data.polynomial.eval ⟷ Mathlib.Data.Polynomial.Eval

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

@@ -163,14 +163,14 @@ def eval₂AddMonoidHom : R[X] →+ S where
 #align polynomial.eval₂_add_monoid_hom Polynomial.eval₂AddMonoidHom
 -/
 
-#print Polynomial.eval₂_nat_cast /-
+#print Polynomial.eval₂_natCast /-
 @[simp]
-theorem eval₂_nat_cast (n : ℕ) : (n : R[X]).eval₂ f x = n :=
+theorem eval₂_natCast (n : ℕ) : (n : R[X]).eval₂ f x = n :=
   by
   induction' n with n ih
   · simp only [eval₂_zero, Nat.cast_zero]
   · rw [n.cast_succ, eval₂_add, ih, eval₂_one, n.cast_succ]
-#align polynomial.eval₂_nat_cast Polynomial.eval₂_nat_cast
+#align polynomial.eval₂_nat_cast Polynomial.eval₂_natCast
 -/
 
 variable [Semiring T]
@@ -434,13 +434,13 @@ theorem eval₂_at_one {S : Type _} [Semiring S] (f : R →+* S) : p.eval₂ f 1
 #align polynomial.eval₂_at_one Polynomial.eval₂_at_one
 -/
 
-#print Polynomial.eval₂_at_nat_cast /-
+#print Polynomial.eval₂_at_natCast /-
 @[simp]
-theorem eval₂_at_nat_cast {S : Type _} [Semiring S] (f : R →+* S) (n : ℕ) :
+theorem eval₂_at_natCast {S : Type _} [Semiring S] (f : R →+* S) (n : ℕ) :
     p.eval₂ f n = f (p.eval n) := by
   convert eval₂_at_apply f n
   simp
-#align polynomial.eval₂_at_nat_cast Polynomial.eval₂_at_nat_cast
+#align polynomial.eval₂_at_nat_cast Polynomial.eval₂_at_natCast
 -/
 
 #print Polynomial.eval_C /-
@@ -450,10 +450,10 @@ theorem eval_C : (C a).eval x = a :=
 #align polynomial.eval_C Polynomial.eval_C
 -/
 
-#print Polynomial.eval_nat_cast /-
+#print Polynomial.eval_natCast /-
 @[simp]
-theorem eval_nat_cast {n : ℕ} : (n : R[X]).eval x = n := by simp only [← C_eq_nat_cast, eval_C]
-#align polynomial.eval_nat_cast Polynomial.eval_nat_cast
+theorem eval_natCast {n : ℕ} : (n : R[X]).eval x = n := by simp only [← C_eq_nat_cast, eval_C]
+#align polynomial.eval_nat_cast Polynomial.eval_natCast
 -/
 
 #print Polynomial.eval_X /-
@@ -561,11 +561,11 @@ def leval {R : Type _} [Semiring R] (r : R) : R[X] →ₗ[R] R
 #align polynomial.leval Polynomial.leval
 -/
 
-#print Polynomial.eval_nat_cast_mul /-
+#print Polynomial.eval_natCast_mul /-
 @[simp]
-theorem eval_nat_cast_mul {n : ℕ} : ((n : R[X]) * p).eval x = n * p.eval x := by
+theorem eval_natCast_mul {n : ℕ} : ((n : R[X]) * p).eval x = n * p.eval x := by
   rw [← C_eq_nat_cast, eval_C_mul]
-#align polynomial.eval_nat_cast_mul Polynomial.eval_nat_cast_mul
+#align polynomial.eval_nat_cast_mul Polynomial.eval_natCast_mul
 -/
 
 #print Polynomial.eval_mul_X /-
@@ -707,10 +707,10 @@ theorem C_comp : (C a).comp p = C a :=
 #align polynomial.C_comp Polynomial.C_comp
 -/
 
-#print Polynomial.nat_cast_comp /-
+#print Polynomial.natCast_comp /-
 @[simp]
-theorem nat_cast_comp {n : ℕ} : (n : R[X]).comp p = n := by rw [← C_eq_nat_cast, C_comp]
-#align polynomial.nat_cast_comp Polynomial.nat_cast_comp
+theorem natCast_comp {n : ℕ} : (n : R[X]).comp p = n := by rw [← C_eq_nat_cast, C_comp]
+#align polynomial.nat_cast_comp Polynomial.natCast_comp
 -/
 
 #print Polynomial.comp_zero /-
@@ -791,11 +791,11 @@ theorem C_mul_comp : (C a * p).comp r = C a * p.comp r :=
 #align polynomial.C_mul_comp Polynomial.C_mul_comp
 -/
 
-#print Polynomial.nat_cast_mul_comp /-
+#print Polynomial.natCast_mul_comp /-
 @[simp]
-theorem nat_cast_mul_comp {n : ℕ} : ((n : R[X]) * p).comp r = n * p.comp r := by
+theorem natCast_mul_comp {n : ℕ} : ((n : R[X]) * p).comp r = n * p.comp r := by
   rw [← C_eq_nat_cast, C_mul_comp, C_eq_nat_cast]
-#align polynomial.nat_cast_mul_comp Polynomial.nat_cast_mul_comp
+#align polynomial.nat_cast_mul_comp Polynomial.natCast_mul_comp
 -/
 
 #print Polynomial.mul_comp /-
@@ -957,12 +957,12 @@ theorem coe_mapRingHom (f : R →+* S) : ⇑(mapRingHom f) = map f :=
 #align polynomial.coe_map_ring_hom Polynomial.coe_mapRingHom
 -/
 
-#print Polynomial.map_nat_cast /-
+#print Polynomial.map_natCast /-
 -- This is protected to not clash with the global `map_nat_cast`.
 @[simp]
-protected theorem map_nat_cast (n : ℕ) : (n : R[X]).map f = n :=
+protected theorem map_natCast (n : ℕ) : (n : R[X]).map f = n :=
   map_natCast (mapRingHom f) n
-#align polynomial.map_nat_cast Polynomial.map_nat_cast
+#align polynomial.map_nat_cast Polynomial.map_natCast
 -/
 
 #print Polynomial.map_bit0 /-
@@ -1221,25 +1221,25 @@ theorem eval_one_map (f : R →+* S) (p : R[X]) : (p.map f).eval 1 = f (p.eval 1
 #align polynomial.eval_one_map Polynomial.eval_one_map
 -/
 
-#print Polynomial.eval_nat_cast_map /-
+#print Polynomial.eval_natCast_map /-
 @[simp]
-theorem eval_nat_cast_map (f : R →+* S) (p : R[X]) (n : ℕ) : (p.map f).eval n = f (p.eval n) :=
+theorem eval_natCast_map (f : R →+* S) (p : R[X]) (n : ℕ) : (p.map f).eval n = f (p.eval n) :=
   by
   apply Polynomial.induction_on' p
   · intro p q hp hq; simp only [hp, hq, Polynomial.map_add, RingHom.map_add, eval_add]
   · intro n r; simp only [map_natCast f, eval_monomial, map_monomial, f.map_pow, f.map_mul]
-#align polynomial.eval_nat_cast_map Polynomial.eval_nat_cast_map
+#align polynomial.eval_nat_cast_map Polynomial.eval_natCast_map
 -/
 
-#print Polynomial.eval_int_cast_map /-
+#print Polynomial.eval_intCast_map /-
 @[simp]
-theorem eval_int_cast_map {R S : Type _} [Ring R] [Ring S] (f : R →+* S) (p : R[X]) (i : ℤ) :
+theorem eval_intCast_map {R S : Type _} [Ring R] [Ring S] (f : R →+* S) (p : R[X]) (i : ℤ) :
     (p.map f).eval i = f (p.eval i) :=
   by
   apply Polynomial.induction_on' p
   · intro p q hp hq; simp only [hp, hq, Polynomial.map_add, RingHom.map_add, eval_add]
   · intro n r; simp only [map_intCast, eval_monomial, map_monomial, map_pow, map_mul]
-#align polynomial.eval_int_cast_map Polynomial.eval_int_cast_map
+#align polynomial.eval_int_cast_map Polynomial.eval_intCast_map
 -/
 
 end Map
@@ -1570,18 +1570,18 @@ protected theorem map_neg {S} [Ring S] (f : R →+* S) : (-p).map f = -p.map f :
 #align polynomial.map_neg Polynomial.map_neg
 -/
 
-#print Polynomial.map_int_cast /-
+#print Polynomial.map_intCast /-
 @[simp]
-theorem map_int_cast {S} [Ring S] (f : R →+* S) (n : ℤ) : map f ↑n = ↑n :=
+theorem map_intCast {S} [Ring S] (f : R →+* S) (n : ℤ) : map f ↑n = ↑n :=
   map_intCast (mapRingHom f) n
-#align polynomial.map_int_cast Polynomial.map_int_cast
+#align polynomial.map_int_cast Polynomial.map_intCast
 -/
 
-#print Polynomial.eval_int_cast /-
+#print Polynomial.eval_intCast /-
 @[simp]
-theorem eval_int_cast {n : ℤ} {x : R} : (n : R[X]).eval x = n := by
+theorem eval_intCast {n : ℤ} {x : R} : (n : R[X]).eval x = n := by
   simp only [← C_eq_int_cast, eval_C]
-#align polynomial.eval_int_cast Polynomial.eval_int_cast
+#align polynomial.eval_int_cast Polynomial.eval_intCast
 -/
 
 #print Polynomial.eval₂_neg /-

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

@@ -991,7 +991,7 @@ theorem map_dvd (f : R →+* S) {x y : R[X]} : x ∣ y → x.map f ∣ y.map f :
 theorem coeff_map (n : ℕ) : coeff (p.map f) n = f (coeff p n) :=
   by
   rw [map, eval₂, coeff_sum, Sum]
-  conv_rhs => rw [← sum_C_mul_X_pow_eq p, coeff_sum, Sum, RingHom.map_sum]
+  conv_rhs => rw [← sum_C_mul_X_pow_eq p, coeff_sum, Sum, map_sum]
   refine' Finset.sum_congr rfl fun x hx => _
   simp [Function.comp, coeff_C_mul_X_pow, f.map_mul]
   split_ifs <;> simp [f.map_zero]

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

@@ -614,11 +614,11 @@ def IsRoot (p : R[X]) (a : R) : Prop :=
 
 instance [DecidableEq R] : Decidable (IsRoot p a) := by unfold is_root <;> infer_instance
 
-#print Polynomial.IsRoot.definition /-
+#print Polynomial.IsRoot.def /-
 @[simp]
-theorem IsRoot.definition : IsRoot p a ↔ p.eval a = 0 :=
+theorem IsRoot.def : IsRoot p a ↔ p.eval a = 0 :=
   Iff.rfl
-#align polynomial.is_root.def Polynomial.IsRoot.definition
+#align polynomial.is_root.def Polynomial.IsRoot.def
 -/
 
 #print Polynomial.IsRoot.eq_zero /-

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

@@ -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 Data.Polynomial.Degree.Definitions
-import Data.Polynomial.Induction
+import Algebra.Polynomial.Degree.Definitions
+import Algebra.Polynomial.Induction
 
 #align_import data.polynomial.eval from "leanprover-community/mathlib"@"728baa2f54e6062c5879a3e397ac6bac323e506f"
 

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

@@ -542,8 +542,8 @@ theorem eval_monomial_one_add_sub [CommRing S] (d : ℕ) (y : S) :
     apply_congr
     skip
     rw [one_pow, mul_one, mul_comm]
-  rw [sum_range_succ, mul_add, Nat.choose_self, Nat.cast_one, one_mul, add_sub_cancel, mul_sum,
-    sum_range_succ', Nat.cast_zero, MulZeroClass.zero_mul, MulZeroClass.mul_zero, add_zero]
+  rw [sum_range_succ, mul_add, Nat.choose_self, Nat.cast_one, one_mul, add_sub_cancel_right,
+    mul_sum, sum_range_succ', Nat.cast_zero, MulZeroClass.zero_mul, MulZeroClass.mul_zero, add_zero]
   apply sum_congr rfl fun y hy => _
   rw [← mul_assoc, ← mul_assoc, ← Nat.cast_mul, Nat.succ_mul_choose_eq, Nat.cast_mul,
     Nat.add_sub_cancel]
@@ -576,7 +576,7 @@ theorem eval_mul_X : (p * X).eval x = p.eval x * x :=
   · intro p q ph qh
     simp only [add_mul, eval_add, ph, qh]
   · intro n a
-    simp only [← monomial_one_one_eq_X, monomial_mul_monomial, eval_monomial, mul_one, pow_succ',
+    simp only [← monomial_one_one_eq_X, monomial_mul_monomial, eval_monomial, mul_one, pow_succ,
       mul_assoc]
 #align polynomial.eval_mul_X Polynomial.eval_mul_X
 -/
@@ -587,7 +587,7 @@ theorem eval_mul_X_pow {k : ℕ} : (p * X ^ k).eval x = p.eval x * x ^ k :=
   by
   induction' k with k ih
   · simp
-  · simp [pow_succ', ← mul_assoc, ih]
+  · simp [pow_succ, ← mul_assoc, ih]
 #align polynomial.eval_mul_X_pow Polynomial.eval_mul_X_pow
 -/
 
@@ -614,11 +614,11 @@ def IsRoot (p : R[X]) (a : R) : Prop :=
 
 instance [DecidableEq R] : Decidable (IsRoot p a) := by unfold is_root <;> infer_instance
 
-#print Polynomial.IsRoot.def /-
+#print Polynomial.IsRoot.definition /-
 @[simp]
-theorem IsRoot.def : IsRoot p a ↔ p.eval a = 0 :=
+theorem IsRoot.definition : IsRoot p a ↔ p.eval a = 0 :=
   Iff.rfl
-#align polynomial.is_root.def Polynomial.IsRoot.def
+#align polynomial.is_root.def Polynomial.IsRoot.definition
 -/
 
 #print Polynomial.IsRoot.eq_zero /-
@@ -757,7 +757,7 @@ theorem mul_X_comp : (p * X).comp r = p.comp r * r :=
   by
   apply Polynomial.induction_on' p
   · intro p q hp hq; simp only [hp, hq, add_mul, add_comp]
-  · intro n b; simp only [pow_succ', mul_assoc, monomial_mul_X, monomial_comp]
+  · intro n b; simp only [pow_succ, mul_assoc, monomial_mul_X, monomial_comp]
 #align polynomial.mul_X_comp Polynomial.mul_X_comp
 -/
 
@@ -767,7 +767,7 @@ theorem X_pow_comp {k : ℕ} : (X ^ k).comp p = p ^ k :=
   by
   induction' k with k ih
   · simp
-  · simp [pow_succ', mul_X_comp, ih]
+  · simp [pow_succ, mul_X_comp, ih]
 #align polynomial.X_pow_comp Polynomial.X_pow_comp
 -/
 
@@ -777,7 +777,7 @@ theorem mul_X_pow_comp {k : ℕ} : (p * X ^ k).comp r = p.comp r * r ^ k :=
   by
   induction' k with k ih
   · simp
-  · simp [ih, pow_succ', ← mul_assoc, mul_X_comp]
+  · simp [ih, pow_succ, ← mul_assoc, mul_X_comp]
 #align polynomial.mul_X_pow_comp Polynomial.mul_X_pow_comp
 -/
 
@@ -839,7 +839,7 @@ theorem smul_comp [Monoid S] [DistribMulAction S R] [IsScalarTower S R R] (s : S
 theorem comp_assoc {R : Type _} [CommSemiring R] (φ ψ χ : R[X]) :
     (φ.comp ψ).comp χ = φ.comp (ψ.comp χ) := by
   apply Polynomial.induction_on φ <;>
-    · intros; simp_all only [add_comp, mul_comp, C_comp, X_comp, pow_succ', ← mul_assoc]
+    · intros; simp_all only [add_comp, mul_comp, C_comp, X_comp, pow_succ, ← mul_assoc]
 #align polynomial.comp_assoc Polynomial.comp_assoc
 -/
 
@@ -1199,7 +1199,7 @@ theorem map_comp (p q : R[X]) : map f (p.comp q) = (map f p).comp (map f q) :=
       simp (config := { contextual := true }) only [Polynomial.map_add, add_comp, forall_const,
         imp_true_iff, eq_self_iff_true])
     (by
-      simp (config := { contextual := true }) only [pow_succ', ← mul_assoc, comp, forall_const,
+      simp (config := { contextual := true }) only [pow_succ, ← mul_assoc, comp, forall_const,
         eval₂_mul_X, imp_true_iff, eq_self_iff_true, map_X, Polynomial.map_mul])
 #align polynomial.map_comp Polynomial.map_comp
 -/

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

@@ -221,7 +221,7 @@ theorem eval₂_mul_noncomm (hf : ∀ k, Commute (f <| q.coeff k) x) :
     eval₂ f x (p * q) = eval₂ f x p * eval₂ f x q :=
   by
   rcases p with ⟨⟩; rcases q with ⟨⟩
-  simp only [coeff] at hf 
+  simp only [coeff] at hf
   simp only [← of_finsupp_mul, eval₂_of_finsupp]
   exact lift_nc_mul _ _ p q fun k n hn => (hf k).pow_right n
 #align polynomial.eval₂_mul_noncomm Polynomial.eval₂_mul_noncomm
@@ -262,7 +262,7 @@ theorem eval₂_list_prod_noncomm (ps : List R[X])
   by
   induction' ps using List.reverseRecOn with ps p ihp
   · simp
-  · simp only [List.forall_mem_append, List.forall_mem_singleton] at hf 
+  · simp only [List.forall_mem_append, List.forall_mem_singleton] at hf
     simp [eval₂_mul_noncomm _ _ hf.2, ihp hf.1]
 #align polynomial.eval₂_list_prod_noncomm Polynomial.eval₂_list_prod_noncomm
 -/
@@ -641,7 +641,7 @@ theorem coeff_zero_eq_eval_zero (p : R[X]) : coeff p 0 = p.eval 0 :=
 
 #print Polynomial.zero_isRoot_of_coeff_zero_eq_zero /-
 theorem zero_isRoot_of_coeff_zero_eq_zero {p : R[X]} (hp : p.coeff 0 = 0) : IsRoot p 0 := by
-  rwa [coeff_zero_eq_eval_zero] at hp 
+  rwa [coeff_zero_eq_eval_zero] at hp
 #align polynomial.zero_is_root_of_coeff_zero_eq_zero Polynomial.zero_isRoot_of_coeff_zero_eq_zero
 -/
 
@@ -1051,7 +1051,7 @@ theorem map_surjective (hf : Function.Surjective f) : Function.Surjective (map f
 theorem degree_map_le (p : R[X]) : degree (p.map f) ≤ degree p :=
   by
   apply (degree_le_iff_coeff_zero _ _).2 fun m hm => _
-  rw [degree_lt_iff_coeff_zero] at hm 
+  rw [degree_lt_iff_coeff_zero] at hm
   simp [hm m le_rfl]
 #align polynomial.degree_map_le Polynomial.degree_map_le
 -/

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

@@ -1331,7 +1331,7 @@ theorem coe_evalRingHom (r : R) : (evalRingHom r : R[X] → R) = eval r :=
 
 #print Polynomial.evalRingHom_zero /-
 theorem evalRingHom_zero : evalRingHom 0 = constantCoeff :=
-  FunLike.ext _ _ fun p => p.coeff_zero_eq_eval_zero.symm
+  DFunLike.ext _ _ fun p => p.coeff_zero_eq_eval_zero.symm
 #align polynomial.eval_ring_hom_zero Polynomial.evalRingHom_zero
 -/
 

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.Degree.Definitions
-import Mathbin.Data.Polynomial.Induction
+import Data.Polynomial.Degree.Definitions
+import Data.Polynomial.Induction
 
 #align_import data.polynomial.eval from "leanprover-community/mathlib"@"728baa2f54e6062c5879a3e397ac6bac323e506f"
 

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.eval
-! leanprover-community/mathlib commit 728baa2f54e6062c5879a3e397ac6bac323e506f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Polynomial.Degree.Definitions
 import Mathbin.Data.Polynomial.Induction
 
+#align_import data.polynomial.eval from "leanprover-community/mathlib"@"728baa2f54e6062c5879a3e397ac6bac323e506f"
+
 /-!
 # Theory of univariate polynomials
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -1355,11 +1355,13 @@ theorem eval_comp : (p.comp q).eval x = p.eval (q.eval x) :=
 #align polynomial.eval_comp Polynomial.eval_comp
 -/
 
+#print Polynomial.iterate_comp_eval /-
 @[simp]
 theorem iterate_comp_eval :
     ∀ (k : ℕ) (t : R), ((p.comp^[k]) q).eval t = ((fun x => p.eval x)^[k]) (q.eval t) :=
   iterate_comp_eval₂ _
 #align polynomial.iterate_comp_eval Polynomial.iterate_comp_eval
+-/
 
 #print Polynomial.compRingHom /-
 /-- `comp p`, regarded as a ring homomorphism from `R[X]` to itself. -/

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

@@ -52,29 +52,39 @@ irreducible_def eval₂ (p : R[X]) : S :=
 #align polynomial.eval₂ Polynomial.eval₂
 -/
 
+#print Polynomial.eval₂_eq_sum /-
 theorem eval₂_eq_sum {f : R →+* S} {x : S} : p.eval₂ f x = p.Sum fun e a => f a * x ^ e := by
   rw [eval₂]
 #align polynomial.eval₂_eq_sum Polynomial.eval₂_eq_sum
+-/
 
+#print Polynomial.eval₂_congr /-
 theorem eval₂_congr {R S : Type _} [Semiring R] [Semiring S] {f g : R →+* S} {s t : S}
     {φ ψ : R[X]} : f = g → s = t → φ = ψ → eval₂ f s φ = eval₂ g t ψ := by
   rintro rfl rfl rfl <;> rfl
 #align polynomial.eval₂_congr Polynomial.eval₂_congr
+-/
 
+#print Polynomial.eval₂_at_zero /-
 @[simp]
 theorem eval₂_at_zero : p.eval₂ f 0 = f (coeff p 0) := by
   simp (config := { contextual := true }) only [eval₂_eq_sum, zero_pow_eq, mul_ite,
     MulZeroClass.mul_zero, mul_one, Sum, Classical.not_not, mem_support_iff, sum_ite_eq',
     ite_eq_left_iff, RingHom.map_zero, imp_true_iff, eq_self_iff_true]
 #align polynomial.eval₂_at_zero Polynomial.eval₂_at_zero
+-/
 
+#print Polynomial.eval₂_zero /-
 @[simp]
 theorem eval₂_zero : (0 : R[X]).eval₂ f x = 0 := by simp [eval₂_eq_sum]
 #align polynomial.eval₂_zero Polynomial.eval₂_zero
+-/
 
+#print Polynomial.eval₂_C /-
 @[simp]
 theorem eval₂_C : (C a).eval₂ f x = f a := by simp [eval₂_eq_sum]
 #align polynomial.eval₂_C Polynomial.eval₂_C
+-/
 
 #print Polynomial.eval₂_X /-
 @[simp]
@@ -82,10 +92,12 @@ theorem eval₂_X : X.eval₂ f x = x := by simp [eval₂_eq_sum]
 #align polynomial.eval₂_X Polynomial.eval₂_X
 -/
 
+#print Polynomial.eval₂_monomial /-
 @[simp]
 theorem eval₂_monomial {n : ℕ} {r : R} : (monomial n r).eval₂ f x = f r * x ^ n := by
   simp [eval₂_eq_sum]
 #align polynomial.eval₂_monomial Polynomial.eval₂_monomial
+-/
 
 #print Polynomial.eval₂_X_pow /-
 @[simp]
@@ -97,10 +109,12 @@ theorem eval₂_X_pow {n : ℕ} : (X ^ n).eval₂ f x = x ^ n :=
 #align polynomial.eval₂_X_pow Polynomial.eval₂_X_pow
 -/
 
+#print Polynomial.eval₂_add /-
 @[simp]
 theorem eval₂_add : (p + q).eval₂ f x = p.eval₂ f x + q.eval₂ f x := by simp only [eval₂_eq_sum];
   apply sum_add_index <;> simp [add_mul]
 #align polynomial.eval₂_add Polynomial.eval₂_add
+-/
 
 #print Polynomial.eval₂_one /-
 @[simp]
@@ -108,15 +122,20 @@ theorem eval₂_one : (1 : R[X]).eval₂ f x = 1 := by rw [← C_1, eval₂_C, f
 #align polynomial.eval₂_one Polynomial.eval₂_one
 -/
 
+#print Polynomial.eval₂_bit0 /-
 @[simp]
 theorem eval₂_bit0 : (bit0 p).eval₂ f x = bit0 (p.eval₂ f x) := by rw [bit0, eval₂_add, bit0]
 #align polynomial.eval₂_bit0 Polynomial.eval₂_bit0
+-/
 
+#print Polynomial.eval₂_bit1 /-
 @[simp]
 theorem eval₂_bit1 : (bit1 p).eval₂ f x = bit1 (p.eval₂ f x) := by
   rw [bit1, eval₂_add, eval₂_bit0, eval₂_one, bit1]
 #align polynomial.eval₂_bit1 Polynomial.eval₂_bit1
+-/
 
+#print Polynomial.eval₂_smul /-
 @[simp]
 theorem eval₂_smul (g : R →+* S) (p : R[X]) (x : S) {s : R} :
     eval₂ g x (s • p) = g s * eval₂ g x p :=
@@ -126,6 +145,7 @@ theorem eval₂_smul (g : R →+* S) (p : R[X]) (x : S) {s : R} :
   rw [eval₂_eq_sum, eval₂_eq_sum, sum_over_range' _ _ _ A, sum_over_range' _ _ _ B] <;>
     simp [mul_sum, mul_assoc]
 #align polynomial.eval₂_smul Polynomial.eval₂_smul
+-/
 
 #print Polynomial.eval₂_C_X /-
 @[simp]
@@ -172,9 +192,11 @@ theorem eval₂_sum (p : T[X]) (g : ℕ → T → R[X]) (x : S) :
 #align polynomial.eval₂_sum Polynomial.eval₂_sum
 -/
 
+#print Polynomial.eval₂_list_sum /-
 theorem eval₂_list_sum (l : List R[X]) (x : S) : eval₂ f x l.Sum = (l.map (eval₂ f x)).Sum :=
   map_list_sum (eval₂AddMonoidHom f x) l
 #align polynomial.eval₂_list_sum Polynomial.eval₂_list_sum
+-/
 
 #print Polynomial.eval₂_multiset_sum /-
 theorem eval₂_multiset_sum (s : Multiset R[X]) (x : S) :
@@ -190,11 +212,14 @@ theorem eval₂_finset_sum (s : Finset ι) (g : ι → R[X]) (x : S) :
 #align polynomial.eval₂_finset_sum Polynomial.eval₂_finset_sum
 -/
 
+#print Polynomial.eval₂_ofFinsupp /-
 theorem eval₂_ofFinsupp {f : R →+* S} {x : S} {p : AddMonoidAlgebra R ℕ} :
     eval₂ f x (⟨p⟩ : R[X]) = liftNC (↑f) (powersHom S x) p := by
   simp only [eval₂_eq_sum, Sum, to_finsupp_sum, support, coeff]; rfl
 #align polynomial.eval₂_of_finsupp Polynomial.eval₂_ofFinsupp
+-/
 
+#print Polynomial.eval₂_mul_noncomm /-
 theorem eval₂_mul_noncomm (hf : ∀ k, Commute (f <| q.coeff k) x) :
     eval₂ f x (p * q) = eval₂ f x p * eval₂ f x q :=
   by
@@ -203,7 +228,9 @@ theorem eval₂_mul_noncomm (hf : ∀ k, Commute (f <| q.coeff k) x) :
   simp only [← of_finsupp_mul, eval₂_of_finsupp]
   exact lift_nc_mul _ _ p q fun k n hn => (hf k).pow_right n
 #align polynomial.eval₂_mul_noncomm Polynomial.eval₂_mul_noncomm
+-/
 
+#print Polynomial.eval₂_mul_X /-
 @[simp]
 theorem eval₂_mul_X : eval₂ f x (p * X) = eval₂ f x p * x :=
   by
@@ -212,11 +239,15 @@ theorem eval₂_mul_X : eval₂ f x (p * X) = eval₂ f x p * x :=
   · simp
   · simp [coeff_X_of_ne_one hk]
 #align polynomial.eval₂_mul_X Polynomial.eval₂_mul_X
+-/
 
+#print Polynomial.eval₂_X_mul /-
 @[simp]
 theorem eval₂_X_mul : eval₂ f x (X * p) = eval₂ f x p * x := by rw [X_mul, eval₂_mul_X]
 #align polynomial.eval₂_X_mul Polynomial.eval₂_X_mul
+-/
 
+#print Polynomial.eval₂_mul_C' /-
 theorem eval₂_mul_C' (h : Commute (f a) x) : eval₂ f x (p * C a) = eval₂ f x p * f a :=
   by
   rw [eval₂_mul_noncomm, eval₂_C]
@@ -225,7 +256,9 @@ theorem eval₂_mul_C' (h : Commute (f a) x) : eval₂ f x (p * C a) = eval₂ f
   · simp only [hk, h, coeff_C_zero, coeff_C_ne_zero]
   · simp only [coeff_C_ne_zero hk, RingHom.map_zero, Commute.zero_left]
 #align polynomial.eval₂_mul_C' Polynomial.eval₂_mul_C'
+-/
 
+#print Polynomial.eval₂_list_prod_noncomm /-
 theorem eval₂_list_prod_noncomm (ps : List R[X])
     (hf : ∀ p ∈ ps, ∀ (k), Commute (f <| coeff p k) x) :
     eval₂ f x ps.Prod = (ps.map (Polynomial.eval₂ f x)).Prod :=
@@ -235,7 +268,9 @@ theorem eval₂_list_prod_noncomm (ps : List R[X])
   · simp only [List.forall_mem_append, List.forall_mem_singleton] at hf 
     simp [eval₂_mul_noncomm _ _ hf.2, ihp hf.1]
 #align polynomial.eval₂_list_prod_noncomm Polynomial.eval₂_list_prod_noncomm
+-/
 
+#print Polynomial.eval₂RingHom' /-
 /-- `eval₂` as a `ring_hom` for noncommutative rings -/
 def eval₂RingHom' (f : R →+* S) (x : S) (hf : ∀ a, Commute (f a) x) : R[X] →+* S
     where
@@ -245,6 +280,7 @@ def eval₂RingHom' (f : R →+* S) (x : S) (hf : ∀ a, Commute (f a) x) : R[X]
   map_mul' p q := eval₂_mul_noncomm f x fun k => hf <| coeff q k
   map_one' := eval₂_one _ _
 #align polynomial.eval₂_ring_hom' Polynomial.eval₂RingHom'
+-/
 
 end
 
@@ -261,11 +297,14 @@ section
 
 variable [Semiring S] (f : R →+* S) (x : S)
 
+#print Polynomial.eval₂_eq_sum_range /-
 theorem eval₂_eq_sum_range :
     p.eval₂ f x = ∑ i in Finset.range (p.natDegree + 1), f (p.coeff i) * x ^ i :=
   trans (congr_arg _ p.as_sum_range) (trans (eval₂_finset_sum f _ _ x) (congr_arg _ (by simp)))
 #align polynomial.eval₂_eq_sum_range Polynomial.eval₂_eq_sum_range
+-/
 
