eq_oneₓ'. -/
 theorem monic_mul_C_of_leadingCoeff_mul_eq_one {b : R} (hp : p.leadingCoeff * b = 1) :
-    Monic (p * C b) := by
-  nontriviality
+    Monic (p * C b) := by nontriviality;
   rw [monic, leading_coeff_mul' _] <;> simp [leading_coeff_C b, hp]
 #align polynomial.monic_mul_C_of_leading_coeff_mul_eq_one Polynomial.monic_mul_C_of_leadingCoeff_mul_eq_one
 
@@ -178,9 +173,7 @@ theorem Monic.mul (hp : Monic p) (hq : Monic q) : Monic (p * q) :=
 #print Polynomial.Monic.pow /-
 theorem Monic.pow (hp : Monic p) : ∀ n : ℕ, Monic (p ^ n)
   | 0 => monic_one
-  | n + 1 => by
-    rw [pow_succ]
-    exact hp.mul (monic.pow n)
+  | n + 1 => by rw [pow_succ]; exact hp.mul (monic.pow n)
 #align polynomial.monic.pow Polynomial.Monic.pow
 -/
 
@@ -229,16 +222,11 @@ namespace Monic
 theorem natDegree_eq_zero_iff_eq_one (hp : p.Monic) : p.natDegree = 0 ↔ p = 1 :=
   by
   constructor <;> intro h
-  swap
-  · rw [h]
-    exact nat_degree_one
+  swap; · rw [h]; exact nat_degree_one
   have : p = C (p.coeff 0) := by
     rw [← Polynomial.degree_le_zero_iff]
     rwa [Polynomial.natDegree_eq_zero_iff_degree_le_zero] at h
-  rw [this]
-  convert C_1
-  rw [← h]
-  apply hp
+  rw [this]; convert C_1; rw [← h]; apply hp
 #align polynomial.monic.nat_degree_eq_zero_iff_eq_one Polynomial.Monic.natDegree_eq_zero_iff_eq_one
 -/
 
@@ -419,8 +407,7 @@ theorem Monic.nextCoeff_multiset_prod (t : Multiset ι) (f : ι → R[X]) (h : 
   refine' Multiset.induction_on t _ fun a t ih ht => _
   · simp only [Multiset.not_mem_zero, forall_prop_of_true, forall_prop_of_false, Multiset.map_zero,
       Multiset.prod_zero, Multiset.sum_zero, not_false_iff, forall_true_iff]
-    rw [← C_1]
-    rw [next_coeff_C_eq_zero]
+    rw [← C_1]; rw [next_coeff_C_eq_zero]
   · rw [Multiset.map_cons, Multiset.prod_cons, Multiset.map_cons, Multiset.sum_cons,
       monic.next_coeff_mul, ih]
     exacts[fun i hi => ht i (Multiset.mem_cons_of_mem hi), ht a (Multiset.mem_cons_self _ _),
@@ -620,10 +607,7 @@ but is expected to have type
   forall {R : Type.{u1}} [_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)}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R _inst_1) p) -> (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)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) q) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) -> (Polynomial.Monic.{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))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic.sub_of_left Polynomial.Monic.sub_of_leftₓ'. -/
 theorem Monic.sub_of_left {p q : R[X]} (hp : Monic p) (hpq : degree q < degree p) : Monic (p - q) :=
-  by
-  rw [sub_eq_add_neg]
-  apply hp.add_of_left
-  rwa [degree_neg]
+  by rw [sub_eq_add_neg]; apply hp.add_of_left; rwa [degree_neg]
 #align polynomial.monic.sub_of_left Polynomial.Monic.sub_of_left
 
 /- warning: polynomial.monic.sub_of_right -> Polynomial.Monic.sub_of_right is a dubious translation:

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

@@ -68,7 +68,7 @@ theorem monic_zero_iff_subsingleton' :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (Polynomial.natDegree.{u1} R _inst_1 p)) (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{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)))) (Finset.range (Polynomial.natDegree.{u1} R _inst_1 p)) (fun (i : Nat) => 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) (Polynomial.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) i)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (Polynomial.natDegree.{u1} R _inst_1 p)) (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{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)))) (Finset.range (Polynomial.natDegree.{u1} R _inst_1 p)) (fun (i : Nat) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Polynomial.coeff.{u1} R _inst_1 p i)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Polynomial.coeff.{u1} R _inst_1 p i)) (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) (Polynomial.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) i)))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (Polynomial.natDegree.{u1} R _inst_1 p)) (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{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)))) (Finset.range (Polynomial.natDegree.{u1} R _inst_1 p)) (fun (i : Nat) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Polynomial.coeff.{u1} R _inst_1 p i)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Polynomial.coeff.{u1} R _inst_1 p i)) (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) (Polynomial.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) i)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic.as_sum Polynomial.Monic.as_sumₓ'. -/
 theorem Monic.as_sum (hp : p.Monic) :
     p = X ^ p.natDegree + ∑ i in range p.natDegree, C (p.coeff i) * X ^ i :=
@@ -106,7 +106,7 @@ theorem Monic.map [Semiring S] (f : R →+* S) (hp : Monic p) : Monic (p.map f)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {b : 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))))) b (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (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)))))))) -> (Polynomial.Monic.{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) b) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {b : 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)))) b (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Polynomial.Monic.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) b) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) b) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) b) (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) b) p))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {b : 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)))) b (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Polynomial.Monic.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) b) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) b) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) b) (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) b) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_C_mul_of_mul_leading_coeff_eq_one Polynomial.monic_C_mul_of_mul_leadingCoeff_eq_oneₓ'. -/
 theorem monic_C_mul_of_mul_leadingCoeff_eq_one {b : R} (hp : b * p.leadingCoeff = 1) :
     Monic (C b * p) := by
@@ -118,7 +118,7 @@ theorem monic_C_mul_of_mul_leadingCoeff_eq_one {b : R} (hp : b * p.leadingCoeff
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {b : 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))))) (Polynomial.leadingCoeff.{u1} R _inst_1 p) b) (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)))))))) -> (Polynomial.Monic.{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) b)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {b : 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)))) (Polynomial.leadingCoeff.{u1} R _inst_1 p) b) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Polynomial.Monic.{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) b) (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) b)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {b : 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)))) (Polynomial.leadingCoeff.{u1} R _inst_1 p) b) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Polynomial.Monic.{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) b) (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) b)))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_mul_C_of_leading_coeff_mul_eq_one Polynomial.monic_mul_C_of_leadingCoeff_mul_eq_oneₓ'. -/
 theorem monic_mul_C_of_leadingCoeff_mul_eq_one {b : R} (hp : p.leadingCoeff * b = 1) :
     Monic (p * C b) := by
@@ -156,7 +156,7 @@ theorem monic_X_pow_add {n : ℕ} (H : degree p ≤ n) : Monic (X ^ (n + 1) + p)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (x : R), Polynomial.Monic.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.X.{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) x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (x : R), Polynomial.Monic.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.X.{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) x))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (x : R), Polynomial.Monic.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.X.{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) x))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_X_add_C Polynomial.monic_X_add_Cₓ'. -/
 theorem monic_X_add_C (x : R) : Monic (X + C x) :=
   pow_one (X : R[X]) ▸ monic_X_pow_add degree_C_le
@@ -363,7 +363,7 @@ end Monic
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Nontrivial.{u1} R] (n : Nat) (r : R), Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.X.{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) r)) n)) n
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Nontrivial.{u1} R] (n : Nat) (r : R), Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.X.{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) r)) n)) n
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Nontrivial.{u1} R] (n : Nat) (r : R), Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.X.{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) r)) n)) n
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_pow_X_add_C Polynomial.natDegree_pow_X_add_Cₓ'. -/
 @[simp]
 theorem natDegree_pow_X_add_C [Nontrivial R] (n : ℕ) (r : R) : ((X + C r) ^ n).natDegree = n := by
@@ -478,7 +478,7 @@ include hf
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R 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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (Polynomial.degree.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (Polynomial.degree.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_map_eq_of_injective Polynomial.degree_map_eq_of_injectiveₓ'. -/
 theorem degree_map_eq_of_injective (p : R[X]) : degree (p.map f) = degree p :=
   if h : p = 0 then by simp [h]
@@ -491,7 +491,7 @@ theorem degree_map_eq_of_injective (p : R[X]) : degree (p.map f) = degree p :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R 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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (Polynomial.natDegree.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (Polynomial.natDegree.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_map_eq_of_injective Polynomial.natDegree_map_eq_of_injectiveₓ'. -/
 theorem natDegree_map_eq_of_injective (p : R[X]) : natDegree (p.map f) = natDegree p :=
   natDegree_eq_of_degree_eq (degree_map_eq_of_injective hf p)
@@ -501,7 +501,7 @@ theorem natDegree_map_eq_of_injective (p : R[X]) : natDegree (p.map f) = natDegr
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R 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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.leadingCoeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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 (Polynomial.leadingCoeff.{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] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.leadingCoeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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 (Polynomial.leadingCoeff.{u1} R _inst_1 p)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.leadingCoeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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 (Polynomial.leadingCoeff.{u1} R _inst_1 p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_map' Polynomial.leadingCoeff_map'ₓ'. -/
 theorem leadingCoeff_map' (p : R[X]) : leadingCoeff (p.map f) = f (leadingCoeff p) :=
   by
@@ -513,7 +513,7 @@ theorem leadingCoeff_map' (p : R[X]) : leadingCoeff (p.map f) = f (leadingCoeff
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R 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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.nextCoeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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 (Polynomial.nextCoeff.{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] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.nextCoeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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 (Polynomial.nextCoeff.{u1} R _inst_1 p)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.nextCoeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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 (Polynomial.nextCoeff.{u1} R _inst_1 p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.next_coeff_map Polynomial.nextCoeff_mapₓ'. -/
 theorem nextCoeff_map (p : R[X]) : (p.map f).nextCoeff = f p.nextCoeff :=
   by
@@ -526,7 +526,7 @@ theorem nextCoeff_map (p : R[X]) : (p.map f).nextCoeff = f p.nextCoeff :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R 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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.leadingCoeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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 (Polynomial.leadingCoeff.{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] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.leadingCoeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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 (Polynomial.leadingCoeff.{u1} R _inst_1 p)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.leadingCoeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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 (Polynomial.leadingCoeff.{u1} R _inst_1 p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_of_injective Polynomial.leadingCoeff_of_injectiveₓ'. -/
 theorem leadingCoeff_of_injective (p : R[X]) : leadingCoeff (p.map f) = f (leadingCoeff p) :=
   by
@@ -538,7 +538,7 @@ theorem leadingCoeff_of_injective (p : R[X]) : leadingCoeff (p.map f) = f (leadi
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R 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)) -> (forall {p : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) -> (Polynomial.Monic.{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] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall {p : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) -> (Polynomial.Monic.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall {p : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) -> (Polynomial.Monic.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_of_injective Polynomial.monic_of_injectiveₓ'. -/
 theorem monic_of_injective {p : R[X]} (hp : (p.map f).Monic) : p.Monic :=
   by
@@ -550,7 +550,7 @@ theorem monic_of_injective {p : R[X]} (hp : (p.map f).Monic) : p.Monic :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R 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)) -> (forall {p : Polynomial.{u1} R _inst_1}, Iff (Polynomial.Monic.{u1} R _inst_1 p) (Polynomial.Monic.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall {p : Polynomial.{u1} R _inst_1}, Iff (Polynomial.Monic.{u1} R _inst_1 p) (Polynomial.Monic.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall {p : Polynomial.{u1} R _inst_1}, Iff (Polynomial.Monic.{u1} R _inst_1 p) (Polynomial.Monic.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)))
 Case conversion may be inaccurate. Consider using '#align function.injective.monic_map_iff Function.Injective.monic_map_iffₓ'. -/
 theorem Function.Injective.monic_map_iff {p : R[X]} : p.Monic ↔ (p.map f).Monic :=
   ⟨Monic.map _, Polynomial.monic_of_injective hf⟩
@@ -568,7 +568,7 @@ variable [Ring R] {p : R[X]}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (x : R), Polynomial.Monic.{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)) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_1)) x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (x : R), Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) x) (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)) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_1)) x))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (x : R), Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) x) (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)) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_1)) x))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_X_sub_C Polynomial.monic_X_sub_Cₓ'. -/
 theorem monic_X_sub_C (x : R) : Monic (X - C x) := by
   simpa only [sub_eq_add_neg, C_neg] using monic_X_add_C (-x)
@@ -588,7 +588,7 @@ theorem monic_X_pow_sub {n : ℕ} (H : degree p ≤ n) : Monic (X ^ (n + 1) - p)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (a : R) {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R _inst_2) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.ring.{u1} R _inst_2)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_2)) n) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_2)) a)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (a : R) {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R _inst_2) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_2)) n) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_2)) a)))
+  forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (a : R) {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R _inst_2) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_2)) n) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_2)) a)))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_X_pow_sub_C Polynomial.monic_X_pow_sub_Cₓ'. -/
 /-- `X ^ n - a` is monic. -/
 theorem monic_X_pow_sub_C {R : Type u} [Ring R] (a : R) {n : ℕ} (h : n ≠ 0) : (X ^ n - C a).Monic :=

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

@@ -126,23 +126,31 @@ theorem monic_mul_C_of_leadingCoeff_mul_eq_one {b : R} (hp : p.leadingCoeff * b
   rw [monic, leading_coeff_mul' _] <;> simp [leading_coeff_C b, hp]
 #align polynomial.monic_mul_C_of_leading_coeff_mul_eq_one Polynomial.monic_mul_C_of_leadingCoeff_mul_eq_one
 
-#print Polynomial.monic_of_degree_le /-
+/- warning: polynomial.monic_of_degree_le -> Polynomial.monic_of_degree_le 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), (LE.le.{0} (WithBot.{0} Nat) (Preorder.toHasLe.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R _inst_1 p) ((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)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R _inst_1 p n) (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)))))))) -> (Polynomial.Monic.{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), (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R _inst_1 p) (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)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R _inst_1 p n) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Polynomial.Monic.{u1} R _inst_1 p)
+Case conversion may be inaccurate. Consider using '#align polynomial.monic_of_degree_le Polynomial.monic_of_degree_leₓ'. -/
 theorem monic_of_degree_le (n : ℕ) (H1 : degree p ≤ n) (H2 : coeff p n = 1) : Monic p :=
   Decidable.byCases
     (fun H : degree p < n => eq_of_zero_eq_one (H2 ▸ (coeff_eq_zero_of_degree_lt H).symm) _ _)
     fun H : ¬degree p < n => by
     rwa [monic, leading_coeff, nat_degree, (lt_or_eq_of_le H1).resolve_left H]
 #align polynomial.monic_of_degree_le Polynomial.monic_of_degree_le
--/
 
-#print Polynomial.monic_X_pow_add /-
+/- warning: polynomial.monic_X_pow_add -> Polynomial.monic_X_pow_add 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}, (LE.le.{0} (WithBot.{0} Nat) (Preorder.toHasLe.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R _inst_1 p) ((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.Monic.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) p))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {n : Nat}, (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R _inst_1 p) (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.Monic.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p))
+Case conversion may be inaccurate. Consider using '#align polynomial.monic_X_pow_add Polynomial.monic_X_pow_addₓ'. -/
 theorem monic_X_pow_add {n : ℕ} (H : degree p ≤ n) : Monic (X ^ (n + 1) + p) :=
   have H1 : degree p < n + 1 := lt_of_le_of_lt H (WithBot.coe_lt_coe.2 (Nat.lt_succ_self n))
   monic_of_degree_le (n + 1)
     (le_trans (degree_add_le _ _) (max_le (degree_X_pow_le _) (le_of_lt H1)))
     (by rw [coeff_add, coeff_X_pow, if_pos rfl, coeff_eq_zero_of_degree_lt H1, add_zero])
 #align polynomial.monic_X_pow_add Polynomial.monic_X_pow_add
--/
 
 /- warning: polynomial.monic_X_add_C -> Polynomial.monic_X_add_C is a dubious translation:
 lean 3 declaration is
@@ -176,17 +184,25 @@ theorem Monic.pow (hp : Monic p) : ∀ n : ℕ, Monic (p ^ n)
 #align polynomial.monic.pow Polynomial.Monic.pow
 -/
 
-#print Polynomial.Monic.add_of_left /-
+/- warning: polynomial.monic.add_of_left -> Polynomial.Monic.add_of_left is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u1} R _inst_1 p) -> (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))))) (Polynomial.degree.{u1} R _inst_1 q) (Polynomial.degree.{u1} R _inst_1 p)) -> (Polynomial.Monic.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) p q))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u1} R _inst_1 p) -> (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)))) (Polynomial.degree.{u1} R _inst_1 q) (Polynomial.degree.{u1} R _inst_1 p)) -> (Polynomial.Monic.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) p q))
+Case conversion may be inaccurate. Consider using '#align polynomial.monic.add_of_left Polynomial.Monic.add_of_leftₓ'. -/
 theorem Monic.add_of_left (hp : Monic p) (hpq : degree q < degree p) : Monic (p + q) := by
   rwa [monic, add_comm, leading_coeff_add_of_degree_lt hpq]
 #align polynomial.monic.add_of_left Polynomial.Monic.add_of_left
--/
 
-#print Polynomial.Monic.add_of_right /-
+/- warning: polynomial.monic.add_of_right -> Polynomial.Monic.add_of_right is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u1} R _inst_1 q) -> (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))))) (Polynomial.degree.{u1} R _inst_1 p) (Polynomial.degree.{u1} R _inst_1 q)) -> (Polynomial.Monic.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) p q))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u1} R _inst_1 q) -> (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)))) (Polynomial.degree.{u1} R _inst_1 p) (Polynomial.degree.{u1} R _inst_1 q)) -> (Polynomial.Monic.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) p q))
+Case conversion may be inaccurate. Consider using '#align polynomial.monic.add_of_right Polynomial.Monic.add_of_rightₓ'. -/
 theorem Monic.add_of_right (hq : Monic q) (hpq : degree p < degree q) : Monic (p + q) := by
   rwa [monic, leading_coeff_add_of_degree_lt hpq]
 #align polynomial.monic.add_of_right Polynomial.Monic.add_of_right
--/
 
 #print Polynomial.Monic.of_mul_monic_left /-
 theorem Monic.of_mul_monic_left (hp : p.Monic) (hpq : (p * q).Monic) : q.Monic :=
@@ -226,12 +242,16 @@ theorem natDegree_eq_zero_iff_eq_one (hp : p.Monic) : p.natDegree = 0 ↔ p = 1
 #align polynomial.monic.nat_degree_eq_zero_iff_eq_one Polynomial.Monic.natDegree_eq_zero_iff_eq_one
 -/
 
-#print Polynomial.Monic.degree_le_zero_iff_eq_one /-
+/- warning: polynomial.monic.degree_le_zero_iff_eq_one -> Polynomial.Monic.degree_le_zero_iff_eq_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Iff (LE.le.{0} (WithBot.{0} Nat) (Preorder.toHasLe.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R _inst_1 p) (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))))) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 1 (One.one.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.hasOne.{u1} R _inst_1))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Iff (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R _inst_1 p) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align polynomial.monic.degree_le_zero_iff_eq_one Polynomial.Monic.degree_le_zero_iff_eq_oneₓ'. -/
 @[simp]
 theorem degree_le_zero_iff_eq_one (hp : p.Monic) : p.degree ≤ 0 ↔ p = 1 := by
   rw [← hp.nat_degree_eq_zero_iff_eq_one, nat_degree_eq_zero_iff_degree_le_zero]
 #align polynomial.monic.degree_le_zero_iff_eq_one Polynomial.Monic.degree_le_zero_iff_eq_one
--/
 
 #print Polynomial.Monic.natDegree_mul /-
 theorem natDegree_mul (hp : p.Monic) (hq : q.Monic) :
@@ -282,11 +302,15 @@ theorem not_dvd_of_natDegree_lt (hp : Monic p) (h0 : q ≠ 0) (hl : natDegree q
 #align polynomial.monic.not_dvd_of_nat_degree_lt Polynomial.Monic.not_dvd_of_natDegree_lt
 -/
 
-#print Polynomial.Monic.not_dvd_of_degree_lt /-
+/- warning: polynomial.monic.not_dvd_of_degree_lt -> Polynomial.Monic.not_dvd_of_degree_lt is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Ne.{succ u1} (Polynomial.{u1} R _inst_1) q (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))))) -> (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))))) (Polynomial.degree.{u1} R _inst_1 q) (Polynomial.degree.{u1} R _inst_1 p)) -> (Not (Dvd.Dvd.{u1} (Polynomial.{u1} R _inst_1) (semigroupDvd.{u1} (Polynomial.{u1} R _inst_1) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R _inst_1) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) p q))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Ne.{succ u1} (Polynomial.{u1} R _inst_1) q (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{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)))) (Polynomial.degree.{u1} R _inst_1 q) (Polynomial.degree.{u1} R _inst_1 p)) -> (Not (Dvd.dvd.{u1} (Polynomial.{u1} R _inst_1) (semigroupDvd.{u1} (Polynomial.{u1} R _inst_1) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R _inst_1) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) p q))
+Case conversion may be inaccurate. Consider using '#align polynomial.monic.not_dvd_of_degree_lt Polynomial.Monic.not_dvd_of_degree_ltₓ'. -/
 theorem not_dvd_of_degree_lt (hp : Monic p) (h0 : q ≠ 0) (hl : degree q < degree p) : ¬p ∣ q :=
   Monic.not_dvd_of_natDegree_lt hp h0 <| natDegree_lt_natDegree h0 hl
 #align polynomial.monic.not_dvd_of_degree_lt Polynomial.Monic.not_dvd_of_degree_lt
--/
 
 /- warning: polynomial.monic.next_coeff_mul -> Polynomial.Monic.nextCoeff_mul is a dubious translation:
 lean 3 declaration is
@@ -552,7 +576,7 @@ theorem monic_X_sub_C (x : R) : Monic (X - C x) := by
 
 /- warning: polynomial.monic_X_pow_sub -> Polynomial.monic_X_pow_sub is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {n : Nat}, (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p) ((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.Monic.{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)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.ring.{u1} R _inst_1)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) p))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {n : Nat}, (LE.le.{0} (WithBot.{0} Nat) (Preorder.toHasLe.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p) ((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.Monic.{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)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.ring.{u1} R _inst_1)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) p))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {n : Nat}, (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p) (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.Monic.{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)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_X_pow_sub Polynomial.monic_X_pow_subₓ'. -/
@@ -589,18 +613,22 @@ theorem not_isUnit_X_pow_sub_one (R : Type _) [CommRing R] [Nontrivial R] (n : 
   rw [← @nat_degree_one R, ← (monic_X_pow_sub_C _ hn).eq_one_of_isUnit h, nat_degree_X_pow_sub_C]
 #align polynomial.not_is_unit_X_pow_sub_one Polynomial.not_isUnit_X_pow_sub_one
 
-#print Polynomial.Monic.sub_of_left /-
+/- warning: polynomial.monic.sub_of_left -> Polynomial.Monic.sub_of_left is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_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)}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R _inst_1) p) -> (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))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) q) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) -> (Polynomial.Monic.{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))
+but is expected to have type
+  forall {R : Type.{u1}} [_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)}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R _inst_1) p) -> (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)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) q) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) -> (Polynomial.Monic.{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))
+Case conversion may be inaccurate. Consider using '#align polynomial.monic.sub_of_left Polynomial.Monic.sub_of_leftₓ'. -/
 theorem Monic.sub_of_left {p q : R[X]} (hp : Monic p) (hpq : degree q < degree p) : Monic (p - q) :=
   by
   rw [sub_eq_add_neg]
   apply hp.add_of_left
   rwa [degree_neg]
 #align polynomial.monic.sub_of_left Polynomial.Monic.sub_of_left
--/
 
 /- warning: polynomial.monic.sub_of_right -> Polynomial.Monic.sub_of_right is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_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)}, (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) q) (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))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{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))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) q)) -> (Polynomial.Monic.{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))
+  forall {R : Type.{u1}} [_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)}, (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) q) (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))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{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))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) q)) -> (Polynomial.Monic.{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))
 but is expected to have type
   forall {R : Type.{u1}} [_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)}, (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) q) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{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)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) q)) -> (Polynomial.Monic.{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))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic.sub_of_right Polynomial.Monic.sub_of_rightₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

@@ -578,7 +578,7 @@ theorem monic_X_pow_sub_C {R : Type u} [Ring R] (a : R) {n : ℕ} (h : n ≠ 0)
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_2 : CommRing.{u1} R] [_inst_3 : Nontrivial.{u1} R] (n : Nat), Not (IsUnit.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_2))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))))))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_2 : CommRing.{u1} R] [_inst_3 : Nontrivial.{u1} R] (n : Nat), Not (IsUnit.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_2))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))))))
+  forall (R : Type.{u1}) [_inst_2 : CommRing.{u1} R] [_inst_3 : Nontrivial.{u1} R] (n : Nat), Not (IsUnit.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_2))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.not_is_unit_X_pow_sub_one Polynomial.not_isUnit_X_pow_sub_oneₓ'. -/
 theorem not_isUnit_X_pow_sub_one (R : Type _) [CommRing R] [Nontrivial R] (n : ℕ) :
     ¬IsUnit (X ^ n - 1 : R[X]) := by
@@ -602,7 +602,7 @@ theorem Monic.sub_of_left {p q : R[X]} (hp : Monic p) (hpq : degree q < degree p
 lean 3 declaration is
   forall {R : Type.{u1}} [_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)}, (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) q) (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))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{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))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) q)) -> (Polynomial.Monic.{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))
 but is expected to have type
-  forall {R : Type.{u1}} [_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)}, (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) q) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{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)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) q)) -> (Polynomial.Monic.{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))
+  forall {R : Type.{u1}} [_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)}, (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) q) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{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)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) q)) -> (Polynomial.Monic.{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))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic.sub_of_right Polynomial.Monic.sub_of_rightₓ'. -/
 theorem Monic.sub_of_right {p q : R[X]} (hq : q.leadingCoeff = -1) (hpq : degree p < degree q) :
     Monic (p - q) :=

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

@@ -335,16 +335,16 @@ theorem natDegree_pow (hp : p.Monic) (n : ℕ) : (p ^ n).natDegree = n * p.natDe
 
 end Monic
 
-/- warning: polynomial.nat_degree_pow_X_add_C -> Polynomial.natDegree_pow_X_add_c is a dubious translation:
+/- warning: polynomial.nat_degree_pow_X_add_C -> Polynomial.natDegree_pow_X_add_C is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Nontrivial.{u1} R] (n : Nat) (r : R), Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.X.{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) r)) n)) n
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Nontrivial.{u1} R] (n : Nat) (r : R), Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.X.{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) r)) n)) n
-Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_pow_X_add_C Polynomial.natDegree_pow_X_add_cₓ'. -/
+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_pow_X_add_C Polynomial.natDegree_pow_X_add_Cₓ'. -/
 @[simp]
-theorem natDegree_pow_X_add_c [Nontrivial R] (n : ℕ) (r : R) : ((X + C r) ^ n).natDegree = n := by
+theorem natDegree_pow_X_add_C [Nontrivial R] (n : ℕ) (r : R) : ((X + C r) ^ n).natDegree = n := by
   rw [(monic_X_add_C r).natDegree_pow, nat_degree_X_add_C, mul_one]
-#align polynomial.nat_degree_pow_X_add_C Polynomial.natDegree_pow_X_add_c
+#align polynomial.nat_degree_pow_X_add_C Polynomial.natDegree_pow_X_add_C
 
 #print Polynomial.Monic.eq_one_of_isUnit /-
 theorem Monic.eq_one_of_isUnit (hm : Monic p) (hpu : IsUnit p) : p = 1 :=

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

@@ -600,7 +600,7 @@ theorem Monic.sub_of_left {p q : R[X]} (hp : Monic p) (hpq : degree q < degree p
 
 /- warning: polynomial.monic.sub_of_right -> Polynomial.Monic.sub_of_right is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_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)}, (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) q) (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))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{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))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) q)) -> (Polynomial.Monic.{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))
+  forall {R : Type.{u1}} [_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)}, (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) q) (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))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{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))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) q)) -> (Polynomial.Monic.{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))
 but is expected to have type
   forall {R : Type.{u1}} [_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)}, (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) q) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{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)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) q)) -> (Polynomial.Monic.{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))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic.sub_of_right Polynomial.Monic.sub_of_rightₓ'. -/

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

@@ -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.monic
-! leanprover-community/mathlib commit cbdf7b565832144d024caa5a550117c6df0204a5
+! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Algebra.Regular.Smul
 /-!
 # Theory of monic polynomials
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We give several tools for proving that polynomials are monic, e.g.
 `monic.mul`, `monic.map`, `monic.pow`.
 -/