+#print Polynomial.eval₂_eq_sum_range' /-
 theorem eval₂_eq_sum_range' (f : R →+* S) {p : R[X]} {n : ℕ} (hn : p.natDegree < n) (x : S) :
     eval₂ f x p = ∑ i in Finset.range n, f (p.coeff i) * x ^ i :=
   by
@@ -273,6 +312,7 @@ theorem eval₂_eq_sum_range' (f : R →+* S) {p : R[X]} {n : ℕ} (hn : p.natDe
   intro i
   rw [f.map_zero, MulZeroClass.zero_mul]
 #align polynomial.eval₂_eq_sum_range' Polynomial.eval₂_eq_sum_range'
+-/
 
 end
 
@@ -280,22 +320,28 @@ section
 
 variable [CommSemiring S] (f : R →+* S) (x : S)
 
+#print Polynomial.eval₂_mul /-
 @[simp]
 theorem eval₂_mul : (p * q).eval₂ f x = p.eval₂ f x * q.eval₂ f x :=
   eval₂_mul_noncomm _ _ fun k => Commute.all _ _
 #align polynomial.eval₂_mul Polynomial.eval₂_mul
+-/
 
+#print Polynomial.eval₂_mul_eq_zero_of_left /-
 theorem eval₂_mul_eq_zero_of_left (q : R[X]) (hp : p.eval₂ f x = 0) : (p * q).eval₂ f x = 0 :=
   by
   rw [eval₂_mul f x]
   exact mul_eq_zero_of_left hp (q.eval₂ f x)
 #align polynomial.eval₂_mul_eq_zero_of_left Polynomial.eval₂_mul_eq_zero_of_left
+-/
 
+#print Polynomial.eval₂_mul_eq_zero_of_right /-
 theorem eval₂_mul_eq_zero_of_right (p : R[X]) (hq : q.eval₂ f x = 0) : (p * q).eval₂ f x = 0 :=
   by
   rw [eval₂_mul f x]
   exact mul_eq_zero_of_right (p.eval₂ f x) hq
 #align polynomial.eval₂_mul_eq_zero_of_right Polynomial.eval₂_mul_eq_zero_of_right
+-/
 
 #print Polynomial.eval₂RingHom /-
 /-- `eval₂` as a `ring_hom` -/
@@ -306,10 +352,12 @@ def eval₂RingHom (f : R →+* S) (x : S) : R[X] →+* S :=
 #align polynomial.eval₂_ring_hom Polynomial.eval₂RingHom
 -/
 
+#print Polynomial.coe_eval₂RingHom /-
 @[simp]
 theorem coe_eval₂RingHom (f : R →+* S) (x) : ⇑(eval₂RingHom f x) = eval₂ f x :=
   rfl
 #align polynomial.coe_eval₂_ring_hom Polynomial.coe_eval₂RingHom
+-/
 
 #print Polynomial.eval₂_pow /-
 theorem eval₂_pow (n : ℕ) : (p ^ n).eval₂ f x = p.eval₂ f x ^ n :=
@@ -323,14 +371,18 @@ theorem eval₂_dvd : p ∣ q → eval₂ f x p ∣ eval₂ f x q :=
 #align polynomial.eval₂_dvd Polynomial.eval₂_dvd
 -/
 
+#print Polynomial.eval₂_eq_zero_of_dvd_of_eval₂_eq_zero /-
 theorem eval₂_eq_zero_of_dvd_of_eval₂_eq_zero (h : p ∣ q) (h0 : eval₂ f x p = 0) :
     eval₂ f x q = 0 :=
   zero_dvd_iff.mp (h0 ▸ eval₂_dvd f x h)
 #align polynomial.eval₂_eq_zero_of_dvd_of_eval₂_eq_zero Polynomial.eval₂_eq_zero_of_dvd_of_eval₂_eq_zero
+-/
 
+#print Polynomial.eval₂_list_prod /-
 theorem eval₂_list_prod (l : List R[X]) (x : S) : eval₂ f x l.Prod = (l.map (eval₂ f x)).Prod :=
   map_list_prod (eval₂RingHom f x) l
 #align polynomial.eval₂_list_prod Polynomial.eval₂_list_prod
+-/
 
 end
 
@@ -347,19 +399,26 @@ def eval : R → R[X] → R :=
 #align polynomial.eval Polynomial.eval
 -/
 
+#print Polynomial.eval_eq_sum /-
 theorem eval_eq_sum : p.eval x = p.Sum fun e a => a * x ^ e := by rw [eval, eval₂_eq_sum]; rfl
 #align polynomial.eval_eq_sum Polynomial.eval_eq_sum
+-/
 
+#print Polynomial.eval_eq_sum_range /-
 theorem eval_eq_sum_range {p : R[X]} (x : R) :
     p.eval x = ∑ i in Finset.range (p.natDegree + 1), p.coeff i * x ^ i := by
   rw [eval_eq_sum, sum_over_range] <;> simp
 #align polynomial.eval_eq_sum_range Polynomial.eval_eq_sum_range
+-/
 
+#print Polynomial.eval_eq_sum_range' /-
 theorem eval_eq_sum_range' {p : R[X]} {n : ℕ} (hn : p.natDegree < n) (x : R) :
     p.eval x = ∑ i in Finset.range n, p.coeff i * x ^ i := by
   rw [eval_eq_sum, p.sum_over_range' _ _ hn] <;> simp
 #align polynomial.eval_eq_sum_range' Polynomial.eval_eq_sum_range'
+-/
 
+#print Polynomial.eval₂_at_apply /-
 @[simp]
 theorem eval₂_at_apply {S : Type _} [Semiring S] (f : R →+* S) (r : R) :
     p.eval₂ f (f r) = f (p.eval r) :=
@@ -367,25 +426,32 @@ theorem eval₂_at_apply {S : Type _} [Semiring S] (f : R →+* S) (r : R) :
   rw [eval₂_eq_sum, eval_eq_sum, Sum, Sum, f.map_sum]
   simp only [f.map_mul, f.map_pow]
 #align polynomial.eval₂_at_apply Polynomial.eval₂_at_apply
+-/
 
+#print Polynomial.eval₂_at_one /-
 @[simp]
 theorem eval₂_at_one {S : Type _} [Semiring S] (f : R →+* S) : p.eval₂ f 1 = f (p.eval 1) :=
   by
   convert eval₂_at_apply f 1
   simp
 #align polynomial.eval₂_at_one Polynomial.eval₂_at_one
+-/
 
+#print Polynomial.eval₂_at_nat_cast /-
 @[simp]
 theorem eval₂_at_nat_cast {S : Type _} [Semiring S] (f : R →+* S) (n : ℕ) :
     p.eval₂ f n = f (p.eval n) := by
   convert eval₂_at_apply f n
   simp
 #align polynomial.eval₂_at_nat_cast Polynomial.eval₂_at_nat_cast
+-/
 
+#print Polynomial.eval_C /-
 @[simp]
 theorem eval_C : (C a).eval x = a :=
   eval₂_C _ _
 #align polynomial.eval_C Polynomial.eval_C
+-/
 
 #print Polynomial.eval_nat_cast /-
 @[simp]
@@ -400,20 +466,26 @@ theorem eval_X : X.eval x = x :=
 #align polynomial.eval_X Polynomial.eval_X
 -/
 
+#print Polynomial.eval_monomial /-
 @[simp]
 theorem eval_monomial {n a} : (monomial n a).eval x = a * x ^ n :=
   eval₂_monomial _ _
 #align polynomial.eval_monomial Polynomial.eval_monomial
+-/
 
+#print Polynomial.eval_zero /-
 @[simp]
 theorem eval_zero : (0 : R[X]).eval x = 0 :=
   eval₂_zero _ _
 #align polynomial.eval_zero Polynomial.eval_zero
+-/
 
+#print Polynomial.eval_add /-
 @[simp]
 theorem eval_add : (p + q).eval x = p.eval x + q.eval x :=
   eval₂_add _ _
 #align polynomial.eval_add Polynomial.eval_add
+-/
 
 #print Polynomial.eval_one /-
 @[simp]
@@ -422,22 +494,29 @@ theorem eval_one : (1 : R[X]).eval x = 1 :=
 #align polynomial.eval_one Polynomial.eval_one
 -/
 
+#print Polynomial.eval_bit0 /-
 @[simp]
 theorem eval_bit0 : (bit0 p).eval x = bit0 (p.eval x) :=
   eval₂_bit0 _ _
 #align polynomial.eval_bit0 Polynomial.eval_bit0
+-/
 
+#print Polynomial.eval_bit1 /-
 @[simp]
 theorem eval_bit1 : (bit1 p).eval x = bit1 (p.eval x) :=
   eval₂_bit1 _ _
 #align polynomial.eval_bit1 Polynomial.eval_bit1
+-/
 
+#print Polynomial.eval_smul /-
 @[simp]
 theorem eval_smul [Monoid S] [DistribMulAction S R] [IsScalarTower S R R] (s : S) (p : R[X])
     (x : R) : (s • p).eval x = s • p.eval x := by
   rw [← smul_one_smul R s p, eval, eval₂_smul, RingHom.id_apply, smul_one_mul]
 #align polynomial.eval_smul Polynomial.eval_smul
+-/
 
+#print Polynomial.eval_C_mul /-
 @[simp]
 theorem eval_C_mul : (C a * p).eval x = a * p.eval x :=
   by
@@ -447,7 +526,9 @@ theorem eval_C_mul : (C a * p).eval x = a * p.eval x :=
   · intro n b
     simp only [mul_assoc, C_mul_monomial, eval_monomial]
 #align polynomial.eval_C_mul Polynomial.eval_C_mul
+-/
 
+#print Polynomial.eval_monomial_one_add_sub /-
 /-- A reformulation of the expansion of (1 + y)^d:
 $$(d + 1) (1 + y)^d - (d + 1)y^d = \sum_{i = 0}^d {d + 1 \choose i} \cdot i \cdot y^{i - 1}.$$
 -/
@@ -470,6 +551,7 @@ theorem eval_monomial_one_add_sub [CommRing S] (d : ℕ) (y : S) :
   rw [← mul_assoc, ← mul_assoc, ← Nat.cast_mul, Nat.succ_mul_choose_eq, Nat.cast_mul,
     Nat.add_sub_cancel]
 #align polynomial.eval_monomial_one_add_sub Polynomial.eval_monomial_one_add_sub
+-/
 
 #print Polynomial.leval /-
 /-- `polynomial.eval` as linear map -/
@@ -482,11 +564,14 @@ def leval {R : Type _} [Semiring R] (r : R) : R[X] →ₗ[R] R
 #align polynomial.leval Polynomial.leval
 -/
 
+#print Polynomial.eval_nat_cast_mul /-
 @[simp]
 theorem eval_nat_cast_mul {n : ℕ} : ((n : R[X]) * p).eval x = n * p.eval x := by
   rw [← C_eq_nat_cast, eval_C_mul]
 #align polynomial.eval_nat_cast_mul Polynomial.eval_nat_cast_mul
+-/
 
+#print Polynomial.eval_mul_X /-
 @[simp]
 theorem eval_mul_X : (p * X).eval x = p.eval x * x :=
   by
@@ -497,7 +582,9 @@ theorem eval_mul_X : (p * X).eval x = p.eval x * x :=
     simp only [← monomial_one_one_eq_X, monomial_mul_monomial, eval_monomial, mul_one, pow_succ',
       mul_assoc]
 #align polynomial.eval_mul_X Polynomial.eval_mul_X
+-/
 
+#print Polynomial.eval_mul_X_pow /-
 @[simp]
 theorem eval_mul_X_pow {k : ℕ} : (p * X ^ k).eval x = p.eval x * x ^ k :=
   by
@@ -505,6 +592,7 @@ theorem eval_mul_X_pow {k : ℕ} : (p * X ^ k).eval x = p.eval x * x ^ k :=
   · simp
   · simp [pow_succ', ← mul_assoc, ih]
 #align polynomial.eval_mul_X_pow Polynomial.eval_mul_X_pow
+-/
 
 #print Polynomial.eval_sum /-
 theorem eval_sum (p : R[X]) (f : ℕ → R → R[X]) (x : R) :
@@ -529,15 +617,20 @@ def IsRoot (p : R[X]) (a : R) : Prop :=
 
 instance [DecidableEq R] : Decidable (IsRoot p a) := by unfold is_root <;> infer_instance
 
+#print Polynomial.IsRoot.def /-
 @[simp]
 theorem IsRoot.def : IsRoot p a ↔ p.eval a = 0 :=
   Iff.rfl
 #align polynomial.is_root.def Polynomial.IsRoot.def
+-/
 
+#print Polynomial.IsRoot.eq_zero /-
 theorem IsRoot.eq_zero (h : IsRoot p x) : eval x p = 0 :=
   h
 #align polynomial.is_root.eq_zero Polynomial.IsRoot.eq_zero
+-/
 
+#print Polynomial.coeff_zero_eq_eval_zero /-
 theorem coeff_zero_eq_eval_zero (p : R[X]) : coeff p 0 = p.eval 0 :=
   calc
     coeff p 0 = coeff p 0 * 0 ^ 0 := by simp
@@ -547,10 +640,13 @@ theorem coeff_zero_eq_eval_zero (p : R[X]) : coeff p 0 = p.eval 0 :=
       exact
         Finset.sum_eq_single _ (fun b _ hb => by simp [zero_pow (Nat.pos_of_ne_zero hb)]) (by simp)
 #align polynomial.coeff_zero_eq_eval_zero Polynomial.coeff_zero_eq_eval_zero
+-/
 
+#print Polynomial.zero_isRoot_of_coeff_zero_eq_zero /-
 theorem zero_isRoot_of_coeff_zero_eq_zero {p : R[X]} (hp : p.coeff 0 = 0) : IsRoot p 0 := by
   rwa [coeff_zero_eq_eval_zero] at hp 
 #align polynomial.zero_is_root_of_coeff_zero_eq_zero Polynomial.zero_isRoot_of_coeff_zero_eq_zero
+-/
 
 #print Polynomial.IsRoot.dvd /-
 theorem IsRoot.dvd {R : Type _} [CommSemiring R] {p q : R[X]} {x : R} (h : p.IsRoot x)
@@ -559,8 +655,10 @@ theorem IsRoot.dvd {R : Type _} [CommSemiring R] {p q : R[X]} {x : R} (h : p.IsR
 #align polynomial.is_root.dvd Polynomial.IsRoot.dvd
 -/
 
+#print Polynomial.not_isRoot_C /-
 theorem not_isRoot_C (r a : R) (hr : r ≠ 0) : ¬IsRoot (C r) a := by simpa using hr
 #align polynomial.not_is_root_C Polynomial.not_isRoot_C
+-/
 
 #print Polynomial.eval_surjective /-
 theorem eval_surjective (x : R) : Function.Surjective <| eval x := fun y => ⟨C y, eval_C⟩
@@ -578,8 +676,10 @@ def comp (p q : R[X]) : R[X] :=
 #align polynomial.comp Polynomial.comp
 -/
 
+#print Polynomial.comp_eq_sum_left /-
 theorem comp_eq_sum_left : p.comp q = p.Sum fun e a => C a * q ^ e := by rw [comp, eval₂_eq_sum]
 #align polynomial.comp_eq_sum_left Polynomial.comp_eq_sum_left
+-/
 
 #print Polynomial.comp_X /-
 @[simp]
@@ -597,14 +697,18 @@ theorem X_comp : X.comp p = p :=
 #align polynomial.X_comp Polynomial.X_comp
 -/
 
+#print Polynomial.comp_C /-
 @[simp]
 theorem comp_C : p.comp (C a) = C (p.eval a) := by simp [comp, (C : R →+* _).map_sum]
 #align polynomial.comp_C Polynomial.comp_C
+-/
 
+#print Polynomial.C_comp /-
 @[simp]
 theorem C_comp : (C a).comp p = C a :=
   eval₂_C _ _
 #align polynomial.C_comp Polynomial.C_comp
+-/
 
 #print Polynomial.nat_cast_comp /-
 @[simp]
@@ -612,9 +716,11 @@ theorem nat_cast_comp {n : ℕ} : (n : R[X]).comp p = n := by rw [← C_eq_nat_c
 #align polynomial.nat_cast_comp Polynomial.nat_cast_comp
 -/
 
+#print Polynomial.comp_zero /-
 @[simp]
 theorem comp_zero : p.comp (0 : R[X]) = C (p.eval 0) := by rw [← C_0, comp_C]
 #align polynomial.comp_zero Polynomial.comp_zero
+-/
 
 #print Polynomial.zero_comp /-
 @[simp]
@@ -622,9 +728,11 @@ theorem zero_comp : comp (0 : R[X]) p = 0 := by rw [← C_0, C_comp]
 #align polynomial.zero_comp Polynomial.zero_comp
 -/
 
+#print Polynomial.comp_one /-
 @[simp]
 theorem comp_one : p.comp 1 = C (p.eval 1) := by rw [← C_1, comp_C]
 #align polynomial.comp_one Polynomial.comp_one
+-/
 
 #print Polynomial.one_comp /-
 @[simp]
@@ -639,10 +747,12 @@ theorem add_comp : (p + q).comp r = p.comp r + q.comp r :=
 #align polynomial.add_comp Polynomial.add_comp
 -/
 
+#print Polynomial.monomial_comp /-
 @[simp]
 theorem monomial_comp (n : ℕ) : (monomial n a).comp p = C a * p ^ n :=
   eval₂_monomial _ _
 #align polynomial.monomial_comp Polynomial.monomial_comp
+-/
 
 #print Polynomial.mul_X_comp /-
 @[simp]
@@ -674,6 +784,7 @@ theorem mul_X_pow_comp {k : ℕ} : (p * X ^ k).comp r = p.comp r * r ^ k :=
 #align polynomial.mul_X_pow_comp Polynomial.mul_X_pow_comp
 -/
 
+#print Polynomial.C_mul_comp /-
 @[simp]
 theorem C_mul_comp : (C a * p).comp r = C a * p.comp r :=
   by
@@ -681,6 +792,7 @@ theorem C_mul_comp : (C a * p).comp r = C a * p.comp r :=
   · intro p q hp hq; simp [hp, hq, mul_add]
   · intro n b; simp [mul_assoc]
 #align polynomial.C_mul_comp Polynomial.C_mul_comp
+-/
 
 #print Polynomial.nat_cast_mul_comp /-
 @[simp]
@@ -718,11 +830,13 @@ theorem bit1_comp : comp (bit1 p : R[X]) q = bit1 (p.comp q) := by
 #align polynomial.bit1_comp Polynomial.bit1_comp
 -/
 
+#print Polynomial.smul_comp /-
 @[simp]
 theorem smul_comp [Monoid S] [DistribMulAction S R] [IsScalarTower S R R] (s : S) (p q : R[X]) :
     (s • p).comp q = s • p.comp q := by
   rw [← smul_one_smul R s p, comp, comp, eval₂_smul, ← smul_eq_C_mul, smul_assoc, one_smul]
 #align polynomial.smul_comp Polynomial.smul_comp
+-/
 
 #print Polynomial.comp_assoc /-
 theorem comp_assoc {R : Type _} [CommSemiring R] (φ ψ χ : R[X]) :
@@ -732,6 +846,7 @@ theorem comp_assoc {R : Type _} [CommSemiring R] (φ ψ χ : R[X]) :
 #align polynomial.comp_assoc Polynomial.comp_assoc
 -/
 
+#print Polynomial.coeff_comp_degree_mul_degree /-
 theorem coeff_comp_degree_mul_degree (hqd0 : natDegree q ≠ 0) :
     coeff (p.comp q) (natDegree p * natDegree q) = leadingCoeff p * leadingCoeff q ^ natDegree p :=
   by
@@ -745,6 +860,7 @@ theorem coeff_comp_degree_mul_degree (hqd0 : natDegree q ≠ 0) :
     exact lt_of_le_of_ne (le_nat_degree_of_mem_supp _ hbs) hbp
   · simp (config := { contextual := true })
 #align polynomial.coeff_comp_degree_mul_degree Polynomial.coeff_comp_degree_mul_degree
+-/
 
 end Comp
 
@@ -761,10 +877,12 @@ def map : R[X] → S[X] :=
 #align polynomial.map Polynomial.map
 -/
 
+#print Polynomial.map_C /-
 @[simp]
 theorem map_C : (C a).map f = C (f a) :=
   eval₂_C _ _
 #align polynomial.map_C Polynomial.map_C
+-/
 
 #print Polynomial.map_X /-
 @[simp]
@@ -773,12 +891,14 @@ theorem map_X : X.map f = X :=
 #align polynomial.map_X Polynomial.map_X
 -/
 
+#print Polynomial.map_monomial /-
 @[simp]
 theorem map_monomial {n a} : (monomial n a).map f = monomial n (f a) :=
   by
   dsimp only [map]
   rw [eval₂_monomial, ← C_mul_X_pow_eq_monomial]; rfl
 #align polynomial.map_monomial Polynomial.map_monomial
+-/
 
 #print Polynomial.map_zero /-
 @[simp]
@@ -808,10 +928,12 @@ protected theorem map_mul : (p * q).map f = p.map f * q.map f := by rw [map, eva
 #align polynomial.map_mul Polynomial.map_mul
 -/
 
+#print Polynomial.map_smul /-
 @[simp]
 protected theorem map_smul (r : R) : (r • p).map f = f r • p.map f := by
   rw [map, eval₂_smul, RingHom.comp_apply, C_mul']
 #align polynomial.map_smul Polynomial.map_smul
+-/
 
 #print Polynomial.mapRingHom /-
 -- `map` is a ring-hom unconditionally, and theoretically the definition could be replaced,
@@ -831,10 +953,12 @@ def mapRingHom (f : R →+* S) : R[X] →+* S[X]
 #align polynomial.map_ring_hom Polynomial.mapRingHom
 -/
 
+#print Polynomial.coe_mapRingHom /-
 @[simp]
 theorem coe_mapRingHom (f : R →+* S) : ⇑(mapRingHom f) = map f :=
   rfl
 #align polynomial.coe_map_ring_hom Polynomial.coe_mapRingHom
+-/
 
 #print Polynomial.map_nat_cast /-
 -- This is protected to not clash with the global `map_nat_cast`.
@@ -865,6 +989,7 @@ theorem map_dvd (f : R →+* S) {x y : R[X]} : x ∣ y → x.map f ∣ y.map f :
 #align polynomial.map_dvd Polynomial.map_dvd
 -/
 
+#print Polynomial.coeff_map /-
 @[simp]
 theorem coeff_map (n : ℕ) : coeff (p.map f) n = f (coeff p n) :=
   by
@@ -874,13 +999,16 @@ theorem coeff_map (n : ℕ) : coeff (p.map f) n = f (coeff p n) :=
   simp [Function.comp, coeff_C_mul_X_pow, f.map_mul]
   split_ifs <;> simp [f.map_zero]
 #align polynomial.coeff_map Polynomial.coeff_map
+-/
 
+#print Polynomial.mapEquiv /-
 /-- If `R` and `S` are isomorphic, then so are their polynomial rings. -/
 @[simps]
 def mapEquiv (e : R ≃+* S) : R[X] ≃+* S[X] :=
   RingEquiv.ofHomInv (mapRingHom (e : R →+* S)) (mapRingHom (e.symm : S →+* R)) (by ext <;> simp)
     (by ext <;> simp)
 #align polynomial.map_equiv Polynomial.mapEquiv
+-/
 
 #print Polynomial.map_map /-
 theorem map_map [Semiring T] (g : S →+* T) (p : R[X]) : (p.map f).map g = p.map (g.comp f) :=
@@ -903,10 +1031,13 @@ theorem eval₂_eq_eval_map {x : S} : p.eval₂ f x = (p.map f).eval x :=
 #align polynomial.eval₂_eq_eval_map Polynomial.eval₂_eq_eval_map
 -/
 
+#print Polynomial.map_injective /-
 theorem map_injective (hf : Function.Injective f) : Function.Injective (map f) := fun p q h =>
   ext fun m => hf <| by rw [← coeff_map f, ← coeff_map f, h]
 #align polynomial.map_injective Polynomial.map_injective
+-/
 
+#print Polynomial.map_surjective /-
 theorem map_surjective (hf : Function.Surjective f) : Function.Surjective (map f) := fun p =>
   Polynomial.induction_on' p
     (fun p q hp hq =>
@@ -917,6 +1048,7 @@ theorem map_surjective (hf : Function.Surjective f) : Function.Surjective (map f
     let ⟨r, hr⟩ := hf s
     ⟨monomial n r, by rw [map_monomial f, hr]⟩
 #align polynomial.map_surjective Polynomial.map_surjective
+-/
 
 #print Polynomial.degree_map_le /-
 theorem degree_map_le (p : R[X]) : degree (p.map f) ≤ degree p :=
@@ -935,14 +1067,19 @@ theorem natDegree_map_le (p : R[X]) : natDegree (p.map f) ≤ natDegree p :=
 
 variable {f}
 
+#print Polynomial.map_eq_zero_iff /-
 protected theorem map_eq_zero_iff (hf : Function.Injective f) : p.map f = 0 ↔ p = 0 :=
   map_eq_zero_iff (mapRingHom f) (map_injective f hf)
 #align polynomial.map_eq_zero_iff Polynomial.map_eq_zero_iff
+-/
 
+#print Polynomial.map_ne_zero_iff /-
 protected theorem map_ne_zero_iff (hf : Function.Injective f) : p.map f ≠ 0 ↔ p ≠ 0 :=
   (Polynomial.map_eq_zero_iff hf).Not
 #align polynomial.map_ne_zero_iff Polynomial.map_ne_zero_iff
+-/
 
+#print Polynomial.map_monic_eq_zero_iff /-
 theorem map_monic_eq_zero_iff (hp : p.Monic) : p.map f = 0 ↔ ∀ x, f x = 0 :=
   ⟨fun hfp x =>
     calc
@@ -951,6 +1088,7 @@ theorem map_monic_eq_zero_iff (hp : p.Monic) : p.map f = 0 ↔ ∀ x, f x = 0 :=
       _ = 0 := by simp only [hfp, MulZeroClass.mul_zero, coeff_zero],
     fun h => ext fun n => by simp only [h, coeff_map, coeff_zero]⟩
 #align polynomial.map_monic_eq_zero_iff Polynomial.map_monic_eq_zero_iff
+-/
 
 #print Polynomial.map_monic_ne_zero /-
 theorem map_monic_ne_zero (hp : p.Monic) [Nontrivial S] : p.map f ≠ 0 := fun h =>
@@ -958,6 +1096,7 @@ theorem map_monic_ne_zero (hp : p.Monic) [Nontrivial S] : p.map f ≠ 0 := fun h
 #align polynomial.map_monic_ne_zero Polynomial.map_monic_ne_zero
 -/
 
+#print Polynomial.degree_map_eq_of_leadingCoeff_ne_zero /-
 theorem degree_map_eq_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCoeff p) ≠ 0) :
     degree (p.map f) = degree p :=
   le_antisymm (degree_map_le f _) <|
@@ -968,18 +1107,23 @@ theorem degree_map_eq_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCo
     rw [coeff_map]
     exact hf
 #align polynomial.degree_map_eq_of_leading_coeff_ne_zero Polynomial.degree_map_eq_of_leadingCoeff_ne_zero
+-/
 
+#print Polynomial.natDegree_map_of_leadingCoeff_ne_zero /-
 theorem natDegree_map_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCoeff p) ≠ 0) :
     natDegree (p.map f) = natDegree p :=
   natDegree_eq_of_degree_eq (degree_map_eq_of_leadingCoeff_ne_zero f hf)
 #align polynomial.nat_degree_map_of_leading_coeff_ne_zero Polynomial.natDegree_map_of_leadingCoeff_ne_zero
+-/
 
+#print Polynomial.leadingCoeff_map_of_leadingCoeff_ne_zero /-
 theorem leadingCoeff_map_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCoeff p) ≠ 0) :
     leadingCoeff (p.map f) = f (leadingCoeff p) :=
   by
   unfold leading_coeff
   rw [coeff_map, nat_degree_map_of_leading_coeff_ne_zero f hf]
 #align polynomial.leading_coeff_map_of_leading_coeff_ne_zero Polynomial.leadingCoeff_map_of_leadingCoeff_ne_zero
+-/
 
 variable (f)
 
@@ -1011,6 +1155,7 @@ protected theorem map_pow (n : ℕ) : (p ^ n).map f = p.map f ^ n :=
 #align polynomial.map_pow Polynomial.map_pow
 -/
 
+#print Polynomial.mem_map_rangeS /-
 theorem mem_map_rangeS {p : S[X]} : p ∈ (mapRingHom f).srange ↔ ∀ n, p.coeff n ∈ f.srange :=
   by
   constructor
@@ -1022,11 +1167,14 @@ theorem mem_map_rangeS {p : S[X]} : p ∈ (mapRingHom f).srange ↔ ∀ n, p.coe
     use C c * X ^ i
     rw [coe_map_ring_hom, Polynomial.map_mul, map_C, hc, Polynomial.map_pow, map_X]
 #align polynomial.mem_map_srange Polynomial.mem_map_rangeS
+-/
 
+#print Polynomial.mem_map_range /-
 theorem mem_map_range {R S : Type _} [Ring R] [Ring S] (f : R →+* S) {p : S[X]} :
     p ∈ (mapRingHom f).range ↔ ∀ n, p.coeff n ∈ f.range :=
   mem_map_rangeS f
 #align polynomial.mem_map_range Polynomial.mem_map_range
+-/
 
 #print Polynomial.eval₂_map /-
 theorem eval₂_map [Semiring T] (g : S →+* T) (x : T) : (p.map f).eval₂ g x = p.eval₂ (g.comp f) x :=
@@ -1040,10 +1188,12 @@ theorem eval_map (x : S) : (p.map f).eval x = p.eval₂ f x :=
 #align polynomial.eval_map Polynomial.eval_map
 -/
 
+#print Polynomial.map_sum /-
 protected theorem map_sum {ι : Type _} (g : ι → R[X]) (s : Finset ι) :
     (∑ i in s, g i).map f = ∑ i in s, (g i).map f :=
   (mapRingHom f).map_sum _ _
 #align polynomial.map_sum Polynomial.map_sum
+-/
 
 #print Polynomial.map_comp /-
 theorem map_comp (p q : R[X]) : map f (p.comp q) = (map f p).comp (map f q) :=
@@ -1057,11 +1207,14 @@ theorem map_comp (p q : R[X]) : map f (p.comp q) = (map f p).comp (map f q) :=
 #align polynomial.map_comp Polynomial.map_comp
 -/
 
+#print Polynomial.eval_zero_map /-
 @[simp]
 theorem eval_zero_map (f : R →+* S) (p : R[X]) : (p.map f).eval 0 = f (p.eval 0) := by
   simp [← coeff_zero_eq_eval_zero]
 #align polynomial.eval_zero_map Polynomial.eval_zero_map
+-/
 
+#print Polynomial.eval_one_map /-
 @[simp]
 theorem eval_one_map (f : R →+* S) (p : R[X]) : (p.map f).eval 1 = f (p.eval 1) :=
   by
@@ -1069,7 +1222,9 @@ theorem eval_one_map (f : R →+* S) (p : R[X]) : (p.map f).eval 1 = f (p.eval 1
   · intro p q hp hq; simp only [hp, hq, Polynomial.map_add, RingHom.map_add, eval_add]
   · intro n r; simp only [one_pow, mul_one, eval_monomial, map_monomial]
 #align polynomial.eval_one_map Polynomial.eval_one_map
+-/
 
+#print Polynomial.eval_nat_cast_map /-
 @[simp]
 theorem eval_nat_cast_map (f : R →+* S) (p : R[X]) (n : ℕ) : (p.map f).eval n = f (p.eval n) :=
   by
@@ -1077,7 +1232,9 @@ theorem eval_nat_cast_map (f : R →+* S) (p : R[X]) (n : ℕ) : (p.map f).eval
   · intro p q hp hq; simp only [hp, hq, Polynomial.map_add, RingHom.map_add, eval_add]
   · intro n r; simp only [map_natCast f, eval_monomial, map_monomial, f.map_pow, f.map_mul]
 #align polynomial.eval_nat_cast_map Polynomial.eval_nat_cast_map
+-/
 
+#print Polynomial.eval_int_cast_map /-
 @[simp]
 theorem eval_int_cast_map {R S : Type _} [Ring R] [Ring S] (f : R →+* S) (p : R[X]) (i : ℤ) :
     (p.map f).eval i = f (p.eval i) :=
@@ -1086,6 +1243,7 @@ theorem eval_int_cast_map {R S : Type _} [Ring R] [Ring S] (f : R →+* S) (p :
   · intro p q hp hq; simp only [hp, hq, Polynomial.map_add, RingHom.map_add, eval_add]
   · intro n r; simp only [map_intCast, eval_monomial, map_monomial, map_pow, map_mul]
 #align polynomial.eval_int_cast_map Polynomial.eval_int_cast_map
+-/
 
 end Map
 
@@ -1100,9 +1258,11 @@ section HomEval₂
 
 variable [Semiring S] [Semiring T] (f : R →+* S) (g : S →+* T) (p)
 
+#print Polynomial.hom_eval₂ /-
 theorem hom_eval₂ (x : S) : g (p.eval₂ f x) = p.eval₂ (g.comp f) (g x) := by
   rw [← eval₂_map, eval₂_at_apply, eval_map]
 #align polynomial.hom_eval₂ Polynomial.hom_eval₂
+-/
 
 end HomEval₂
 
@@ -1116,9 +1276,11 @@ section
 
 variable [Semiring R] {p q : R[X]} {x : R} [Semiring S] (f : R →+* S)
 
+#print Polynomial.eval₂_hom /-
 theorem eval₂_hom (x : R) : p.eval₂ f (f x) = f (p.eval x) :=
   RingHom.comp_id f ▸ (hom_eval₂ p (RingHom.id R) f x).symm
 #align polynomial.eval₂_hom Polynomial.eval₂_hom
+-/
 
 end
 
@@ -1149,10 +1311,12 @@ section
 
 variable [CommSemiring R] {p q : R[X]} {x : R} [CommSemiring S] (f : R →+* S)
 
+#print Polynomial.eval_mul /-
 @[simp]
 theorem eval_mul : (p * q).eval x = p.eval x * q.eval x :=
   eval₂_mul _ _
 #align polynomial.eval_mul Polynomial.eval_mul
+-/
 
 #print Polynomial.evalRingHom /-
 /-- `eval r`, regarded as a ring homomorphism from `R[X]` to `R`. -/
@@ -1161,10 +1325,12 @@ def evalRingHom : R → R[X] →+* R :=
 #align polynomial.eval_ring_hom Polynomial.evalRingHom
 -/
 
+#print Polynomial.coe_evalRingHom /-
 @[simp]
 theorem coe_evalRingHom (r : R) : (evalRingHom r : R[X] → R) = eval r :=
   rfl
 #align polynomial.coe_eval_ring_hom Polynomial.coe_evalRingHom
+-/
 
 #print Polynomial.evalRingHom_zero /-
 theorem evalRingHom_zero : evalRingHom 0 = constantCoeff :=
@@ -1202,14 +1368,18 @@ def compRingHom : R[X] → R[X] →+* R[X] :=
 #align polynomial.comp_ring_hom Polynomial.compRingHom
 -/
 
+#print Polynomial.coe_compRingHom /-
 @[simp]
 theorem coe_compRingHom (q : R[X]) : (compRingHom q : R[X] → R[X]) = fun p => comp p q :=
   rfl
 #align polynomial.coe_comp_ring_hom Polynomial.coe_compRingHom
+-/
 
+#print Polynomial.coe_compRingHom_apply /-
 theorem coe_compRingHom_apply (p q : R[X]) : (compRingHom q : R[X] → R[X]) p = comp p q :=
   rfl
 #align polynomial.coe_comp_ring_hom_apply Polynomial.coe_compRingHom_apply
+-/
 
 #print Polynomial.root_mul_left_of_isRoot /-
 theorem root_mul_left_of_isRoot (p : R[X]) {q : R[X]} : IsRoot q a → IsRoot (p * q) a := fun H => by
@@ -1237,11 +1407,13 @@ theorem eval₂_finset_prod (s : Finset ι) (g : ι → R[X]) (x : S) :
 #align polynomial.eval₂_finset_prod Polynomial.eval₂_finset_prod
 -/
 
+#print Polynomial.eval_list_prod /-
 /-- Polynomial evaluation commutes with `list.prod`
 -/
 theorem eval_list_prod (l : List R[X]) (x : R) : eval x l.Prod = (l.map (eval x)).Prod :=
   (evalRingHom x).map_list_prod l
 #align polynomial.eval_list_prod Polynomial.eval_list_prod
+-/
 
 #print Polynomial.eval_multiset_prod /-
 /-- Polynomial evaluation commutes with `multiset.prod`
@@ -1251,12 +1423,14 @@ theorem eval_multiset_prod (s : Multiset R[X]) (x : R) : eval x s.Prod = (s.map
 #align polynomial.eval_multiset_prod Polynomial.eval_multiset_prod
 -/
 
+#print Polynomial.eval_prod /-
 /-- Polynomial evaluation commutes with `finset.prod`
 -/
 theorem eval_prod {ι : Type _} (s : Finset ι) (p : ι → R[X]) (x : R) :
     eval x (∏ j in s, p j) = ∏ j in s, eval x (p j) :=
   (evalRingHom x).map_prod _ _
 #align polynomial.eval_prod Polynomial.eval_prod
+-/
 
 #print Polynomial.list_prod_comp /-
 theorem list_prod_comp (l : List R[X]) (q : R[X]) :
@@ -1272,15 +1446,19 @@ theorem multiset_prod_comp (s : Multiset R[X]) (q : R[X]) :
 #align polynomial.multiset_prod_comp Polynomial.multiset_prod_comp
 -/
 
+#print Polynomial.prod_comp /-
 theorem prod_comp {ι : Type _} (s : Finset ι) (p : ι → R[X]) (q : R[X]) :
     (∏ j in s, p j).comp q = ∏ j in s, (p j).comp q :=
   map_prod (compRingHom q) _ _
 #align polynomial.prod_comp Polynomial.prod_comp
+-/
 
+#print Polynomial.isRoot_prod /-
 theorem isRoot_prod {R} [CommRing R] [IsDomain R] {ι : Type _} (s : Finset ι) (p : ι → R[X])
     (x : R) : IsRoot (∏ j in s, p j) x ↔ ∃ i ∈ s, IsRoot (p i) x := by
   simp only [is_root, eval_prod, Finset.prod_eq_zero_iff]
 #align polynomial.is_root_prod Polynomial.isRoot_prod
+-/
 
 #print Polynomial.eval_dvd /-
 theorem eval_dvd : p ∣ q → eval x p ∣ eval x q :=
@@ -1288,9 +1466,11 @@ theorem eval_dvd : p ∣ q → eval x p ∣ eval x q :=
 #align polynomial.eval_dvd Polynomial.eval_dvd
 -/
 
+#print Polynomial.eval_eq_zero_of_dvd_of_eval_eq_zero /-
 theorem eval_eq_zero_of_dvd_of_eval_eq_zero : p ∣ q → eval x p = 0 → eval x q = 0 :=
   eval₂_eq_zero_of_dvd_of_eval₂_eq_zero _ _
 #align polynomial.eval_eq_zero_of_dvd_of_eval_eq_zero Polynomial.eval_eq_zero_of_dvd_of_eval_eq_zero
+-/
 
 #print Polynomial.eval_geom_sum /-
 @[simp]
@@ -1314,11 +1494,13 @@ theorem support_map_subset [Semiring R] [Semiring S] (f : R →+* S) (p : R[X])
 #align polynomial.support_map_subset Polynomial.support_map_subset
 -/
 
+#print Polynomial.support_map_of_injective /-
 theorem support_map_of_injective [Semiring R] [Semiring S] (p : R[X]) {f : R →+* S}
     (hf : Function.Injective f) : (map f p).support = p.support := by
   simp_rw [Finset.ext_iff, mem_support_iff, coeff_map, ← map_zero f, hf.ne_iff, iff_self_iff,
     forall_const]
 #align polynomial.support_map_of_injective Polynomial.support_map_of_injective
+-/
 
 variable [CommSemiring R] [CommSemiring S] (f : R →+* S)
 
@@ -1328,24 +1510,32 @@ protected theorem map_multiset_prod (m : Multiset R[X]) : m.Prod.map f = (m.map
 #align polynomial.map_multiset_prod Polynomial.map_multiset_prod
 -/
 
+#print Polynomial.map_prod /-
 protected theorem map_prod {ι : Type _} (g : ι → R[X]) (s : Finset ι) :
     (∏ i in s, g i).map f = ∏ i in s, (g i).map f :=
   (mapRingHom f).map_prod _ _
 #align polynomial.map_prod Polynomial.map_prod
+-/
 
+#print Polynomial.IsRoot.map /-
 theorem IsRoot.map {f : R →+* S} {x : R} {p : R[X]} (h : IsRoot p x) : IsRoot (p.map f) (f x) := by
   rw [is_root, eval_map, eval₂_hom, h.eq_zero, f.map_zero]
 #align polynomial.is_root.map Polynomial.IsRoot.map
+-/
 
+#print Polynomial.IsRoot.of_map /-
 theorem IsRoot.of_map {R} [CommRing R] {f : R →+* S} {x : R} {p : R[X]} (h : IsRoot (p.map f) (f x))
     (hf : Function.Injective f) : IsRoot p x := by
   rwa [is_root, ← (injective_iff_map_eq_zero' f).mp hf, ← eval₂_hom, ← eval_map]
 #align polynomial.is_root.of_map Polynomial.IsRoot.of_map
+-/
 
+#print Polynomial.isRoot_map_iff /-
 theorem isRoot_map_iff {R : Type _} [CommRing R] {f : R →+* S} {x : R} {p : R[X]}
     (hf : Function.Injective f) : IsRoot (p.map f) (f x) ↔ IsRoot p x :=
   ⟨fun h => h.of_map hf, fun h => h.map⟩
 #align polynomial.is_root_map_iff Polynomial.isRoot_map_iff
+-/
 
 end Map
 
@@ -1355,58 +1545,80 @@ section Ring
 
 variable [Ring R] {p q r : R[X]}
 
+#print Polynomial.C_neg /-
 theorem C_neg : C (-a) = -C a :=
   RingHom.map_neg C a
 #align polynomial.C_neg Polynomial.C_neg
+-/
 
+#print Polynomial.C_sub /-
 theorem C_sub : C (a - b) = C a - C b :=
   RingHom.map_sub C a b
 #align polynomial.C_sub Polynomial.C_sub
+-/
 
+#print Polynomial.map_sub /-
 @[simp]
 protected theorem map_sub {S} [Ring S] (f : R →+* S) : (p - q).map f = p.map f - q.map f :=
   (mapRingHom f).map_sub p q
 #align polynomial.map_sub Polynomial.map_sub
+-/
 
+#print Polynomial.map_neg /-
 @[simp]
 protected theorem map_neg {S} [Ring S] (f : R →+* S) : (-p).map f = -p.map f :=
   (mapRingHom f).map_neg p
 #align polynomial.map_neg Polynomial.map_neg
+-/
 
+#print Polynomial.map_int_cast /-
 @[simp]
 theorem map_int_cast {S} [Ring S] (f : R →+* S) (n : ℤ) : map f ↑n = ↑n :=
   map_intCast (mapRingHom f) n
 #align polynomial.map_int_cast Polynomial.map_int_cast
+-/
 
+#print Polynomial.eval_int_cast /-
 @[simp]
 theorem eval_int_cast {n : ℤ} {x : R} : (n : R[X]).eval x = n := by
   simp only [← C_eq_int_cast, eval_C]
 #align polynomial.eval_int_cast Polynomial.eval_int_cast
+-/
 
+#print Polynomial.eval₂_neg /-
 @[simp]
 theorem eval₂_neg {S} [Ring S] (f : R →+* S) {x : S} : (-p).eval₂ f x = -p.eval₂ f x := by
   rw [eq_neg_iff_add_eq_zero, ← eval₂_add, add_left_neg, eval₂_zero]
 #align polynomial.eval₂_neg Polynomial.eval₂_neg
+-/
 
+#print Polynomial.eval₂_sub /-
 @[simp]
 theorem eval₂_sub {S} [Ring S] (f : R →+* S) {x : S} :
     (p - q).eval₂ f x = p.eval₂ f x - q.eval₂ f x := by
   rw [sub_eq_add_neg, eval₂_add, eval₂_neg, sub_eq_add_neg]
 #align polynomial.eval₂_sub Polynomial.eval₂_sub
+-/
 
+#print Polynomial.eval_neg /-
 @[simp]
 theorem eval_neg (p : R[X]) (x : R) : (-p).eval x = -p.eval x :=
   eval₂_neg _
 #align polynomial.eval_neg Polynomial.eval_neg
+-/
 
+#print Polynomial.eval_sub /-
 @[simp]
 theorem eval_sub (p q : R[X]) (x : R) : (p - q).eval x = p.eval x - q.eval x :=
   eval₂_sub _
 #align polynomial.eval_sub Polynomial.eval_sub
+-/
 
+#print Polynomial.root_X_sub_C /-
 theorem root_X_sub_C : IsRoot (X - C a) b ↔ a = b := by
   rw [is_root.def, eval_sub, eval_X, eval_C, sub_eq_zero, eq_comm]
 #align polynomial.root_X_sub_C Polynomial.root_X_sub_C
+-/
 
 #print Polynomial.neg_comp /-
 @[simp]

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

@@ -546,7 +546,6 @@ theorem coeff_zero_eq_eval_zero (p : R[X]) : coeff p 0 = p.eval 0 :=
       rw [eval_eq_sum]
       exact
         Finset.sum_eq_single _ (fun b _ hb => by simp [zero_pow (Nat.pos_of_ne_zero hb)]) (by simp)
-    
 #align polynomial.coeff_zero_eq_eval_zero Polynomial.coeff_zero_eq_eval_zero
 
 theorem zero_isRoot_of_coeff_zero_eq_zero {p : R[X]} (hp : p.coeff 0 = 0) : IsRoot p 0 := by
@@ -949,8 +948,7 @@ theorem map_monic_eq_zero_iff (hp : p.Monic) : p.map f = 0 ↔ ∀ x, f x = 0 :=
     calc
       f x = f x * f p.leadingCoeff := by simp only [mul_one, hp.leading_coeff, f.map_one]
       _ = f x * (p.map f).coeff p.natDegree := (congr_arg _ (coeff_map _ _).symm)
-      _ = 0 := by simp only [hfp, MulZeroClass.mul_zero, coeff_zero]
-      ,
+      _ = 0 := by simp only [hfp, MulZeroClass.mul_zero, coeff_zero],
     fun h => ext fun n => by simp only [h, coeff_map, coeff_zero]⟩
 #align polynomial.map_monic_eq_zero_iff Polynomial.map_monic_eq_zero_iff
 

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

@@ -199,7 +199,7 @@ theorem eval₂_mul_noncomm (hf : ∀ k, Commute (f <| q.coeff k) x) :
     eval₂ f x (p * q) = eval₂ f x p * eval₂ f x q :=
   by
   rcases p with ⟨⟩; rcases q with ⟨⟩
-  simp only [coeff] at hf
+  simp only [coeff] at hf 
   simp only [← of_finsupp_mul, eval₂_of_finsupp]
   exact lift_nc_mul _ _ p q fun k n hn => (hf k).pow_right n
 #align polynomial.eval₂_mul_noncomm Polynomial.eval₂_mul_noncomm
@@ -232,7 +232,7 @@ theorem eval₂_list_prod_noncomm (ps : List R[X])
   by
   induction' ps using List.reverseRecOn with ps p ihp
   · simp
-  · simp only [List.forall_mem_append, List.forall_mem_singleton] at hf
+  · simp only [List.forall_mem_append, List.forall_mem_singleton] at hf 
     simp [eval₂_mul_noncomm _ _ hf.2, ihp hf.1]
 #align polynomial.eval₂_list_prod_noncomm Polynomial.eval₂_list_prod_noncomm
 
@@ -550,7 +550,7 @@ theorem coeff_zero_eq_eval_zero (p : R[X]) : coeff p 0 = p.eval 0 :=
 #align polynomial.coeff_zero_eq_eval_zero Polynomial.coeff_zero_eq_eval_zero
 
 theorem zero_isRoot_of_coeff_zero_eq_zero {p : R[X]} (hp : p.coeff 0 = 0) : IsRoot p 0 := by
-  rwa [coeff_zero_eq_eval_zero] at hp
+  rwa [coeff_zero_eq_eval_zero] at hp 
 #align polynomial.zero_is_root_of_coeff_zero_eq_zero Polynomial.zero_isRoot_of_coeff_zero_eq_zero
 
 #print Polynomial.IsRoot.dvd /-
@@ -729,7 +729,7 @@ theorem smul_comp [Monoid S] [DistribMulAction S R] [IsScalarTower S R R] (s : S
 theorem comp_assoc {R : Type _} [CommSemiring R] (φ ψ χ : R[X]) :
     (φ.comp ψ).comp χ = φ.comp (ψ.comp χ) := by
   apply Polynomial.induction_on φ <;>
-    · intros ; simp_all only [add_comp, mul_comp, C_comp, X_comp, pow_succ', ← mul_assoc]
+    · intros; simp_all only [add_comp, mul_comp, C_comp, X_comp, pow_succ', ← mul_assoc]
 #align polynomial.comp_assoc Polynomial.comp_assoc
 -/
 
@@ -923,7 +923,7 @@ theorem map_surjective (hf : Function.Surjective f) : Function.Surjective (map f
 theorem degree_map_le (p : R[X]) : degree (p.map f) ≤ degree p :=
   by
   apply (degree_le_iff_coeff_zero _ _).2 fun m hm => _
-  rw [degree_lt_iff_coeff_zero] at hm
+  rw [degree_lt_iff_coeff_zero] at hm 
   simp [hm m le_rfl]
 #align polynomial.degree_map_le Polynomial.degree_map_le
 -/

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

@@ -26,7 +26,7 @@ noncomputable section
 
 open Finset AddMonoidAlgebra
 
-open BigOperators Polynomial
+open scoped BigOperators Polynomial
 
 namespace Polynomial
 
@@ -919,12 +919,14 @@ theorem map_surjective (hf : Function.Surjective f) : Function.Surjective (map f
     ⟨monomial n r, by rw [map_monomial f, hr]⟩
 #align polynomial.map_surjective Polynomial.map_surjective
 
+#print Polynomial.degree_map_le /-
 theorem degree_map_le (p : R[X]) : degree (p.map f) ≤ degree p :=
   by
   apply (degree_le_iff_coeff_zero _ _).2 fun m hm => _
   rw [degree_lt_iff_coeff_zero] at hm
   simp [hm m le_rfl]
 #align polynomial.degree_map_le Polynomial.degree_map_le
+-/
 
 #print Polynomial.natDegree_map_le /-
 theorem natDegree_map_le (p : R[X]) : natDegree (p.map f) ≤ natDegree p :=

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

@@ -52,33 +52,15 @@ irreducible_def eval₂ (p : R[X]) : S :=
 #align polynomial.eval₂ Polynomial.eval₂
 -/
 
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 theorem eval₂_eq_sum {f : R →+* S} {x : S} : p.eval₂ f x = p.Sum fun e a => f a * x ^ e := by
   rw [eval₂]
 #align polynomial.eval₂_eq_sum Polynomial.eval₂_eq_sum
 
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 theorem eval₂_congr {R S : Type _} [Semiring R] [Semiring S] {f g : R →+* S} {s t : S}
     {φ ψ : R[X]} : f = g → s = t → φ = ψ → eval₂ f s φ = eval₂ g t ψ := by
   rintro rfl rfl rfl <;> rfl
 #align polynomial.eval₂_congr Polynomial.eval₂_congr
 
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 @[simp]
 theorem eval₂_at_zero : p.eval₂ f 0 = f (coeff p 0) := by
   simp (config := { contextual := true }) only [eval₂_eq_sum, zero_pow_eq, mul_ite,
@@ -86,22 +68,10 @@ theorem eval₂_at_zero : p.eval₂ f 0 = f (coeff p 0) := by
     ite_eq_left_iff, RingHom.map_zero, imp_true_iff, eq_self_iff_true]
 #align polynomial.eval₂_at_zero Polynomial.eval₂_at_zero
 
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 @[simp]
 theorem eval₂_zero : (0 : R[X]).eval₂ f x = 0 := by simp [eval₂_eq_sum]
 #align polynomial.eval₂_zero Polynomial.eval₂_zero
 
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 @[simp]
 theorem eval₂_C : (C a).eval₂ f x = f a := by simp [eval₂_eq_sum]
 #align polynomial.eval₂_C Polynomial.eval₂_C
@@ -112,12 +82,6 @@ theorem eval₂_X : X.eval₂ f x = x := by simp [eval₂_eq_sum]
 #align polynomial.eval₂_X Polynomial.eval₂_X
 -/
 
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 @[simp]
 theorem eval₂_monomial {n : ℕ} {r : R} : (monomial n r).eval₂ f x = f r * x ^ n := by
   simp [eval₂_eq_sum]
@@ -133,12 +97,6 @@ theorem eval₂_X_pow {n : ℕ} : (X ^ n).eval₂ f x = x ^ n :=
 #align polynomial.eval₂_X_pow Polynomial.eval₂_X_pow
 -/
 
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 @[simp]
 theorem eval₂_add : (p + q).eval₂ f x = p.eval₂ f x + q.eval₂ f x := by simp only [eval₂_eq_sum];
   apply sum_add_index <;> simp [add_mul]
@@ -150,33 +108,15 @@ theorem eval₂_one : (1 : R[X]).eval₂ f x = 1 := by rw [← C_1, eval₂_C, f
 #align polynomial.eval₂_one Polynomial.eval₂_one
 -/
 
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 @[simp]
 theorem eval₂_bit0 : (bit0 p).eval₂ f x = bit0 (p.eval₂ f x) := by rw [bit0, eval₂_add, bit0]
 #align polynomial.eval₂_bit0 Polynomial.eval₂_bit0
 
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 @[simp]
 theorem eval₂_bit1 : (bit1 p).eval₂ f x = bit1 (p.eval₂ f x) := by
   rw [bit1, eval₂_add, eval₂_bit0, eval₂_one, bit1]
 #align polynomial.eval₂_bit1 Polynomial.eval₂_bit1
 
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 @[simp]
 theorem eval₂_smul (g : R →+* S) (p : R[X]) (x : S) {s : R} :
     eval₂ g x (s • p) = g s * eval₂ g x p :=
@@ -232,12 +172,6 @@ theorem eval₂_sum (p : T[X]) (g : ℕ → T → R[X]) (x : S) :
 #align polynomial.eval₂_sum Polynomial.eval₂_sum
 -/
 
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 theorem eval₂_list_sum (l : List R[X]) (x : S) : eval₂ f x l.Sum = (l.map (eval₂ f x)).Sum :=
   map_list_sum (eval₂AddMonoidHom f x) l
 #align polynomial.eval₂_list_sum Polynomial.eval₂_list_sum
@@ -256,20 +190,11 @@ theorem eval₂_finset_sum (s : Finset ι) (g : ι → R[X]) (x : S) :
 #align polynomial.eval₂_finset_sum Polynomial.eval₂_finset_sum
 -/
 
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 theorem eval₂_ofFinsupp {f : R →+* S} {x : S} {p : AddMonoidAlgebra R ℕ} :
     eval₂ f x (⟨p⟩ : R[X]) = liftNC (↑f) (powersHom S x) p := by
   simp only [eval₂_eq_sum, Sum, to_finsupp_sum, support, coeff]; rfl
 #align polynomial.eval₂_of_finsupp Polynomial.eval₂_ofFinsupp
 
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 theorem eval₂_mul_noncomm (hf : ∀ k, Commute (f <| q.coeff k) x) :
     eval₂ f x (p * q) = eval₂ f x p * eval₂ f x q :=
   by
@@ -279,12 +204,6 @@ theorem eval₂_mul_noncomm (hf : ∀ k, Commute (f <| q.coeff k) x) :
   exact lift_nc_mul _ _ p q fun k n hn => (hf k).pow_right n
 #align polynomial.eval₂_mul_noncomm Polynomial.eval₂_mul_noncomm
 
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 @[simp]
 theorem eval₂_mul_X : eval₂ f x (p * X) = eval₂ f x p * x :=
   by
@@ -294,22 +213,10 @@ theorem eval₂_mul_X : eval₂ f x (p * X) = eval₂ f x p * x :=
   · simp [coeff_X_of_ne_one hk]
 #align polynomial.eval₂_mul_X Polynomial.eval₂_mul_X
 
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 @[simp]
 theorem eval₂_X_mul : eval₂ f x (X * p) = eval₂ f x p * x := by rw [X_mul, eval₂_mul_X]
 #align polynomial.eval₂_X_mul Polynomial.eval₂_X_mul
 
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(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 a)))
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 theorem eval₂_mul_C' (h : Commute (f a) x) : eval₂ f x (p * C a) = eval₂ f x p * f a :=
   by
   rw [eval₂_mul_noncomm, eval₂_C]
@@ -319,12 +226,6 @@ theorem eval₂_mul_C' (h : Commute (f a) x) : eval₂ f x (p * C a) = eval₂ f
   · simp only [coeff_C_ne_zero hk, RingHom.map_zero, Commute.zero_left]
 #align polynomial.eval₂_mul_C' Polynomial.eval₂_mul_C'
 
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 theorem eval₂_list_prod_noncomm (ps : List R[X])
     (hf : ∀ p ∈ ps, ∀ (k), Commute (f <| coeff p k) x) :
     eval₂ f x ps.Prod = (ps.map (Polynomial.eval₂ f x)).Prod :=
@@ -335,12 +236,6 @@ theorem eval₂_list_prod_noncomm (ps : List R[X])
     simp [eval₂_mul_noncomm _ _ hf.2, ihp hf.1]
 #align polynomial.eval₂_list_prod_noncomm Polynomial.eval₂_list_prod_noncomm
 
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 /-- `eval₂` as a `ring_hom` for noncommutative rings -/
 def eval₂RingHom' (f : R →+* S) (x : S) (hf : ∀ a, Commute (f a) x) : R[X] →+* S
     where
@@ -366,23 +261,11 @@ section
 
 variable [Semiring S] (f : R →+* S) (x : S)
 
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 theorem eval₂_eq_sum_range :
     p.eval₂ f x = ∑ i in Finset.range (p.natDegree + 1), f (p.coeff i) * x ^ i :=
   trans (congr_arg _ p.as_sum_range) (trans (eval₂_finset_sum f _ _ x) (congr_arg _ (by simp)))
 #align polynomial.eval₂_eq_sum_range Polynomial.eval₂_eq_sum_range
 
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 theorem eval₂_eq_sum_range' (f : R →+* S) {p : R[X]} {n : ℕ} (hn : p.natDegree < n) (x : S) :
     eval₂ f x p = ∑ i in Finset.range n, f (p.coeff i) * x ^ i :=
   by
@@ -397,35 +280,17 @@ section
 
 variable [CommSemiring S] (f : R →+* S) (x : S)
 
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 @[simp]
 theorem eval₂_mul : (p * q).eval₂ f x = p.eval₂ f x * q.eval₂ f x :=
   eval₂_mul_noncomm _ _ fun k => Commute.all _ _
 #align polynomial.eval₂_mul Polynomial.eval₂_mul
 
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 theorem eval₂_mul_eq_zero_of_left (q : R[X]) (hp : p.eval₂ f x = 0) : (p * q).eval₂ f x = 0 :=
   by
   rw [eval₂_mul f x]
   exact mul_eq_zero_of_left hp (q.eval₂ f x)
 #align polynomial.eval₂_mul_eq_zero_of_left Polynomial.eval₂_mul_eq_zero_of_left
 
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 theorem eval₂_mul_eq_zero_of_right (p : R[X]) (hq : q.eval₂ f x = 0) : (p * q).eval₂ f x = 0 :=
   by
   rw [eval₂_mul f x]
@@ -441,12 +306,6 @@ def eval₂RingHom (f : R →+* S) (x : S) : R[X] →+* S :=
 #align polynomial.eval₂_ring_hom Polynomial.eval₂RingHom
 -/
 
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 @[simp]
 theorem coe_eval₂RingHom (f : R →+* S) (x) : ⇑(eval₂RingHom f x) = eval₂ f x :=
   rfl
@@ -464,23 +323,11 @@ theorem eval₂_dvd : p ∣ q → eval₂ f x p ∣ eval₂ f x q :=
 #align polynomial.eval₂_dvd Polynomial.eval₂_dvd
 -/
 
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 theorem eval₂_eq_zero_of_dvd_of_eval₂_eq_zero (h : p ∣ q) (h0 : eval₂ f x p = 0) :
     eval₂ f x q = 0 :=
   zero_dvd_iff.mp (h0 ▸ eval₂_dvd f x h)
 #align polynomial.eval₂_eq_zero_of_dvd_of_eval₂_eq_zero Polynomial.eval₂_eq_zero_of_dvd_of_eval₂_eq_zero
 
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 theorem eval₂_list_prod (l : List R[X]) (x : S) : eval₂ f x l.Prod = (l.map (eval₂ f x)).Prod :=
   map_list_prod (eval₂RingHom f x) l
 #align polynomial.eval₂_list_prod Polynomial.eval₂_list_prod
@@ -500,43 +347,19 @@ def eval : R → R[X] → R :=
 #align polynomial.eval Polynomial.eval
 -/
 
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 theorem eval_eq_sum : p.eval x = p.Sum fun e a => a * x ^ e := by rw [eval, eval₂_eq_sum]; rfl
 #align polynomial.eval_eq_sum Polynomial.eval_eq_sum
 
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 theorem eval_eq_sum_range {p : R[X]} (x : R) :
     p.eval x = ∑ i in Finset.range (p.natDegree + 1), p.coeff i * x ^ i := by
   rw [eval_eq_sum, sum_over_range] <;> simp
 #align polynomial.eval_eq_sum_range Polynomial.eval_eq_sum_range
 