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

@@ -65,7 +65,7 @@ theorem monic_zero_iff_subsingleton' :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (Polynomial.natDegree.{u1} R _inst_1 p)) (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{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)))) (Finset.range (Polynomial.natDegree.{u1} R _inst_1 p)) (fun (i : Nat) => 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) (Polynomial.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) i)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (Polynomial.natDegree.{u1} R _inst_1 p)) (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{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)))) (Finset.range (Polynomial.natDegree.{u1} R _inst_1 p)) (fun (i : Nat) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) (Polynomial.coeff.{u1} R _inst_1 p i)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) (Polynomial.coeff.{u1} R _inst_1 p i)) (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) (Polynomial.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) i)))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (Polynomial.natDegree.{u1} R _inst_1 p)) (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{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)))) (Finset.range (Polynomial.natDegree.{u1} R _inst_1 p)) (fun (i : Nat) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Polynomial.coeff.{u1} R _inst_1 p i)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Polynomial.coeff.{u1} R _inst_1 p i)) (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) (Polynomial.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) i)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic.as_sum Polynomial.Monic.as_sumₓ'. -/
 theorem Monic.as_sum (hp : p.Monic) :
     p = X ^ p.natDegree + ∑ i in range p.natDegree, C (p.coeff i) * X ^ i :=
@@ -103,7 +103,7 @@ theorem Monic.map [Semiring S] (f : R →+* S) (hp : Monic p) : Monic (p.map f)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {b : 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))))) b (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (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)))))))) -> (Polynomial.Monic.{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) b) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {b : 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)))) b (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Polynomial.Monic.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) b) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) b) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) b) (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) b) p))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {b : 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)))) b (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Polynomial.Monic.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) b) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) b) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) b) (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) b) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_C_mul_of_mul_leading_coeff_eq_one Polynomial.monic_C_mul_of_mul_leadingCoeff_eq_oneₓ'. -/
 theorem monic_C_mul_of_mul_leadingCoeff_eq_one {b : R} (hp : b * p.leadingCoeff = 1) :
     Monic (C b * p) := by
@@ -115,7 +115,7 @@ theorem monic_C_mul_of_mul_leadingCoeff_eq_one {b : R} (hp : b * p.leadingCoeff
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {b : 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))))) (Polynomial.leadingCoeff.{u1} R _inst_1 p) b) (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)))))))) -> (Polynomial.Monic.{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) b)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {b : 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)))) (Polynomial.leadingCoeff.{u1} R _inst_1 p) b) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Polynomial.Monic.{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) b) (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) b)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {b : 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)))) (Polynomial.leadingCoeff.{u1} R _inst_1 p) b) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Polynomial.Monic.{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) b) (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) b)))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_mul_C_of_leading_coeff_mul_eq_one Polynomial.monic_mul_C_of_leadingCoeff_mul_eq_oneₓ'. -/
 theorem monic_mul_C_of_leadingCoeff_mul_eq_one {b : R} (hp : p.leadingCoeff * b = 1) :
     Monic (p * C b) := by
@@ -145,7 +145,7 @@ theorem monic_X_pow_add {n : ℕ} (H : degree p ≤ n) : Monic (X ^ (n + 1) + p)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (x : R), Polynomial.Monic.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.X.{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) x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (x : R), Polynomial.Monic.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.X.{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) x))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (x : R), Polynomial.Monic.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.X.{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) x))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_X_add_C Polynomial.monic_X_add_Cₓ'. -/
 theorem monic_X_add_C (x : R) : Monic (X + C x) :=
   pow_one (X : R[X]) ▸ monic_X_pow_add degree_C_le
@@ -336,7 +336,7 @@ end Monic
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Nontrivial.{u1} R] (n : Nat) (r : R), Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.X.{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) r)) n)) n
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Nontrivial.{u1} R] (n : Nat) (r : R), Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.X.{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) r)) n)) n
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Nontrivial.{u1} R] (n : Nat) (r : R), Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.X.{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) r)) n)) n
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_pow_X_add_C Polynomial.natDegree_pow_X_add_cₓ'. -/
 @[simp]
 theorem natDegree_pow_X_add_c [Nontrivial R] (n : ℕ) (r : R) : ((X + C r) ^ n).natDegree = n := by
@@ -451,7 +451,7 @@ include hf
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R 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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (Polynomial.degree.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (Polynomial.degree.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_map_eq_of_injective Polynomial.degree_map_eq_of_injectiveₓ'. -/
 theorem degree_map_eq_of_injective (p : R[X]) : degree (p.map f) = degree p :=
   if h : p = 0 then by simp [h]
@@ -464,7 +464,7 @@ theorem degree_map_eq_of_injective (p : R[X]) : degree (p.map f) = degree p :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R 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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (Polynomial.natDegree.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (Polynomial.natDegree.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_map_eq_of_injective Polynomial.natDegree_map_eq_of_injectiveₓ'. -/
 theorem natDegree_map_eq_of_injective (p : R[X]) : natDegree (p.map f) = natDegree p :=
   natDegree_eq_of_degree_eq (degree_map_eq_of_injective hf p)
@@ -474,7 +474,7 @@ theorem natDegree_map_eq_of_injective (p : R[X]) : natDegree (p.map f) = natDegr
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R 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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.leadingCoeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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 (Polynomial.leadingCoeff.{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] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.leadingCoeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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 (Polynomial.leadingCoeff.{u1} R _inst_1 p)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.leadingCoeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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 (Polynomial.leadingCoeff.{u1} R _inst_1 p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_map' Polynomial.leadingCoeff_map'ₓ'. -/
 theorem leadingCoeff_map' (p : R[X]) : leadingCoeff (p.map f) = f (leadingCoeff p) :=
   by
@@ -486,7 +486,7 @@ theorem leadingCoeff_map' (p : R[X]) : leadingCoeff (p.map f) = f (leadingCoeff
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R 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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.nextCoeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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 (Polynomial.nextCoeff.{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] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.nextCoeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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 (Polynomial.nextCoeff.{u1} R _inst_1 p)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.nextCoeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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 (Polynomial.nextCoeff.{u1} R _inst_1 p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.next_coeff_map Polynomial.nextCoeff_mapₓ'. -/
 theorem nextCoeff_map (p : R[X]) : (p.map f).nextCoeff = f p.nextCoeff :=
   by
@@ -499,7 +499,7 @@ theorem nextCoeff_map (p : R[X]) : (p.map f).nextCoeff = f p.nextCoeff :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R 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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.leadingCoeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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 (Polynomial.leadingCoeff.{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] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.leadingCoeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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 (Polynomial.leadingCoeff.{u1} R _inst_1 p)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.leadingCoeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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 (Polynomial.leadingCoeff.{u1} R _inst_1 p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_of_injective Polynomial.leadingCoeff_of_injectiveₓ'. -/
 theorem leadingCoeff_of_injective (p : R[X]) : leadingCoeff (p.map f) = f (leadingCoeff p) :=
   by
@@ -511,7 +511,7 @@ theorem leadingCoeff_of_injective (p : R[X]) : leadingCoeff (p.map f) = f (leadi
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R 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)) -> (forall {p : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) -> (Polynomial.Monic.{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] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall {p : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) -> (Polynomial.Monic.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall {p : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) -> (Polynomial.Monic.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_of_injective Polynomial.monic_of_injectiveₓ'. -/
 theorem monic_of_injective {p : R[X]} (hp : (p.map f).Monic) : p.Monic :=
   by
@@ -523,7 +523,7 @@ theorem monic_of_injective {p : R[X]} (hp : (p.map f).Monic) : p.Monic :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R 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)) -> (forall {p : Polynomial.{u1} R _inst_1}, Iff (Polynomial.Monic.{u1} R _inst_1 p) (Polynomial.Monic.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall {p : Polynomial.{u1} R _inst_1}, Iff (Polynomial.Monic.{u1} R _inst_1 p) (Polynomial.Monic.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R S (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)) -> (forall {p : Polynomial.{u1} R _inst_1}, Iff (Polynomial.Monic.{u1} R _inst_1 p) (Polynomial.Monic.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)))
 Case conversion may be inaccurate. Consider using '#align function.injective.monic_map_iff Function.Injective.monic_map_iffₓ'. -/
 theorem Function.Injective.monic_map_iff {p : R[X]} : p.Monic ↔ (p.map f).Monic :=
   ⟨Monic.map _, Polynomial.monic_of_injective hf⟩
@@ -541,7 +541,7 @@ variable [Ring R] {p : R[X]}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (x : R), Polynomial.Monic.{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)) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_1)) x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (x : R), Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) x) (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)) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_1)) x))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (x : R), Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) x) (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)) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_1)) x))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_X_sub_C Polynomial.monic_X_sub_Cₓ'. -/
 theorem monic_X_sub_C (x : R) : Monic (X - C x) := by
   simpa only [sub_eq_add_neg, C_neg] using monic_X_add_C (-x)
@@ -561,7 +561,7 @@ theorem monic_X_pow_sub {n : ℕ} (H : degree p ≤ n) : Monic (X ^ (n + 1) - p)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (a : R) {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R _inst_2) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.ring.{u1} R _inst_2)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_2)) n) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_2)) a)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (a : R) {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R _inst_2) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_2)) n) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_2)) a)))
+  forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (a : R) {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R _inst_2) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_2)) n) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_2)) a)))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_X_pow_sub_C Polynomial.monic_X_pow_sub_Cₓ'. -/
 /-- `X ^ n - a` is monic. -/
 theorem monic_X_pow_sub_C {R : Type u} [Ring R] (a : R) {n : ℕ} (h : n ≠ 0) : (X ^ n - C a).Monic :=

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

@@ -80,7 +80,7 @@ theorem ne_zero_of_ne_zero_of_monic (hp : p ≠ 0) (hq : Monic q) : q ≠ 0 :=
   by
   rintro rfl
   rw [monic.def, leading_coeff_zero] at hq
-  rw [← mul_one p, ← C_1, ← hq, C_0, mul_zero] at hp
+  rw [← mul_one p, ← C_1, ← hq, C_0, MulZeroClass.mul_zero] at hp
   exact hp rfl
 #align polynomial.ne_zero_of_ne_zero_of_monic Polynomial.ne_zero_of_ne_zero_of_monic
 -/
@@ -778,12 +778,12 @@ theorem isUnit_leadingCoeff_mul_left_eq_zero_iff (h : IsUnit p.leadingCoeff) {q
   constructor
   · intro hp
     replace hp := congr_arg (· * C ↑h.unit⁻¹) hp
-    simp only [zero_mul] at hp
+    simp only [MulZeroClass.zero_mul] at hp
     rwa [mul_assoc, monic.mul_left_eq_zero_iff] at hp
     refine' monic_mul_C_of_leading_coeff_mul_eq_one _
     simp [Units.mul_inv_eq_iff_eq_mul, IsUnit.unit_spec]
   · rintro rfl
-    rw [zero_mul]
+    rw [MulZeroClass.zero_mul]
 #align polynomial.is_unit_leading_coeff_mul_left_eq_zero_iff Polynomial.isUnit_leadingCoeff_mul_left_eq_zero_iff
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936

@@ -35,14 +35,23 @@ section Semiring
 
 variable [Semiring R] {p q r : R[X]}
 
+#print Polynomial.monic_zero_iff_subsingleton /-
 theorem monic_zero_iff_subsingleton : Monic (0 : R[X]) ↔ Subsingleton R :=
   subsingleton_iff_zero_eq_one
 #align polynomial.monic_zero_iff_subsingleton Polynomial.monic_zero_iff_subsingleton
+-/
 
+/- warning: polynomial.not_monic_zero_iff -> Polynomial.not_monic_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Iff (Not (Polynomial.Monic.{u1} R _inst_1 (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)))))) (Ne.{succ u1} R (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))))))) (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))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Iff (Not (Polynomial.Monic.{u1} R _inst_1 (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) (Ne.{succ u1} R (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))
+Case conversion may be inaccurate. Consider using '#align polynomial.not_monic_zero_iff Polynomial.not_monic_zero_iffₓ'. -/
 theorem not_monic_zero_iff : ¬Monic (0 : R[X]) ↔ (0 : R) ≠ 1 :=
   (monic_zero_iff_subsingleton.trans subsingleton_iff_zero_eq_one.symm).Not
 #align polynomial.not_monic_zero_iff Polynomial.not_monic_zero_iff
 
+#print Polynomial.monic_zero_iff_subsingleton' /-
 theorem monic_zero_iff_subsingleton' :
     Monic (0 : R[X]) ↔ (∀ f g : R[X], f = g) ∧ ∀ a b : R, a = b :=
   Polynomial.monic_zero_iff_subsingleton.trans
@@ -50,7 +59,14 @@ theorem monic_zero_iff_subsingleton' :
       intro
       simp, fun h => subsingleton_iff.mpr h.2⟩
 #align polynomial.monic_zero_iff_subsingleton' Polynomial.monic_zero_iff_subsingleton'
+-/
 
+/- warning: polynomial.monic.as_sum -> Polynomial.Monic.as_sum is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (Polynomial.natDegree.{u1} R _inst_1 p)) (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{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)))) (Finset.range (Polynomial.natDegree.{u1} R _inst_1 p)) (fun (i : Nat) => 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) (Polynomial.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) i)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (Polynomial.natDegree.{u1} R _inst_1 p)) (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{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)))) (Finset.range (Polynomial.natDegree.{u1} R _inst_1 p)) (fun (i : Nat) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) (Polynomial.coeff.{u1} R _inst_1 p i)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) (Polynomial.coeff.{u1} R _inst_1 p i)) (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) (Polynomial.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) i)))))
+Case conversion may be inaccurate. Consider using '#align polynomial.monic.as_sum Polynomial.Monic.as_sumₓ'. -/
 theorem Monic.as_sum (hp : p.Monic) :
     p = X ^ p.natDegree + ∑ i in range p.natDegree, C (p.coeff i) * X ^ i :=
   by
@@ -59,6 +75,7 @@ theorem Monic.as_sum (hp : p.Monic) :
   exact congr_arg C hp
 #align polynomial.monic.as_sum Polynomial.Monic.as_sum
 
+#print Polynomial.ne_zero_of_ne_zero_of_monic /-
 theorem ne_zero_of_ne_zero_of_monic (hp : p ≠ 0) (hq : Monic q) : q ≠ 0 :=
   by
   rintro rfl
@@ -66,7 +83,9 @@ theorem ne_zero_of_ne_zero_of_monic (hp : p ≠ 0) (hq : Monic q) : q ≠ 0 :=
   rw [← mul_one p, ← C_1, ← hq, C_0, mul_zero] at hp
   exact hp rfl
 #align polynomial.ne_zero_of_ne_zero_of_monic Polynomial.ne_zero_of_ne_zero_of_monic
+-/
 
+#print Polynomial.Monic.map /-
 theorem Monic.map [Semiring S] (f : R →+* S) (hp : Monic p) : Monic (p.map f) :=
   by
   nontriviality
@@ -78,37 +97,61 @@ theorem Monic.map [Semiring S] (f : R →+* S) (hp : Monic p) : Monic (p.map f)
   suffices p.coeff (map f p).natDegree = 1 by simp [this]
   rwa [nat_degree_eq_of_degree_eq (degree_map_eq_of_leading_coeff_ne_zero f this)]
 #align polynomial.monic.map Polynomial.Monic.map
+-/
 
-theorem monic_c_mul_of_mul_leadingCoeff_eq_one {b : R} (hp : b * p.leadingCoeff = 1) :
+/- warning: polynomial.monic_C_mul_of_mul_leading_coeff_eq_one -> Polynomial.monic_C_mul_of_mul_leadingCoeff_eq_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {b : 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))))) b (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (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)))))))) -> (Polynomial.Monic.{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) b) p))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {b : 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)))) b (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Polynomial.Monic.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) b) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) b) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) b) (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) b) p))
+Case conversion may be inaccurate. Consider using '#align polynomial.monic_C_mul_of_mul_leading_coeff_eq_one Polynomial.monic_C_mul_of_mul_leadingCoeff_eq_oneₓ'. -/
+theorem monic_C_mul_of_mul_leadingCoeff_eq_one {b : R} (hp : b * p.leadingCoeff = 1) :
     Monic (C b * p) := by
   nontriviality
   rw [monic, leading_coeff_mul' _] <;> simp [leading_coeff_C b, hp]
-#align polynomial.monic_C_mul_of_mul_leading_coeff_eq_one Polynomial.monic_c_mul_of_mul_leadingCoeff_eq_one
-
-theorem monic_mul_c_of_leadingCoeff_mul_eq_one {b : R} (hp : p.leadingCoeff * b = 1) :
+#align polynomial.monic_C_mul_of_mul_leading_coeff_eq_one Polynomial.monic_C_mul_of_mul_leadingCoeff_eq_one
+
+/- warning: polynomial.monic_mul_C_of_leading_coeff_mul_eq_one -> Polynomial.monic_mul_C_of_leadingCoeff_mul_eq_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {b : 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))))) (Polynomial.leadingCoeff.{u1} R _inst_1 p) b) (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)))))))) -> (Polynomial.Monic.{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) b)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {b : 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)))) (Polynomial.leadingCoeff.{u1} R _inst_1 p) b) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Polynomial.Monic.{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) b) (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) b)))
+Case conversion may be inaccurate. Consider using '#align polynomial.monic_mul_C_of_leading_coeff_mul_eq_one Polynomial.monic_mul_C_of_leadingCoeff_mul_eq_oneₓ'. -/
+theorem monic_mul_C_of_leadingCoeff_mul_eq_one {b : R} (hp : p.leadingCoeff * b = 1) :
     Monic (p * C b) := by
   nontriviality
   rw [monic, leading_coeff_mul' _] <;> simp [leading_coeff_C b, hp]
-#align polynomial.monic_mul_C_of_leading_coeff_mul_eq_one Polynomial.monic_mul_c_of_leadingCoeff_mul_eq_one
+#align polynomial.monic_mul_C_of_leading_coeff_mul_eq_one Polynomial.monic_mul_C_of_leadingCoeff_mul_eq_one
 
+#print Polynomial.monic_of_degree_le /-
 theorem monic_of_degree_le (n : ℕ) (H1 : degree p ≤ n) (H2 : coeff p n = 1) : Monic p :=
   Decidable.byCases
     (fun H : degree p < n => eq_of_zero_eq_one (H2 ▸ (coeff_eq_zero_of_degree_lt H).symm) _ _)
     fun H : ¬degree p < n => by
     rwa [monic, leading_coeff, nat_degree, (lt_or_eq_of_le H1).resolve_left H]
 #align polynomial.monic_of_degree_le Polynomial.monic_of_degree_le
+-/
 
-theorem monic_x_pow_add {n : ℕ} (H : degree p ≤ n) : Monic (X ^ (n + 1) + p) :=
+#print Polynomial.monic_X_pow_add /-
+theorem monic_X_pow_add {n : ℕ} (H : degree p ≤ n) : Monic (X ^ (n + 1) + p) :=
   have H1 : degree p < n + 1 := lt_of_le_of_lt H (WithBot.coe_lt_coe.2 (Nat.lt_succ_self n))
   monic_of_degree_le (n + 1)
     (le_trans (degree_add_le _ _) (max_le (degree_X_pow_le _) (le_of_lt H1)))
     (by rw [coeff_add, coeff_X_pow, if_pos rfl, coeff_eq_zero_of_degree_lt H1, add_zero])
-#align polynomial.monic_X_pow_add Polynomial.monic_x_pow_add
-
-theorem monic_x_add_c (x : R) : Monic (X + C x) :=
-  pow_one (X : R[X]) ▸ monic_x_pow_add degree_C_le
-#align polynomial.monic_X_add_C Polynomial.monic_x_add_c
+#align polynomial.monic_X_pow_add Polynomial.monic_X_pow_add
+-/
 