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 theorem eval_eq_sum_range' {p : R[X]} {n : ℕ} (hn : p.natDegree < n) (x : R) :
     p.eval x = ∑ i in Finset.range n, p.coeff i * x ^ i := by
   rw [eval_eq_sum, p.sum_over_range' _ _ hn] <;> simp
 #align polynomial.eval_eq_sum_range' Polynomial.eval_eq_sum_range'
 
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 @[simp]
 theorem eval₂_at_apply {S : Type _} [Semiring S] (f : R →+* S) (r : R) :
     p.eval₂ f (f r) = f (p.eval r) :=
@@ -545,12 +368,6 @@ theorem eval₂_at_apply {S : Type _} [Semiring S] (f : R →+* S) (r : R) :
   simp only [f.map_mul, f.map_pow]
 #align polynomial.eval₂_at_apply Polynomial.eval₂_at_apply
 
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 @[simp]
 theorem eval₂_at_one {S : Type _} [Semiring S] (f : R →+* S) : p.eval₂ f 1 = f (p.eval 1) :=
   by
@@ -558,12 +375,6 @@ theorem eval₂_at_one {S : Type _} [Semiring S] (f : R →+* S) : p.eval₂ f 1
   simp
 #align polynomial.eval₂_at_one Polynomial.eval₂_at_one
 
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 @[simp]
 theorem eval₂_at_nat_cast {S : Type _} [Semiring S] (f : R →+* S) (n : ℕ) :
     p.eval₂ f n = f (p.eval n) := by
@@ -571,12 +382,6 @@ theorem eval₂_at_nat_cast {S : Type _} [Semiring S] (f : R →+* S) (n : ℕ)
   simp
 #align polynomial.eval₂_at_nat_cast Polynomial.eval₂_at_nat_cast
 
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 @[simp]
 theorem eval_C : (C a).eval x = a :=
   eval₂_C _ _
@@ -595,34 +400,16 @@ theorem eval_X : X.eval x = x :=
 #align polynomial.eval_X Polynomial.eval_X
 -/
 
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 @[simp]
 theorem eval_monomial {n a} : (monomial n a).eval x = a * x ^ n :=
   eval₂_monomial _ _
 #align polynomial.eval_monomial Polynomial.eval_monomial
 
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 @[simp]
 theorem eval_zero : (0 : R[X]).eval x = 0 :=
   eval₂_zero _ _
 #align polynomial.eval_zero Polynomial.eval_zero
 
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 @[simp]
 theorem eval_add : (p + q).eval x = p.eval x + q.eval x :=
   eval₂_add _ _
@@ -635,46 +422,22 @@ theorem eval_one : (1 : R[X]).eval x = 1 :=
 #align polynomial.eval_one Polynomial.eval_one
 -/
 
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 @[simp]
 theorem eval_bit0 : (bit0 p).eval x = bit0 (p.eval x) :=
   eval₂_bit0 _ _
 #align polynomial.eval_bit0 Polynomial.eval_bit0
 
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 @[simp]
 theorem eval_bit1 : (bit1 p).eval x = bit1 (p.eval x) :=
   eval₂_bit1 _ _
 #align polynomial.eval_bit1 Polynomial.eval_bit1
 
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 @[simp]
 theorem eval_smul [Monoid S] [DistribMulAction S R] [IsScalarTower S R R] (s : S) (p : R[X])
     (x : R) : (s • p).eval x = s • p.eval x := by
   rw [← smul_one_smul R s p, eval, eval₂_smul, RingHom.id_apply, smul_one_mul]
 #align polynomial.eval_smul Polynomial.eval_smul
 
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 @[simp]
 theorem eval_C_mul : (C a * p).eval x = a * p.eval x :=
   by
@@ -685,9 +448,6 @@ theorem eval_C_mul : (C a * p).eval x = a * p.eval x :=
     simp only [mul_assoc, C_mul_monomial, eval_monomial]
 #align polynomial.eval_C_mul Polynomial.eval_C_mul
 
-/- warning: polynomial.eval_monomial_one_add_sub -> Polynomial.eval_monomial_one_add_sub is a dubious translation:
-<too large>
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 /-- A reformulation of the expansion of (1 + y)^d:
 $$(d + 1) (1 + y)^d - (d + 1)y^d = \sum_{i = 0}^d {d + 1 \choose i} \cdot i \cdot y^{i - 1}.$$
 -/
@@ -722,23 +482,11 @@ def leval {R : Type _} [Semiring R] (r : R) : R[X] →ₗ[R] R
 #align polynomial.leval Polynomial.leval
 -/
 
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 @[simp]
 theorem eval_nat_cast_mul {n : ℕ} : ((n : R[X]) * p).eval x = n * p.eval x := by
   rw [← C_eq_nat_cast, eval_C_mul]
 #align polynomial.eval_nat_cast_mul Polynomial.eval_nat_cast_mul
 
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 @[simp]
 theorem eval_mul_X : (p * X).eval x = p.eval x * x :=
   by
@@ -750,12 +498,6 @@ theorem eval_mul_X : (p * X).eval x = p.eval x * x :=
       mul_assoc]
 #align polynomial.eval_mul_X Polynomial.eval_mul_X
 
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 @[simp]
 theorem eval_mul_X_pow {k : ℕ} : (p * X ^ k).eval x = p.eval x * x ^ k :=
   by
@@ -787,33 +529,15 @@ def IsRoot (p : R[X]) (a : R) : Prop :=
 
 instance [DecidableEq R] : Decidable (IsRoot p a) := by unfold is_root <;> infer_instance
 
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 @[simp]
 theorem IsRoot.def : IsRoot p a ↔ p.eval a = 0 :=
   Iff.rfl
 #align polynomial.is_root.def Polynomial.IsRoot.def
 
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 theorem IsRoot.eq_zero (h : IsRoot p x) : eval x p = 0 :=
   h
 #align polynomial.is_root.eq_zero Polynomial.IsRoot.eq_zero
 
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 theorem coeff_zero_eq_eval_zero (p : R[X]) : coeff p 0 = p.eval 0 :=
   calc
     coeff p 0 = coeff p 0 * 0 ^ 0 := by simp
@@ -825,12 +549,6 @@ theorem coeff_zero_eq_eval_zero (p : R[X]) : coeff p 0 = p.eval 0 :=
     
 #align polynomial.coeff_zero_eq_eval_zero Polynomial.coeff_zero_eq_eval_zero
 
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 theorem zero_isRoot_of_coeff_zero_eq_zero {p : R[X]} (hp : p.coeff 0 = 0) : IsRoot p 0 := by
   rwa [coeff_zero_eq_eval_zero] at hp
 #align polynomial.zero_is_root_of_coeff_zero_eq_zero Polynomial.zero_isRoot_of_coeff_zero_eq_zero
@@ -842,12 +560,6 @@ theorem IsRoot.dvd {R : Type _} [CommSemiring R] {p q : R[X]} {x : R} (h : p.IsR
 #align polynomial.is_root.dvd Polynomial.IsRoot.dvd
 -/
 
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 theorem not_isRoot_C (r a : R) (hr : r ≠ 0) : ¬IsRoot (C r) a := by simpa using hr
 #align polynomial.not_is_root_C Polynomial.not_isRoot_C
 
@@ -867,12 +579,6 @@ def comp (p q : R[X]) : R[X] :=
 #align polynomial.comp Polynomial.comp
 -/
 
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 theorem comp_eq_sum_left : p.comp q = p.Sum fun e a => C a * q ^ e := by rw [comp, eval₂_eq_sum]
 #align polynomial.comp_eq_sum_left Polynomial.comp_eq_sum_left
 
@@ -892,22 +598,10 @@ theorem X_comp : X.comp p = p :=
 #align polynomial.X_comp Polynomial.X_comp
 -/
 
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 @[simp]
 theorem comp_C : p.comp (C a) = C (p.eval a) := by simp [comp, (C : R →+* _).map_sum]
 #align polynomial.comp_C Polynomial.comp_C
 
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 @[simp]
 theorem C_comp : (C a).comp p = C a :=
   eval₂_C _ _
@@ -919,12 +613,6 @@ theorem nat_cast_comp {n : ℕ} : (n : R[X]).comp p = n := by rw [← C_eq_nat_c
 #align polynomial.nat_cast_comp Polynomial.nat_cast_comp
 -/
 
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 @[simp]
 theorem comp_zero : p.comp (0 : R[X]) = C (p.eval 0) := by rw [← C_0, comp_C]
 #align polynomial.comp_zero Polynomial.comp_zero
@@ -935,12 +623,6 @@ theorem zero_comp : comp (0 : R[X]) p = 0 := by rw [← C_0, C_comp]
 #align polynomial.zero_comp Polynomial.zero_comp
 -/
 
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 @[simp]
 theorem comp_one : p.comp 1 = C (p.eval 1) := by rw [← C_1, comp_C]
 #align polynomial.comp_one Polynomial.comp_one
@@ -958,12 +640,6 @@ theorem add_comp : (p + q).comp r = p.comp r + q.comp r :=
 #align polynomial.add_comp Polynomial.add_comp
 -/
 
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 @[simp]
 theorem monomial_comp (n : ℕ) : (monomial n a).comp p = C a * p ^ n :=
   eval₂_monomial _ _
@@ -999,12 +675,6 @@ theorem mul_X_pow_comp {k : ℕ} : (p * X ^ k).comp r = p.comp r * r ^ k :=
 #align polynomial.mul_X_pow_comp Polynomial.mul_X_pow_comp
 -/
 
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 @[simp]
 theorem C_mul_comp : (C a * p).comp r = C a * p.comp r :=
   by
@@ -1049,12 +719,6 @@ theorem bit1_comp : comp (bit1 p : R[X]) q = bit1 (p.comp q) := by
 #align polynomial.bit1_comp Polynomial.bit1_comp
 -/
 
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-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_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))))] [_inst_4 : IsScalarTower.{u2, u1, u1} S R 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))) (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (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)))] (s : S) (p : Polynomial.{u1} R _inst_1) (q : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{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)))) s p) q) (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)))) s (Polynomial.comp.{u1} R _inst_1 p q))
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-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_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))))] [_inst_4 : IsScalarTower.{u2, u1, u1} S R R (SMulZeroClass.toSMul.{u2, u1} S R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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))) (SMulZeroClass.toSMul.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u2, u1} S R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))] (s : S) (p : Polynomial.{u1} R _inst_1) (q : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (HSMul.hSMul.{u2, u1, u1} S (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHSMul.{u2, u1} S (Polynomial.{u1} R _inst_1) (SMulZeroClass.toSMul.{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))))) s p) q) (HSMul.hSMul.{u2, u1, u1} S (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHSMul.{u2, u1} S (Polynomial.{u1} R _inst_1) (SMulZeroClass.toSMul.{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))))) s (Polynomial.comp.{u1} R _inst_1 p q))
-Case conversion may be inaccurate. Consider using '#align polynomial.smul_comp Polynomial.smul_compₓ'. -/
 @[simp]
 theorem smul_comp [Monoid S] [DistribMulAction S R] [IsScalarTower S R R] (s : S) (p q : R[X]) :
     (s • p).comp q = s • p.comp q := by
@@ -1069,12 +733,6 @@ theorem comp_assoc {R : Type _} [CommSemiring R] (φ ψ χ : R[X]) :
 #align polynomial.comp_assoc Polynomial.comp_assoc
 -/
 
-/- warning: polynomial.coeff_comp_degree_mul_degree -> Polynomial.coeff_comp_degree_mul_degree is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align polynomial.coeff_comp_degree_mul_degree Polynomial.coeff_comp_degree_mul_degreeₓ'. -/
 theorem coeff_comp_degree_mul_degree (hqd0 : natDegree q ≠ 0) :
     coeff (p.comp q) (natDegree p * natDegree q) = leadingCoeff p * leadingCoeff q ^ natDegree p :=
   by
@@ -1104,9 +762,6 @@ def map : R[X] → S[X] :=
 #align polynomial.map Polynomial.map
 -/
 
-/- warning: polynomial.map_C -> Polynomial.map_C is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.map_C Polynomial.map_Cₓ'. -/
 @[simp]
 theorem map_C : (C a).map f = C (f a) :=
   eval₂_C _ _
@@ -1119,9 +774,6 @@ theorem map_X : X.map f = X :=
 #align polynomial.map_X Polynomial.map_X
 -/
 
-/- warning: polynomial.map_monomial -> Polynomial.map_monomial is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.map_monomial Polynomial.map_monomialₓ'. -/
 @[simp]
 theorem map_monomial {n a} : (monomial n a).map f = monomial n (f a) :=
   by
@@ -1157,12 +809,6 @@ protected theorem map_mul : (p * q).map f = p.map f * q.map f := by rw [map, eva
 #align polynomial.map_mul Polynomial.map_mul
 -/
 
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 @[simp]
 protected theorem map_smul (r : R) : (r • p).map f = f r • p.map f := by
   rw [map, eval₂_smul, RingHom.comp_apply, C_mul']
@@ -1186,12 +832,6 @@ def mapRingHom (f : R →+* S) : R[X] →+* S[X]
 #align polynomial.map_ring_hom Polynomial.mapRingHom
 -/
 
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 @[simp]
 theorem coe_mapRingHom (f : R →+* S) : ⇑(mapRingHom f) = map f :=
   rfl
@@ -1226,12 +866,6 @@ theorem map_dvd (f : R →+* S) {x y : R[X]} : x ∣ y → x.map f ∣ y.map f :
 #align polynomial.map_dvd Polynomial.map_dvd
 -/
 
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 @[simp]
 theorem coeff_map (n : ℕ) : coeff (p.map f) n = f (coeff p n) :=
   by
@@ -1242,12 +876,6 @@ theorem coeff_map (n : ℕ) : coeff (p.map f) n = f (coeff p n) :=
   split_ifs <;> simp [f.map_zero]
 #align polynomial.coeff_map Polynomial.coeff_map
 
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 /-- If `R` and `S` are isomorphic, then so are their polynomial rings. -/
 @[simps]
 def mapEquiv (e : R ≃+* S) : R[X] ≃+* S[X] :=
@@ -1276,22 +904,10 @@ theorem eval₂_eq_eval_map {x : S} : p.eval₂ f x = (p.map f).eval x :=
 #align polynomial.eval₂_eq_eval_map Polynomial.eval₂_eq_eval_map
 -/
 
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 theorem map_injective (hf : Function.Injective f) : Function.Injective (map f) := fun p q h =>
   ext fun m => hf <| by rw [← coeff_map f, ← coeff_map f, h]
 #align polynomial.map_injective Polynomial.map_injective
 
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 theorem map_surjective (hf : Function.Surjective f) : Function.Surjective (map f) := fun p =>
   Polynomial.induction_on' p
     (fun p q hp hq =>
@@ -1303,12 +919,6 @@ theorem map_surjective (hf : Function.Surjective f) : Function.Surjective (map f
     ⟨monomial n r, by rw [map_monomial f, hr]⟩
 #align polynomial.map_surjective Polynomial.map_surjective
 
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 theorem degree_map_le (p : R[X]) : degree (p.map f) ≤ degree p :=
   by
   apply (degree_le_iff_coeff_zero _ _).2 fun m hm => _
@@ -1324,32 +934,14 @@ theorem natDegree_map_le (p : R[X]) : natDegree (p.map f) ≤ natDegree p :=
 
 variable {f}
 
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 protected theorem map_eq_zero_iff (hf : Function.Injective f) : p.map f = 0 ↔ p = 0 :=
   map_eq_zero_iff (mapRingHom f) (map_injective f hf)
 #align polynomial.map_eq_zero_iff Polynomial.map_eq_zero_iff
 
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 protected theorem map_ne_zero_iff (hf : Function.Injective f) : p.map f ≠ 0 ↔ p ≠ 0 :=
   (Polynomial.map_eq_zero_iff hf).Not
 #align polynomial.map_ne_zero_iff Polynomial.map_ne_zero_iff
 
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 theorem map_monic_eq_zero_iff (hp : p.Monic) : p.map f = 0 ↔ ∀ x, f x = 0 :=
   ⟨fun hfp x =>
     calc
@@ -1366,12 +958,6 @@ theorem map_monic_ne_zero (hp : p.Monic) [Nontrivial S] : p.map f ≠ 0 := fun h
 #align polynomial.map_monic_ne_zero Polynomial.map_monic_ne_zero
 -/
 
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 theorem degree_map_eq_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCoeff p) ≠ 0) :
     degree (p.map f) = degree p :=
   le_antisymm (degree_map_le f _) <|
@@ -1383,23 +969,11 @@ theorem degree_map_eq_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCo
     exact hf
 #align polynomial.degree_map_eq_of_leading_coeff_ne_zero Polynomial.degree_map_eq_of_leadingCoeff_ne_zero
 
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 theorem natDegree_map_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCoeff p) ≠ 0) :
     natDegree (p.map f) = natDegree p :=
   natDegree_eq_of_degree_eq (degree_map_eq_of_leadingCoeff_ne_zero f hf)
 #align polynomial.nat_degree_map_of_leading_coeff_ne_zero Polynomial.natDegree_map_of_leadingCoeff_ne_zero
 
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 theorem leadingCoeff_map_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCoeff p) ≠ 0) :
     leadingCoeff (p.map f) = f (leadingCoeff p) :=
   by
@@ -1437,12 +1011,6 @@ protected theorem map_pow (n : ℕ) : (p ^ n).map f = p.map f ^ n :=
 #align polynomial.map_pow Polynomial.map_pow
 -/
 
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 theorem mem_map_rangeS {p : S[X]} : p ∈ (mapRingHom f).srange ↔ ∀ n, p.coeff n ∈ f.srange :=
   by
   constructor
@@ -1455,12 +1023,6 @@ theorem mem_map_rangeS {p : S[X]} : p ∈ (mapRingHom f).srange ↔ ∀ n, p.coe
     rw [coe_map_ring_hom, Polynomial.map_mul, map_C, hc, Polynomial.map_pow, map_X]
 #align polynomial.mem_map_srange Polynomial.mem_map_rangeS
 
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 theorem mem_map_range {R S : Type _} [Ring R] [Ring S] (f : R →+* S) {p : S[X]} :
     p ∈ (mapRingHom f).range ↔ ∀ n, p.coeff n ∈ f.range :=
   mem_map_rangeS f
@@ -1478,12 +1040,6 @@ theorem eval_map (x : S) : (p.map f).eval x = p.eval₂ f x :=
 #align polynomial.eval_map Polynomial.eval_map
 -/
 
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 protected theorem map_sum {ι : Type _} (g : ι → R[X]) (s : Finset ι) :
     (∑ i in s, g i).map f = ∑ i in s, (g i).map f :=
   (mapRingHom f).map_sum _ _
@@ -1501,23 +1057,11 @@ theorem map_comp (p q : R[X]) : map f (p.comp q) = (map f p).comp (map f q) :=
 #align polynomial.map_comp Polynomial.map_comp
 -/
 
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 @[simp]
 theorem eval_zero_map (f : R →+* S) (p : R[X]) : (p.map f).eval 0 = f (p.eval 0) := by
   simp [← coeff_zero_eq_eval_zero]
 #align polynomial.eval_zero_map Polynomial.eval_zero_map
 
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 @[simp]
 theorem eval_one_map (f : R →+* S) (p : R[X]) : (p.map f).eval 1 = f (p.eval 1) :=
   by
@@ -1526,12 +1070,6 @@ theorem eval_one_map (f : R →+* S) (p : R[X]) : (p.map f).eval 1 = f (p.eval 1
   · intro n r; simp only [one_pow, mul_one, eval_monomial, map_monomial]
 #align polynomial.eval_one_map Polynomial.eval_one_map
 
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 @[simp]
 theorem eval_nat_cast_map (f : R →+* S) (p : R[X]) (n : ℕ) : (p.map f).eval n = f (p.eval n) :=
   by
@@ -1540,12 +1078,6 @@ theorem eval_nat_cast_map (f : R →+* S) (p : R[X]) (n : ℕ) : (p.map f).eval
   · intro n r; simp only [map_natCast f, eval_monomial, map_monomial, f.map_pow, f.map_mul]
 #align polynomial.eval_nat_cast_map Polynomial.eval_nat_cast_map
 
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 @[simp]
 theorem eval_int_cast_map {R S : Type _} [Ring R] [Ring S] (f : R →+* S) (p : R[X]) (i : ℤ) :
     (p.map f).eval i = f (p.eval i) :=
@@ -1568,12 +1100,6 @@ section HomEval₂
 
 variable [Semiring S] [Semiring T] (f : R →+* S) (g : S →+* T) (p)
 
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 theorem hom_eval₂ (x : S) : g (p.eval₂ f x) = p.eval₂ (g.comp f) (g x) := by
   rw [← eval₂_map, eval₂_at_apply, eval_map]
 #align polynomial.hom_eval₂ Polynomial.hom_eval₂
@@ -1590,12 +1116,6 @@ section
 
 variable [Semiring R] {p q : R[X]} {x : R} [Semiring S] (f : R →+* S)
 
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 theorem eval₂_hom (x : R) : p.eval₂ f (f x) = f (p.eval x) :=
   RingHom.comp_id f ▸ (hom_eval₂ p (RingHom.id R) f x).symm
 #align polynomial.eval₂_hom Polynomial.eval₂_hom
@@ -1629,12 +1149,6 @@ section
 
 variable [CommSemiring R] {p q : R[X]} {x : R} [CommSemiring S] (f : R →+* S)
 
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 @[simp]
 theorem eval_mul : (p * q).eval x = p.eval x * q.eval x :=
   eval₂_mul _ _
@@ -1647,12 +1161,6 @@ def evalRingHom : R → R[X] →+* R :=
 #align polynomial.eval_ring_hom Polynomial.evalRingHom
 -/
 
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 @[simp]
 theorem coe_evalRingHom (r : R) : (evalRingHom r : R[X] → R) = eval r :=
   rfl
@@ -1694,23 +1202,11 @@ def compRingHom : R[X] → R[X] →+* R[X] :=
 #align polynomial.comp_ring_hom Polynomial.compRingHom
 -/
 
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 @[simp]
 theorem coe_compRingHom (q : R[X]) : (compRingHom q : R[X] → R[X]) = fun p => comp p q :=
   rfl
 #align polynomial.coe_comp_ring_hom Polynomial.coe_compRingHom
 
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 theorem coe_compRingHom_apply (p q : R[X]) : (compRingHom q : R[X] → R[X]) p = comp p q :=
   rfl
 #align polynomial.coe_comp_ring_hom_apply Polynomial.coe_compRingHom_apply
@@ -1741,12 +1237,6 @@ theorem eval₂_finset_prod (s : Finset ι) (g : ι → R[X]) (x : S) :
 #align polynomial.eval₂_finset_prod Polynomial.eval₂_finset_prod
 -/
 
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 /-- Polynomial evaluation commutes with `list.prod`
 -/
 theorem eval_list_prod (l : List R[X]) (x : R) : eval x l.Prod = (l.map (eval x)).Prod :=
@@ -1761,12 +1251,6 @@ theorem eval_multiset_prod (s : Multiset R[X]) (x : R) : eval x s.Prod = (s.map
 #align polynomial.eval_multiset_prod Polynomial.eval_multiset_prod
 -/
 
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 /-- Polynomial evaluation commutes with `finset.prod`
 -/
 theorem eval_prod {ι : Type _} (s : Finset ι) (p : ι → R[X]) (x : R) :
@@ -1788,23 +1272,11 @@ theorem multiset_prod_comp (s : Multiset R[X]) (q : R[X]) :
 #align polynomial.multiset_prod_comp Polynomial.multiset_prod_comp
 -/
 
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 theorem prod_comp {ι : Type _} (s : Finset ι) (p : ι → R[X]) (q : R[X]) :
     (∏ j in s, p j).comp q = ∏ j in s, (p j).comp q :=
   map_prod (compRingHom q) _ _
 #align polynomial.prod_comp Polynomial.prod_comp
 
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 theorem isRoot_prod {R} [CommRing R] [IsDomain R] {ι : Type _} (s : Finset ι) (p : ι → R[X])
     (x : R) : IsRoot (∏ j in s, p j) x ↔ ∃ i ∈ s, IsRoot (p i) x := by
   simp only [is_root, eval_prod, Finset.prod_eq_zero_iff]
@@ -1816,12 +1288,6 @@ theorem eval_dvd : p ∣ q → eval x p ∣ eval x q :=
 #align polynomial.eval_dvd Polynomial.eval_dvd
 -/
 
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 theorem eval_eq_zero_of_dvd_of_eval_eq_zero : p ∣ q → eval x p = 0 → eval x q = 0 :=
   eval₂_eq_zero_of_dvd_of_eval₂_eq_zero _ _
 #align polynomial.eval_eq_zero_of_dvd_of_eval_eq_zero Polynomial.eval_eq_zero_of_dvd_of_eval_eq_zero
@@ -1848,12 +1314,6 @@ theorem support_map_subset [Semiring R] [Semiring S] (f : R →+* S) (p : R[X])
 #align polynomial.support_map_subset Polynomial.support_map_subset
 -/
 
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 theorem support_map_of_injective [Semiring R] [Semiring S] (p : R[X]) {f : R →+* S}
     (hf : Function.Injective f) : (map f p).support = p.support := by
   simp_rw [Finset.ext_iff, mem_support_iff, coeff_map, ← map_zero f, hf.ne_iff, iff_self_iff,
@@ -1868,44 +1328,20 @@ protected theorem map_multiset_prod (m : Multiset R[X]) : m.Prod.map f = (m.map
 #align polynomial.map_multiset_prod Polynomial.map_multiset_prod
 -/
 
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 protected theorem map_prod {ι : Type _} (g : ι → R[X]) (s : Finset ι) :
     (∏ i in s, g i).map f = ∏ i in s, (g i).map f :=
   (mapRingHom f).map_prod _ _
 #align polynomial.map_prod Polynomial.map_prod
 
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 theorem IsRoot.map {f : R →+* S} {x : R} {p : R[X]} (h : IsRoot p x) : IsRoot (p.map f) (f x) := by
   rw [is_root, eval_map, eval₂_hom, h.eq_zero, f.map_zero]
 #align polynomial.is_root.map Polynomial.IsRoot.map
 
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 theorem IsRoot.of_map {R} [CommRing R] {f : R →+* S} {x : R} {p : R[X]} (h : IsRoot (p.map f) (f x))
     (hf : Function.Injective f) : IsRoot p x := by
   rwa [is_root, ← (injective_iff_map_eq_zero' f).mp hf, ← eval₂_hom, ← eval_map]
 #align polynomial.is_root.of_map Polynomial.IsRoot.of_map
 
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 theorem isRoot_map_iff {R : Type _} [CommRing R] {f : R →+* S} {x : R} {p : R[X]}
     (hf : Function.Injective f) : IsRoot (p.map f) (f x) ↔ IsRoot p x :=
   ⟨fun h => h.of_map hf, fun h => h.map⟩
@@ -1919,118 +1355,55 @@ section Ring
 
 variable [Ring R] {p q r : R[X]}
 
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 theorem C_neg : C (-a) = -C a :=
   RingHom.map_neg C a
 #align polynomial.C_neg Polynomial.C_neg
 
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 theorem C_sub : C (a - b) = C a - C b :=
   RingHom.map_sub C a b
 #align polynomial.C_sub Polynomial.C_sub
 
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 @[simp]
 protected theorem map_sub {S} [Ring S] (f : R →+* S) : (p - q).map f = p.map f - q.map f :=
   (mapRingHom f).map_sub p q
 #align polynomial.map_sub Polynomial.map_sub
 
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 @[simp]
 protected theorem map_neg {S} [Ring S] (f : R →+* S) : (-p).map f = -p.map f :=
   (mapRingHom f).map_neg p
 #align polynomial.map_neg Polynomial.map_neg
 
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 @[simp]
 theorem map_int_cast {S} [Ring S] (f : R →+* S) (n : ℤ) : map f ↑n = ↑n :=
   map_intCast (mapRingHom f) n
 #align polynomial.map_int_cast Polynomial.map_int_cast
 
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 @[simp]
 theorem eval_int_cast {n : ℤ} {x : R} : (n : R[X]).eval x = n := by
   simp only [← C_eq_int_cast, eval_C]
 #align polynomial.eval_int_cast Polynomial.eval_int_cast
 
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 @[simp]
 theorem eval₂_neg {S} [Ring S] (f : R →+* S) {x : S} : (-p).eval₂ f x = -p.eval₂ f x := by
   rw [eq_neg_iff_add_eq_zero, ← eval₂_add, add_left_neg, eval₂_zero]
 #align polynomial.eval₂_neg Polynomial.eval₂_neg
 
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 @[simp]
 theorem eval₂_sub {S} [Ring S] (f : R →+* S) {x : S} :
     (p - q).eval₂ f x = p.eval₂ f x - q.eval₂ f x := by
   rw [sub_eq_add_neg, eval₂_add, eval₂_neg, sub_eq_add_neg]
 #align polynomial.eval₂_sub Polynomial.eval₂_sub
 
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 @[simp]
 theorem eval_neg (p : R[X]) (x : R) : (-p).eval x = -p.eval x :=
   eval₂_neg _
 #align polynomial.eval_neg Polynomial.eval_neg
 
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 @[simp]
 theorem eval_sub (p q : R[X]) (x : R) : (p - q).eval x = p.eval x - q.eval x :=
   eval₂_sub _
 #align polynomial.eval_sub Polynomial.eval_sub
 
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 theorem root_X_sub_C : IsRoot (X - C a) b ↔ a = b := by
   rw [is_root.def, eval_sub, eval_X, eval_C, sub_eq_zero, eq_comm]
 #align polynomial.root_X_sub_C Polynomial.root_X_sub_C

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

@@ -140,9 +140,7 @@ but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_add Polynomial.eval₂_addₓ'. -/
 @[simp]
-theorem eval₂_add : (p + q).eval₂ f x = p.eval₂ f x + q.eval₂ f x :=
-  by
-  simp only [eval₂_eq_sum]
+theorem eval₂_add : (p + q).eval₂ f x = p.eval₂ f x + q.eval₂ f x := by simp only [eval₂_eq_sum];
   apply sum_add_index <;> simp [add_mul]
 #align polynomial.eval₂_add Polynomial.eval₂_add
 
@@ -262,10 +260,8 @@ theorem eval₂_finset_sum (s : Finset ι) (g : ι → R[X]) (x : S) :
 <too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_of_finsupp Polynomial.eval₂_ofFinsuppₓ'. -/
 theorem eval₂_ofFinsupp {f : R →+* S} {x : S} {p : AddMonoidAlgebra R ℕ} :
-    eval₂ f x (⟨p⟩ : R[X]) = liftNC (↑f) (powersHom S x) p :=
-  by
-  simp only [eval₂_eq_sum, Sum, to_finsupp_sum, support, coeff]
-  rfl
+    eval₂ f x (⟨p⟩ : R[X]) = liftNC (↑f) (powersHom S x) p := by
+  simp only [eval₂_eq_sum, Sum, to_finsupp_sum, support, coeff]; rfl
 #align polynomial.eval₂_of_finsupp Polynomial.eval₂_ofFinsupp
 
 /- warning: polynomial.eval₂_mul_noncomm -> Polynomial.eval₂_mul_noncomm is a dubious translation:
@@ -510,10 +506,7 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x p) (Polynomial.sum.{u1, u1} R _inst_1 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) p (fun (e : Nat) (a : R) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x e)))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_eq_sum Polynomial.eval_eq_sumₓ'. -/
-theorem eval_eq_sum : p.eval x = p.Sum fun e a => a * x ^ e :=
-  by
-  rw [eval, eval₂_eq_sum]
-  rfl
+theorem eval_eq_sum : p.eval x = p.Sum fun e a => a * x ^ e := by rw [eval, eval₂_eq_sum]; rfl
 #align polynomial.eval_eq_sum Polynomial.eval_eq_sum
 
 /- warning: polynomial.eval_eq_sum_range -> Polynomial.eval_eq_sum_range is a dubious translation:
@@ -981,10 +974,8 @@ theorem monomial_comp (n : ℕ) : (monomial n a).comp p = C a * p ^ n :=
 theorem mul_X_comp : (p * X).comp r = p.comp r * r :=
   by
   apply Polynomial.induction_on' p
-  · intro p q hp hq
-    simp only [hp, hq, add_mul, add_comp]
-  · intro n b
-    simp only [pow_succ', mul_assoc, monomial_mul_X, monomial_comp]
+  · intro p q hp hq; simp only [hp, hq, add_mul, add_comp]
+  · intro n b; simp only [pow_succ', mul_assoc, monomial_mul_X, monomial_comp]
 #align polynomial.mul_X_comp Polynomial.mul_X_comp
 -/
 
@@ -1018,10 +1009,8 @@ Case conversion may be inaccurate. Consider using '#align polynomial.C_mul_comp
 theorem C_mul_comp : (C a * p).comp r = C a * p.comp r :=
   by
   apply Polynomial.induction_on' p
-  · intro p q hp hq
-    simp [hp, hq, mul_add]
-  · intro n b
-    simp [mul_assoc]
+  · intro p q hp hq; simp [hp, hq, mul_add]
+  · intro n b; simp [mul_assoc]
 #align polynomial.C_mul_comp Polynomial.C_mul_comp
 
 #print Polynomial.nat_cast_mul_comp /-
@@ -1076,8 +1065,7 @@ theorem smul_comp [Monoid S] [DistribMulAction S R] [IsScalarTower S R R] (s : S
 theorem comp_assoc {R : Type _} [CommSemiring R] (φ ψ χ : R[X]) :
     (φ.comp ψ).comp χ = φ.comp (ψ.comp χ) := by
   apply Polynomial.induction_on φ <;>
-    · intros
-      simp_all only [add_comp, mul_comp, C_comp, X_comp, pow_succ', ← mul_assoc]
+    · intros ; simp_all only [add_comp, mul_comp, C_comp, X_comp, pow_succ', ← mul_assoc]
 #align polynomial.comp_assoc Polynomial.comp_assoc
 -/
 
@@ -1164,9 +1152,7 @@ protected theorem map_one : (1 : R[X]).map f = 1 :=
 
 #print Polynomial.map_mul /-
 @[simp]
-protected theorem map_mul : (p * q).map f = p.map f * q.map f :=
-  by
-  rw [map, eval₂_mul_noncomm]
+protected theorem map_mul : (p * q).map f = p.map f * q.map f := by rw [map, eval₂_mul_noncomm];
   exact fun k => (commute_X _).symm
 #align polynomial.map_mul Polynomial.map_mul
 -/
@@ -1285,10 +1271,8 @@ theorem map_id : p.map (RingHom.id _) = p := by simp [Polynomial.ext_iff, coeff_
 theorem eval₂_eq_eval_map {x : S} : p.eval₂ f x = (p.map f).eval x :=
   by
   apply Polynomial.induction_on' p
-  · intro p q hp hq
-    simp [hp, hq]
-  · intro n r
-    simp
+  · intro p q hp hq; simp [hp, hq]
+  · intro n r; simp
 #align polynomial.eval₂_eq_eval_map Polynomial.eval₂_eq_eval_map
 -/
 
@@ -1462,11 +1446,8 @@ Case conversion may be inaccurate. Consider using '#align polynomial.mem_map_sra
 theorem mem_map_rangeS {p : S[X]} : p ∈ (mapRingHom f).srange ↔ ∀ n, p.coeff n ∈ f.srange :=
   by
   constructor
-  · rintro ⟨p, rfl⟩ n
-    rw [coe_map_ring_hom, coeff_map]
-    exact Set.mem_range_self _
-  · intro h
-    rw [p.as_sum_range_C_mul_X_pow]
+  · rintro ⟨p, rfl⟩ n; rw [coe_map_ring_hom, coeff_map]; exact Set.mem_range_self _
+  · intro h; rw [p.as_sum_range_C_mul_X_pow]
     refine' (map_ring_hom f).srange.sum_mem _
     intro i hi
     rcases h i with ⟨c, hc⟩
@@ -1541,10 +1522,8 @@ Case conversion may be inaccurate. Consider using '#align polynomial.eval_one_ma
 theorem eval_one_map (f : R →+* S) (p : R[X]) : (p.map f).eval 1 = f (p.eval 1) :=
   by
   apply Polynomial.induction_on' p
-  · intro p q hp hq
-    simp only [hp, hq, Polynomial.map_add, RingHom.map_add, eval_add]
-  · intro n r
-    simp only [one_pow, mul_one, eval_monomial, map_monomial]
+  · intro p q hp hq; simp only [hp, hq, Polynomial.map_add, RingHom.map_add, eval_add]
+  · intro n r; simp only [one_pow, mul_one, eval_monomial, map_monomial]
 #align polynomial.eval_one_map Polynomial.eval_one_map
 
 /- warning: polynomial.eval_nat_cast_map -> Polynomial.eval_nat_cast_map is a dubious translation:
@@ -1557,10 +1536,8 @@ Case conversion may be inaccurate. Consider using '#align polynomial.eval_nat_ca
 theorem eval_nat_cast_map (f : R →+* S) (p : R[X]) (n : ℕ) : (p.map f).eval n = f (p.eval n) :=
   by
   apply Polynomial.induction_on' p
-  · intro p q hp hq
-    simp only [hp, hq, Polynomial.map_add, RingHom.map_add, eval_add]
-  · intro n r
-    simp only [map_natCast f, eval_monomial, map_monomial, f.map_pow, f.map_mul]
+  · intro p q hp hq; simp only [hp, hq, Polynomial.map_add, RingHom.map_add, eval_add]
+  · intro n r; simp only [map_natCast f, eval_monomial, map_monomial, f.map_pow, f.map_mul]
 #align polynomial.eval_nat_cast_map Polynomial.eval_nat_cast_map
 
 /- warning: polynomial.eval_int_cast_map -> Polynomial.eval_int_cast_map is a dubious translation:
@@ -1574,10 +1551,8 @@ theorem eval_int_cast_map {R S : Type _} [Ring R] [Ring S] (f : R →+* S) (p :
     (p.map f).eval i = f (p.eval i) :=
   by
   apply Polynomial.induction_on' p
-  · intro p q hp hq
-    simp only [hp, hq, Polynomial.map_add, RingHom.map_add, eval_add]
-  · intro n r
-    simp only [map_intCast, eval_monomial, map_monomial, map_pow, map_mul]
+  · intro p q hp hq; simp only [hp, hq, Polynomial.map_add, RingHom.map_add, eval_add]
+  · intro n r; simp only [map_intCast, eval_monomial, map_monomial, map_pow, map_mul]
 #align polynomial.eval_int_cast_map Polynomial.eval_int_cast_map
 
 end Map
@@ -1701,10 +1676,8 @@ theorem eval_pow (n : ℕ) : (p ^ n).eval x = p.eval x ^ n :=
 theorem eval_comp : (p.comp q).eval x = p.eval (q.eval x) :=
   by
   apply Polynomial.induction_on' p
-  · intro r s hr hs
-    simp [add_comp, hr, hs]
-  · intro n a
-    simp
+  · intro r s hr hs; simp [add_comp, hr, hs]
+  · intro n a; simp
 #align polynomial.eval_comp Polynomial.eval_comp
 -/
 

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

@@ -259,10 +259,7 @@ theorem eval₂_finset_sum (s : Finset ι) (g : ι → R[X]) (x : S) :
 -/
 
 /- warning: polynomial.eval₂_of_finsupp -> Polynomial.eval₂_ofFinsupp is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_of_finsupp Polynomial.eval₂_ofFinsuppₓ'. -/
 theorem eval₂_ofFinsupp {f : R →+* S} {x : S} {p : AddMonoidAlgebra R ℕ} :
     eval₂ f x (⟨p⟩ : R[X]) = liftNC (↑f) (powersHom S x) p :=
@@ -696,10 +693,7 @@ theorem eval_C_mul : (C a * p).eval x = a * p.eval x :=
 #align polynomial.eval_C_mul Polynomial.eval_C_mul
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_monomial_one_add_sub Polynomial.eval_monomial_one_add_subₓ'. -/
 /-- A reformulation of the expansion of (1 + y)^d:
 $$(d + 1) (1 + y)^d - (d + 1)y^d = \sum_{i = 0}^d {d + 1 \choose i} \cdot i \cdot y^{i - 1}.$$
@@ -1123,10 +1117,7 @@ def map : R[X] → S[X] :=
 -/
 
 /- warning: polynomial.map_C -> Polynomial.map_C is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.map_C Polynomial.map_Cₓ'. -/
 @[simp]
 theorem map_C : (C a).map f = C (f a) :=
@@ -1141,10 +1132,7 @@ theorem map_X : X.map f = X :=
 -/
 
 /- warning: polynomial.map_monomial -> Polynomial.map_monomial is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align polynomial.map_monomial Polynomial.map_monomialₓ'. -/
 @[simp]
 theorem map_monomial {n a} : (monomial n a).map f = monomial n (f a) :=
@@ -1969,10 +1957,7 @@ theorem C_neg : C (-a) = -C a :=
 #align polynomial.C_neg Polynomial.C_neg
 
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(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)) a) (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)) b))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.C_sub Polynomial.C_subₓ'. -/
 theorem C_sub : C (a - b) = C a - C b :=
   RingHom.map_sub C a b

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -116,7 +116,7 @@ theorem eval₂_X : X.eval₂ f x = x := by simp [eval₂_eq_sum]
 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)) (x : S) {n : Nat} {r : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (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 r) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x n))
 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)) (x : S) {n : Nat} {r : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2)))) (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 r) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x n))
+  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)) (x : S) {n : Nat} {r : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2)))) (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 r) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x n))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_monomial Polynomial.eval₂_monomialₓ'. -/
 @[simp]
 theorem eval₂_monomial {n : ℕ} {r : R} : (monomial n r).eval₂ f x = f r * x ^ n := by
@@ -609,7 +609,7 @@ theorem eval_X : X.eval x = x :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {x : R} {n : Nat} {a : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {x : R} {n : Nat} {a : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x n))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {x : R} {n : Nat} {a : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x n))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_monomial Polynomial.eval_monomialₓ'. -/
 @[simp]
 theorem eval_monomial {n a} : (monomial n a).eval x = a * x ^ n :=
@@ -699,7 +699,7 @@ theorem eval_C_mul : (C a * p).eval x = a * p.eval x :=
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (d : Nat) (y : S), Eq.{succ u1} S (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (SubNegMonoid.toHasSub.{u1} S (AddGroup.toSubNegMonoid.{u1} S (AddGroupWithOne.toAddGroup.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) y) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) d) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2))))))))))) (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) y (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) d) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))))))) (Finset.sum.{u1, 0} S Nat (AddCommGroup.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toAddCommGroup.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) d (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (x_1 : Nat) => HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Nat.choose (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) d (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x_1)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) x_1) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (Ring.toMonoid.{u1} S (CommRing.toRing.{u1} S _inst_2)))) y (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) x_1 (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
 but is expected to have type
-  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (d : Nat) (y : S), Eq.{succ u1} S (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (Ring.toSub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.eval.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) y) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) d) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.eval.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) y (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) d) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))))) (Finset.sum.{u1, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) d (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x_1 : Nat) => HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Nat.choose (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) d (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x_1)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) x_1) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) y (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) x_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (d : Nat) (y : S), Eq.{succ u1} S (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (Ring.toSub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.eval.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) y) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) d) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.eval.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) y (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) d) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))))) (Finset.sum.{u1, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) d (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x_1 : Nat) => HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Nat.choose (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) d (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x_1)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) x_1) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) y (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) x_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_monomial_one_add_sub Polynomial.eval_monomial_one_add_subₓ'. -/
 /-- A reformulation of the expansion of (1 + y)^d:
 $$(d + 1) (1 + y)^d - (d + 1)y^d = \sum_{i = 0}^d {d + 1 \choose i} \cdot i \cdot y^{i - 1}.$$
@@ -975,7 +975,7 @@ theorem add_comp : (p + q).comp r = p.comp r + q.comp r :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a) p) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) (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))))) p n))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a) p) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (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))))) p n))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a) p) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (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))))) p n))
 Case conversion may be inaccurate. Consider using '#align polynomial.monomial_comp Polynomial.monomial_compₓ'. -/
 @[simp]
 theorem monomial_comp (n : ℕ) : (monomial n a).comp p = C a * p ^ n :=
@@ -1144,7 +1144,7 @@ theorem map_X : X.map f = X :=
 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)) {n : Nat} {a : R}, Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a)) (coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) (fun (_x : LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) => S -> (Polynomial.{u2} S _inst_2)) (LinearMap.hasCoeToFun.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) (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 a))
 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)) {n : Nat} {a : R}, Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2 _inst_2 (RingHom.id.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2)))) (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Polynomial.module.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2 (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2)))) (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Polynomial.module.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2 (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2)) (RingHom.id.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2))) (Polynomial.monomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2 n) (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 a))
+  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)) {n : Nat} {a : R}, Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2 _inst_2 (RingHom.id.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2)))) (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Polynomial.module.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2 (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2)))) (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Polynomial.module.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2 (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2)) (RingHom.id.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2))) (Polynomial.monomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2 n) (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 a))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_monomial Polynomial.map_monomialₓ'. -/
 @[simp]
 theorem map_monomial {n a} : (monomial n a).map f = monomial n (f a) :=