+/- warning: polynomial.monic_X_add_C -> Polynomial.monic_X_add_C is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (x : R), Polynomial.Monic.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.X.{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) x))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (x : R), Polynomial.Monic.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.X.{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) x))
+Case conversion may be inaccurate. Consider using '#align polynomial.monic_X_add_C Polynomial.monic_X_add_Cₓ'. -/
+theorem monic_X_add_C (x : R) : Monic (X + C x) :=
+  pow_one (X : R[X]) ▸ monic_X_pow_add degree_C_le
+#align polynomial.monic_X_add_C Polynomial.monic_X_add_C
+
+#print Polynomial.Monic.mul /-
 theorem Monic.mul (hp : Monic p) (hq : Monic q) : Monic (p * q) :=
   if h0 : (0 : R) = 1 then
     haveI := subsingleton_of_zero_eq_one h0
@@ -119,38 +162,50 @@ theorem Monic.mul (hp : Monic p) (hq : Monic q) : Monic (p * q) :=
       simp [monic.def.1 hp, monic.def.1 hq, Ne.symm h0]
     rw [monic.def, leading_coeff_mul' this, monic.def.1 hp, monic.def.1 hq, one_mul]
 #align polynomial.monic.mul Polynomial.Monic.mul
+-/
 
+#print Polynomial.Monic.pow /-
 theorem Monic.pow (hp : Monic p) : ∀ n : ℕ, Monic (p ^ n)
   | 0 => monic_one
   | n + 1 => by
     rw [pow_succ]
     exact hp.mul (monic.pow n)
 #align polynomial.monic.pow Polynomial.Monic.pow
+-/
 
+#print Polynomial.Monic.add_of_left /-
 theorem Monic.add_of_left (hp : Monic p) (hpq : degree q < degree p) : Monic (p + q) := by
   rwa [monic, add_comm, leading_coeff_add_of_degree_lt hpq]
 #align polynomial.monic.add_of_left Polynomial.Monic.add_of_left
+-/
 
+#print Polynomial.Monic.add_of_right /-
 theorem Monic.add_of_right (hq : Monic q) (hpq : degree p < degree q) : Monic (p + q) := by
   rwa [monic, leading_coeff_add_of_degree_lt hpq]
 #align polynomial.monic.add_of_right Polynomial.Monic.add_of_right
+-/
 
+#print Polynomial.Monic.of_mul_monic_left /-
 theorem Monic.of_mul_monic_left (hp : p.Monic) (hpq : (p * q).Monic) : q.Monic :=
   by
   contrapose! hpq
   rw [monic.def] at hpq⊢
   rwa [leading_coeff_monic_mul hp]
 #align polynomial.monic.of_mul_monic_left Polynomial.Monic.of_mul_monic_left
+-/
 
+#print Polynomial.Monic.of_mul_monic_right /-
 theorem Monic.of_mul_monic_right (hq : q.Monic) (hpq : (p * q).Monic) : p.Monic :=
   by
   contrapose! hpq
   rw [monic.def] at hpq⊢
   rwa [leading_coeff_mul_monic hq]
 #align polynomial.monic.of_mul_monic_right Polynomial.Monic.of_mul_monic_right
+-/
 
 namespace Monic
 
+#print Polynomial.Monic.natDegree_eq_zero_iff_eq_one /-
 @[simp]
 theorem natDegree_eq_zero_iff_eq_one (hp : p.Monic) : p.natDegree = 0 ↔ p = 1 :=
   by
@@ -166,12 +221,16 @@ theorem natDegree_eq_zero_iff_eq_one (hp : p.Monic) : p.natDegree = 0 ↔ p = 1
   rw [← h]
   apply hp
 #align polynomial.monic.nat_degree_eq_zero_iff_eq_one Polynomial.Monic.natDegree_eq_zero_iff_eq_one
+-/
 
+#print Polynomial.Monic.degree_le_zero_iff_eq_one /-
 @[simp]
 theorem degree_le_zero_iff_eq_one (hp : p.Monic) : p.degree ≤ 0 ↔ p = 1 := by
   rw [← hp.nat_degree_eq_zero_iff_eq_one, nat_degree_eq_zero_iff_degree_le_zero]
 #align polynomial.monic.degree_le_zero_iff_eq_one Polynomial.Monic.degree_le_zero_iff_eq_one
+-/
 
+#print Polynomial.Monic.natDegree_mul /-
 theorem natDegree_mul (hp : p.Monic) (hq : q.Monic) :
     (p * q).natDegree = p.natDegree + q.natDegree :=
   by
@@ -179,7 +238,9 @@ theorem natDegree_mul (hp : p.Monic) (hq : q.Monic) :
   apply nat_degree_mul'
   simp [hp.leading_coeff, hq.leading_coeff]
 #align polynomial.monic.nat_degree_mul Polynomial.Monic.natDegree_mul
+-/
 
+#print Polynomial.Monic.degree_mul_comm /-
 theorem degree_mul_comm (hp : p.Monic) (q : R[X]) : (p * q).degree = (q * p).degree :=
   by
   by_cases h : q = 0
@@ -188,14 +249,18 @@ theorem degree_mul_comm (hp : p.Monic) (q : R[X]) : (p * q).degree = (q * p).deg
   · exact add_comm _ _
   · rwa [hp.leading_coeff, one_mul, leading_coeff_ne_zero]
 #align polynomial.monic.degree_mul_comm Polynomial.Monic.degree_mul_comm
+-/
 
+#print Polynomial.Monic.natDegree_mul' /-
 theorem natDegree_mul' (hp : p.Monic) (hq : q ≠ 0) :
     (p * q).natDegree = p.natDegree + q.natDegree :=
   by
   rw [nat_degree_mul', add_comm]
   simpa [hp.leading_coeff, leading_coeff_ne_zero]
 #align polynomial.monic.nat_degree_mul' Polynomial.Monic.natDegree_mul'
+-/
 
+#print Polynomial.Monic.natDegree_mul_comm /-
 theorem natDegree_mul_comm (hp : p.Monic) (q : R[X]) : (p * q).natDegree = (q * p).natDegree :=
   by
   by_cases h : q = 0
@@ -203,18 +268,29 @@ theorem natDegree_mul_comm (hp : p.Monic) (q : R[X]) : (p * q).natDegree = (q *
   rw [hp.nat_degree_mul' h, Polynomial.natDegree_mul', add_comm]
   simpa [hp.leading_coeff, leading_coeff_ne_zero]
 #align polynomial.monic.nat_degree_mul_comm Polynomial.Monic.natDegree_mul_comm
+-/
 
+#print Polynomial.Monic.not_dvd_of_natDegree_lt /-
 theorem not_dvd_of_natDegree_lt (hp : Monic p) (h0 : q ≠ 0) (hl : natDegree q < natDegree p) :
     ¬p ∣ q := by
   rintro ⟨r, rfl⟩
   rw [hp.nat_degree_mul' <| right_ne_zero_of_mul h0] at hl
   exact hl.not_le (Nat.le_add_right _ _)
 #align polynomial.monic.not_dvd_of_nat_degree_lt Polynomial.Monic.not_dvd_of_natDegree_lt
+-/
 
+#print Polynomial.Monic.not_dvd_of_degree_lt /-
 theorem not_dvd_of_degree_lt (hp : Monic p) (h0 : q ≠ 0) (hl : degree q < degree p) : ¬p ∣ q :=
   Monic.not_dvd_of_natDegree_lt hp h0 <| natDegree_lt_natDegree h0 hl
 #align polynomial.monic.not_dvd_of_degree_lt Polynomial.Monic.not_dvd_of_degree_lt
+-/
 
+/- warning: polynomial.monic.next_coeff_mul -> Polynomial.Monic.nextCoeff_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Polynomial.Monic.{u1} R _inst_1 q) -> (Eq.{succ u1} R (Polynomial.nextCoeff.{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.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Polynomial.nextCoeff.{u1} R _inst_1 p) (Polynomial.nextCoeff.{u1} R _inst_1 q)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Polynomial.Monic.{u1} R _inst_1 q) -> (Eq.{succ u1} R (Polynomial.nextCoeff.{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.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Polynomial.nextCoeff.{u1} R _inst_1 p) (Polynomial.nextCoeff.{u1} R _inst_1 q)))
+Case conversion may be inaccurate. Consider using '#align polynomial.monic.next_coeff_mul Polynomial.Monic.nextCoeff_mulₓ'. -/
 theorem nextCoeff_mul (hp : Monic p) (hq : Monic q) :
     nextCoeff (p * q) = nextCoeff p + nextCoeff q :=
   by
@@ -224,6 +300,12 @@ theorem nextCoeff_mul (hp : Monic p) (hq : Monic q) :
     simp [coeff_mul, nat.antidiagonal, hp.leading_coeff, hq.leading_coeff, add_comm]
 #align polynomial.monic.next_coeff_mul Polynomial.Monic.nextCoeff_mul
 
+/- warning: polynomial.monic.eq_one_of_map_eq_one -> Polynomial.Monic.eq_one_of_map_eq_one is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.monic.eq_one_of_map_eq_one Polynomial.Monic.eq_one_of_map_eq_oneₓ'. -/
 theorem eq_one_of_map_eq_one {S : Type _} [Semiring S] [Nontrivial S] (f : R →+* S) (hp : p.Monic)
     (map_eq : p.map f = 1) : p = 1 := by
   nontriviality R
@@ -238,6 +320,7 @@ theorem eq_one_of_map_eq_one {S : Type _} [Semiring S] [Nontrivial S] (f : R →
   rw [← hndeg, ← Polynomial.leadingCoeff, hp.leading_coeff, C.map_one]
 #align polynomial.monic.eq_one_of_map_eq_one Polynomial.Monic.eq_one_of_map_eq_one
 
+#print Polynomial.Monic.natDegree_pow /-
 theorem natDegree_pow (hp : p.Monic) (n : ℕ) : (p ^ n).natDegree = n * p.natDegree :=
   by
   induction' n with n hn
@@ -245,14 +328,22 @@ theorem natDegree_pow (hp : p.Monic) (n : ℕ) : (p ^ n).natDegree = n * p.natDe
   · rw [pow_succ, hp.nat_degree_mul (hp.pow n), hn]
     ring
 #align polynomial.monic.nat_degree_pow Polynomial.Monic.natDegree_pow
+-/
 
 end Monic
 
+/- warning: polynomial.nat_degree_pow_X_add_C -> Polynomial.natDegree_pow_X_add_c is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_pow_X_add_C Polynomial.natDegree_pow_X_add_cₓ'. -/
 @[simp]
-theorem natDegree_pow_x_add_c [Nontrivial R] (n : ℕ) (r : R) : ((X + C r) ^ n).natDegree = n := by
+theorem natDegree_pow_X_add_c [Nontrivial R] (n : ℕ) (r : R) : ((X + C r) ^ n).natDegree = n := by
   rw [(monic_X_add_C r).natDegree_pow, nat_degree_X_add_C, mul_one]
-#align polynomial.nat_degree_pow_X_add_C Polynomial.natDegree_pow_x_add_c
+#align polynomial.nat_degree_pow_X_add_C Polynomial.natDegree_pow_X_add_c
 
+#print Polynomial.Monic.eq_one_of_isUnit /-
 theorem Monic.eq_one_of_isUnit (hm : Monic p) (hpu : IsUnit p) : p = 1 :=
   by
   nontriviality R
@@ -261,10 +352,13 @@ theorem Monic.eq_one_of_isUnit (hm : Monic p) (hpu : IsUnit p) : p = 1 :=
   rw [h, nat_degree_one, eq_comm, add_eq_zero_iff] at this
   exact hm.nat_degree_eq_zero_iff_eq_one.mp this.1
 #align polynomial.monic.eq_one_of_is_unit Polynomial.Monic.eq_one_of_isUnit
+-/
 
+#print Polynomial.Monic.isUnit_iff /-
 theorem Monic.isUnit_iff (hm : p.Monic) : IsUnit p ↔ p = 1 :=
   ⟨hm.eq_one_of_isUnit, fun h => h.symm ▸ isUnit_one⟩
 #align polynomial.monic.is_unit_iff Polynomial.Monic.isUnit_iff
+-/
 
 end Semiring
 
@@ -272,6 +366,7 @@ section CommSemiring
 
 variable [CommSemiring R] {p : R[X]}
 
+#print Polynomial.monic_multiset_prod_of_monic /-
 theorem monic_multiset_prod_of_monic (t : Multiset ι) (f : ι → R[X]) (ht : ∀ i ∈ t, Monic (f i)) :
     Monic (t.map f).Prod := by
   revert ht
@@ -280,12 +375,16 @@ theorem monic_multiset_prod_of_monic (t : Multiset ι) (f : ι → R[X]) (ht : 
   rw [Multiset.map_cons, Multiset.prod_cons]
   exact (ht _ (Multiset.mem_cons_self _ _)).mul (ih fun _ hi => ht _ (Multiset.mem_cons_of_mem hi))
 #align polynomial.monic_multiset_prod_of_monic Polynomial.monic_multiset_prod_of_monic
+-/
 
+#print Polynomial.monic_prod_of_monic /-
 theorem monic_prod_of_monic (s : Finset ι) (f : ι → R[X]) (hs : ∀ i ∈ s, Monic (f i)) :
     Monic (∏ i in s, f i) :=
   monic_multiset_prod_of_monic s.1 f hs
 #align polynomial.monic_prod_of_monic Polynomial.monic_prod_of_monic
+-/
 
+#print Polynomial.Monic.nextCoeff_multiset_prod /-
 theorem Monic.nextCoeff_multiset_prod (t : Multiset ι) (f : ι → R[X]) (h : ∀ i ∈ t, Monic (f i)) :
     nextCoeff (t.map f).Prod = (t.map fun i => nextCoeff (f i)).Sum :=
   by
@@ -300,11 +399,14 @@ theorem Monic.nextCoeff_multiset_prod (t : Multiset ι) (f : ι → R[X]) (h : 
     exacts[fun i hi => ht i (Multiset.mem_cons_of_mem hi), ht a (Multiset.mem_cons_self _ _),
       monic_multiset_prod_of_monic _ _ fun b bs => ht _ (Multiset.mem_cons_of_mem bs)]
 #align polynomial.monic.next_coeff_multiset_prod Polynomial.Monic.nextCoeff_multiset_prod
+-/
 
+#print Polynomial.Monic.nextCoeff_prod /-
 theorem Monic.nextCoeff_prod (s : Finset ι) (f : ι → R[X]) (h : ∀ i ∈ s, Monic (f i)) :
     nextCoeff (∏ i in s, f i) = ∑ i in s, nextCoeff (f i) :=
   Monic.nextCoeff_multiset_prod s.1 f h
 #align polynomial.monic.next_coeff_prod Polynomial.Monic.nextCoeff_prod
+-/
 
 end CommSemiring
 
@@ -312,6 +414,7 @@ section Semiring
 
 variable [Semiring R]
 
+#print Polynomial.Monic.natDegree_map /-
 @[simp]
 theorem Monic.natDegree_map [Semiring S] [Nontrivial S] {P : R[X]} (hmo : P.Monic) (f : R →+* S) :
     (P.map f).natDegree = P.natDegree :=
@@ -320,7 +423,9 @@ theorem Monic.natDegree_map [Semiring S] [Nontrivial S] {P : R[X]} (hmo : P.Moni
   rw [coeff_map, monic.coeff_nat_degree hmo, RingHom.map_one]
   exact one_ne_zero
 #align polynomial.monic.nat_degree_map Polynomial.Monic.natDegree_map
+-/
 
+#print Polynomial.Monic.degree_map /-
 @[simp]
 theorem Monic.degree_map [Semiring S] [Nontrivial S] {P : R[X]} (hmo : P.Monic) (f : R →+* S) :
     (P.map f).degree = P.degree := by
@@ -332,6 +437,7 @@ theorem Monic.degree_map [Semiring S] [Nontrivial S] {P : R[X]} (hmo : P.Monic)
     rw [coeff_map, monic.coeff_nat_degree hmo, RingHom.map_one]
     exact one_ne_zero
 #align polynomial.monic.degree_map Polynomial.Monic.degree_map
+-/
 
 section Injective
 
@@ -341,6 +447,12 @@ variable [Semiring S] {f : R →+* S} (hf : Injective f)
 
 include hf
 
+/- warning: polynomial.degree_map_eq_of_injective -> Polynomial.degree_map_eq_of_injective is a dubious translation:
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+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Function.Injective.{succ u1, succ u2} R 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)) -> (forall (p : Polynomial.{u1} R _inst_1), Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (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_map_eq_of_injective Polynomial.degree_map_eq_of_injectiveₓ'. -/
 theorem degree_map_eq_of_injective (p : R[X]) : degree (p.map f) = degree p :=
   if h : p = 0 then by simp [h]
   else
@@ -348,16 +460,34 @@ theorem degree_map_eq_of_injective (p : R[X]) : degree (p.map f) = degree p :=
       (by rw [← f.map_zero] <;> exact mt hf.eq_iff.1 (mt leading_coeff_eq_zero.1 h))
 #align polynomial.degree_map_eq_of_injective Polynomial.degree_map_eq_of_injective
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_map_eq_of_injective Polynomial.natDegree_map_eq_of_injectiveₓ'. -/
 theorem natDegree_map_eq_of_injective (p : R[X]) : natDegree (p.map f) = natDegree p :=
   natDegree_eq_of_degree_eq (degree_map_eq_of_injective hf p)
 #align polynomial.nat_degree_map_eq_of_injective Polynomial.natDegree_map_eq_of_injective
 