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

@@ -56,7 +56,7 @@ irreducible_def eval₂ (p : R[X]) : S :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {x : S}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Polynomial.sum.{u1, u2} R _inst_1 S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) p (fun (e : Nat) (a : R) => HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (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 a) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x e)))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {x : S}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Polynomial.sum.{u1, u2} R _inst_1 S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) p (fun (e : Nat) (a : R) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2)))) (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 a) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x e)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {x : S}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Polynomial.sum.{u1, u2} R _inst_1 S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) p (fun (e : Nat) (a : R) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2)))) (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 a) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x e)))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_eq_sum Polynomial.eval₂_eq_sumₓ'. -/
 theorem eval₂_eq_sum {f : R →+* S} {x : S} : p.eval₂ f x = p.Sum fun e a => f a * x ^ e := by
   rw [eval₂]
@@ -77,7 +77,7 @@ theorem eval₂_congr {R S : Type _} [Semiring R] [Semiring S] {f g : R →+* S}
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))))) 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.coeff.{u1} R _inst_1 p (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) 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.coeff.{u1} R _inst_1 p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) 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.coeff.{u1} R _inst_1 p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_at_zero Polynomial.eval₂_at_zeroₓ'. -/
 @[simp]
 theorem eval₂_at_zero : p.eval₂ f 0 = f (coeff p 0) := by
@@ -100,7 +100,7 @@ theorem eval₂_zero : (0 : R[X]).eval₂ f x = 0 := by simp [eval₂_eq_sum]
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_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)) (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a)) (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 a)
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_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)) (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) (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 a)
+  forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_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)) (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) (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 a)
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_C Polynomial.eval₂_Cₓ'. -/
 @[simp]
 theorem eval₂_C : (C a).eval₂ f x = f a := by simp [eval₂_eq_sum]
@@ -116,7 +116,7 @@ theorem eval₂_X : X.eval₂ f x = x := by simp [eval₂_eq_sum]
 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)) (x : S) {n : Nat} {r : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (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 r) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x n))
 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)) (x : S) {n : Nat} {r : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2)))) (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 r) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x n))
+  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)) (x : S) {n : Nat} {r : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2)))) (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 r) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x n))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_monomial Polynomial.eval₂_monomialₓ'. -/
 @[simp]
 theorem eval₂_monomial {n : ℕ} {r : R} : (monomial n r).eval₂ f x = f r * x ^ n := by
@@ -177,7 +177,7 @@ theorem eval₂_bit1 : (bit1 p).eval₂ f x = bit1 (p.eval₂ f x) := by
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (p : Polynomial.{u1} R _inst_1) (x : S) {s : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 g x (SMul.smul.{u1, u1} R (Polynomial.{u1} R _inst_1) (SMulZeroClass.toHasSmul.{u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1) (Polynomial.smulZeroClass.{u1, u1} R _inst_1 R (SMulWithZero.toSmulZeroClass.{u1, u1} R R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) s p)) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (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)) g s) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 g x p))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (p : Polynomial.{u1} R _inst_1) (x : S) {s : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 g x (HSMul.hSMul.{u1, u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1) (Polynomial.smulZeroClass.{u1, u1} R _inst_1 R (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) s p)) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) s) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) s) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) s) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) s) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) s) _inst_2)))) (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))))) g s) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 g x p))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (p : Polynomial.{u1} R _inst_1) (x : S) {s : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 g x (HSMul.hSMul.{u1, u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1) (Polynomial.smulZeroClass.{u1, u1} R _inst_1 R (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) s p)) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) s) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) s) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) s) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) s) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) s) _inst_2)))) (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))))) g s) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 g x p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_smul Polynomial.eval₂_smulₓ'. -/
 @[simp]
 theorem eval₂_smul (g : R →+* S) (p : R[X]) (x : S) {s : R} :
@@ -262,7 +262,7 @@ theorem eval₂_finset_sum (s : Finset ι) (g : ι → R[X]) (x : S) :
 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)} {x : S} {p : AddMonoidAlgebra.{u1, 0} R Nat _inst_1}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (Polynomial.ofFinsupp.{u1} R _inst_1 p)) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{0, u1} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (fun (_x : AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{0, u1} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) => (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) -> S) (AddMonoidHom.hasCoeToFun.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{0, u1} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidAlgebra.liftNC.{u1, 0, u2} R Nat S _inst_1 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) ((fun (a : Sort.{max (succ u1) (succ u2)}) (b : Sort.{max (succ u2) (succ u1)}) [self : HasLiftT.{max (succ u1) (succ u2), max (succ u2) (succ u1)} a b] => self.0) (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoidHom.{u1, u2} R S (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (HasLiftT.mk.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoidHom.{u1, u2} R S (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (CoeTCₓ.coe.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoidHom.{u1, u2} R S (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidHom.hasCoeT.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (RingHomClass.toAddMonoidHomClass.{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.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) f) (coeFn.{succ u2, succ u2} (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (fun (_x : MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) => (Multiplicative.{0} Nat) -> S) (MonoidHom.hasCoeToFun.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} S (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) (fun (_x : Equiv.{succ u2, succ u2} S (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) => S -> (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) (Equiv.hasCoeToFun.{succ u2, succ u2} S (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) (powersHom.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) x))) 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)} {x : S} {p : AddMonoidAlgebra.{u1, 0} R Nat _inst_1}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (Polynomial.ofFinsupp.{u1} R _inst_1 p)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (fun (_x : AddMonoidAlgebra.{u1, 0} R Nat _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : AddMonoidAlgebra.{u1, 0} R Nat _inst_1) => S) _x) (AddHomClass.toFunLike.{max u2 u1, u1, u2} (AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddZeroClass.toAdd.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1)))) (AddZeroClass.toAdd.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidHomClass.toAddHomClass.{max u2 u1, u1, u2} (AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (AddMonoidHom.addMonoidHomClass.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) (AddMonoidAlgebra.liftNC.{u1, 0, u2} R Nat S _inst_1 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoidHomClass.toAddMonoidHom.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (RingHomClass.toAddMonoidHomClass.{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) (FunLike.coe.{succ u2, 1, succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x) (Multiplicative.{0} Nat) (fun (_x : Multiplicative.{0} Nat) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Multiplicative.{0} Nat) => S) _x) (MulHomClass.toFunLike.{u2, 0, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x) (Multiplicative.{0} Nat) S (MulOneClass.toMul.{0} (Multiplicative.{0} Nat) (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (MulOneClass.toMul.{u2} S (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (MonoidHomClass.toMulHomClass.{u2, 0, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x) (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (MonoidHom.monoidHomClass.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} S (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} S (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) (powersHom.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) x))) 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)} {x : S} {p : AddMonoidAlgebra.{u1, 0} R Nat _inst_1}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (Polynomial.ofFinsupp.{u1} R _inst_1 p)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (fun (_x : AddMonoidAlgebra.{u1, 0} R Nat _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : AddMonoidAlgebra.{u1, 0} R Nat _inst_1) => S) _x) (AddHomClass.toFunLike.{max u2 u1, u1, u2} (AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddZeroClass.toAdd.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1)))) (AddZeroClass.toAdd.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidHomClass.toAddHomClass.{max u2 u1, u1, u2} (AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (AddMonoidHom.addMonoidHomClass.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) (AddMonoidAlgebra.liftNC.{u1, 0, u2} R Nat S _inst_1 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoidHomClass.toAddMonoidHom.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (RingHomClass.toAddMonoidHomClass.{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) (FunLike.coe.{succ u2, 1, succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x) (Multiplicative.{0} Nat) (fun (_x : Multiplicative.{0} Nat) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Multiplicative.{0} Nat) => S) _x) (MulHomClass.toFunLike.{u2, 0, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x) (Multiplicative.{0} Nat) S (MulOneClass.toMul.{0} (Multiplicative.{0} Nat) (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (MulOneClass.toMul.{u2} S (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (MonoidHomClass.toMulHomClass.{u2, 0, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x) (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (MonoidHom.monoidHomClass.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} S (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} S (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) (powersHom.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) x))) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_of_finsupp Polynomial.eval₂_ofFinsuppₓ'. -/
 theorem eval₂_ofFinsupp {f : R →+* S} {x : S} {p : AddMonoidAlgebra R ℕ} :
     eval₂ f x (⟨p⟩ : R[X]) = liftNC (↑f) (powersHom S x) p :=
@@ -275,7 +275,7 @@ theorem eval₂_ofFinsupp {f : R →+* S} {x : S} {p : AddMonoidAlgebra R ℕ} :
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), (forall (k : Nat), Commute.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (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.coeff.{u1} R _inst_1 q k)) x) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (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)) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x q)))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), (forall (k : Nat), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) _inst_2))) (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.coeff.{u1} R _inst_1 q k)) x) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (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)) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x q)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), (forall (k : Nat), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) _inst_2))) (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.coeff.{u1} R _inst_1 q k)) x) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (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)) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x q)))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_mul_noncomm Polynomial.eval₂_mul_noncommₓ'. -/
 theorem eval₂_mul_noncomm (hf : ∀ k, Commute (f <| q.coeff k) x) :
     eval₂ f x (p * q) = eval₂ f x p * eval₂ f x q :=
@@ -315,7 +315,7 @@ theorem eval₂_X_mul : eval₂ f x (X * p) = eval₂ f x p * x := by rw [X_mul,
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), (Commute.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (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 a) x) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a))) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x 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 a)))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), (Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) (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 a) x) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) 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_inst_1 _inst_2 f x 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 a)))
+  forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), (Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2))) (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 a) x) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a))) (HMul.hMul.{u2, u2, u2} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) S (instHMul.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x 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 a)))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_mul_C' Polynomial.eval₂_mul_C'ₓ'. -/
 theorem eval₂_mul_C' (h : Commute (f a) x) : eval₂ f x (p * C a) = eval₂ f x p * f a :=
   by
@@ -330,7 +330,7 @@ theorem eval₂_mul_C' (h : Commute (f a) x) : eval₂ f x (p * C a) = eval₂ f
 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)) (x : S) (ps : List.{u1} (Polynomial.{u1} R _inst_1)), (forall (p : Polynomial.{u1} R _inst_1), (Membership.Mem.{u1, u1} (Polynomial.{u1} R _inst_1) (List.{u1} (Polynomial.{u1} R _inst_1)) (List.hasMem.{u1} (Polynomial.{u1} R _inst_1)) p ps) -> (forall (k : Nat), Commute.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (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.coeff.{u1} R _inst_1 p k)) x)) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (List.prod.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1) (Polynomial.hasOne.{u1} R _inst_1) ps)) (List.prod.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (AddMonoidWithOne.toOne.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (List.map.{u1, u2} (Polynomial.{u1} R _inst_1) S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x) ps)))
 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)) (x : S) (ps : List.{u1} (Polynomial.{u1} R _inst_1)), (forall (p : Polynomial.{u1} R _inst_1), (Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (List.{u1} (Polynomial.{u1} R _inst_1)) (List.instMembershipList.{u1} (Polynomial.{u1} R _inst_1)) p ps) -> (forall (k : Nat), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) _inst_2))) (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.coeff.{u1} R _inst_1 p k)) x)) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (List.prod.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1) ps)) (List.prod.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toOne.{u2} S _inst_2) (List.map.{u1, u2} (Polynomial.{u1} R _inst_1) S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x) ps)))
+  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)) (x : S) (ps : List.{u1} (Polynomial.{u1} R _inst_1)), (forall (p : Polynomial.{u1} R _inst_1), (Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (List.{u1} (Polynomial.{u1} R _inst_1)) (List.instMembershipList.{u1} (Polynomial.{u1} R _inst_1)) p ps) -> (forall (k : Nat), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) _inst_2))) (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.coeff.{u1} R _inst_1 p k)) x)) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (List.prod.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1) ps)) (List.prod.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toOne.{u2} S _inst_2) (List.map.{u1, u2} (Polynomial.{u1} R _inst_1) S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x) ps)))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_list_prod_noncomm Polynomial.eval₂_list_prod_noncommₓ'. -/
 theorem eval₂_list_prod_noncomm (ps : List R[X])
     (hf : ∀ p ∈ ps, ∀ (k), Commute (f <| coeff p k) x) :
@@ -346,7 +346,7 @@ theorem eval₂_list_prod_noncomm (ps : List R[X])
 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)) (x : S), (forall (a : R), Commute.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (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 a) x) -> (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2))
 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)) (x : S), (forall (a : R), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) (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 a) x) -> (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2))
+  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)) (x : S), (forall (a : R), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2))) (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 a) x) -> (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_ring_hom' Polynomial.eval₂RingHom'ₓ'. -/
 /-- `eval₂` as a `ring_hom` for noncommutative rings -/
 def eval₂RingHom' (f : R →+* S) (x : S) (hf : ∀ a, Commute (f a) x) : R[X] →+* S
@@ -377,7 +377,7 @@ variable [Semiring S] (f : R →+* S) (x : S)
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Finset.sum.{u2, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Polynomial.natDegree.{u1} R _inst_1 p) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (i : Nat) => HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (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.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x i)))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Finset.sum.{u2, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Polynomial.natDegree.{u1} R _inst_1 p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (i : Nat) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) _inst_2)))) (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.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x i)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Finset.sum.{u2, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Polynomial.natDegree.{u1} R _inst_1 p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (i : Nat) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) _inst_2)))) (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.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x i)))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_eq_sum_range Polynomial.eval₂_eq_sum_rangeₓ'. -/
 theorem eval₂_eq_sum_range :
     p.eval₂ f x = ∑ i in Finset.range (p.natDegree + 1), f (p.coeff i) * x ^ i :=
@@ -388,7 +388,7 @@ theorem eval₂_eq_sum_range :
 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)) {p : Polynomial.{u1} R _inst_1} {n : Nat}, (LT.lt.{0} Nat Nat.hasLt (Polynomial.natDegree.{u1} R _inst_1 p) n) -> (forall (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Finset.sum.{u2, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finset.range n) (fun (i : Nat) => HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (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.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x i))))
 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)) {p : Polynomial.{u1} R _inst_1} {n : Nat}, (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 p) n) -> (forall (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Finset.sum.{u2, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finset.range n) (fun (i : Nat) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) _inst_2)))) (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.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x i))))
+  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)) {p : Polynomial.{u1} R _inst_1} {n : Nat}, (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 p) n) -> (forall (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Finset.sum.{u2, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finset.range n) (fun (i : Nat) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) _inst_2)))) (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.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x i))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_eq_sum_range' Polynomial.eval₂_eq_sum_range'ₓ'. -/
 theorem eval₂_eq_sum_range' (f : R →+* S) {p : R[X]} {n : ℕ} (hn : p.natDegree < n) (x : S) :
     eval₂ f x p = ∑ i in Finset.range n, f (p.coeff i) * x ^ i :=
@@ -452,7 +452,7 @@ def eval₂RingHom (f : R →+* S) (x : S) : R[X] →+* S :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (x : S), Eq.{max (succ u1) (succ u2)} ((Polynomial.{u1} R _inst_1) -> S) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => (Polynomial.{u1} R _inst_1) -> S) (RingHom.hasCoeToFun.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.eval₂RingHom.{u1, u2} R S _inst_1 _inst_2 f x)) (Polynomial.eval₂.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) f x)
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (x : S), Eq.{max (succ u1) (succ u2)} (forall (ᾰ : Polynomial.{u1} R _inst_1), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => S) ᾰ) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) S (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)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (Polynomial.eval₂RingHom.{u1, u2} R S _inst_1 _inst_2 f x)) (Polynomial.eval₂.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) f x)
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (x : S), Eq.{max (succ u1) (succ u2)} (forall (ᾰ : Polynomial.{u1} R _inst_1), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => S) ᾰ) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) S (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)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (Polynomial.eval₂RingHom.{u1, u2} R S _inst_1 _inst_2 f x)) (Polynomial.eval₂.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) f x)
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_eval₂_ring_hom Polynomial.coe_eval₂RingHomₓ'. -/
 @[simp]
 theorem coe_eval₂RingHom (f : R →+* S) (x) : ⇑(eval₂RingHom f x) = eval₂ f x :=
@@ -545,7 +545,7 @@ theorem eval_eq_sum_range' {p : R[X]} {n : ℕ} (hn : p.natDegree < n) (x : R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (r : R), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (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 r) 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.eval.{u1} R _inst_1 r p))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {p : Polynomial.{u2} R _inst_1} {S : Type.{u1}} [_inst_2 : Semiring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (r : R), Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S _inst_1 _inst_2 f (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f r) p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f (Polynomial.eval.{u2} R _inst_1 r p))
+  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {p : Polynomial.{u2} R _inst_1} {S : Type.{u1}} [_inst_2 : Semiring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (r : R), Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S _inst_1 _inst_2 f (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f r) p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f (Polynomial.eval.{u2} R _inst_1 r p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_at_apply Polynomial.eval₂_at_applyₓ'. -/
 @[simp]
 theorem eval₂_at_apply {S : Type _} [Semiring S] (f : R →+* S) (r : R) :
@@ -559,7 +559,7 @@ theorem eval₂_at_apply {S : Type _} [Semiring S] (f : R →+* S) (r : R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (OfNat.ofNat.{u2} S 1 (OfNat.mk.{u2} S 1 (One.one.{u2} S (AddMonoidWithOne.toOne.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))))) 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.eval.{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))))))) p))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {p : Polynomial.{u2} R _inst_1} {S : Type.{u1}} [_inst_2 : Semiring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)), Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S _inst_1 _inst_2 f (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S _inst_2))) p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f (Polynomial.eval.{u2} R _inst_1 (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R _inst_1))) p))
+  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {p : Polynomial.{u2} R _inst_1} {S : Type.{u1}} [_inst_2 : Semiring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)), Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S _inst_1 _inst_2 f (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S _inst_2))) p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f (Polynomial.eval.{u2} R _inst_1 (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R _inst_1))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_at_one Polynomial.eval₂_at_oneₓ'. -/
 @[simp]
 theorem eval₂_at_one {S : Type _} [Semiring S] (f : R →+* S) : p.eval₂ f 1 = f (p.eval 1) :=
@@ -572,7 +572,7 @@ theorem eval₂_at_one {S : Type _} [Semiring S] (f : R →+* S) : p.eval₂ f 1
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (n : Nat), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u2} Nat S (CoeTCₓ.coe.{1, succ u2} Nat S (Nat.castCoe.{u2} S (AddMonoidWithOne.toNatCast.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))))) n) 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.eval.{u1} R _inst_1 ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) n) p))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {p : Polynomial.{u2} R _inst_1} {S : Type.{u1}} [_inst_2 : Semiring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (n : Nat), Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S _inst_1 _inst_2 f (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S _inst_2) n) p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f (Polynomial.eval.{u2} R _inst_1 (Nat.cast.{u2} R (Semiring.toNatCast.{u2} R _inst_1) n) p))
+  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {p : Polynomial.{u2} R _inst_1} {S : Type.{u1}} [_inst_2 : Semiring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (n : Nat), Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S _inst_1 _inst_2 f (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S _inst_2) n) p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f (Polynomial.eval.{u2} R _inst_1 (Nat.cast.{u2} R (Semiring.toNatCast.{u2} R _inst_1) n) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_at_nat_cast Polynomial.eval₂_at_nat_castₓ'. -/
 @[simp]
 theorem eval₂_at_nat_cast {S : Type _} [Semiring S] (f : R →+* S) (n : ℕ) :
@@ -585,7 +585,7 @@ theorem eval₂_at_nat_cast {S : Type _} [Semiring S] (f : R →+* S) (n : ℕ)
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a)) a
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) a
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) a
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_C Polynomial.eval_Cₓ'. -/
 @[simp]
 theorem eval_C : (C a).eval x = a :=
@@ -683,7 +683,7 @@ theorem eval_smul [Monoid S] [DistribMulAction S R] [IsScalarTower S R R] (s : S
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) p)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a (Polynomial.eval.{u1} R _inst_1 x p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (Polynomial.eval.{u1} R _inst_1 x p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (Polynomial.eval.{u1} R _inst_1 x p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_C_mul Polynomial.eval_C_mulₓ'. -/
 @[simp]
 theorem eval_C_mul : (C a * p).eval x = a * p.eval x :=
@@ -859,7 +859,7 @@ theorem IsRoot.dvd {R : Type _} [CommSemiring R] {p q : R[X]} {x : R} (h : p.IsR
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (a : R), (Ne.{succ u1} R 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)))))))) -> (Not (Polynomial.IsRoot.{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) a))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (a : R), (Ne.{succ u1} R r (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Not (Polynomial.IsRoot.{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) a))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (a : R), (Ne.{succ u1} R r (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Not (Polynomial.IsRoot.{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) a))
 Case conversion may be inaccurate. Consider using '#align polynomial.not_is_root_C Polynomial.not_isRoot_Cₓ'. -/
 theorem not_isRoot_C (r a : R) (hr : r ≠ 0) : ¬IsRoot (C r) a := by simpa using hr
 #align polynomial.not_is_root_C Polynomial.not_isRoot_C
@@ -884,7 +884,7 @@ def comp (p q : R[X]) : R[X] :=
 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}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p q) (Polynomial.sum.{u1, u1} R _inst_1 (Polynomial.{u1} R _inst_1) (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)))) p (fun (e : Nat) (a : R) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) (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))))) q e)))
 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}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p q) (Polynomial.sum.{u1, u1} R _inst_1 (Polynomial.{u1} R _inst_1) (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)))) p (fun (e : Nat) (a : R) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (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))))) q e)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p q) (Polynomial.sum.{u1, u1} R _inst_1 (Polynomial.{u1} R _inst_1) (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)))) p (fun (e : Nat) (a : R) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (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))))) q e)))
 Case conversion may be inaccurate. Consider using '#align polynomial.comp_eq_sum_left Polynomial.comp_eq_sum_leftₓ'. -/
 theorem comp_eq_sum_left : p.comp q = p.Sum fun e a => C a * q ^ e := by rw [comp, eval₂_eq_sum]
 #align polynomial.comp_eq_sum_left Polynomial.comp_eq_sum_left
@@ -909,7 +909,7 @@ theorem X_comp : X.comp p = p :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a)) (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.eval.{u1} R _inst_1 a p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) (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.eval.{u1} R _inst_1 a p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) (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.eval.{u1} R _inst_1 a p))
 Case conversion may be inaccurate. Consider using '#align polynomial.comp_C Polynomial.comp_Cₓ'. -/
 @[simp]
 theorem comp_C : p.comp (C a) = C (p.eval a) := by simp [comp, (C : R →+* _).map_sum]
@@ -919,7 +919,7 @@ theorem comp_C : p.comp (C a) = C (p.eval a) := by simp [comp, (C : R →+* _).m
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) p) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a)
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)
 Case conversion may be inaccurate. Consider using '#align polynomial.C_comp Polynomial.C_compₓ'. -/
 @[simp]
 theorem C_comp : (C a).comp p = C a :=
@@ -936,7 +936,7 @@ theorem nat_cast_comp {n : ℕ} : (n : R[X]).comp p = n := by rw [← C_eq_nat_c
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) (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.eval.{u1} R _inst_1 (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))))))) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) (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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) p))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) (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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.comp_zero Polynomial.comp_zeroₓ'. -/
 @[simp]
 theorem comp_zero : p.comp (0 : R[X]) = C (p.eval 0) := by rw [← C_0, comp_C]
@@ -952,7 +952,7 @@ theorem zero_comp : comp (0 : R[X]) p = 0 := by rw [← C_0, C_comp]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{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))))) (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.eval.{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))))))) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{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)))) (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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))) p))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{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)))) (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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.comp_one Polynomial.comp_oneₓ'. -/
 @[simp]
 theorem comp_one : p.comp 1 = C (p.eval 1) := by rw [← C_1, comp_C]
@@ -975,7 +975,7 @@ theorem add_comp : (p + q).comp r = p.comp r + q.comp r :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a) p) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) (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))))) p n))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a) p) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (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))))) p n))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a) p) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (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))))) p n))
 Case conversion may be inaccurate. Consider using '#align polynomial.monomial_comp Polynomial.monomial_compₓ'. -/
 @[simp]
 theorem monomial_comp (n : ℕ) : (monomial n a).comp p = C a * p ^ n :=
@@ -1018,7 +1018,7 @@ theorem mul_X_pow_comp {k : ℕ} : (p * X ^ k).comp r = p.comp r * r ^ k :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {r : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) p) r) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) (Polynomial.comp.{u1} R _inst_1 p r))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {r : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p) r) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (Polynomial.comp.{u1} R _inst_1 p r))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {r : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p) r) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (Polynomial.comp.{u1} R _inst_1 p r))
 Case conversion may be inaccurate. Consider using '#align polynomial.C_mul_comp Polynomial.C_mul_compₓ'. -/
 @[simp]
 theorem C_mul_comp : (C a * p).comp r = C a * p.comp r :=
@@ -1126,7 +1126,7 @@ def map : R[X] → S[X] :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_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)), Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a)) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (fun (_x : RingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) => S -> (Polynomial.{u2} S _inst_2)) (RingHom.hasCoeToFun.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.C.{u2} S _inst_2) (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 a))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_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)), Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2)))))) (Polynomial.C.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (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 a))
+  forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_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)), Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2)))))) (Polynomial.C.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (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 a))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_C Polynomial.map_Cₓ'. -/
 @[simp]
 theorem map_C : (C a).map f = C (f a) :=
@@ -1144,7 +1144,7 @@ theorem map_X : X.map f = X :=
 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)) {n : Nat} {a : R}, Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) 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 but is expected to have type
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(Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 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(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) 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(Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2 _inst_2 (RingHom.id.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2)))) (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Polynomial.module.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2 (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2)))) (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2) (Polynomial.module.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2 (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2)) (RingHom.id.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2))) (Polynomial.monomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) _inst_2 n) (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 a))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_monomial Polynomial.map_monomialₓ'. -/
 @[simp]
 theorem map_monomial {n a} : (monomial n a).map f = monomial n (f a) :=
@@ -1187,7 +1187,7 @@ protected theorem map_mul : (p * q).map f = p.map f * q.map f :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (r : R), Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (SMul.smul.{u1, u1} R (Polynomial.{u1} R _inst_1) (SMulZeroClass.toHasSmul.{u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1) (Polynomial.smulZeroClass.{u1, u1} R _inst_1 R (SMulWithZero.toSmulZeroClass.{u1, u1} R R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) r p)) (SMul.smul.{u2, u2} S (Polynomial.{u2} S _inst_2) (SMulZeroClass.toHasSmul.{u2, u2} S (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2) (Polynomial.smulZeroClass.{u2, u2} S _inst_2 S (SMulWithZero.toSmulZeroClass.{u2, u2} S S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (MulZeroClass.toSMulWithZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))))) (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 r) (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] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (r : R), Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (HSMul.hSMul.{u1, u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1) (Polynomial.smulZeroClass.{u1, u1} R _inst_1 R (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) r p)) (HSMul.hSMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Polynomial.{u2} S _inst_2) (Polynomial.{u2} S _inst_2) (instHSMul.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Polynomial.{u2} S _inst_2) (SMulZeroClass.toSMul.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2) (Polynomial.smulZeroClass.{u2, u2} S _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (SMulWithZero.toSMulZeroClass.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) S (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (MulZeroClass.toSMulWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2)))))))) (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 r) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (r : R), Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (HSMul.hSMul.{u1, u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1) (Polynomial.smulZeroClass.{u1, u1} R _inst_1 R (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) r p)) (HSMul.hSMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Polynomial.{u2} S _inst_2) (Polynomial.{u2} S _inst_2) (instHSMul.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Polynomial.{u2} S _inst_2) (SMulZeroClass.toSMul.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2) (Polynomial.smulZeroClass.{u2, u2} S _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (SMulWithZero.toSMulZeroClass.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) S (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (MulZeroClass.toSMulWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2)))))))) (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 r) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_smul Polynomial.map_smulₓ'. -/
 @[simp]
 protected theorem map_smul (r : R) : (r • p).map f = f r • p.map f := by
@@ -1216,7 +1216,7 @@ def mapRingHom (f : R →+* S) : R[X] →+* S[X]
 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)), Eq.{max (succ u1) (succ u2)} ((Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (RingHom.hasCoeToFun.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.mapRingHom.{u1, u2} R S _inst_1 _inst_2 f)) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f)
 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)), Eq.{max (succ u1) (succ u2)} (forall (ᾰ : Polynomial.{u1} R _inst_1), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) ᾰ) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (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)))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) (Polynomial.mapRingHom.{u1, u2} R S _inst_1 _inst_2 f)) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f)
+  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)), Eq.{max (succ u1) (succ u2)} (forall (ᾰ : Polynomial.{u1} R _inst_1), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) ᾰ) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (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)))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) (Polynomial.mapRingHom.{u1, u2} R S _inst_1 _inst_2 f)) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f)
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_map_ring_hom Polynomial.coe_mapRingHomₓ'. -/
 @[simp]
 theorem coe_mapRingHom (f : R →+* S) : ⇑(mapRingHom f) = map f :=
@@ -1256,7 +1256,7 @@ theorem map_dvd (f : R →+* S) {x y : R[X]} : x ∣ y → x.map f ∣ y.map f :
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (n : Nat), Eq.{succ u2} S (Polynomial.coeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) n) (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.coeff.{u1} R _inst_1 p n))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (n : Nat), Eq.{succ u2} S (Polynomial.coeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) n) (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.coeff.{u1} R _inst_1 p n))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (n : Nat), Eq.{succ u2} S (Polynomial.coeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) n) (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.coeff.{u1} R _inst_1 p n))
 Case conversion may be inaccurate. Consider using '#align polynomial.coeff_map Polynomial.coeff_mapₓ'. -/
 @[simp]
 theorem coeff_map (n : ℕ) : coeff (p.map f) n = f (coeff p n) :=
@@ -1308,7 +1308,7 @@ theorem eval₂_eq_eval_map {x : S} : p.eval₂ f x = (p.map f).eval x :=
 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)) -> (Function.Injective.{succ u1, succ u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f))
 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)) -> (Function.Injective.{succ u1, succ u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f))
+  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)) -> (Function.Injective.{succ u1, succ u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_injective Polynomial.map_injectiveₓ'. -/
 theorem map_injective (hf : Function.Injective f) : Function.Injective (map f) := fun p q h =>
   ext fun m => hf <| by rw [← coeff_map f, ← coeff_map f, h]
@@ -1318,7 +1318,7 @@ theorem map_injective (hf : Function.Injective f) : Function.Injective (map f) :
 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.Surjective.{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)) -> (Function.Surjective.{succ u1, succ u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f))
 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.Surjective.{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)) -> (Function.Surjective.{succ u1, succ u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f))
+  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.Surjective.{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)) -> (Function.Surjective.{succ u1, succ u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_surjective Polynomial.map_surjectiveₓ'. -/
 theorem map_surjective (hf : Function.Surjective f) : Function.Surjective (map f) := fun p =>
   Polynomial.induction_on' p
@@ -1356,7 +1356,7 @@ variable {f}
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_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)) -> (Iff (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (OfNat.mk.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.zero.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2))))) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_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)) -> (Iff (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_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)) -> (Iff (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_eq_zero_iff Polynomial.map_eq_zero_iffₓ'. -/
 protected theorem map_eq_zero_iff (hf : Function.Injective f) : p.map f = 0 ↔ p = 0 :=
   map_eq_zero_iff (mapRingHom f) (map_injective f hf)
@@ -1366,7 +1366,7 @@ protected theorem map_eq_zero_iff (hf : Function.Injective f) : p.map f = 0 ↔
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_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)) -> (Iff (Ne.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (OfNat.mk.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.zero.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2))))) (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_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)) -> (Iff (Ne.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))) (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_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)) -> (Iff (Ne.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))) (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_ne_zero_iff Polynomial.map_ne_zero_iffₓ'. -/
 protected theorem map_ne_zero_iff (hf : Function.Injective f) : p.map f ≠ 0 ↔ p ≠ 0 :=
   (Polynomial.map_eq_zero_iff hf).Not
@@ -1376,7 +1376,7 @@ protected theorem map_ne_zero_iff (hf : Function.Injective f) : p.map f ≠ 0 
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Iff (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (OfNat.mk.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.zero.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2))))) (forall (x : R), Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f x) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Iff (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))) (forall (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2))))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Iff (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))) (forall (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_monic_eq_zero_iff Polynomial.map_monic_eq_zero_iffₓ'. -/
 theorem map_monic_eq_zero_iff (hp : p.Monic) : p.map f = 0 ↔ ∀ x, f x = 0 :=
   ⟨fun hfp x =>
@@ -1398,7 +1398,7 @@ theorem map_monic_ne_zero (hp : p.Monic) [Nontrivial S] : p.map f ≠ 0 := fun h
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (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] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 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)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) _inst_2))))) -> (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] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 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)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) _inst_2))))) -> (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_leading_coeff_ne_zero Polynomial.degree_map_eq_of_leadingCoeff_ne_zeroₓ'. -/
 theorem degree_map_eq_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCoeff p) ≠ 0) :
     degree (p.map f) = degree p :=
@@ -1415,7 +1415,7 @@ theorem degree_map_eq_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCo
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (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] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 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)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) _inst_2))))) -> (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] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 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)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) _inst_2))))) -> (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_of_leading_coeff_ne_zero Polynomial.natDegree_map_of_leadingCoeff_ne_zeroₓ'. -/
 theorem natDegree_map_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCoeff p) ≠ 0) :
     natDegree (p.map f) = natDegree p :=
@@ -1426,7 +1426,7 @@ theorem natDegree_map_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCo
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (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] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 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)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) _inst_2))))) -> (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] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 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)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) _inst_2))))) -> (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_of_leading_coeff_ne_zero Polynomial.leadingCoeff_map_of_leadingCoeff_ne_zeroₓ'. -/
 theorem leadingCoeff_map_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCoeff p) ≠ 0) :
     leadingCoeff (p.map f) = f (leadingCoeff p) :=
@@ -1536,7 +1536,7 @@ theorem map_comp (p q : R[X]) : map f (p.comp q) = (map f p).comp (map f q) :=
 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)) (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))))) (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.eval.{u1} R _inst_1 (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))))))) 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)) (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)) (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_zero_map Polynomial.eval_zero_mapₓ'. -/
 @[simp]
 theorem eval_zero_map (f : R →+* S) (p : R[X]) : (p.map f).eval 0 = f (p.eval 0) := by
@@ -1547,7 +1547,7 @@ theorem eval_zero_map (f : R →+* S) (p : R[X]) : (p.map f).eval 0 = f (p.eval
 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)) (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (OfNat.ofNat.{u2} S 1 (OfNat.mk.{u2} S 1 (One.one.{u2} S (AddMonoidWithOne.toOne.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{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.eval.{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))))))) 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)) (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{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)) (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_one_map Polynomial.eval_one_mapₓ'. -/
 @[simp]
 theorem eval_one_map (f : R →+* S) (p : R[X]) : (p.map f).eval 1 = f (p.eval 1) :=
@@ -1563,7 +1563,7 @@ theorem eval_one_map (f : R →+* S) (p : R[X]) : (p.map f).eval 1 = f (p.eval 1
 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)) (p : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u2} Nat S (CoeTCₓ.coe.{1, succ u2} Nat S (Nat.castCoe.{u2} S (AddMonoidWithOne.toNatCast.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))))) n) (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.eval.{u1} R _inst_1 ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) n) 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)) (p : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (Nat.cast.{u2} S (Semiring.toNatCast.{u2} S _inst_2) n) (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.eval.{u1} R _inst_1 (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R _inst_1) n) 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)) (p : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (Nat.cast.{u2} S (Semiring.toNatCast.{u2} S _inst_2) n) (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.eval.{u1} R _inst_1 (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R _inst_1) n) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_nat_cast_map Polynomial.eval_nat_cast_mapₓ'. -/
 @[simp]
 theorem eval_nat_cast_map (f : R →+* S) (p : R[X]) (n : ℕ) : (p.map f).eval n = f (p.eval n) :=
@@ -1579,7 +1579,7 @@ theorem eval_nat_cast_map (f : R →+* S) (p : R[X]) (n : ℕ) : (p.map f).eval
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_3 : Ring.{u1} R] [_inst_4 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (i : Int), Eq.{succ u2} S (Polynomial.eval.{u2} S (Ring.toSemiring.{u2} S _inst_4) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Int S (HasLiftT.mk.{1, succ u2} Int S (CoeTCₓ.coe.{1, succ u2} Int S (Int.castCoe.{u2} S (AddGroupWithOne.toHasIntCast.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S _inst_4)))))) i) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u2} S _inst_4) f p)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) f (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_3) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_3)))))) i) p))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_3 : Ring.{u2} R] [_inst_4 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4))) (p : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (i : Int), Eq.{succ u1} S (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S _inst_4) (Int.cast.{u1} S (Ring.toIntCast.{u1} S _inst_4) i) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u1} S _inst_4) f p)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4))) R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4)))))) f (Polynomial.eval.{u2} R (Ring.toSemiring.{u2} R _inst_3) (Int.cast.{u2} R (Ring.toIntCast.{u2} R _inst_3) i) p))
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_3 : Ring.{u2} R] [_inst_4 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4))) (p : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (i : Int), Eq.{succ u1} S (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S _inst_4) (Int.cast.{u1} S (Ring.toIntCast.{u1} S _inst_4) i) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u1} S _inst_4) f p)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4))) R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4)))))) f (Polynomial.eval.{u2} R (Ring.toSemiring.{u2} R _inst_3) (Int.cast.{u2} R (Ring.toIntCast.{u2} R _inst_3) i) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_int_cast_map Polynomial.eval_int_cast_mapₓ'. -/
 @[simp]
 theorem eval_int_cast_map {R S : Type _} [Ring R] [Ring S] (f : R →+* S) (p : R[X]) (i : ℤ) :
@@ -1609,7 +1609,7 @@ variable [Semiring S] [Semiring T] (f : R →+* S) (g : S →+* T) (p)
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) [_inst_2 : Semiring.{u2} S] [_inst_3 : Semiring.{u3} T] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (g : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (x : S), Eq.{succ u3} T (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (fun (_x : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) => S -> T) (RingHom.hasCoeToFun.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) g (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p)) (Polynomial.eval₂.{u1, u3} R T _inst_1 _inst_3 (RingHom.comp.{u1, u2, u3} R S T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3) g f) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (fun (_x : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) => S -> T) (RingHom.hasCoeToFun.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) g x) p)
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) [_inst_2 : Semiring.{u2} S] [_inst_3 : Semiring.{u3} T] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (g : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (x : S), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => T) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3))))) g (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p)) (Polynomial.eval₂.{u1, u3} R T _inst_1 _inst_3 (RingHom.comp.{u1, u2, u3} R S T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3) g f) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3))))) g x) p)
+  forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) [_inst_2 : Semiring.{u2} S] [_inst_3 : Semiring.{u3} T] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (g : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (x : S), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => T) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3))))) g (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p)) (Polynomial.eval₂.{u1, u3} R T _inst_1 _inst_3 (RingHom.comp.{u1, u2, u3} R S T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3) g f) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3))))) g x) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.hom_eval₂ Polynomial.hom_eval₂ₓ'. -/
 theorem hom_eval₂ (x : S) : g (p.eval₂ f x) = p.eval₂ (g.comp f) (g x) := by
   rw [← eval₂_map, eval₂_at_apply, eval_map]
@@ -1631,7 +1631,7 @@ variable [Semiring R] {p q : R[X]} {x : R} [Semiring S] (f : R →+* S)
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : R), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f x) 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.eval.{u1} R _inst_1 x p))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : R), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f x) 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.eval.{u1} R _inst_1 x p))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : R), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f x) 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.eval.{u1} R _inst_1 x p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_hom Polynomial.eval₂_homₓ'. -/
 theorem eval₂_hom (x : R) : p.eval₂ f (f x) = f (p.eval x) :=
   RingHom.comp_id f ▸ (hom_eval₂ p (RingHom.id R) f x).symm
@@ -1688,7 +1688,7 @@ def evalRingHom : R → R[X] →+* R :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (r : R), Eq.{succ u1} ((fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> R) (Polynomial.evalRingHom.{u1} R _inst_1 r)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> R) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.evalRingHom.{u1} R _inst_1 r)) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) r)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (r : R), Eq.{succ u1} (forall (a : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => R) a) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Polynomial.evalRingHom.{u1} R _inst_1 r)) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) r)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (r : R), Eq.{succ u1} (forall (a : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => R) a) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Polynomial.evalRingHom.{u1} R _inst_1 r)) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) r)
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_eval_ring_hom Polynomial.coe_evalRingHomₓ'. -/
 @[simp]
 theorem coe_evalRingHom (r : R) : (evalRingHom r : R[X] → R) = eval r :=
@@ -1737,7 +1737,7 @@ def compRingHom : R[X] → R[X] →+* R[X] :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} ((fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.compRingHom.{u1} R _inst_1 q)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.compRingHom.{u1} R _inst_1 q)) (fun (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p q)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} (forall (a : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.compRingHom.{u1} R _inst_1 q)) (fun (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p q)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} (forall (a : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.compRingHom.{u1} R _inst_1 q)) (fun (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p q)
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_comp_ring_hom Polynomial.coe_compRingHomₓ'. -/
 @[simp]
 theorem coe_compRingHom (q : R[X]) : (compRingHom q : R[X] → R[X]) = fun p => comp p q :=
@@ -1748,7 +1748,7 @@ theorem coe_compRingHom (q : R[X]) : (compRingHom q : R[X] → R[X]) = fun p =>
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.compRingHom.{u1} R _inst_1 q) p) (Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p q)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) p) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.compRingHom.{u1} R _inst_1 q) p) (Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p q)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) p) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.compRingHom.{u1} R _inst_1 q) p) (Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p q)
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_comp_ring_hom_apply Polynomial.coe_compRingHom_applyₓ'. -/
 theorem coe_compRingHom_apply (p q : R[X]) : (compRingHom q : R[X] → R[X]) p = comp p q :=
   rfl
@@ -1891,7 +1891,7 @@ theorem support_map_subset [Semiring R] [Semiring S] (f : R →+* S) (p : R[X])
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] (p : Polynomial.{u1} R _inst_1) {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)) -> (Eq.{1} (Finset.{0} Nat) (Polynomial.support.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (Polynomial.support.{u1} R _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] (p : Polynomial.{u1} R _inst_1) {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)) -> (Eq.{1} (Finset.{0} Nat) (Polynomial.support.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (Polynomial.support.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] (p : Polynomial.{u1} R _inst_1) {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)) -> (Eq.{1} (Finset.{0} Nat) (Polynomial.support.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (Polynomial.support.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.support_map_of_injective Polynomial.support_map_of_injectiveₓ'. -/
 theorem support_map_of_injective [Semiring R] [Semiring S] (p : R[X]) {f : R →+* S}
     (hf : Function.Injective f) : (map f p).support = p.support := by
@@ -1922,7 +1922,7 @@ protected theorem map_prod {ι : Type _} (g : ι → R[X]) (s : Finset ι) :
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p x) -> (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) f x))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p x) -> (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{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 (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p x) -> (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{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 (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x))
 Case conversion may be inaccurate. Consider using '#align polynomial.is_root.map Polynomial.IsRoot.mapₓ'. -/
 theorem IsRoot.map {f : R →+* S} {x : R} {p : R[X]} (h : IsRoot p x) : IsRoot (p.map f) (f x) := by
   rw [is_root, eval_map, eval₂_hom, h.eq_zero, f.map_zero]
@@ -1932,7 +1932,7 @@ theorem IsRoot.map {f : R →+* S} {x : R} {p : R[X]} (h : IsRoot p x) : IsRoot
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))} {x : R} {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))}, (Polynomial.IsRoot.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (CommSemiring.toSemiring.{u1} S _inst_2) f p) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) f x)) -> (Function.Injective.{succ u2, succ u1} R S (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) f)) -> (Polynomial.IsRoot.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) p x)
 but is expected to have type
-  forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))}, (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x)) -> (Function.Injective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f)) -> (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) p x)
+  forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))}, (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x)) -> (Function.Injective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f)) -> (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) p x)
 Case conversion may be inaccurate. Consider using '#align polynomial.is_root.of_map Polynomial.IsRoot.of_mapₓ'. -/
 theorem IsRoot.of_map {R} [CommRing R] {f : R →+* S} {x : R} {p : R[X]} (h : IsRoot (p.map f) (f x))
     (hf : Function.Injective f) : IsRoot p x := by
@@ -1943,7 +1943,7 @@ theorem IsRoot.of_map {R} [CommRing R] {f : R →+* S} {x : R} {p : R[X]} (h : I
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))} {x : R} {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))}, (Function.Injective.{succ u2, succ u1} R S (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) f)) -> (Iff (Polynomial.IsRoot.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (CommSemiring.toSemiring.{u1} S _inst_2) f p) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) f x)) (Polynomial.IsRoot.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) p x))
 but is expected to have type
-  forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))}, (Function.Injective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f)) -> (Iff (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x)) (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) p x))
+  forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))}, (Function.Injective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f)) -> (Iff (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x)) (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) p x))
 Case conversion may be inaccurate. Consider using '#align polynomial.is_root_map_iff Polynomial.isRoot_map_iffₓ'. -/
 theorem isRoot_map_iff {R : Type _} [CommRing R] {f : R →+* S} {x : R} {p : R[X]}
     (hf : Function.Injective f) : IsRoot (p.map f) (f x) ↔ IsRoot p x :=
@@ -1962,7 +1962,7 @@ variable [Ring R] {p q r : R[X]}
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} (Polynomial.{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)) (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))))) a)) (Neg.neg.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.neg'.{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)) a))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) a)) (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)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) a)) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (Polynomial.neg'.{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)) a))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) a)) (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)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) a)) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (Polynomial.neg'.{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)) a))
 Case conversion may be inaccurate. Consider using '#align polynomial.C_neg Polynomial.C_negₓ'. -/
 theorem C_neg : C (-a) = -C a :=
   RingHom.map_neg C a
@@ -1972,7 +1972,7 @@ theorem C_neg : C (-a) = -C a :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} {b : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} (Polynomial.{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)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) a b)) (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)) (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)) a) (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)) b))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} {b : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) a b)) (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)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) a b)) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) b) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (instHSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (Polynomial.sub.{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)) a) (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)) b))
+  forall {R : Type.{u1}} {a : R} {b : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) a b)) (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)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) a b)) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) b) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (instHSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (Polynomial.sub.{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)) a) (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)) b))
 Case conversion may be inaccurate. Consider using '#align polynomial.C_sub Polynomial.C_subₓ'. -/
 theorem C_sub : C (a - b) = C a - C b :=
   RingHom.map_sub C a b
@@ -2071,7 +2071,7 @@ theorem eval_sub (p q : R[X]) (x : R) : (p - q).eval x = p.eval x - q.eval x :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} {b : R} [_inst_1 : Ring.{u1} R], Iff (Polynomial.IsRoot.{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)) a)) b) (Eq.{succ u1} R a b)
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} {b : R} [_inst_1 : Ring.{u1} R], Iff (Polynomial.IsRoot.{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)) a) (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)) a)) b) (Eq.{succ u1} R a b)
+  forall {R : Type.{u1}} {a : R} {b : R} [_inst_1 : Ring.{u1} R], Iff (Polynomial.IsRoot.{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)) a) (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)) a)) b) (Eq.{succ u1} R a b)
 Case conversion may be inaccurate. Consider using '#align polynomial.root_X_sub_C Polynomial.root_X_sub_Cₓ'. -/
 theorem root_X_sub_C : IsRoot (X - C a) b ↔ a = b := by
   rw [is_root.def, eval_sub, eval_X, eval_C, sub_eq_zero, eq_comm]

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

@@ -116,7 +116,7 @@ theorem eval₂_X : X.eval₂ f x = x := by simp [eval₂_eq_sum]
 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)) (x : S) {n : Nat} {r : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (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 r) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x n))
 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)) (x : S) {n : Nat} {r : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2)))) (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 r) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x n))
+  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)) (x : S) {n : Nat} {r : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2)))) (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 r) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x n))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_monomial Polynomial.eval₂_monomialₓ'. -/
 @[simp]
 theorem eval₂_monomial {n : ℕ} {r : R} : (monomial n r).eval₂ f x = f r * x ^ n := by
@@ -609,7 +609,7 @@ theorem eval_X : X.eval x = x :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {x : R} {n : Nat} {a : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {x : R} {n : Nat} {a : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x n))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {x : R} {n : Nat} {a : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x n))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_monomial Polynomial.eval_monomialₓ'. -/
 @[simp]
 theorem eval_monomial {n a} : (monomial n a).eval x = a * x ^ n :=
@@ -699,7 +699,7 @@ theorem eval_C_mul : (C a * p).eval x = a * p.eval x :=
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (d : Nat) (y : S), Eq.{succ u1} S (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (SubNegMonoid.toHasSub.{u1} S (AddGroup.toSubNegMonoid.{u1} S (AddGroupWithOne.toAddGroup.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) y) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) d) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2))))))))))) (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) y (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) d) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))))))) (Finset.sum.{u1, 0} S Nat (AddCommGroup.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toAddCommGroup.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) d (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (x_1 : Nat) => HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Nat.choose (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) d (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x_1)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) x_1) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (Ring.toMonoid.{u1} S (CommRing.toRing.{u1} S _inst_2)))) y (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) x_1 (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
 but is expected to have type
-  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (d : Nat) (y : S), Eq.{succ u1} S (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (Ring.toSub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.eval.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) y) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) d) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.eval.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) y (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) d) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))))) (Finset.sum.{u1, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) d (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x_1 : Nat) => HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Nat.choose (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) d (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x_1)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) x_1) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) y (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) x_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (d : Nat) (y : S), Eq.{succ u1} S (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (Ring.toSub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.eval.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) y) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) d) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.eval.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) y (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) d) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))))) (Finset.sum.{u1, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) d (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x_1 : Nat) => HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Nat.choose (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) d (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x_1)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) x_1) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) y (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) x_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_monomial_one_add_sub Polynomial.eval_monomial_one_add_subₓ'. -/
 /-- A reformulation of the expansion of (1 + y)^d:
 $$(d + 1) (1 + y)^d - (d + 1)y^d = \sum_{i = 0}^d {d + 1 \choose i} \cdot i \cdot y^{i - 1}.$$
@@ -975,7 +975,7 @@ theorem add_comp : (p + q).comp r = p.comp r + q.comp r :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a) p) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) (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))))) p n))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a) p) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (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))))) p n))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a) p) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (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))))) p n))
 Case conversion may be inaccurate. Consider using '#align polynomial.monomial_comp Polynomial.monomial_compₓ'. -/
 @[simp]
 theorem monomial_comp (n : ℕ) : (monomial n a).comp p = C a * p ^ n :=
@@ -1144,7 +1144,7 @@ theorem map_X : X.map f = X :=
 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)) {n : Nat} {a : R}, Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a)) (coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) (fun (_x : LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) => S -> (Polynomial.{u2} S _inst_2)) (LinearMap.hasCoeToFun.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) (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 a))
 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)) {n : Nat} {a : R}, Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2 _inst_2 (RingHom.id.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2)))) (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.module.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2 (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2)))) (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.module.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2 (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2)) (RingHom.id.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) (Polynomial.monomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2 n) (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 a))
+  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)) {n : Nat} {a : R}, Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2 _inst_2 (RingHom.id.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2)))) (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.module.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2 (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2)))) (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.module.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2 (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2)) (RingHom.id.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) (Polynomial.monomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2 n) (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 a))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_monomial Polynomial.map_monomialₓ'. -/
 @[simp]
 theorem map_monomial {n a} : (monomial n a).map f = monomial n (f a) :=

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

@@ -1331,14 +1331,18 @@ theorem map_surjective (hf : Function.Surjective f) : Function.Surjective (map f
     ⟨monomial n r, by rw [map_monomial f, hr]⟩
 #align polynomial.map_surjective Polynomial.map_surjective
 
-#print Polynomial.degree_map_le /-
+/- warning: polynomial.degree_map_le -> Polynomial.degree_map_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (p : Polynomial.{u1} R _inst_1), 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.{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)) (p : Polynomial.{u1} R _inst_1), 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.{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_le Polynomial.degree_map_leₓ'. -/
 theorem degree_map_le (p : R[X]) : degree (p.map f) ≤ degree p :=
   by
   apply (degree_le_iff_coeff_zero _ _).2 fun m hm => _
   rw [degree_lt_iff_coeff_zero] at hm
   simp [hm m le_rfl]
 #align polynomial.degree_map_le Polynomial.degree_map_le
--/
 
 #print Polynomial.natDegree_map_le /-
 theorem natDegree_map_le (p : R[X]) : natDegree (p.map f) ≤ natDegree p :=

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

@@ -699,7 +699,7 @@ theorem eval_C_mul : (C a * p).eval x = a * p.eval x :=
 lean 3 declaration is
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(CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) d) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))))))) (Finset.sum.{u1, 0} S Nat (AddCommGroup.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toAddCommGroup.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) d (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (x_1 : Nat) => HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Nat.choose (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) d (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x_1)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) x_1) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (Ring.toMonoid.{u1} S (CommRing.toRing.{u1} S _inst_2)))) y (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) x_1 (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
 but is expected to have type
-  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (d : Nat) (y : S), Eq.{succ u1} S (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (Ring.toSub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (NonAssocRing.toOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) y) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))) d) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (NonAssocRing.toOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) y (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))) d) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (NonAssocRing.toOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))))) (Finset.sum.{u1, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) d (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x_1 : Nat) => HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Nat.choose (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) d (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x_1)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))) x_1) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) y (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) x_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (d : Nat) (y : S), Eq.{succ u1} S (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (Ring.toSub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.eval.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) y) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) d) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.eval.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) y (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) d) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))))) (Finset.sum.{u1, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) d (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x_1 : Nat) => HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Nat.choose (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) d (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x_1)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) x_1) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) y (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) x_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_monomial_one_add_sub Polynomial.eval_monomial_one_add_subₓ'. -/
 /-- A reformulation of the expansion of (1 + y)^d:
 $$(d + 1) (1 + y)^d - (d + 1)y^d = \sum_{i = 0}^d {d + 1 \choose i} \cdot i \cdot y^{i - 1}.$$
@@ -1486,7 +1486,7 @@ theorem mem_map_rangeS {p : S[X]} : p ∈ (mapRingHom f).srange ↔ ∀ n, p.coe
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_3 : Ring.{u1} R] [_inst_4 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) {p : Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_4)}, Iff (Membership.Mem.{u2, u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_4)) (Subring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_4)) (Polynomial.ring.{u2} S _inst_4)) (SetLike.hasMem.{u2, u2} (Subring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_4)) (Polynomial.ring.{u2} S _inst_4)) (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_4)) (Subring.setLike.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_4)) (Polynomial.ring.{u2} S _inst_4))) p (RingHom.range.{u1, u2} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_4)) (Polynomial.ring.{u1} R _inst_3) (Polynomial.ring.{u2} S _inst_4) (Polynomial.mapRingHom.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u2} S _inst_4) f))) (forall (n : Nat), Membership.Mem.{u2, u2} S (Subring.{u2} S _inst_4) (SetLike.hasMem.{u2, u2} (Subring.{u2} S _inst_4) S (Subring.setLike.{u2} S _inst_4)) (Polynomial.coeff.{u2} S (Ring.toSemiring.{u2} S _inst_4) p n) (RingHom.range.{u1, u2} R S _inst_3 _inst_4 f))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_3 : Ring.{u2} R] [_inst_4 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) {p : Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_4)}, Iff (Membership.mem.{u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_4)) (Subring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_4)) (Polynomial.ring.{u1} S _inst_4)) (SetLike.instMembership.{u1, u1} (Subring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_4)) (Polynomial.ring.{u1} S _inst_4)) (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_4)) (Subring.instSetLikeSubring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_4)) (Polynomial.ring.{u1} S _inst_4))) p (RingHom.range.{u2, u1} (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_4)) (Polynomial.ring.{u2} R _inst_3) (Polynomial.ring.{u1} S _inst_4) (Polynomial.mapRingHom.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u1} S _inst_4) f))) (forall (n : Nat), Membership.mem.{u1, u1} S (Subring.{u1} S _inst_4) (SetLike.instMembership.{u1, u1} (Subring.{u1} S _inst_4) S (Subring.instSetLikeSubring.{u1} S _inst_4)) (Polynomial.coeff.{u1} S (Ring.toSemiring.{u1} S _inst_4) p n) (RingHom.range.{u2, u1} R S _inst_3 _inst_4 f))
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_3 : Ring.{u2} R] [_inst_4 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4))) {p : Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_4)}, Iff (Membership.mem.{u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_4)) (Subring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_4)) (Polynomial.ring.{u1} S _inst_4)) (SetLike.instMembership.{u1, u1} (Subring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_4)) (Polynomial.ring.{u1} S _inst_4)) (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_4)) (Subring.instSetLikeSubring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_4)) (Polynomial.ring.{u1} S _inst_4))) p (RingHom.range.{u2, u1} (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_4)) (Polynomial.ring.{u2} R _inst_3) (Polynomial.ring.{u1} S _inst_4) (Polynomial.mapRingHom.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u1} S _inst_4) f))) (forall (n : Nat), Membership.mem.{u1, u1} S (Subring.{u1} S _inst_4) (SetLike.instMembership.{u1, u1} (Subring.{u1} S _inst_4) S (Subring.instSetLikeSubring.{u1} S _inst_4)) (Polynomial.coeff.{u1} S (Ring.toSemiring.{u1} S _inst_4) p n) (RingHom.range.{u2, u1} R S _inst_3 _inst_4 f))
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_map_range Polynomial.mem_map_rangeₓ'. -/
 theorem mem_map_range {R S : Type _} [Ring R] [Ring S] (f : R →+* S) {p : S[X]} :
     p ∈ (mapRingHom f).range ↔ ∀ n, p.coeff n ∈ f.range :=
@@ -1575,7 +1575,7 @@ theorem eval_nat_cast_map (f : R →+* S) (p : R[X]) (n : ℕ) : (p.map f).eval
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_3 : Ring.{u1} R] [_inst_4 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (i : Int), Eq.{succ u2} S (Polynomial.eval.{u2} S (Ring.toSemiring.{u2} S _inst_4) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Int S (HasLiftT.mk.{1, succ u2} Int S (CoeTCₓ.coe.{1, succ u2} Int S (Int.castCoe.{u2} S (AddGroupWithOne.toHasIntCast.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S _inst_4)))))) i) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u2} S _inst_4) f p)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) f (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_3) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_3)))))) i) p))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_3 : Ring.{u2} R] [_inst_4 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) (p : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (i : Int), Eq.{succ u1} S (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S _inst_4) (Int.cast.{u1} S (Ring.toIntCast.{u1} S _inst_4) i) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u1} S _inst_4) f p)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4)))))) f (Polynomial.eval.{u2} R (Ring.toSemiring.{u2} R _inst_3) (Int.cast.{u2} R (Ring.toIntCast.{u2} R _inst_3) i) p))
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_3 : Ring.{u2} R] [_inst_4 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4))) (p : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (i : Int), Eq.{succ u1} S (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S _inst_4) (Int.cast.{u1} S (Ring.toIntCast.{u1} S _inst_4) i) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u1} S _inst_4) f p)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4))) R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_4)))))) f (Polynomial.eval.{u2} R (Ring.toSemiring.{u2} R _inst_3) (Int.cast.{u2} R (Ring.toIntCast.{u2} R _inst_3) i) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_int_cast_map Polynomial.eval_int_cast_mapₓ'. -/
 @[simp]
 theorem eval_int_cast_map {R S : Type _} [Ring R] [Ring S] (f : R →+* S) (p : R[X]) (i : ℤ) :
@@ -1838,7 +1838,7 @@ theorem prod_comp {ι : Type _} (s : Finset ι) (p : ι → R[X]) (q : R[X]) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] [_inst_4 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))] {ι : Type.{u2}} (s : Finset.{u2} ι) (p : ι -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (x : R), Iff (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) (Finset.prod.{u1, u2} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.commRing.{u1} R _inst_3)) s (fun (j : ι) => p j)) x) (Exists.{succ u2} ι (fun (i : ι) => Exists.{0} (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) (fun (H : Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) => Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) (p i) x)))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] [_inst_4 : IsDomain.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))] {ι : Type.{u1}} (s : Finset.{u1} ι) (p : ι -> (Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)))) (x : R), Iff (Polynomial.IsRoot.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Finset.prod.{u2, u1} (Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Polynomial.commRing.{u2} R _inst_3)) s (fun (j : ι) => p j)) x) (Exists.{succ u1} ι (fun (i : ι) => And (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) (Polynomial.IsRoot.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (p i) x)))
+  forall {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] [_inst_4 : IsDomain.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))] {ι : Type.{u1}} (s : Finset.{u1} ι) (p : ι -> (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (x : R), Iff (Polynomial.IsRoot.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Finset.prod.{u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.commRing.{u2} R _inst_3)) s (fun (j : ι) => p j)) x) (Exists.{succ u1} ι (fun (i : ι) => And (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) (Polynomial.IsRoot.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (p i) x)))
 Case conversion may be inaccurate. Consider using '#align polynomial.is_root_prod Polynomial.isRoot_prodₓ'. -/
 theorem isRoot_prod {R} [CommRing R] [IsDomain R] {ι : Type _} (s : Finset ι) (p : ι → R[X])
     (x : R) : IsRoot (∏ j in s, p j) x ↔ ∃ i ∈ s, IsRoot (p i) x := by
@@ -1928,7 +1928,7 @@ theorem IsRoot.map {f : R →+* S} {x : R} {p : R[X]} (h : IsRoot p x) : IsRoot
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))} {x : R} {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))}, (Polynomial.IsRoot.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (CommSemiring.toSemiring.{u1} S _inst_2) f p) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) f x)) -> (Function.Injective.{succ u2, succ u1} R S (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) f)) -> (Polynomial.IsRoot.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) p x)
 but is expected to have type
-  forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))}, (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x)) -> (Function.Injective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f)) -> (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p x)
+  forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))}, (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x)) -> (Function.Injective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f)) -> (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) p x)
 Case conversion may be inaccurate. Consider using '#align polynomial.is_root.of_map Polynomial.IsRoot.of_mapₓ'. -/
 theorem IsRoot.of_map {R} [CommRing R] {f : R →+* S} {x : R} {p : R[X]} (h : IsRoot (p.map f) (f x))
     (hf : Function.Injective f) : IsRoot p x := by
@@ -1939,7 +1939,7 @@ theorem IsRoot.of_map {R} [CommRing R] {f : R →+* S} {x : R} {p : R[X]} (h : I
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))} {x : R} {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))}, (Function.Injective.{succ u2, succ u1} R S (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) f)) -> (Iff (Polynomial.IsRoot.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (CommSemiring.toSemiring.{u1} S _inst_2) f p) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) f x)) (Polynomial.IsRoot.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) p x))
 but is expected to have type
-  forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))}, (Function.Injective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f)) -> (Iff (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x)) (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p x))
+  forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))}, (Function.Injective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f)) -> (Iff (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x)) (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) p x))
 Case conversion may be inaccurate. Consider using '#align polynomial.is_root_map_iff Polynomial.isRoot_map_iffₓ'. -/
 theorem isRoot_map_iff {R : Type _} [CommRing R] {f : R →+* S} {x : R} {p : R[X]}
     (hf : Function.Injective f) : IsRoot (p.map f) (f x) ↔ IsRoot p x :=
@@ -1978,7 +1978,7 @@ theorem C_sub : C (a - b) = C a - C b :=
 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)} {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))), Eq.{succ u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) f (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)) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (instHSub.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.sub.{u2} S _inst_2)) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) f p) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) f q))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)} {q : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)} {S : Type.{u1}} [_inst_2 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2))), Eq.{succ u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_2)) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (instHSub.{u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Polynomial.sub.{u2} R _inst_1)) p q)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_2)) (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_2)) (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_2)) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_2)) (Polynomial.sub.{u1} S _inst_2)) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f p) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f q))
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)} {q : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)} {S : Type.{u1}} [_inst_2 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))), Eq.{succ u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_2)) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (instHSub.{u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Polynomial.sub.{u2} R _inst_1)) p q)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_2)) (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_2)) (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_2)) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_2)) (Polynomial.sub.{u1} S _inst_2)) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f p) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f q))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_sub Polynomial.map_subₓ'. -/
 @[simp]
 protected theorem map_sub {S} [Ring S] (f : R →+* S) : (p - q).map f = p.map f - q.map f :=
@@ -1989,7 +1989,7 @@ protected theorem map_sub {S} [Ring S] (f : R →+* S) : (p - q).map f = p.map f
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))), Eq.{succ u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) f (Neg.neg.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.neg'.{u1} R _inst_1) p)) (Neg.neg.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.neg'.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) f p))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)} {S : Type.{u1}} [_inst_2 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2))), Eq.{succ u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_2)) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f (Neg.neg.{u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Polynomial.neg'.{u2} R _inst_1) p)) (Neg.neg.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_2)) (Polynomial.neg'.{u1} S _inst_2) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f p))
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)} {S : Type.{u1}} [_inst_2 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))), Eq.{succ u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_2)) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f (Neg.neg.{u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Polynomial.neg'.{u2} R _inst_1) p)) (Neg.neg.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_2)) (Polynomial.neg'.{u1} S _inst_2) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f p))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_neg Polynomial.map_negₓ'. -/
 @[simp]
 protected theorem map_neg {S} [Ring S] (f : R →+* S) : (-p).map f = -p.map f :=
@@ -2000,7 +2000,7 @@ protected theorem map_neg {S} [Ring S] (f : R →+* S) : (-p).map f = -p.map f :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (n : Int), Eq.{succ u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) f ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasLiftT.mk.{1, succ u1} Int (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (CoeTCₓ.coe.{1, succ u1} Int (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Int.castCoe.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.intCast.{u1} R _inst_1)))) n)) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Int (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (HasLiftT.mk.{1, succ u2} Int (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (CoeTCₓ.coe.{1, succ u2} Int (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Int.castCoe.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.intCast.{u2} S _inst_2)))) n)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {S : Type.{u1}} [_inst_2 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2))) (n : Int), Eq.{succ u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_2)) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f (Int.cast.{u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Polynomial.intCast.{u2} R _inst_1) n)) (Int.cast.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_2)) (Polynomial.intCast.{u1} S _inst_2) n)
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {S : Type.{u1}} [_inst_2 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) (n : Int), Eq.{succ u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_2)) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f (Int.cast.{u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Polynomial.intCast.{u2} R _inst_1) n)) (Int.cast.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S _inst_2)) (Polynomial.intCast.{u1} S _inst_2) n)
 Case conversion may be inaccurate. Consider using '#align polynomial.map_int_cast Polynomial.map_int_castₓ'. -/
 @[simp]
 theorem map_int_cast {S} [Ring S] (f : R →+* S) (n : ℤ) : map f ↑n = ↑n :=
@@ -2022,7 +2022,7 @@ theorem eval_int_cast {n : ℤ} {x : R} : (n : R[X]).eval x = n := by
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) {x : S}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) f x (Neg.neg.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.neg'.{u1} R _inst_1) p)) (Neg.neg.{u2} S (SubNegMonoid.toHasNeg.{u2} S (AddGroup.toSubNegMonoid.{u2} S (AddGroupWithOne.toAddGroup.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S _inst_2))))) (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) f x p))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)} {S : Type.{u1}} [_inst_2 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2))) {x : S}, Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f x (Neg.neg.{u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Polynomial.neg'.{u2} R _inst_1) p)) (Neg.neg.{u1} S (Ring.toNeg.{u1} S _inst_2) (Polynomial.eval₂.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f x p))
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)} {S : Type.{u1}} [_inst_2 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) {x : S}, Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f x (Neg.neg.{u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Polynomial.neg'.{u2} R _inst_1) p)) (Neg.neg.{u1} S (Ring.toNeg.{u1} S _inst_2) (Polynomial.eval₂.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f x p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_neg Polynomial.eval₂_negₓ'. -/
 @[simp]
 theorem eval₂_neg {S} [Ring S] (f : R →+* S) {x : S} : (-p).eval₂ f x = -p.eval₂ f x := by
@@ -2033,7 +2033,7 @@ theorem eval₂_neg {S} [Ring S] (f : R →+* S) {x : S} : (-p).eval₂ f x = -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)} {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) {x : S}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) f x (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)) (HSub.hSub.{u2, u2, u2} S S S (instHSub.{u2} S (SubNegMonoid.toHasSub.{u2} S (AddGroup.toSubNegMonoid.{u2} S (AddGroupWithOne.toAddGroup.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S _inst_2)))))) (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) f x p) (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) f x q))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)} {q : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)} {S : Type.{u1}} [_inst_2 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2))) {x : S}, Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f x (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (instHSub.{u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Polynomial.sub.{u2} R _inst_1)) p q)) (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (Ring.toSub.{u1} S _inst_2)) (Polynomial.eval₂.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f x p) (Polynomial.eval₂.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f x q))
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)} {q : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)} {S : Type.{u1}} [_inst_2 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) {x : S}, Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f x (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (instHSub.{u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Polynomial.sub.{u2} R _inst_1)) p q)) (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (Ring.toSub.{u1} S _inst_2)) (Polynomial.eval₂.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f x p) (Polynomial.eval₂.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f x q))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_sub Polynomial.eval₂_subₓ'. -/
 @[simp]
 theorem eval₂_sub {S} [Ring S] (f : R →+* S) {x : S} :

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

@@ -1645,6 +1645,7 @@ theorem eval₂_comp {x : S} : eval₂ f x (p.comp q) = eval₂ f (eval₂ f x q
 #align polynomial.eval₂_comp Polynomial.eval₂_comp
 -/
 
+#print Polynomial.iterate_comp_eval₂ /-
 @[simp]
 theorem iterate_comp_eval₂ (k : ℕ) (t : S) :
     eval₂ f t ((p.comp^[k]) q) = ((fun x => eval₂ f x p)^[k]) (eval₂ f t q) :=
@@ -1653,6 +1654,7 @@ theorem iterate_comp_eval₂ (k : ℕ) (t : S) :
   · simp
   · rw [Function.iterate_succ_apply', Function.iterate_succ_apply', eval₂_comp, IH]
 #align polynomial.iterate_comp_eval₂ Polynomial.iterate_comp_eval₂
+-/
 
 end
 

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

@@ -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.eval
-! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
+! leanprover-community/mathlib commit 728baa2f54e6062c5879a3e397ac6bac323e506f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1645,6 +1645,15 @@ theorem eval₂_comp {x : S} : eval₂ f x (p.comp q) = eval₂ f (eval₂ f x q
 #align polynomial.eval₂_comp Polynomial.eval₂_comp
 -/
 
+@[simp]
+theorem iterate_comp_eval₂ (k : ℕ) (t : S) :
+    eval₂ f t ((p.comp^[k]) q) = ((fun x => eval₂ f x p)^[k]) (eval₂ f t q) :=
+  by
+  induction' k with k IH
+  · simp
+  · rw [Function.iterate_succ_apply', Function.iterate_succ_apply', eval₂_comp, IH]
+#align polynomial.iterate_comp_eval₂ Polynomial.iterate_comp_eval₂
+
 end
 
 section
@@ -1705,6 +1714,12 @@ theorem eval_comp : (p.comp q).eval x = p.eval (q.eval x) :=
 #align polynomial.eval_comp Polynomial.eval_comp
 -/
 
+@[simp]
+theorem iterate_comp_eval :
+    ∀ (k : ℕ) (t : R), ((p.comp^[k]) q).eval t = ((fun x => p.eval x)^[k]) (q.eval t) :=
+  iterate_comp_eval₂ _
+#align polynomial.iterate_comp_eval Polynomial.iterate_comp_eval
+
 #print Polynomial.compRingHom /-
 /-- `comp p`, regarded as a ring homomorphism from `R[X]` to itself. -/
 def compRingHom : R[X] → R[X] →+* R[X] :=

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

@@ -697,7 +697,7 @@ theorem eval_C_mul : (C a * p).eval x = a * p.eval x :=
 
 /- warning: polynomial.eval_monomial_one_add_sub -> Polynomial.eval_monomial_one_add_sub is a dubious translation:
 lean 3 declaration is
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(HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) d) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))))))) (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) y (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) d) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))))))) (Finset.sum.{u1, 0} S Nat (AddCommGroup.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toAddCommGroup.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) d (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (x_1 : Nat) => HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Nat.choose (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) d (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x_1)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) x_1) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (Ring.toMonoid.{u1} S (CommRing.toRing.{u1} S _inst_2)))) y (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) x_1 (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (d : Nat) (y : S), Eq.{succ u1} S (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (SubNegMonoid.toHasSub.{u1} S (AddGroup.toSubNegMonoid.{u1} S (AddGroupWithOne.toAddGroup.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) y) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) d) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2))))))))))) (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) y (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) d) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))))))) (Finset.sum.{u1, 0} S Nat (AddCommGroup.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toAddCommGroup.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) d (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (x_1 : Nat) => HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Nat.choose (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) d (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x_1)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) x_1) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (Ring.toMonoid.{u1} S (CommRing.toRing.{u1} S _inst_2)))) y (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) x_1 (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
 but is expected to have type
   forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (d : Nat) (y : S), Eq.{succ u1} S (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (Ring.toSub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (NonAssocRing.toOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) y) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))) d) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (NonAssocRing.toOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) y (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))) d) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (NonAssocRing.toOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))))) (Finset.sum.{u1, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) d (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x_1 : Nat) => HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Nat.choose (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) d (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x_1)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))) x_1) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) y (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) x_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_monomial_one_add_sub Polynomial.eval_monomial_one_add_subₓ'. -/
@@ -1573,7 +1573,7 @@ theorem eval_nat_cast_map (f : R →+* S) (p : R[X]) (n : ℕ) : (p.map f).eval
 
 /- warning: polynomial.eval_int_cast_map -> Polynomial.eval_int_cast_map is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_3 : Ring.{u1} R] [_inst_4 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (i : Int), Eq.{succ u2} S (Polynomial.eval.{u2} S (Ring.toSemiring.{u2} S _inst_4) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Int S (HasLiftT.mk.{1, succ u2} Int S (CoeTCₓ.coe.{1, succ u2} Int S (Int.castCoe.{u2} S (AddGroupWithOne.toHasIntCast.{u2} S (NonAssocRing.toAddGroupWithOne.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4)))))) i) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u2} S _inst_4) f p)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) f (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_3) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)))))) i) p))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_3 : Ring.{u1} R] [_inst_4 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (i : Int), Eq.{succ u2} S (Polynomial.eval.{u2} S (Ring.toSemiring.{u2} S _inst_4) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Int S (HasLiftT.mk.{1, succ u2} Int S (CoeTCₓ.coe.{1, succ u2} Int S (Int.castCoe.{u2} S (AddGroupWithOne.toHasIntCast.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S _inst_4)))))) i) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u2} S _inst_4) f p)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) f (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_3) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_3)))))) i) p))
 but is expected to have type
   forall {R : Type.{u2}} {S : Type.{u1}} [_inst_3 : Ring.{u2} R] [_inst_4 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) (p : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (i : Int), Eq.{succ u1} S (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S _inst_4) (Int.cast.{u1} S (Ring.toIntCast.{u1} S _inst_4) i) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u1} S _inst_4) f p)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4)))))) f (Polynomial.eval.{u2} R (Ring.toSemiring.{u2} R _inst_3) (Int.cast.{u2} R (Ring.toIntCast.{u2} R _inst_3) i) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_int_cast_map Polynomial.eval_int_cast_mapₓ'. -/
@@ -1939,7 +1939,7 @@ variable [Ring R] {p q r : R[X]}
 
 /- warning: polynomial.C_neg -> Polynomial.C_neg is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} (Polynomial.{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)) (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))))) a)) (Neg.neg.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.neg'.{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)) a))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} (Polynomial.{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)) (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))))) a)) (Neg.neg.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.neg'.{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)) a))
 but is expected to have type
   forall {R : Type.{u1}} {a : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) a)) (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)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) a)) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (Polynomial.neg'.{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)) a))
 Case conversion may be inaccurate. Consider using '#align polynomial.C_neg Polynomial.C_negₓ'. -/
@@ -1949,7 +1949,7 @@ theorem C_neg : C (-a) = -C a :=
 
 /- warning: polynomial.C_sub -> Polynomial.C_sub is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} {a : R} {b : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} (Polynomial.{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)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) a b)) (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)) (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)) a) (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)) b))
 but is expected to have type
   forall {R : Type.{u1}} {a : R} {b : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) a b)) (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)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) a b)) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) b) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (instHSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (Polynomial.sub.{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)) a) (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)) b))
 Case conversion may be inaccurate. Consider using '#align polynomial.C_sub Polynomial.C_subₓ'. -/
@@ -1992,7 +1992,7 @@ theorem map_int_cast {S} [Ring S] (f : R →+* S) (n : ℤ) : map f ↑n = ↑n
 
 /- warning: polynomial.eval_int_cast -> Polynomial.eval_int_cast is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {n : Int} {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasLiftT.mk.{1, succ u1} Int (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (CoeTCₓ.coe.{1, succ u1} Int (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Int.castCoe.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.intCast.{u1} R _inst_1)))) n)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) n)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {n : Int} {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasLiftT.mk.{1, succ u1} Int (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (CoeTCₓ.coe.{1, succ u1} Int (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Int.castCoe.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.intCast.{u1} R _inst_1)))) n)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) n)
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {n : Int} {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x (Int.cast.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.intCast.{u1} R _inst_1) n)) (Int.cast.{u1} R (Ring.toIntCast.{u1} R _inst_1) n)
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_int_cast Polynomial.eval_int_castₓ'. -/
@@ -2003,7 +2003,7 @@ theorem eval_int_cast {n : ℤ} {x : R} : (n : R[X]).eval x = n := by
 
 /- warning: polynomial.eval₂_neg -> Polynomial.eval₂_neg 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)} {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) {x : S}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) f x (Neg.neg.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.neg'.{u1} R _inst_1) p)) (Neg.neg.{u2} S (SubNegMonoid.toHasNeg.{u2} S (AddGroup.toSubNegMonoid.{u2} S (AddGroupWithOne.toAddGroup.{u2} S (NonAssocRing.toAddGroupWithOne.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))))) (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) f x p))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) {x : S}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) f x (Neg.neg.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.neg'.{u1} R _inst_1) p)) (Neg.neg.{u2} S (SubNegMonoid.toHasNeg.{u2} S (AddGroup.toSubNegMonoid.{u2} S (AddGroupWithOne.toAddGroup.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S _inst_2))))) (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) f x p))
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)} {S : Type.{u1}} [_inst_2 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2))) {x : S}, Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f x (Neg.neg.{u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Polynomial.neg'.{u2} R _inst_1) p)) (Neg.neg.{u1} S (Ring.toNeg.{u1} S _inst_2) (Polynomial.eval₂.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f x p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_neg Polynomial.eval₂_negₓ'. -/
@@ -2014,7 +2014,7 @@ theorem eval₂_neg {S} [Ring S] (f : R →+* S) {x : S} : (-p).eval₂ f x = -p
 
 /- warning: polynomial.eval₂_sub -> Polynomial.eval₂_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)} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) {x : S}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) f x (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)) (HSub.hSub.{u2, u2, u2} S S S (instHSub.{u2} S (SubNegMonoid.toHasSub.{u2} S (AddGroup.toSubNegMonoid.{u2} S (AddGroupWithOne.toAddGroup.{u2} S (NonAssocRing.toAddGroupWithOne.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2)))))) (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) f x p) (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) f x 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)} {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) {x : S}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) f x (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)) (HSub.hSub.{u2, u2, u2} S S S (instHSub.{u2} S (SubNegMonoid.toHasSub.{u2} S (AddGroup.toSubNegMonoid.{u2} S (AddGroupWithOne.toAddGroup.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S _inst_2)))))) (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) f x p) (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) f x q))
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)} {q : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)} {S : Type.{u1}} [_inst_2 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2))) {x : S}, Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f x (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (instHSub.{u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Polynomial.sub.{u2} R _inst_1)) p q)) (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (Ring.toSub.{u1} S _inst_2)) (Polynomial.eval₂.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f x p) (Polynomial.eval₂.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S _inst_2) f x q))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_sub Polynomial.eval₂_subₓ'. -/
@@ -2026,7 +2026,7 @@ theorem eval₂_sub {S} [Ring S] (f : R →+* S) {x : S} :
 