+/- warning: polynomial.leading_coeff_map' -> Polynomial.leadingCoeff_map' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_map' Polynomial.leadingCoeff_map'ₓ'. -/
 theorem leadingCoeff_map' (p : R[X]) : leadingCoeff (p.map f) = f (leadingCoeff p) :=
   by
   unfold leading_coeff
   rw [coeff_map, nat_degree_map_eq_of_injective hf p]
 #align polynomial.leading_coeff_map' Polynomial.leadingCoeff_map'
 
+/- warning: polynomial.next_coeff_map -> Polynomial.nextCoeff_map is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.next_coeff_map Polynomial.nextCoeff_mapₓ'. -/
 theorem nextCoeff_map (p : R[X]) : (p.map f).nextCoeff = f p.nextCoeff :=
   by
   unfold next_coeff
@@ -365,18 +495,36 @@ theorem nextCoeff_map (p : R[X]) : (p.map f).nextCoeff = f p.nextCoeff :=
   split_ifs <;> simp
 #align polynomial.next_coeff_map Polynomial.nextCoeff_map
 
+/- warning: polynomial.leading_coeff_of_injective -> Polynomial.leadingCoeff_of_injective is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_of_injective Polynomial.leadingCoeff_of_injectiveₓ'. -/
 theorem leadingCoeff_of_injective (p : R[X]) : leadingCoeff (p.map f) = f (leadingCoeff p) :=
   by
   delta leading_coeff
   rw [coeff_map f, nat_degree_map_eq_of_injective hf p]
 #align polynomial.leading_coeff_of_injective Polynomial.leadingCoeff_of_injective
 
+/- warning: polynomial.monic_of_injective -> Polynomial.monic_of_injective is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.monic_of_injective Polynomial.monic_of_injectiveₓ'. -/
 theorem monic_of_injective {p : R[X]} (hp : (p.map f).Monic) : p.Monic :=
   by
   apply hf
   rw [← leading_coeff_of_injective hf, hp.leading_coeff, f.map_one]
 #align polynomial.monic_of_injective Polynomial.monic_of_injective
 
+/- warning: function.injective.monic_map_iff -> Function.Injective.monic_map_iff is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align function.injective.monic_map_iff Function.Injective.monic_map_iffₓ'. -/
 theorem Function.Injective.monic_map_iff {p : R[X]} : p.Monic ↔ (p.map f).Monic :=
   ⟨Monic.map _, Polynomial.monic_of_injective hf⟩
 #align function.injective.monic_map_iff Function.Injective.monic_map_iff
@@ -389,38 +537,70 @@ section Ring
 
 variable [Ring R] {p : R[X]}
 
-theorem monic_x_sub_c (x : R) : Monic (X - C x) := by
+/- warning: polynomial.monic_X_sub_C -> Polynomial.monic_X_sub_C is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.monic_X_sub_C Polynomial.monic_X_sub_Cₓ'. -/
+theorem monic_X_sub_C (x : R) : Monic (X - C x) := by
   simpa only [sub_eq_add_neg, C_neg] using monic_X_add_C (-x)
-#align polynomial.monic_X_sub_C Polynomial.monic_x_sub_c
-
-theorem monic_x_pow_sub {n : ℕ} (H : degree p ≤ n) : Monic (X ^ (n + 1) - p) := by
+#align polynomial.monic_X_sub_C Polynomial.monic_X_sub_C
+
+/- warning: polynomial.monic_X_pow_sub -> Polynomial.monic_X_pow_sub 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.monic_X_pow_sub Polynomial.monic_X_pow_subₓ'. -/
+theorem monic_X_pow_sub {n : ℕ} (H : degree p ≤ n) : Monic (X ^ (n + 1) - p) := by
   simpa [sub_eq_add_neg] using monic_X_pow_add (show degree (-p) ≤ n by rwa [← degree_neg p] at H)
-#align polynomial.monic_X_pow_sub Polynomial.monic_x_pow_sub
-
+#align polynomial.monic_X_pow_sub Polynomial.monic_X_pow_sub
+
+/- warning: polynomial.monic_X_pow_sub_C -> Polynomial.monic_X_pow_sub_C is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.monic_X_pow_sub_C Polynomial.monic_X_pow_sub_Cₓ'. -/
 /-- `X ^ n - a` is monic. -/
-theorem monic_x_pow_sub_c {R : Type u} [Ring R] (a : R) {n : ℕ} (h : n ≠ 0) : (X ^ n - C a).Monic :=
+theorem monic_X_pow_sub_C {R : Type u} [Ring R] (a : R) {n : ℕ} (h : n ≠ 0) : (X ^ n - C a).Monic :=
   by
   obtain ⟨k, hk⟩ := Nat.exists_eq_succ_of_ne_zero h
   convert monic_X_pow_sub _
   exact le_trans degree_C_le Nat.WithBot.coe_nonneg
-#align polynomial.monic_X_pow_sub_C Polynomial.monic_x_pow_sub_c
-
-theorem not_isUnit_x_pow_sub_one (R : Type _) [CommRing R] [Nontrivial R] (n : ℕ) :
+#align polynomial.monic_X_pow_sub_C Polynomial.monic_X_pow_sub_C
+
+/- warning: polynomial.not_is_unit_X_pow_sub_one -> Polynomial.not_isUnit_X_pow_sub_one is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_2 : CommRing.{u1} R] [_inst_3 : Nontrivial.{u1} R] (n : Nat), Not (IsUnit.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_2))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))))))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_2 : CommRing.{u1} R] [_inst_3 : Nontrivial.{u1} R] (n : Nat), Not (IsUnit.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_2))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.not_is_unit_X_pow_sub_one Polynomial.not_isUnit_X_pow_sub_oneₓ'. -/
+theorem not_isUnit_X_pow_sub_one (R : Type _) [CommRing R] [Nontrivial R] (n : ℕ) :
     ¬IsUnit (X ^ n - 1 : R[X]) := by
   intro h
   rcases eq_or_ne n 0 with (rfl | hn)
   · simpa using h
   apply hn
   rw [← @nat_degree_one R, ← (monic_X_pow_sub_C _ hn).eq_one_of_isUnit h, nat_degree_X_pow_sub_C]
-#align polynomial.not_is_unit_X_pow_sub_one Polynomial.not_isUnit_x_pow_sub_one
+#align polynomial.not_is_unit_X_pow_sub_one Polynomial.not_isUnit_X_pow_sub_one
 
+#print Polynomial.Monic.sub_of_left /-
 theorem Monic.sub_of_left {p q : R[X]} (hp : Monic p) (hpq : degree q < degree p) : Monic (p - q) :=
   by
   rw [sub_eq_add_neg]
   apply hp.add_of_left
   rwa [degree_neg]
 #align polynomial.monic.sub_of_left Polynomial.Monic.sub_of_left
+-/
 
+/- warning: polynomial.monic.sub_of_right -> Polynomial.Monic.sub_of_right is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_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)}, (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) q) (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))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{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))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) q)) -> (Polynomial.Monic.{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))
+but is expected to have type
+  forall {R : Type.{u1}} [_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)}, (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) q) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{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)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) q)) -> (Polynomial.Monic.{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))
+Case conversion may be inaccurate. Consider using '#align polynomial.monic.sub_of_right Polynomial.Monic.sub_of_rightₓ'. -/
 theorem Monic.sub_of_right {p q : R[X]} (hq : q.leadingCoeff = -1) (hpq : degree p < degree q) :
     Monic (p - q) :=
   by
@@ -437,10 +617,12 @@ section NonzeroSemiring
 
 variable [Semiring R] [Nontrivial R] {p q : R[X]}
 
+#print Polynomial.not_monic_zero /-
 @[simp]
 theorem not_monic_zero : ¬Monic (0 : R[X]) :=
   not_monic_zero_iff.mp zero_ne_one
 #align polynomial.not_monic_zero Polynomial.not_monic_zero
+-/
 
 end NonzeroSemiring
 
@@ -449,6 +631,7 @@ section NotZeroDivisor
 -- TODO: using gh-8537, rephrase lemmas that involve commutation around `*` using the op-ring
 variable [Semiring R] {p : R[X]}
 
+#print Polynomial.Monic.mul_left_ne_zero /-
 theorem Monic.mul_left_ne_zero (hp : Monic p) {q : R[X]} (hq : q ≠ 0) : q * p ≠ 0 :=
   by
   by_cases h : p = 1
@@ -459,7 +642,9 @@ theorem Monic.mul_left_ne_zero (hp : Monic p) {q : R[X]} (hq : q ≠ 0) : q * p
   refine' (lt_trans _ h).ne'
   simp
 #align polynomial.monic.mul_left_ne_zero Polynomial.Monic.mul_left_ne_zero
+-/
 
+#print Polynomial.Monic.mul_right_ne_zero /-
 theorem Monic.mul_right_ne_zero (hp : Monic p) {q : R[X]} (hq : q ≠ 0) : p * q ≠ 0 :=
   by
   by_cases h : p = 1
@@ -471,7 +656,9 @@ theorem Monic.mul_right_ne_zero (hp : Monic p) {q : R[X]} (hq : q ≠ 0) : p * q
   refine' (lt_trans _ h).ne'
   simp
 #align polynomial.monic.mul_right_ne_zero Polynomial.Monic.mul_right_ne_zero
+-/
 
+#print Polynomial.Monic.mul_natDegree_lt_iff /-
 theorem Monic.mul_natDegree_lt_iff (h : Monic p) {q : R[X]} :
     (p * q).natDegree < p.natDegree ↔ p ≠ 1 ∧ q = 0 :=
   by
@@ -480,15 +667,21 @@ theorem Monic.mul_natDegree_lt_iff (h : Monic p) {q : R[X]} :
     exact ⟨fun h => h.ne', fun h => lt_of_le_of_ne (Nat.zero_le _) h.symm⟩
   · simp [h.nat_degree_mul', hq]
 #align polynomial.monic.mul_nat_degree_lt_iff Polynomial.Monic.mul_natDegree_lt_iff
+-/
 
+#print Polynomial.Monic.mul_right_eq_zero_iff /-
 theorem Monic.mul_right_eq_zero_iff (h : Monic p) {q : R[X]} : p * q = 0 ↔ q = 0 := by
   by_cases hq : q = 0 <;> simp [h.mul_right_ne_zero, hq]
 #align polynomial.monic.mul_right_eq_zero_iff Polynomial.Monic.mul_right_eq_zero_iff
+-/
 
+#print Polynomial.Monic.mul_left_eq_zero_iff /-
 theorem Monic.mul_left_eq_zero_iff (h : Monic p) {q : R[X]} : q * p = 0 ↔ q = 0 := by
   by_cases hq : q = 0 <;> simp [h.mul_left_ne_zero, hq]
 #align polynomial.monic.mul_left_eq_zero_iff Polynomial.Monic.mul_left_eq_zero_iff
+-/
 
+#print Polynomial.Monic.isRegular /-
 theorem Monic.isRegular {R : Type _} [Ring R] {p : R[X]} (hp : Monic p) : IsRegular p :=
   by
   constructor
@@ -498,7 +691,14 @@ theorem Monic.isRegular {R : Type _} [Ring R] {p : R[X]} (hp : Monic p) : IsRegu
     simp only at h
     rw [← sub_eq_zero, ← hp.mul_left_eq_zero_iff, sub_mul, h, sub_self]
 #align polynomial.monic.is_regular Polynomial.Monic.isRegular
+-/
 
+/- warning: polynomial.degree_smul_of_smul_regular -> Polynomial.degree_smul_of_smul_regular is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Monoid.{u2} S] [_inst_3 : DistribMulAction.{u2, u1} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {k : S} (p : Polynomial.{u1} R _inst_1), (IsSMulRegular.{u2, u1} S R (SMulZeroClass.toHasSmul.{u2, u1} S R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribSMul.toSmulZeroClass.{u2, u1} S R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (DistribMulAction.toDistribSMul.{u2, u1} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3))) k) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 (SMul.smul.{u2, u1} S (Polynomial.{u1} R _inst_1) (SMulZeroClass.toHasSmul.{u2, u1} S (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1) (Polynomial.smulZeroClass.{u1, u2} R _inst_1 S (DistribSMul.toSmulZeroClass.{u2, u1} S R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (DistribMulAction.toDistribSMul.{u2, u1} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3)))) k p)) (Polynomial.degree.{u1} R _inst_1 p))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {S : Type.{u1}} [_inst_2 : Monoid.{u1} S] [_inst_3 : DistribMulAction.{u1, u2} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))] {k : S} (p : Polynomial.{u2} R _inst_1), (IsSMulRegular.{u1, u2} S R (SMulZeroClass.toSMul.{u1, u2} S R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (DistribSMul.toSMulZeroClass.{u1, u2} S R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, u2} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3))) k) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} R _inst_1 (HSMul.hSMul.{u1, u2, u2} S (Polynomial.{u2} R _inst_1) (Polynomial.{u2} R _inst_1) (instHSMul.{u1, u2} S (Polynomial.{u2} R _inst_1) (SMulZeroClass.toSMul.{u1, u2} S (Polynomial.{u2} R _inst_1) (Polynomial.zero.{u2} R _inst_1) (Polynomial.smulZeroClass.{u2, u1} R _inst_1 S (DistribSMul.toSMulZeroClass.{u1, u2} S R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, u2} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3))))) k p)) (Polynomial.degree.{u2} R _inst_1 p))
+Case conversion may be inaccurate. Consider using '#align polynomial.degree_smul_of_smul_regular Polynomial.degree_smul_of_smul_regularₓ'. -/
 theorem degree_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction S R] {k : S}
     (p : R[X]) (h : IsSMulRegular R k) : (k • p).degree = p.degree :=
   by
@@ -514,6 +714,12 @@ theorem degree_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction S
     simpa using hm m le_rfl
 #align polynomial.degree_smul_of_smul_regular Polynomial.degree_smul_of_smul_regular
 
+/- warning: polynomial.nat_degree_smul_of_smul_regular -> Polynomial.natDegree_smul_of_smul_regular is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Monoid.{u2} S] [_inst_3 : DistribMulAction.{u2, u1} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {k : S} (p : Polynomial.{u1} R _inst_1), (IsSMulRegular.{u2, u1} S R (SMulZeroClass.toHasSmul.{u2, u1} S R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribSMul.toSmulZeroClass.{u2, u1} S R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (DistribMulAction.toDistribSMul.{u2, u1} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3))) k) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (SMul.smul.{u2, u1} S (Polynomial.{u1} R _inst_1) (SMulZeroClass.toHasSmul.{u2, u1} S (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1) (Polynomial.smulZeroClass.{u1, u2} R _inst_1 S (DistribSMul.toSmulZeroClass.{u2, u1} S R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (DistribMulAction.toDistribSMul.{u2, u1} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3)))) k p)) (Polynomial.natDegree.{u1} R _inst_1 p))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {S : Type.{u1}} [_inst_2 : Monoid.{u1} S] [_inst_3 : DistribMulAction.{u1, u2} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))] {k : S} (p : Polynomial.{u2} R _inst_1), (IsSMulRegular.{u1, u2} S R (SMulZeroClass.toSMul.{u1, u2} S R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (DistribSMul.toSMulZeroClass.{u1, u2} S R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, u2} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3))) k) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} R _inst_1 (HSMul.hSMul.{u1, u2, u2} S (Polynomial.{u2} R _inst_1) (Polynomial.{u2} R _inst_1) (instHSMul.{u1, u2} S (Polynomial.{u2} R _inst_1) (SMulZeroClass.toSMul.{u1, u2} S (Polynomial.{u2} R _inst_1) (Polynomial.zero.{u2} R _inst_1) (Polynomial.smulZeroClass.{u2, u1} R _inst_1 S (DistribSMul.toSMulZeroClass.{u1, u2} S R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, u2} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3))))) k p)) (Polynomial.natDegree.{u2} R _inst_1 p))
+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_smul_of_smul_regular Polynomial.natDegree_smul_of_smul_regularₓ'. -/
 theorem natDegree_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction S R] {k : S}
     (p : R[X]) (h : IsSMulRegular R k) : (k • p).natDegree = p.natDegree :=
   by
@@ -526,11 +732,18 @@ theorem natDegree_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction
   exact h.polynomial hp
 #align polynomial.nat_degree_smul_of_smul_regular Polynomial.natDegree_smul_of_smul_regular
 
+/- warning: polynomial.leading_coeff_smul_of_smul_regular -> Polynomial.leadingCoeff_smul_of_smul_regular is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Monoid.{u2} S] [_inst_3 : DistribMulAction.{u2, u1} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {k : S} (p : Polynomial.{u1} R _inst_1), (IsSMulRegular.{u2, u1} S R (SMulZeroClass.toHasSmul.{u2, u1} S R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribSMul.toSmulZeroClass.{u2, u1} S R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (DistribMulAction.toDistribSMul.{u2, u1} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3))) k) -> (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R _inst_1 (SMul.smul.{u2, u1} S (Polynomial.{u1} R _inst_1) (SMulZeroClass.toHasSmul.{u2, u1} S (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1) (Polynomial.smulZeroClass.{u1, u2} R _inst_1 S (DistribSMul.toSmulZeroClass.{u2, u1} S R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (DistribMulAction.toDistribSMul.{u2, u1} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3)))) k p)) (SMul.smul.{u2, u1} S R (SMulZeroClass.toHasSmul.{u2, u1} S R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribSMul.toSmulZeroClass.{u2, u1} S R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (DistribMulAction.toDistribSMul.{u2, u1} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3))) k (Polynomial.leadingCoeff.{u1} R _inst_1 p)))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {S : Type.{u1}} [_inst_2 : Monoid.{u1} S] [_inst_3 : DistribMulAction.{u1, u2} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))] {k : S} (p : Polynomial.{u2} R _inst_1), (IsSMulRegular.{u1, u2} S R (SMulZeroClass.toSMul.{u1, u2} S R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (DistribSMul.toSMulZeroClass.{u1, u2} S R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, u2} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3))) k) -> (Eq.{succ u2} R (Polynomial.leadingCoeff.{u2} R _inst_1 (HSMul.hSMul.{u1, u2, u2} S (Polynomial.{u2} R _inst_1) (Polynomial.{u2} R _inst_1) (instHSMul.{u1, u2} S (Polynomial.{u2} R _inst_1) (SMulZeroClass.toSMul.{u1, u2} S (Polynomial.{u2} R _inst_1) (Polynomial.zero.{u2} R _inst_1) (Polynomial.smulZeroClass.{u2, u1} R _inst_1 S (DistribSMul.toSMulZeroClass.{u1, u2} S R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, u2} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3))))) k p)) (HSMul.hSMul.{u1, u2, u2} S R R (instHSMul.{u1, u2} S R (SMulZeroClass.toSMul.{u1, u2} S R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (DistribSMul.toSMulZeroClass.{u1, u2} S R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{u1, u2} S R _inst_2 (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_3)))) k (Polynomial.leadingCoeff.{u2} R _inst_1 p)))
+Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_smul_of_smul_regular Polynomial.leadingCoeff_smul_of_smul_regularₓ'. -/
 theorem leadingCoeff_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction S R] {k : S}
     (p : R[X]) (h : IsSMulRegular R k) : (k • p).leadingCoeff = k • p.leadingCoeff := by
   rw [leading_coeff, leading_coeff, coeff_smul, nat_degree_smul_of_smul_regular p h]
 #align polynomial.leading_coeff_smul_of_smul_regular Polynomial.leadingCoeff_smul_of_smul_regular
 
+#print Polynomial.monic_of_isUnit_leadingCoeff_inv_smul /-
 theorem monic_of_isUnit_leadingCoeff_inv_smul (h : IsUnit p.leadingCoeff) : Monic (h.Unit⁻¹ • p) :=
   by
   rw [monic.def, leading_coeff_smul_of_smul_regular _ (isSMulRegular_of_group _), Units.smul_def]
@@ -538,7 +751,9 @@ theorem monic_of_isUnit_leadingCoeff_inv_smul (h : IsUnit p.leadingCoeff) : Moni
   simp only [← hk, smul_eq_mul, ← Units.val_mul, Units.val_eq_one, inv_mul_eq_iff_eq_mul]
   simp [Units.ext_iff, IsUnit.unit_spec]
 #align polynomial.monic_of_is_unit_leading_coeff_inv_smul Polynomial.monic_of_isUnit_leadingCoeff_inv_smul
+-/
 
+#print Polynomial.isUnit_leadingCoeff_mul_right_eq_zero_iff /-
 theorem isUnit_leadingCoeff_mul_right_eq_zero_iff (h : IsUnit p.leadingCoeff) {q : R[X]} :
     p * q = 0 ↔ q = 0 := by
   constructor
@@ -555,7 +770,9 @@ theorem isUnit_leadingCoeff_mul_right_eq_zero_iff (h : IsUnit p.leadingCoeff) {q
   · rintro rfl
     simp
 #align polynomial.is_unit_leading_coeff_mul_right_eq_zero_iff Polynomial.isUnit_leadingCoeff_mul_right_eq_zero_iff
+-/
 
+#print Polynomial.isUnit_leadingCoeff_mul_left_eq_zero_iff /-
 theorem isUnit_leadingCoeff_mul_left_eq_zero_iff (h : IsUnit p.leadingCoeff) {q : R[X]} :
     q * p = 0 ↔ q = 0 := by
   constructor
@@ -568,6 +785,7 @@ theorem isUnit_leadingCoeff_mul_left_eq_zero_iff (h : IsUnit p.leadingCoeff) {q
   · rintro rfl
     rw [zero_mul]
 #align polynomial.is_unit_leading_coeff_mul_left_eq_zero_iff Polynomial.isUnit_leadingCoeff_mul_left_eq_zero_iff
+-/
 
 end NotZeroDivisor
 

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

@@ -101,12 +101,12 @@ theorem monic_of_degree_le (n : ℕ) (H1 : degree p ≤ n) (H2 : coeff p n = 1)
 theorem monic_x_pow_add {n : ℕ} (H : degree p ≤ n) : Monic (X ^ (n + 1) + p) :=
   have H1 : degree p < n + 1 := lt_of_le_of_lt H (WithBot.coe_lt_coe.2 (Nat.lt_succ_self n))
   monic_of_degree_le (n + 1)
-    (le_trans (degree_add_le _ _) (max_le (degree_x_pow_le _) (le_of_lt H1)))
+    (le_trans (degree_add_le _ _) (max_le (degree_X_pow_le _) (le_of_lt H1)))
     (by rw [coeff_add, coeff_X_pow, if_pos rfl, coeff_eq_zero_of_degree_lt H1, add_zero])
 #align polynomial.monic_X_pow_add Polynomial.monic_x_pow_add
 
 theorem monic_x_add_c (x : R) : Monic (X + C x) :=
-  pow_one (X : R[X]) ▸ monic_x_pow_add degree_c_le
+  pow_one (X : R[X]) ▸ monic_x_pow_add degree_C_le
 #align polynomial.monic_X_add_C Polynomial.monic_x_add_c
 
 theorem Monic.mul (hp : Monic p) (hq : Monic q) : Monic (p * q) :=

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

@@ -52,7 +52,7 @@ theorem monic_zero_iff_subsingleton' :
 #align polynomial.monic_zero_iff_subsingleton' Polynomial.monic_zero_iff_subsingleton'
 
 theorem Monic.as_sum (hp : p.Monic) :
-    p = x ^ p.natDegree + ∑ i in range p.natDegree, c (p.coeff i) * x ^ i :=
+    p = X ^ p.natDegree + ∑ i in range p.natDegree, C (p.coeff i) * X ^ i :=
   by
   conv_lhs => rw [p.as_sum_range_C_mul_X_pow, sum_range_succ_comm]
   suffices C (p.coeff p.nat_degree) = 1 by rw [this, one_mul]
@@ -80,13 +80,13 @@ theorem Monic.map [Semiring S] (f : R →+* S) (hp : Monic p) : Monic (p.map f)
 #align polynomial.monic.map Polynomial.Monic.map
 
 theorem monic_c_mul_of_mul_leadingCoeff_eq_one {b : R} (hp : b * p.leadingCoeff = 1) :
-    Monic (c b * p) := by
+    Monic (C b * p) := by
   nontriviality
   rw [monic, leading_coeff_mul' _] <;> simp [leading_coeff_C b, hp]
 #align polynomial.monic_C_mul_of_mul_leading_coeff_eq_one Polynomial.monic_c_mul_of_mul_leadingCoeff_eq_one
 
 theorem monic_mul_c_of_leadingCoeff_mul_eq_one {b : R} (hp : p.leadingCoeff * b = 1) :
-    Monic (p * c b) := by
+    Monic (p * C b) := by
   nontriviality
   rw [monic, leading_coeff_mul' _] <;> simp [leading_coeff_C b, hp]
 #align polynomial.monic_mul_C_of_leading_coeff_mul_eq_one Polynomial.monic_mul_c_of_leadingCoeff_mul_eq_one
@@ -98,15 +98,15 @@ theorem monic_of_degree_le (n : ℕ) (H1 : degree p ≤ n) (H2 : coeff p n = 1)
     rwa [monic, leading_coeff, nat_degree, (lt_or_eq_of_le H1).resolve_left H]
 #align polynomial.monic_of_degree_le Polynomial.monic_of_degree_le
 
-theorem monic_x_pow_add {n : ℕ} (H : degree p ≤ n) : Monic (x ^ (n + 1) + p) :=
+theorem monic_x_pow_add {n : ℕ} (H : degree p ≤ n) : Monic (X ^ (n + 1) + p) :=
   have H1 : degree p < n + 1 := lt_of_le_of_lt H (WithBot.coe_lt_coe.2 (Nat.lt_succ_self n))
   monic_of_degree_le (n + 1)
     (le_trans (degree_add_le _ _) (max_le (degree_x_pow_le _) (le_of_lt H1)))
     (by rw [coeff_add, coeff_X_pow, if_pos rfl, coeff_eq_zero_of_degree_lt H1, add_zero])
 #align polynomial.monic_X_pow_add Polynomial.monic_x_pow_add
 
-theorem monic_x_add_c (x : R) : Monic (x + c x) :=
-  pow_one (x : R[X]) ▸ monic_x_pow_add degree_c_le
+theorem monic_x_add_c (x : R) : Monic (X + C x) :=
+  pow_one (X : R[X]) ▸ monic_x_pow_add degree_c_le
 #align polynomial.monic_X_add_C Polynomial.monic_x_add_c
 
 theorem Monic.mul (hp : Monic p) (hq : Monic q) : Monic (p * q) :=
@@ -249,7 +249,7 @@ theorem natDegree_pow (hp : p.Monic) (n : ℕ) : (p ^ n).natDegree = n * p.natDe
 end Monic
 
 @[simp]
-theorem natDegree_pow_x_add_c [Nontrivial R] (n : ℕ) (r : R) : ((x + c r) ^ n).natDegree = n := by
+theorem natDegree_pow_x_add_c [Nontrivial R] (n : ℕ) (r : R) : ((X + C r) ^ n).natDegree = n := by
   rw [(monic_X_add_C r).natDegree_pow, nat_degree_X_add_C, mul_one]
 #align polynomial.nat_degree_pow_X_add_C Polynomial.natDegree_pow_x_add_c
 
@@ -389,16 +389,16 @@ section Ring
 
 variable [Ring R] {p : R[X]}
 
-theorem monic_x_sub_c (x : R) : Monic (x - c x) := by
+theorem monic_x_sub_c (x : R) : Monic (X - C x) := by
   simpa only [sub_eq_add_neg, C_neg] using monic_X_add_C (-x)
 #align polynomial.monic_X_sub_C Polynomial.monic_x_sub_c
 
-theorem monic_x_pow_sub {n : ℕ} (H : degree p ≤ n) : Monic (x ^ (n + 1) - p) := by
+theorem monic_x_pow_sub {n : ℕ} (H : degree p ≤ n) : Monic (X ^ (n + 1) - p) := by
   simpa [sub_eq_add_neg] using monic_X_pow_add (show degree (-p) ≤ n by rwa [← degree_neg p] at H)
 #align polynomial.monic_X_pow_sub Polynomial.monic_x_pow_sub
 
 /-- `X ^ n - a` is monic. -/
-theorem monic_x_pow_sub_c {R : Type u} [Ring R] (a : R) {n : ℕ} (h : n ≠ 0) : (x ^ n - c a).Monic :=
+theorem monic_x_pow_sub_c {R : Type u} [Ring R] (a : R) {n : ℕ} (h : n ≠ 0) : (X ^ n - C a).Monic :=
   by
   obtain ⟨k, hk⟩ := Nat.exists_eq_succ_of_ne_zero h
   convert monic_X_pow_sub _
@@ -406,7 +406,7 @@ theorem monic_x_pow_sub_c {R : Type u} [Ring R] (a : R) {n : ℕ} (h : n ≠ 0)
 #align polynomial.monic_X_pow_sub_C Polynomial.monic_x_pow_sub_c
 
 theorem not_isUnit_x_pow_sub_one (R : Type _) [CommRing R] [Nontrivial R] (n : ℕ) :
-    ¬IsUnit (x ^ n - 1 : R[X]) := by
+    ¬IsUnit (X ^ n - 1 : R[X]) := by
   intro h
   rcases eq_or_ne n 0 with (rfl | hn)
   · simpa using h

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

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -57,7 +57,7 @@ theorem Monic.as_sum (hp : p.Monic) :
 
 theorem ne_zero_of_ne_zero_of_monic (hp : p ≠ 0) (hq : Monic q) : q ≠ 0 := by
   rintro rfl
-  rw [Monic.def', leadingCoeff_zero] at hq
+  rw [Monic.def, leadingCoeff_zero] at hq
   rw [← mul_one p, ← C_1, ← hq, C_0, mul_zero] at hp
   exact hp rfl
 #align polynomial.ne_zero_of_ne_zero_of_monic Polynomial.ne_zero_of_ne_zero_of_monic
@@ -121,8 +121,8 @@ theorem Monic.mul (hp : Monic p) (hq : Monic q) : Monic (p * q) :=
     Subsingleton.elim _ _
   else by
     have : p.leadingCoeff * q.leadingCoeff ≠ 0 := by
-      simp [Monic.def'.1 hp, Monic.def'.1 hq, Ne.symm h0]
-    rw [Monic.def', leadingCoeff_mul' this, Monic.def'.1 hp, Monic.def'.1 hq, one_mul]
+      simp [Monic.def.1 hp, Monic.def.1 hq, Ne.symm h0]
+    rw [Monic.def, leadingCoeff_mul' this, Monic.def.1 hp, Monic.def.1 hq, one_mul]
 #align polynomial.monic.mul Polynomial.Monic.mul
 
 theorem Monic.pow (hp : Monic p) : ∀ n : ℕ, Monic (p ^ n)
@@ -142,13 +142,13 @@ theorem Monic.add_of_right (hq : Monic q) (hpq : degree p < degree q) : Monic (p
 
 theorem Monic.of_mul_monic_left (hp : p.Monic) (hpq : (p * q).Monic) : q.Monic := by
   contrapose! hpq
-  rw [Monic.def'] at hpq ⊢
+  rw [Monic.def] at hpq ⊢
   rwa [leadingCoeff_monic_mul hp]
 #align polynomial.monic.of_mul_monic_left Polynomial.Monic.of_mul_monic_left
 
 theorem Monic.of_mul_monic_right (hq : q.Monic) (hpq : (p * q).Monic) : p.Monic := by
   contrapose! hpq
-  rw [Monic.def'] at hpq ⊢
+  rw [Monic.def] at hpq ⊢
   rwa [leadingCoeff_mul_monic hq]
 #align polynomial.monic.of_mul_monic_right Polynomial.Monic.of_mul_monic_right
 
@@ -164,7 +164,7 @@ theorem natDegree_eq_zero_iff_eq_one (hp : p.Monic) : p.natDegree = 0 ↔ p = 1
     rw [← Polynomial.degree_le_zero_iff]
     rwa [Polynomial.natDegree_eq_zero_iff_degree_le_zero] at h
   rw [this]
-  rw [← h, ← Polynomial.leadingCoeff, Monic.def'.1 hp, C_1]
+  rw [← h, ← Polynomial.leadingCoeff, Monic.def.1 hp, C_1]
 #align polynomial.monic.nat_degree_eq_zero_iff_eq_one Polynomial.Monic.natDegree_eq_zero_iff_eq_one
 
 @[simp]
@@ -526,7 +526,7 @@ theorem leadingCoeff_smul_of_smul_regular {S : Type*} [Monoid S] [DistribMulActi
 
 theorem monic_of_isUnit_leadingCoeff_inv_smul (h : IsUnit p.leadingCoeff) :
     Monic (h.unit⁻¹ • p) := by
-  rw [Monic.def', leadingCoeff_smul_of_smul_regular _ (isSMulRegular_of_group _), Units.smul_def]
+  rw [Monic.def, leadingCoeff_smul_of_smul_regular _ (isSMulRegular_of_group _), Units.smul_def]
   obtain ⟨k, hk⟩ := h
   simp only [← hk, smul_eq_mul, ← Units.val_mul, Units.val_eq_one, inv_mul_eq_iff_eq_mul]
   simp [Units.ext_iff, IsUnit.unit_spec]

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

@@ -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.Reverse
+import Mathlib.Algebra.Polynomial.Reverse
 import Mathlib.Algebra.Regular.SMul
 
 #align_import data.polynomial.monic from "leanprover-community/mathlib"@"cbdf7b565832144d024caa5a550117c6df0204a5"

@@ -449,7 +449,7 @@ variable [Semiring R] {p : R[X]}
 theorem Monic.mul_left_ne_zero (hp : Monic p) {q : R[X]} (hq : q ≠ 0) : q * p ≠ 0 := by
   by_cases h : p = 1
   · simpa [h]
-  rw [Ne.def, ← degree_eq_bot, hp.degree_mul, WithBot.add_eq_bot, not_or, degree_eq_bot]
+  rw [Ne, ← degree_eq_bot, hp.degree_mul, WithBot.add_eq_bot, not_or, degree_eq_bot]
   refine' ⟨hq, _⟩
   rw [← hp.degree_le_zero_iff_eq_one, not_le] at h
   refine' (lt_trans _ h).ne'
@@ -459,7 +459,7 @@ theorem Monic.mul_left_ne_zero (hp : Monic p) {q : R[X]} (hq : q ≠ 0) : q * p
 theorem Monic.mul_right_ne_zero (hp : Monic p) {q : R[X]} (hq : q ≠ 0) : p * q ≠ 0 := by
   by_cases h : p = 1
   · simpa [h]
-  rw [Ne.def, ← degree_eq_bot, hp.degree_mul_comm, hp.degree_mul, WithBot.add_eq_bot, not_or,
+  rw [Ne, ← degree_eq_bot, hp.degree_mul_comm, hp.degree_mul, WithBot.add_eq_bot, not_or,
     degree_eq_bot]
   refine' ⟨hq, _⟩
   rw [← hp.degree_le_zero_iff_eq_one, not_le] at h

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.

@@ -129,7 +129,7 @@ theorem Monic.pow (hp : Monic p) : ∀ n : ℕ, Monic (p ^ n)
   | 0 => monic_one
   | n + 1 => by
     rw [pow_succ]
-    exact hp.mul (Monic.pow hp n)
+    exact (Monic.pow hp n).mul hp
 #align polynomial.monic.pow Polynomial.Monic.pow
 
 theorem Monic.add_of_left (hp : Monic p) (hpq : degree q < degree p) : Monic (p + q) := by
@@ -223,7 +223,7 @@ theorem nextCoeff_mul (hp : Monic p) (hq : Monic q) :
 theorem nextCoeff_pow (hp : p.Monic) (n : ℕ) : (p ^ n).nextCoeff = n • p.nextCoeff := by
   induction n with
   | zero => rw [pow_zero, Nat.zero_eq, zero_smul, ← map_one (f := C), nextCoeff_C_eq_zero]
-  | succ n ih => rw [pow_succ, hp.nextCoeff_mul (hp.pow n), ih, succ_nsmul]
+  | succ n ih => rw [pow_succ, (hp.pow n).nextCoeff_mul hp, ih, succ_nsmul]
 
 theorem eq_one_of_map_eq_one {S : Type*} [Semiring S] [Nontrivial S] (f : R →+* S) (hp : p.Monic)
     (map_eq : p.map f = 1) : p = 1 := by
@@ -241,7 +241,7 @@ theorem eq_one_of_map_eq_one {S : Type*} [Semiring S] [Nontrivial S] (f : R →+
 theorem natDegree_pow (hp : p.Monic) (n : ℕ) : (p ^ n).natDegree = n * p.natDegree := by
   induction' n with n hn
   · simp
-  · rw [pow_succ, hp.natDegree_mul (hp.pow n), hn, Nat.succ_mul, add_comm]
+  · rw [pow_succ, (hp.pow n).natDegree_mul hp, hn, Nat.succ_mul, add_comm]
 #align polynomial.monic.nat_degree_pow Polynomial.Monic.natDegree_pow
 
 end Monic

This will become an error in 2024-03-16 nightly, possibly not permanently.

Co-authored-by: Scott Morrison <scott@tqft.net>

@@ -57,7 +57,7 @@ theorem Monic.as_sum (hp : p.Monic) :
 
 theorem ne_zero_of_ne_zero_of_monic (hp : p ≠ 0) (hq : Monic q) : q ≠ 0 := by
   rintro rfl
-  rw [Monic.def, leadingCoeff_zero] at hq
+  rw [Monic.def', leadingCoeff_zero] at hq
   rw [← mul_one p, ← C_1, ← hq, C_0, mul_zero] at hp
   exact hp rfl
 #align polynomial.ne_zero_of_ne_zero_of_monic Polynomial.ne_zero_of_ne_zero_of_monic
@@ -121,8 +121,8 @@ theorem Monic.mul (hp : Monic p) (hq : Monic q) : Monic (p * q) :=
     Subsingleton.elim _ _
   else by
     have : p.leadingCoeff * q.leadingCoeff ≠ 0 := by
-      simp [Monic.def.1 hp, Monic.def.1 hq, Ne.symm h0]
-    rw [Monic.def, leadingCoeff_mul' this, Monic.def.1 hp, Monic.def.1 hq, one_mul]
+      simp [Monic.def'.1 hp, Monic.def'.1 hq, Ne.symm h0]
+    rw [Monic.def', leadingCoeff_mul' this, Monic.def'.1 hp, Monic.def'.1 hq, one_mul]
 #align polynomial.monic.mul Polynomial.Monic.mul
 
 theorem Monic.pow (hp : Monic p) : ∀ n : ℕ, Monic (p ^ n)
@@ -142,13 +142,13 @@ theorem Monic.add_of_right (hq : Monic q) (hpq : degree p < degree q) : Monic (p
 
 theorem Monic.of_mul_monic_left (hp : p.Monic) (hpq : (p * q).Monic) : q.Monic := by
   contrapose! hpq
-  rw [Monic.def] at hpq ⊢
+  rw [Monic.def'] at hpq ⊢
   rwa [leadingCoeff_monic_mul hp]
 #align polynomial.monic.of_mul_monic_left Polynomial.Monic.of_mul_monic_left
 
 theorem Monic.of_mul_monic_right (hq : q.Monic) (hpq : (p * q).Monic) : p.Monic := by
   contrapose! hpq
-  rw [Monic.def] at hpq ⊢
+  rw [Monic.def'] at hpq ⊢
   rwa [leadingCoeff_mul_monic hq]
 #align polynomial.monic.of_mul_monic_right Polynomial.Monic.of_mul_monic_right
 
@@ -164,7 +164,7 @@ theorem natDegree_eq_zero_iff_eq_one (hp : p.Monic) : p.natDegree = 0 ↔ p = 1
     rw [← Polynomial.degree_le_zero_iff]
     rwa [Polynomial.natDegree_eq_zero_iff_degree_le_zero] at h
   rw [this]
-  rw [← h, ← Polynomial.leadingCoeff, Monic.def.1 hp, C_1]
+  rw [← h, ← Polynomial.leadingCoeff, Monic.def'.1 hp, C_1]
 #align polynomial.monic.nat_degree_eq_zero_iff_eq_one Polynomial.Monic.natDegree_eq_zero_iff_eq_one
 
 @[simp]
@@ -526,7 +526,7 @@ theorem leadingCoeff_smul_of_smul_regular {S : Type*} [Monoid S] [DistribMulActi
 
 theorem monic_of_isUnit_leadingCoeff_inv_smul (h : IsUnit p.leadingCoeff) :
     Monic (h.unit⁻¹ • p) := by
-  rw [Monic.def, leadingCoeff_smul_of_smul_regular _ (isSMulRegular_of_group _), Units.smul_def]
+  rw [Monic.def', leadingCoeff_smul_of_smul_regular _ (isSMulRegular_of_group _), Units.smul_def]
   obtain ⟨k, hk⟩ := h
   simp only [← hk, smul_eq_mul, ← Units.val_mul, Units.val_eq_one, inv_mul_eq_iff_eq_mul]
   simp [Units.ext_iff, IsUnit.unit_spec]

Remove unnecessary "rw"s.

@@ -189,7 +189,7 @@ theorem degree_mul_comm (hp : p.Monic) (q : R[X]) : (p * q).degree = (q * p).deg
 
 nonrec theorem natDegree_mul' (hp : p.Monic) (hq : q ≠ 0) :
     (p * q).natDegree = p.natDegree + q.natDegree := by
-  rw [natDegree_mul', add_comm]
+  rw [natDegree_mul']
   simpa [hp.leadingCoeff, leadingCoeff_ne_zero]
 #align polynomial.monic.nat_degree_mul' Polynomial.Monic.natDegree_mul'
 

@@ -104,8 +104,13 @@ theorem monic_X_pow_add {n : ℕ} (H : degree p ≤ n) : Monic (X ^ (n + 1) + p)
 set_option linter.uppercaseLean3 false in
 #align polynomial.monic_X_pow_add Polynomial.monic_X_pow_add
 
+variable (a) in
+theorem monic_X_pow_add_C {n : ℕ} (h : n ≠ 0) : (X ^ n + C a).Monic := by
+  obtain ⟨k, rfl⟩ := Nat.exists_eq_succ_of_ne_zero h
+  exact monic_X_pow_add <| degree_C_le.trans Nat.WithBot.coe_nonneg
+
 theorem monic_X_add_C (x : R) : Monic (X + C x) :=
-  pow_one (X : R[X]) ▸ monic_X_pow_add degree_C_le
+  pow_one (X : R[X]) ▸ monic_X_pow_add_C x one_ne_zero
 set_option linter.uppercaseLean3 false in
 #align polynomial.monic_X_add_C Polynomial.monic_X_add_C
 
@@ -393,9 +398,7 @@ set_option linter.uppercaseLean3 false in
 /-- `X ^ n - a` is monic. -/
 theorem monic_X_pow_sub_C {R : Type u} [Ring R] (a : R) {n : ℕ} (h : n ≠ 0) :
     (X ^ n - C a).Monic := by
-  obtain ⟨k, rfl⟩ := Nat.exists_eq_succ_of_ne_zero h
-  apply monic_X_pow_sub _
-  exact le_trans degree_C_le Nat.WithBot.coe_nonneg
+  simpa only [map_neg, ← sub_eq_add_neg] using monic_X_pow_add_C (-a) h
 set_option linter.uppercaseLean3 false in
 #align polynomial.monic_X_pow_sub_C Polynomial.monic_X_pow_sub_C
 

• Polynomial.map_contract: Polynomial.map and Polynomial.contract commutes
• Irreducible.natDegree_pos: an irreducible polynomial over a field must have positive degree (not true if it's not a field)
• Polynomial.Monic.nextCoeff_pow: corollary of Polynomial.Monic.nextCoeff_mul
• Polynomial.exists_monic_irreducible_factor: a polynomial over a field which is not a unit must have a monic irreducible factor (not true if it's not a field)

@@ -215,6 +215,11 @@ theorem nextCoeff_mul (hp : Monic p) (hq : Monic q) :
       show Nat.succ 0 = 1 from rfl]
 #align polynomial.monic.next_coeff_mul Polynomial.Monic.nextCoeff_mul
 
+theorem nextCoeff_pow (hp : p.Monic) (n : ℕ) : (p ^ n).nextCoeff = n • p.nextCoeff := by
+  induction n with
+  | zero => rw [pow_zero, Nat.zero_eq, zero_smul, ← map_one (f := C), nextCoeff_C_eq_zero]
+  | succ n ih => rw [pow_succ, hp.nextCoeff_mul (hp.pow n), ih, succ_nsmul]
+
 theorem eq_one_of_map_eq_one {S : Type*} [Semiring S] [Nontrivial S] (f : R →+* S) (hp : p.Monic)
     (map_eq : p.map f = 1) : p = 1 := by
   nontriviality R

Main changes:

• add Monic.mem_nonZeroDivisors and mem_nonZeroDivisors_of_leadingCoeff which states that a monic polynomial (resp. a polynomial whose leading coefficient is not zero divisor) is not a zero divisor.
• add rootMultiplicity_mul_X_sub_C_pow which states that * (X - a) ^ n adds the root multiplicity at a by n.
• change the conditions in rootMultiplicity_X_sub_C_self, rootMultiplicity_X_sub_C and rootMultiplicity_X_sub_C_pow from IsDomain to Nontrivial.
• add rootMultiplicity_eq_natTrailingDegree which relates rootMultiplicity and natTrailingDegree, and eval_divByMonic_eq_trailingCoeff_comp.
• add le_rootMultiplicity_mul which is similar to le_trailingDegree_mul.
• add rootMultiplicity_mul' which slightly generalizes rootMultiplicity_mul

In Data/Polynomial/FieldDivision:

• add rootMultiplicity_sub_one_le_derivative_rootMultiplicity_of_ne_zero which slightly generalizes rootMultiplicity_sub_one_le_derivative_rootMultiplicity.
• add derivative_rootMultiplicity_of_root_of_mem_nonZeroDivisors which slightly generalizes derivative_rootMultiplicity_of_root.
• add several theorems relating roots of iterate derivative to rootMultiplicity

In addition:

• move eq_of_monic_of_associated from RingDivision to Monic and generalize.
• add dvd_cancel lemmas to NonZeroDivisors.
• add algEquivOfCompEqX: two polynomials that compose to X both ways induces an isomorphism of the polynomial algebra.
• add divisibility lemmas to Polynomial/Derivative.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -254,6 +254,11 @@ theorem Monic.isUnit_iff (hm : p.Monic) : IsUnit p ↔ p = 1 :=
   ⟨hm.eq_one_of_isUnit, fun h => h.symm ▸ isUnit_one⟩
 #align polynomial.monic.is_unit_iff Polynomial.Monic.isUnit_iff
 
+theorem eq_of_monic_of_associated (hp : p.Monic) (hq : q.Monic) (hpq : Associated p q) : p = q := by
+  obtain ⟨u, rfl⟩ := hpq
+  rw [(hp.of_mul_monic_left hq).eq_one_of_isUnit u.isUnit, mul_one]
+#align polynomial.eq_of_monic_of_associated Polynomial.eq_of_monic_of_associated
+
 end Semiring
 
 section CommSemiring

Mathlib.Logic.Unique contains the line attribute [simp] eq_iff_true_of_subsingleton in ...:

https://github.com/leanprover-community/mathlib4/blob/96a11c7aac574c00370c2b3dab483cb676405c5d/Mathlib/Logic/Unique.lean#L255-L256

Despite what the in part may imply, this adds the lemma to the simp set "globally", including for downstream files; it is likely that attribute [local simp] eq_iff_true_of_subsingleton in ... was meant instead (or maybe scoped simp, but I think "scoped" refers to the current namespace). Indeed, the relevant lemma is not marked with @[simp] for possible slowness: https://github.com/leanprover/std4/blob/846e9e1d6bb534774d1acd2dc430e70987da3c18/Std/Logic.lean#L749. Adding it to the simp set causes the example at https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Regression.20in.20simp to slow down.

This PR changes this and fixes the relevant downstream simps. There was also one ocurrence of attribute [simp] FullSubcategory.comp_def FullSubcategory.id_def in in Mathlib.CategoryTheory.Monoidal.Subcategory but that was much easier to fix.

https://github.com/leanprover-community/mathlib4/blob/bc49eb9ba756a233370b4b68bcdedd60402f71ed/Mathlib/CategoryTheory/Monoidal/Subcategory.lean#L118-L119

@@ -45,7 +45,7 @@ theorem monic_zero_iff_subsingleton' :
   Polynomial.monic_zero_iff_subsingleton.trans
     ⟨by
       intro
-      simp, fun h => subsingleton_iff.mpr h.2⟩
+      simp [eq_iff_true_of_subsingleton], fun h => subsingleton_iff.mpr h.2⟩
 #align polynomial.monic_zero_iff_subsingleton' Polynomial.monic_zero_iff_subsingleton'
 
 theorem Monic.as_sum (hp : p.Monic) :

We define a type class Finset.HasAntidiagonal A which contains a function antidiagonal : A → Finset (A × A) such that antidiagonal n is the Finset of all pairs adding to n, as witnessed by mem_antidiagonal.

When A is a canonically ordered add monoid with locally finite order this typeclass can be instantiated with Finset.antidiagonalOfLocallyFinite. This applies in particular when A is ℕ, more generally or σ →₀ ℕ, or even ι →₀ A under the additional assumption OrderedSub A that make it a canonically ordered add monoid. (In fact, we would just need an AddMonoid with a compatible order, finite Iic, such that if a + b = n, then a, b ≤ n, and any finiteness condition would be OK.)

For computational reasons it is better to manually provide instances for ℕ and σ →₀ ℕ, to avoid quadratic runtime performance. These instances are provided as Finset.Nat.instHasAntidiagonal and Finsupp.instHasAntidiagonal. This is why Finset.antidiagonalOfLocallyFinite is an abbrev and not an instance.

This definition does not exactly match with that of Multiset.antidiagonal defined in Mathlib.Data.Multiset.Antidiagonal, because of the multiplicities. Indeed, by counting multiplicities, Multiset α is equivalent to α →₀ ℕ, but Finset.antidiagonal and Multiset.antidiagonal will return different objects. For example, for s : Multiset ℕ := {0,0,0}, Multiset.antidiagonal s has 8 elements but Finset.antidiagonal s has only 4.

def s : Multiset ℕ := {0, 0, 0}
#eval (Finset.antidiagonal s).card -- 4
#eval Multiset.card (Multiset.antidiagonal s) -- 8

TODO

• Define HasMulAntidiagonal (for monoids). For PNat, we will recover the set of divisors of a strictly positive integer.

This closes #7917

Co-authored by: María Inés de Frutos-Fernández <mariaines.dff@gmail.com> and Eric Wieser <efw27@cam.ac.uk>

Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -211,7 +211,7 @@ theorem nextCoeff_mul (hp : Monic p) (hq : Monic q) :
   nontriviality
   simp only [← coeff_one_reverse]
   rw [reverse_mul] <;>
-    simp [coeff_mul, Nat.antidiagonal, hp.leadingCoeff, hq.leadingCoeff, add_comm,
+    simp [coeff_mul, antidiagonal, hp.leadingCoeff, hq.leadingCoeff, add_comm,
       show Nat.succ 0 = 1 from rfl]
 #align polynomial.monic.next_coeff_mul Polynomial.Monic.nextCoeff_mul
 

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.

@@ -20,7 +20,7 @@ noncomputable section
 
 open Finset
 
-open BigOperators Classical Polynomial
+open BigOperators Polynomial
 
 namespace Polynomial
 
@@ -110,6 +110,7 @@ set_option linter.uppercaseLean3 false in
 #align polynomial.monic_X_add_C Polynomial.monic_X_add_C
 
 theorem Monic.mul (hp : Monic p) (hq : Monic q) : Monic (p * q) :=
+  letI := Classical.decEq R
   if h0 : (0 : R) = 1 then
     haveI := subsingleton_of_zero_eq_one h0
     Subsingleton.elim _ _
@@ -325,6 +326,7 @@ open Function
 variable [Semiring S] {f : R →+* S} (hf : Injective f)
 
 theorem degree_map_eq_of_injective (p : R[X]) : degree (p.map f) = degree p :=
+  letI := Classical.decEq R
   if h : p = 0 then by simp [h]
   else
     degree_map_eq_of_leadingCoeff_ne_zero _

Also WithBot.charZero

@@ -496,8 +496,7 @@ theorem natDegree_smul_of_smul_regular {S : Type*} [Monoid S] [DistribMulAction
     (p : R[X]) (h : IsSMulRegular R k) : (k • p).natDegree = p.natDegree := by
   by_cases hp : p = 0
   · simp [hp]
-  rw [← WithBot.coe_eq_coe, ← Nat.cast_withBot, ←Nat.cast_withBot,
-      ← degree_eq_natDegree hp, ← degree_eq_natDegree,
+  rw [← Nat.cast_inj (R := WithBot ℕ), ← degree_eq_natDegree hp, ← degree_eq_natDegree,
     degree_smul_of_smul_regular p h]
   contrapose! hp
   rw [← smul_zero k] at hp

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -214,7 +214,7 @@ theorem nextCoeff_mul (hp : Monic p) (hq : Monic q) :
       show Nat.succ 0 = 1 from rfl]
 #align polynomial.monic.next_coeff_mul Polynomial.Monic.nextCoeff_mul
 
-theorem eq_one_of_map_eq_one {S : Type _} [Semiring S] [Nontrivial S] (f : R →+* S) (hp : p.Monic)
+theorem eq_one_of_map_eq_one {S : Type*} [Semiring S] [Nontrivial S] (f : R →+* S) (hp : p.Monic)
     (map_eq : p.map f = 1) : p = 1 := by
   nontriviality R
   have hdeg : p.degree = 0 := by
@@ -387,7 +387,7 @@ theorem monic_X_pow_sub_C {R : Type u} [Ring R] (a : R) {n : ℕ} (h : n ≠ 0)
 set_option linter.uppercaseLean3 false in
 #align polynomial.monic_X_pow_sub_C Polynomial.monic_X_pow_sub_C
 
-theorem not_isUnit_X_pow_sub_one (R : Type _) [CommRing R] [Nontrivial R] (n : ℕ) :
+theorem not_isUnit_X_pow_sub_one (R : Type*) [CommRing R] [Nontrivial R] (n : ℕ) :
     ¬IsUnit (X ^ n - 1 : R[X]) := by
   intro h
   rcases eq_or_ne n 0 with (rfl | hn)
@@ -468,7 +468,7 @@ theorem Monic.mul_left_eq_zero_iff (h : Monic p) {q : R[X]} : q * p = 0 ↔ q =
   by_cases hq : q = 0 <;> simp [h.mul_left_ne_zero, hq]
 #align polynomial.monic.mul_left_eq_zero_iff Polynomial.Monic.mul_left_eq_zero_iff
 
-theorem Monic.isRegular {R : Type _} [Ring R] {p : R[X]} (hp : Monic p) : IsRegular p := by
+theorem Monic.isRegular {R : Type*} [Ring R] {p : R[X]} (hp : Monic p) : IsRegular p := by
   constructor
   · intro q r h
     dsimp only at h
@@ -478,7 +478,7 @@ theorem Monic.isRegular {R : Type _} [Ring R] {p : R[X]} (hp : Monic p) : IsRegu
     rw [← sub_eq_zero, ← hp.mul_left_eq_zero_iff, sub_mul, h, sub_self]
 #align polynomial.monic.is_regular Polynomial.Monic.isRegular
 
-theorem degree_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction S R] {k : S}
+theorem degree_smul_of_smul_regular {S : Type*} [Monoid S] [DistribMulAction S R] {k : S}
     (p : R[X]) (h : IsSMulRegular R k) : (k • p).degree = p.degree := by
   refine' le_antisymm _ _
   · rw [degree_le_iff_coeff_zero]
@@ -492,7 +492,7 @@ theorem degree_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction S
     simpa using hm m le_rfl
 #align polynomial.degree_smul_of_smul_regular Polynomial.degree_smul_of_smul_regular
 
-theorem natDegree_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction S R] {k : S}
+theorem natDegree_smul_of_smul_regular {S : Type*} [Monoid S] [DistribMulAction S R] {k : S}
     (p : R[X]) (h : IsSMulRegular R k) : (k • p).natDegree = p.natDegree := by
   by_cases hp : p = 0
   · simp [hp]
@@ -504,7 +504,7 @@ theorem natDegree_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction
   exact h.polynomial hp
 #align polynomial.nat_degree_smul_of_smul_regular Polynomial.natDegree_smul_of_smul_regular
 
-theorem leadingCoeff_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAction S R] {k : S}
+theorem leadingCoeff_smul_of_smul_regular {S : Type*} [Monoid S] [DistribMulAction S R] {k : S}
     (p : R[X]) (h : IsSMulRegular R k) : (k • p).leadingCoeff = k • p.leadingCoeff := by
   rw [Polynomial.leadingCoeff, Polynomial.leadingCoeff, coeff_smul,
     natDegree_smul_of_smul_regular p h]

• depends on: #5966

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

@@ -2,15 +2,12 @@
 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.monic
-! leanprover-community/mathlib commit cbdf7b565832144d024caa5a550117c6df0204a5
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Polynomial.Reverse
 import Mathlib.Algebra.Regular.SMul
 
+#align_import data.polynomial.monic from "leanprover-community/mathlib"@"cbdf7b565832144d024caa5a550117c6df0204a5"
+
 /-!
 # Theory of monic polynomials
 

Changes are of the form

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

@@ -139,13 +139,13 @@ theorem Monic.add_of_right (hq : Monic q) (hpq : degree p < degree q) : Monic (p
 
 theorem Monic.of_mul_monic_left (hp : p.Monic) (hpq : (p * q).Monic) : q.Monic := by
   contrapose! hpq
-  rw [Monic.def] at hpq⊢
+  rw [Monic.def] at hpq ⊢
   rwa [leadingCoeff_monic_mul hp]
 #align polynomial.monic.of_mul_monic_left Polynomial.Monic.of_mul_monic_left
 
 theorem Monic.of_mul_monic_right (hq : q.Monic) (hpq : (p * q).Monic) : p.Monic := by
   contrapose! hpq
-  rw [Monic.def] at hpq⊢
+  rw [Monic.def] at hpq ⊢
   rwa [leadingCoeff_mul_monic hq]
 #align polynomial.monic.of_mul_monic_right Polynomial.Monic.of_mul_monic_right
 

Too often tempted to change these during other PRs, so doing a mass edit here.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

@@ -286,7 +286,7 @@ theorem Monic.nextCoeff_multiset_prod (t : Multiset ι) (f : ι → R[X]) (h : 
     rw [nextCoeff_C_eq_zero]
   · rw [Multiset.map_cons, Multiset.prod_cons, Multiset.map_cons, Multiset.sum_cons,
       Monic.nextCoeff_mul, ih]
-    exacts[fun i hi => ht i (Multiset.mem_cons_of_mem hi), ht a (Multiset.mem_cons_self _ _),
+    exacts [fun i hi => ht i (Multiset.mem_cons_of_mem hi), ht a (Multiset.mem_cons_self _ _),
       monic_multiset_prod_of_monic _ _ fun b bs => ht _ (Multiset.mem_cons_of_mem bs)]
 #align polynomial.monic.next_coeff_multiset_prod Polynomial.Monic.nextCoeff_multiset_prod
 

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".

@@ -68,8 +68,7 @@ theorem ne_zero_of_ne_zero_of_monic (hp : p ≠ 0) (hq : Monic q) : q ≠ 0 := b
 theorem Monic.map [Semiring S] (f : R →+* S) (hp : Monic p) : Monic (p.map f) := by
   unfold Monic
   nontriviality
-  have : f p.leadingCoeff ≠ 0 :=
-    by
+  have : f p.leadingCoeff ≠ 0 := by
     rw [show _ = _ from hp, f.map_one]
     exact one_ne_zero
   rw [Polynomial.leadingCoeff, coeff_map]
@@ -221,8 +220,7 @@ theorem nextCoeff_mul (hp : Monic p) (hq : Monic q) :
 theorem eq_one_of_map_eq_one {S : Type _} [Semiring S] [Nontrivial S] (f : R →+* S) (hp : p.Monic)
     (map_eq : p.map f = 1) : p = 1 := by
   nontriviality R
-  have hdeg : p.degree = 0 :=
-    by
+  have hdeg : p.degree = 0 := by
     rw [← degree_map_eq_of_leadingCoeff_ne_zero f _, map_eq, degree_one]
     · rw [hp.leadingCoeff, f.map_one]
       exact one_ne_zero
@@ -384,8 +382,8 @@ set_option linter.uppercaseLean3 false in
 #align polynomial.monic_X_pow_sub Polynomial.monic_X_pow_sub
 
 /-- `X ^ n - a` is monic. -/
-theorem monic_X_pow_sub_C {R : Type u} [Ring R] (a : R) {n : ℕ} (h : n ≠ 0) : (X ^ n - C a).Monic :=
-  by
+theorem monic_X_pow_sub_C {R : Type u} [Ring R] (a : R) {n : ℕ} (h : n ≠ 0) :
+    (X ^ n - C a).Monic := by
   obtain ⟨k, rfl⟩ := Nat.exists_eq_succ_of_ne_zero h
   apply monic_X_pow_sub _
   exact le_trans degree_C_le Nat.WithBot.coe_nonneg
@@ -402,8 +400,8 @@ theorem not_isUnit_X_pow_sub_one (R : Type _) [CommRing R] [Nontrivial R] (n : 
 set_option linter.uppercaseLean3 false in
 #align polynomial.not_is_unit_X_pow_sub_one Polynomial.not_isUnit_X_pow_sub_one
 
-theorem Monic.sub_of_left {p q : R[X]} (hp : Monic p) (hpq : degree q < degree p) : Monic (p - q) :=
-  by
+theorem Monic.sub_of_left {p q : R[X]} (hp : Monic p) (hpq : degree q < degree p) :
+    Monic (p - q) := by
   rw [sub_eq_add_neg]
   apply hp.add_of_left
   rwa [degree_neg]
@@ -515,8 +513,8 @@ theorem leadingCoeff_smul_of_smul_regular {S : Type _} [Monoid S] [DistribMulAct
     natDegree_smul_of_smul_regular p h]
 #align polynomial.leading_coeff_smul_of_smul_regular Polynomial.leadingCoeff_smul_of_smul_regular
 
-theorem monic_of_isUnit_leadingCoeff_inv_smul (h : IsUnit p.leadingCoeff) : Monic (h.unit⁻¹ • p) :=
-  by
+theorem monic_of_isUnit_leadingCoeff_inv_smul (h : IsUnit p.leadingCoeff) :
+    Monic (h.unit⁻¹ • p) := by
   rw [Monic.def, leadingCoeff_smul_of_smul_regular _ (isSMulRegular_of_group _), Units.smul_def]
   obtain ⟨k, hk⟩ := h
   simp only [← hk, smul_eq_mul, ← Units.val_mul, Units.val_eq_one, inv_mul_eq_iff_eq_mul]
@@ -528,8 +526,7 @@ theorem isUnit_leadingCoeff_mul_right_eq_zero_iff (h : IsUnit p.leadingCoeff) {q
   constructor
   · intro hp
     rw [← smul_eq_zero_iff_eq h.unit⁻¹] at hp
-    have : h.unit⁻¹ • (p * q) = h.unit⁻¹ • p * q :=
-      by
+    have : h.unit⁻¹ • (p * q) = h.unit⁻¹ • p * q := by
       ext
       simp only [Units.smul_def, coeff_smul, coeff_mul, smul_eq_mul, mul_sum]
       refine' sum_congr rfl fun x _ => _

@@ -241,10 +241,10 @@ theorem natDegree_pow (hp : p.Monic) (n : ℕ) : (p ^ n).natDegree = n * p.natDe
 end Monic
 
 @[simp]
-theorem natDegree_pow_X_add_c [Nontrivial R] (n : ℕ) (r : R) : ((X + C r) ^ n).natDegree = n := by
+theorem natDegree_pow_X_add_C [Nontrivial R] (n : ℕ) (r : R) : ((X + C r) ^ n).natDegree = n := by
   rw [(monic_X_add_C r).natDegree_pow, natDegree_X_add_C, mul_one]
 set_option linter.uppercaseLean3 false in
-#align polynomial.nat_degree_pow_X_add_C Polynomial.natDegree_pow_X_add_c
+#align polynomial.nat_degree_pow_X_add_C Polynomial.natDegree_pow_X_add_C
 
 theorem Monic.eq_one_of_isUnit (hm : Monic p) (hpu : IsUnit p) : p = 1 := by
   nontriviality R