 /- warning: polynomial.eval_neg -> Polynomial.eval_neg 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)) (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x (Neg.neg.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.neg'.{u1} R _inst_1) p)) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x p))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x (Neg.neg.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.neg'.{u1} R _inst_1) p)) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x 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)) (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x (Neg.neg.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.neg'.{u1} R _inst_1) p)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_neg Polynomial.eval_negₓ'. -/
@@ -2037,7 +2037,7 @@ theorem eval_neg (p : R[X]) (x : R) : (-p).eval x = -p.eval x :=
 
 /- warning: polynomial.eval_sub -> Polynomial.eval_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)) (q : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x (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)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x p) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x 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)) (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x (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)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x p) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x 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)) (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x (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)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x p) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x q))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_sub Polynomial.eval_subₓ'. -/

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.eval
-! leanprover-community/mathlib commit e064a7bf82ad94c3c17b5128bbd860d1ec34874e
+! 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.Data.Polynomial.Induction
 /-!
 # Theory of univariate polynomials
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The main defs here are `eval₂`, `eval`, and `map`.
 We give several lemmas about their interaction with each other and with module operations.
 -/

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

@@ -53,7 +53,7 @@ irreducible_def eval₂ (p : R[X]) : S :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {x : S}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Polynomial.sum.{u1, u2} R _inst_1 S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) p (fun (e : Nat) (a : R) => HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (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 a) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x e)))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {x : S}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Polynomial.sum.{u1, u2} R _inst_1 S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) p (fun (e : Nat) (a : R) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2)))) (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 a) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x e)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {x : S}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Polynomial.sum.{u1, u2} R _inst_1 S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) p (fun (e : Nat) (a : R) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2)))) (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 a) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x e)))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_eq_sum Polynomial.eval₂_eq_sumₓ'. -/
 theorem eval₂_eq_sum {f : R →+* S} {x : S} : p.eval₂ f x = p.Sum fun e a => f a * x ^ e := by
   rw [eval₂]
@@ -74,7 +74,7 @@ theorem eval₂_congr {R S : Type _} [Semiring R] [Semiring S] {f g : R →+* S}
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))))) 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.coeff.{u1} R _inst_1 p (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) 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.coeff.{u1} R _inst_1 p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) 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.coeff.{u1} R _inst_1 p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_at_zero Polynomial.eval₂_at_zeroₓ'. -/
 @[simp]
 theorem eval₂_at_zero : p.eval₂ f 0 = f (coeff p 0) := by
@@ -97,7 +97,7 @@ theorem eval₂_zero : (0 : R[X]).eval₂ f x = 0 := by simp [eval₂_eq_sum]
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_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)) (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a)) (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 a)
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_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)) (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) (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 a)
+  forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_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)) (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) (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 a)
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_C Polynomial.eval₂_Cₓ'. -/
 @[simp]
 theorem eval₂_C : (C a).eval₂ f x = f a := by simp [eval₂_eq_sum]
@@ -113,7 +113,7 @@ theorem eval₂_X : X.eval₂ f x = x := by simp [eval₂_eq_sum]
 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)) (x : S) {n : Nat} {r : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (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 r) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x n))
 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)) (x : S) {n : Nat} {r : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) _inst_2)))) (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 r) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x n))
+  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)) (x : S) {n : Nat} {r : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2)))) (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 r) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x n))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_monomial Polynomial.eval₂_monomialₓ'. -/
 @[simp]
 theorem eval₂_monomial {n : ℕ} {r : R} : (monomial n r).eval₂ f x = f r * x ^ n := by
@@ -174,7 +174,7 @@ theorem eval₂_bit1 : (bit1 p).eval₂ f x = bit1 (p.eval₂ f x) := by
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (p : Polynomial.{u1} R _inst_1) (x : S) {s : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 g x (SMul.smul.{u1, u1} R (Polynomial.{u1} R _inst_1) (SMulZeroClass.toHasSmul.{u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1) (Polynomial.smulZeroClass.{u1, u1} R _inst_1 R (SMulWithZero.toSmulZeroClass.{u1, u1} R R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) s p)) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (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)) g s) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 g x p))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (p : Polynomial.{u1} R _inst_1) (x : S) {s : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 g x (HSMul.hSMul.{u1, u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1) (Polynomial.smulZeroClass.{u1, u1} R _inst_1 R (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) s p)) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) s) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) s) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) s) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) s) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) s) _inst_2)))) (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))))) g s) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 g x p))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (p : Polynomial.{u1} R _inst_1) (x : S) {s : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 g x (HSMul.hSMul.{u1, u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1) (Polynomial.smulZeroClass.{u1, u1} R _inst_1 R (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) s p)) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) s) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) s) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) s) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) s) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) s) _inst_2)))) (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))))) g s) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 g x p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_smul Polynomial.eval₂_smulₓ'. -/
 @[simp]
 theorem eval₂_smul (g : R →+* S) (p : R[X]) (x : S) {s : R} :
@@ -259,7 +259,7 @@ theorem eval₂_finset_sum (s : Finset ι) (g : ι → R[X]) (x : S) :
 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)} {x : S} {p : AddMonoidAlgebra.{u1, 0} R Nat _inst_1}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (Polynomial.ofFinsupp.{u1} R _inst_1 p)) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{0, u1} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (fun (_x : AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{0, u1} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) => (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) -> S) (AddMonoidHom.hasCoeToFun.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{0, u1} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidAlgebra.liftNC.{u1, 0, u2} R Nat S _inst_1 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) ((fun (a : Sort.{max (succ u1) (succ u2)}) (b : Sort.{max (succ u2) (succ u1)}) [self : HasLiftT.{max (succ u1) (succ u2), max (succ u2) (succ u1)} a b] => self.0) (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoidHom.{u1, u2} R S (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (HasLiftT.mk.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoidHom.{u1, u2} R S (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (CoeTCₓ.coe.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoidHom.{u1, u2} R S (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidHom.hasCoeT.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (RingHomClass.toAddMonoidHomClass.{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.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) f) (coeFn.{succ u2, succ u2} (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (fun (_x : MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) => (Multiplicative.{0} Nat) -> S) (MonoidHom.hasCoeToFun.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} S (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) (fun (_x : Equiv.{succ u2, succ u2} S (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) => S -> (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) (Equiv.hasCoeToFun.{succ u2, succ u2} S (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) (powersHom.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) x))) 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)} {x : S} {p : AddMonoidAlgebra.{u1, 0} R Nat _inst_1}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (Polynomial.ofFinsupp.{u1} R _inst_1 p)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (fun (_x : AddMonoidAlgebra.{u1, 0} R Nat _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : AddMonoidAlgebra.{u1, 0} R Nat _inst_1) => S) _x) (AddHomClass.toFunLike.{max u2 u1, u1, u2} (AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddZeroClass.toAdd.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1)))) (AddZeroClass.toAdd.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidHomClass.toAddHomClass.{max u2 u1, u1, u2} (AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (AddMonoidHom.addMonoidHomClass.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) (AddMonoidAlgebra.liftNC.{u1, 0, u2} R Nat S _inst_1 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoidHomClass.toAddMonoidHom.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (RingHomClass.toAddMonoidHomClass.{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) (FunLike.coe.{succ u2, 1, succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x) (Multiplicative.{0} Nat) (fun (_x : Multiplicative.{0} Nat) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Multiplicative.{0} Nat) => S) _x) (MulHomClass.toFunLike.{u2, 0, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x) (Multiplicative.{0} Nat) S (MulOneClass.toMul.{0} (Multiplicative.{0} Nat) (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (MulOneClass.toMul.{u2} S (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (MonoidHomClass.toMulHomClass.{u2, 0, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x) (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (MonoidHom.monoidHomClass.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} S (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} S (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) (powersHom.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) x))) 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)} {x : S} {p : AddMonoidAlgebra.{u1, 0} R Nat _inst_1}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (Polynomial.ofFinsupp.{u1} R _inst_1 p)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (fun (_x : AddMonoidAlgebra.{u1, 0} R Nat _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : AddMonoidAlgebra.{u1, 0} R Nat _inst_1) => S) _x) (AddHomClass.toFunLike.{max u2 u1, u1, u2} (AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddZeroClass.toAdd.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1)))) (AddZeroClass.toAdd.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidHomClass.toAddHomClass.{max u2 u1, u1, u2} (AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (AddMonoidHom.addMonoidHomClass.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) (AddMonoidAlgebra.liftNC.{u1, 0, u2} R Nat S _inst_1 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoidHomClass.toAddMonoidHom.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (RingHomClass.toAddMonoidHomClass.{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) (FunLike.coe.{succ u2, 1, succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x) (Multiplicative.{0} Nat) (fun (_x : Multiplicative.{0} Nat) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Multiplicative.{0} Nat) => S) _x) (MulHomClass.toFunLike.{u2, 0, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x) (Multiplicative.{0} Nat) S (MulOneClass.toMul.{0} (Multiplicative.{0} Nat) (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (MulOneClass.toMul.{u2} S (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (MonoidHomClass.toMulHomClass.{u2, 0, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x) (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (MonoidHom.monoidHomClass.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} S (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} S (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) (powersHom.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) x))) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_of_finsupp Polynomial.eval₂_ofFinsuppₓ'. -/
 theorem eval₂_ofFinsupp {f : R →+* S} {x : S} {p : AddMonoidAlgebra R ℕ} :
     eval₂ f x (⟨p⟩ : R[X]) = liftNC (↑f) (powersHom S x) p :=
@@ -272,7 +272,7 @@ theorem eval₂_ofFinsupp {f : R →+* S} {x : S} {p : AddMonoidAlgebra R ℕ} :
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), (forall (k : Nat), Commute.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (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.coeff.{u1} R _inst_1 q k)) x) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (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)) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x q)))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), (forall (k : Nat), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) _inst_2))) (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.coeff.{u1} R _inst_1 q k)) x) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (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)) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x q)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), (forall (k : Nat), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) _inst_2))) (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.coeff.{u1} R _inst_1 q k)) x) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (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)) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x q)))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_mul_noncomm Polynomial.eval₂_mul_noncommₓ'. -/
 theorem eval₂_mul_noncomm (hf : ∀ k, Commute (f <| q.coeff k) x) :
     eval₂ f x (p * q) = eval₂ f x p * eval₂ f x q :=
@@ -312,7 +312,7 @@ theorem eval₂_X_mul : eval₂ f x (X * p) = eval₂ f x p * x := by rw [X_mul,
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), (Commute.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (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 a) x) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a))) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x 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 a)))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), (Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2))) (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 a) x) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) 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_inst_1 _inst_2 f x 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 a)))
+  forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), (Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) (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 a) x) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a))) (HMul.hMul.{u2, u2, u2} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) S (instHMul.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x 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 a)))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_mul_C' Polynomial.eval₂_mul_C'ₓ'. -/
 theorem eval₂_mul_C' (h : Commute (f a) x) : eval₂ f x (p * C a) = eval₂ f x p * f a :=
   by
@@ -327,7 +327,7 @@ theorem eval₂_mul_C' (h : Commute (f a) x) : eval₂ f x (p * C a) = eval₂ f
 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)) (x : S) (ps : List.{u1} (Polynomial.{u1} R _inst_1)), (forall (p : Polynomial.{u1} R _inst_1), (Membership.Mem.{u1, u1} (Polynomial.{u1} R _inst_1) (List.{u1} (Polynomial.{u1} R _inst_1)) (List.hasMem.{u1} (Polynomial.{u1} R _inst_1)) p ps) -> (forall (k : Nat), Commute.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (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.coeff.{u1} R _inst_1 p k)) x)) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (List.prod.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1) (Polynomial.hasOne.{u1} R _inst_1) ps)) (List.prod.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (AddMonoidWithOne.toOne.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (List.map.{u1, u2} (Polynomial.{u1} R _inst_1) S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x) ps)))
 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)) (x : S) (ps : List.{u1} (Polynomial.{u1} R _inst_1)), (forall (p : Polynomial.{u1} R _inst_1), (Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (List.{u1} (Polynomial.{u1} R _inst_1)) (List.instMembershipList.{u1} (Polynomial.{u1} R _inst_1)) p ps) -> (forall (k : Nat), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) _inst_2))) (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.coeff.{u1} R _inst_1 p k)) x)) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (List.prod.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1) ps)) (List.prod.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toOne.{u2} S _inst_2) (List.map.{u1, u2} (Polynomial.{u1} R _inst_1) S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x) ps)))
+  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)) (x : S) (ps : List.{u1} (Polynomial.{u1} R _inst_1)), (forall (p : Polynomial.{u1} R _inst_1), (Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (List.{u1} (Polynomial.{u1} R _inst_1)) (List.instMembershipList.{u1} (Polynomial.{u1} R _inst_1)) p ps) -> (forall (k : Nat), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) _inst_2))) (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.coeff.{u1} R _inst_1 p k)) x)) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (List.prod.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1) ps)) (List.prod.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toOne.{u2} S _inst_2) (List.map.{u1, u2} (Polynomial.{u1} R _inst_1) S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x) ps)))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_list_prod_noncomm Polynomial.eval₂_list_prod_noncommₓ'. -/
 theorem eval₂_list_prod_noncomm (ps : List R[X])
     (hf : ∀ p ∈ ps, ∀ (k), Commute (f <| coeff p k) x) :
@@ -343,7 +343,7 @@ theorem eval₂_list_prod_noncomm (ps : List R[X])
 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)) (x : S), (forall (a : R), Commute.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (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 a) x) -> (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2))
 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)) (x : S), (forall (a : R), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2))) (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 a) x) -> (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2))
+  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)) (x : S), (forall (a : R), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) (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 a) x) -> (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_ring_hom' Polynomial.eval₂RingHom'ₓ'. -/
 /-- `eval₂` as a `ring_hom` for noncommutative rings -/
 def eval₂RingHom' (f : R →+* S) (x : S) (hf : ∀ a, Commute (f a) x) : R[X] →+* S
@@ -374,7 +374,7 @@ variable [Semiring S] (f : R →+* S) (x : S)
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Finset.sum.{u2, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Polynomial.natDegree.{u1} R _inst_1 p) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (i : Nat) => HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (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.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x i)))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Finset.sum.{u2, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Polynomial.natDegree.{u1} R _inst_1 p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (i : Nat) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) _inst_2)))) (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.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x i)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Finset.sum.{u2, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Polynomial.natDegree.{u1} R _inst_1 p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (i : Nat) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) _inst_2)))) (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.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x i)))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_eq_sum_range Polynomial.eval₂_eq_sum_rangeₓ'. -/
 theorem eval₂_eq_sum_range :
     p.eval₂ f x = ∑ i in Finset.range (p.natDegree + 1), f (p.coeff i) * x ^ i :=
@@ -385,7 +385,7 @@ theorem eval₂_eq_sum_range :
 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)) {p : Polynomial.{u1} R _inst_1} {n : Nat}, (LT.lt.{0} Nat Nat.hasLt (Polynomial.natDegree.{u1} R _inst_1 p) n) -> (forall (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Finset.sum.{u2, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finset.range n) (fun (i : Nat) => HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (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.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x i))))
 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)) {p : Polynomial.{u1} R _inst_1} {n : Nat}, (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 p) n) -> (forall (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Finset.sum.{u2, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finset.range n) (fun (i : Nat) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) _inst_2)))) (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.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x i))))
+  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)) {p : Polynomial.{u1} R _inst_1} {n : Nat}, (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 p) n) -> (forall (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Finset.sum.{u2, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finset.range n) (fun (i : Nat) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) _inst_2)))) (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.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x i))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_eq_sum_range' Polynomial.eval₂_eq_sum_range'ₓ'. -/
 theorem eval₂_eq_sum_range' (f : R →+* S) {p : R[X]} {n : ℕ} (hn : p.natDegree < n) (x : S) :
     eval₂ f x p = ∑ i in Finset.range n, f (p.coeff i) * x ^ i :=
@@ -449,7 +449,7 @@ def eval₂RingHom (f : R →+* S) (x : S) : R[X] →+* S :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (x : S), Eq.{max (succ u1) (succ u2)} ((Polynomial.{u1} R _inst_1) -> S) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => (Polynomial.{u1} R _inst_1) -> S) (RingHom.hasCoeToFun.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.eval₂RingHom.{u1, u2} R S _inst_1 _inst_2 f x)) (Polynomial.eval₂.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) f x)
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (x : S), Eq.{max (succ u1) (succ u2)} (forall (ᾰ : Polynomial.{u1} R _inst_1), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Polynomial.{u1} R _inst_1) => S) ᾰ) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Polynomial.{u1} R _inst_1) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) S (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)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (Polynomial.eval₂RingHom.{u1, u2} R S _inst_1 _inst_2 f x)) (Polynomial.eval₂.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) f x)
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (x : S), Eq.{max (succ u1) (succ u2)} (forall (ᾰ : Polynomial.{u1} R _inst_1), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => S) ᾰ) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) S (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)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (Polynomial.eval₂RingHom.{u1, u2} R S _inst_1 _inst_2 f x)) (Polynomial.eval₂.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) f x)
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_eval₂_ring_hom Polynomial.coe_eval₂RingHomₓ'. -/
 @[simp]
 theorem coe_eval₂RingHom (f : R →+* S) (x) : ⇑(eval₂RingHom f x) = eval₂ f x :=
@@ -542,7 +542,7 @@ theorem eval_eq_sum_range' {p : R[X]} {n : ℕ} (hn : p.natDegree < n) (x : R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (r : R), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (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 r) 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.eval.{u1} R _inst_1 r p))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {p : Polynomial.{u2} R _inst_1} {S : Type.{u1}} [_inst_2 : Semiring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (r : R), Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S _inst_1 _inst_2 f (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f r) p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f (Polynomial.eval.{u2} R _inst_1 r p))
+  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {p : Polynomial.{u2} R _inst_1} {S : Type.{u1}} [_inst_2 : Semiring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (r : R), Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S _inst_1 _inst_2 f (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f r) p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f (Polynomial.eval.{u2} R _inst_1 r p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_at_apply Polynomial.eval₂_at_applyₓ'. -/
 @[simp]
 theorem eval₂_at_apply {S : Type _} [Semiring S] (f : R →+* S) (r : R) :
@@ -556,7 +556,7 @@ theorem eval₂_at_apply {S : Type _} [Semiring S] (f : R →+* S) (r : R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (OfNat.ofNat.{u2} S 1 (OfNat.mk.{u2} S 1 (One.one.{u2} S (AddMonoidWithOne.toOne.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))))) 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.eval.{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))))))) p))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {p : Polynomial.{u2} R _inst_1} {S : Type.{u1}} [_inst_2 : Semiring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)), Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S _inst_1 _inst_2 f (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S _inst_2))) p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f (Polynomial.eval.{u2} R _inst_1 (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R _inst_1))) p))
+  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {p : Polynomial.{u2} R _inst_1} {S : Type.{u1}} [_inst_2 : Semiring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)), Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S _inst_1 _inst_2 f (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S _inst_2))) p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f (Polynomial.eval.{u2} R _inst_1 (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R _inst_1))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_at_one Polynomial.eval₂_at_oneₓ'. -/
 @[simp]
 theorem eval₂_at_one {S : Type _} [Semiring S] (f : R →+* S) : p.eval₂ f 1 = f (p.eval 1) :=
@@ -569,7 +569,7 @@ theorem eval₂_at_one {S : Type _} [Semiring S] (f : R →+* S) : p.eval₂ f 1
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (n : Nat), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u2} Nat S (CoeTCₓ.coe.{1, succ u2} Nat S (Nat.castCoe.{u2} S (AddMonoidWithOne.toNatCast.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))))) n) 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.eval.{u1} R _inst_1 ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) n) p))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {p : Polynomial.{u2} R _inst_1} {S : Type.{u1}} [_inst_2 : Semiring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (n : Nat), Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S _inst_1 _inst_2 f (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S _inst_2) n) p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f (Polynomial.eval.{u2} R _inst_1 (Nat.cast.{u2} R (Semiring.toNatCast.{u2} R _inst_1) n) p))
+  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {p : Polynomial.{u2} R _inst_1} {S : Type.{u1}} [_inst_2 : Semiring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (n : Nat), Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S _inst_1 _inst_2 f (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S _inst_2) n) p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f (Polynomial.eval.{u2} R _inst_1 (Nat.cast.{u2} R (Semiring.toNatCast.{u2} R _inst_1) n) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_at_nat_cast Polynomial.eval₂_at_nat_castₓ'. -/
 @[simp]
 theorem eval₂_at_nat_cast {S : Type _} [Semiring S] (f : R →+* S) (n : ℕ) :
@@ -582,7 +582,7 @@ theorem eval₂_at_nat_cast {S : Type _} [Semiring S] (f : R →+* S) (n : ℕ)
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a)) a
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) a
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) a
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_C Polynomial.eval_Cₓ'. -/
 @[simp]
 theorem eval_C : (C a).eval x = a :=
@@ -606,7 +606,7 @@ theorem eval_X : X.eval x = x :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {x : R} {n : Nat} {a : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {x : R} {n : Nat} {a : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x n))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {x : R} {n : Nat} {a : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x n))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_monomial Polynomial.eval_monomialₓ'. -/
 @[simp]
 theorem eval_monomial {n a} : (monomial n a).eval x = a * x ^ n :=
@@ -680,7 +680,7 @@ theorem eval_smul [Monoid S] [DistribMulAction S R] [IsScalarTower S R R] (s : S
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) p)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a (Polynomial.eval.{u1} R _inst_1 x p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (Polynomial.eval.{u1} R _inst_1 x p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (Polynomial.eval.{u1} R _inst_1 x p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_C_mul Polynomial.eval_C_mulₓ'. -/
 @[simp]
 theorem eval_C_mul : (C a * p).eval x = a * p.eval x :=
@@ -696,7 +696,7 @@ theorem eval_C_mul : (C a * p).eval x = a * p.eval x :=
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (d : Nat) (y : S), Eq.{succ u1} S (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (SubNegMonoid.toHasSub.{u1} S (AddGroup.toSubNegMonoid.{u1} S (AddGroupWithOne.toAddGroup.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) y) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) d) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))))))) (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) y (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) d) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))))))) (Finset.sum.{u1, 0} S Nat (AddCommGroup.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toAddCommGroup.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) d (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (x_1 : Nat) => HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Nat.choose (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) d (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x_1)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) x_1) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (Ring.toMonoid.{u1} S (CommRing.toRing.{u1} S _inst_2)))) y (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) x_1 (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
 but is expected to have type
-  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (d : Nat) (y : S), Eq.{succ u1} S (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (Ring.toSub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (NonAssocRing.toOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) y) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))) d) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (NonAssocRing.toOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) y (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))) d) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (NonAssocRing.toOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))))) (Finset.sum.{u1, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) d (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x_1 : Nat) => HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Nat.choose (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) d (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x_1)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))) x_1) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) y (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) x_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (d : Nat) (y : S), Eq.{succ u1} S (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (Ring.toSub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (NonAssocRing.toOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) y) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))) d) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (NonAssocRing.toOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) y (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))) d) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (NonAssocRing.toOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))))) (Finset.sum.{u1, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) d (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x_1 : Nat) => HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Nat.choose (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) d (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x_1)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Nat.cast.{u1} S (NonAssocRing.toNatCast.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))) x_1) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) y (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) x_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_monomial_one_add_sub Polynomial.eval_monomial_one_add_subₓ'. -/
 /-- A reformulation of the expansion of (1 + y)^d:
 $$(d + 1) (1 + y)^d - (d + 1)y^d = \sum_{i = 0}^d {d + 1 \choose i} \cdot i \cdot y^{i - 1}.$$
@@ -856,7 +856,7 @@ theorem IsRoot.dvd {R : Type _} [CommSemiring R] {p q : R[X]} {x : R} (h : p.IsR
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (a : R), (Ne.{succ u1} R 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)))))))) -> (Not (Polynomial.IsRoot.{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) a))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (a : R), (Ne.{succ u1} R r (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Not (Polynomial.IsRoot.{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) a))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (a : R), (Ne.{succ u1} R r (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Not (Polynomial.IsRoot.{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) a))
 Case conversion may be inaccurate. Consider using '#align polynomial.not_is_root_C Polynomial.not_isRoot_Cₓ'. -/
 theorem not_isRoot_C (r a : R) (hr : r ≠ 0) : ¬IsRoot (C r) a := by simpa using hr
 #align polynomial.not_is_root_C Polynomial.not_isRoot_C
@@ -881,7 +881,7 @@ def comp (p q : R[X]) : R[X] :=
 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}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p q) (Polynomial.sum.{u1, u1} R _inst_1 (Polynomial.{u1} R _inst_1) (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)))) p (fun (e : Nat) (a : R) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) (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))))) q e)))
 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}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p q) (Polynomial.sum.{u1, u1} R _inst_1 (Polynomial.{u1} R _inst_1) (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)))) p (fun (e : Nat) (a : R) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (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))))) q e)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p q) (Polynomial.sum.{u1, u1} R _inst_1 (Polynomial.{u1} R _inst_1) (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)))) p (fun (e : Nat) (a : R) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (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))))) q e)))
 Case conversion may be inaccurate. Consider using '#align polynomial.comp_eq_sum_left Polynomial.comp_eq_sum_leftₓ'. -/
 theorem comp_eq_sum_left : p.comp q = p.Sum fun e a => C a * q ^ e := by rw [comp, eval₂_eq_sum]
 #align polynomial.comp_eq_sum_left Polynomial.comp_eq_sum_left
@@ -906,7 +906,7 @@ theorem X_comp : X.comp p = p :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a)) (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.eval.{u1} R _inst_1 a p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) (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.eval.{u1} R _inst_1 a p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) (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.eval.{u1} R _inst_1 a p))
 Case conversion may be inaccurate. Consider using '#align polynomial.comp_C Polynomial.comp_Cₓ'. -/
 @[simp]
 theorem comp_C : p.comp (C a) = C (p.eval a) := by simp [comp, (C : R →+* _).map_sum]
@@ -916,7 +916,7 @@ theorem comp_C : p.comp (C a) = C (p.eval a) := by simp [comp, (C : R →+* _).m
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) p) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a)
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)
 Case conversion may be inaccurate. Consider using '#align polynomial.C_comp Polynomial.C_compₓ'. -/
 @[simp]
 theorem C_comp : (C a).comp p = C a :=
@@ -933,7 +933,7 @@ theorem nat_cast_comp {n : ℕ} : (n : R[X]).comp p = n := by rw [← C_eq_nat_c
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) (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.eval.{u1} R _inst_1 (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))))))) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) (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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) p))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) (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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.comp_zero Polynomial.comp_zeroₓ'. -/
 @[simp]
 theorem comp_zero : p.comp (0 : R[X]) = C (p.eval 0) := by rw [← C_0, comp_C]
@@ -949,7 +949,7 @@ theorem zero_comp : comp (0 : R[X]) p = 0 := by rw [← C_0, C_comp]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{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))))) (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.eval.{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))))))) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{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)))) (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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))) p))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{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)))) (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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.comp_one Polynomial.comp_oneₓ'. -/
 @[simp]
 theorem comp_one : p.comp 1 = C (p.eval 1) := by rw [← C_1, comp_C]
@@ -972,7 +972,7 @@ theorem add_comp : (p + q).comp r = p.comp r + q.comp r :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a) p) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) (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))))) p n))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a) p) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (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))))) p n))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a) p) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (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))))) p n))
 Case conversion may be inaccurate. Consider using '#align polynomial.monomial_comp Polynomial.monomial_compₓ'. -/
 @[simp]
 theorem monomial_comp (n : ℕ) : (monomial n a).comp p = C a * p ^ n :=
@@ -1015,7 +1015,7 @@ theorem mul_X_pow_comp {k : ℕ} : (p * X ^ k).comp r = p.comp r * r ^ k :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {r : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) p) r) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) (Polynomial.comp.{u1} R _inst_1 p r))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {r : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p) r) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (Polynomial.comp.{u1} R _inst_1 p r))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {r : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p) r) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (Polynomial.comp.{u1} R _inst_1 p r))
 Case conversion may be inaccurate. Consider using '#align polynomial.C_mul_comp Polynomial.C_mul_compₓ'. -/
 @[simp]
 theorem C_mul_comp : (C a * p).comp r = C a * p.comp r :=
@@ -1123,7 +1123,7 @@ def map : R[X] → S[X] :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_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)), Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a)) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (fun (_x : RingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) => S -> (Polynomial.{u2} S _inst_2)) (RingHom.hasCoeToFun.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.C.{u2} S _inst_2) (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 a))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_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)), Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2)))))) (Polynomial.C.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (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 a))
+  forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_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)), Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2)))))) (Polynomial.C.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (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 a))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_C Polynomial.map_Cₓ'. -/
 @[simp]
 theorem map_C : (C a).map f = C (f a) :=
@@ -1141,7 +1141,7 @@ theorem map_X : X.map f = X :=
 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)) {n : Nat} {a : R}, Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) 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 but is expected to have type
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(Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 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(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 a))
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(Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2 _inst_2 (RingHom.id.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2)))) (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.module.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2 (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2)))) (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2) (Polynomial.module.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2 (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2)) (RingHom.id.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2))) (Polynomial.monomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) _inst_2 n) (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 a))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_monomial Polynomial.map_monomialₓ'. -/
 @[simp]
 theorem map_monomial {n a} : (monomial n a).map f = monomial n (f a) :=
@@ -1184,7 +1184,7 @@ protected theorem map_mul : (p * q).map f = p.map f * q.map f :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (r : R), Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (SMul.smul.{u1, u1} R (Polynomial.{u1} R _inst_1) (SMulZeroClass.toHasSmul.{u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1) (Polynomial.smulZeroClass.{u1, u1} R _inst_1 R (SMulWithZero.toSmulZeroClass.{u1, u1} R R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) r p)) (SMul.smul.{u2, u2} S (Polynomial.{u2} S _inst_2) (SMulZeroClass.toHasSmul.{u2, u2} S (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2) (Polynomial.smulZeroClass.{u2, u2} S _inst_2 S (SMulWithZero.toSmulZeroClass.{u2, u2} S S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (MulZeroClass.toSMulWithZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))))) (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 r) (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] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (r : R), Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (HSMul.hSMul.{u1, u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1) (Polynomial.smulZeroClass.{u1, u1} R _inst_1 R (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) r p)) (HSMul.hSMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (Polynomial.{u2} S _inst_2) (Polynomial.{u2} S _inst_2) (instHSMul.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (Polynomial.{u2} S _inst_2) (SMulZeroClass.toSMul.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2) (Polynomial.smulZeroClass.{u2, u2} S _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (SMulWithZero.toSMulZeroClass.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) S (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) _inst_2)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (MulZeroClass.toSMulWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) _inst_2)))))))) (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 r) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (r : R), Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (HSMul.hSMul.{u1, u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1) (Polynomial.smulZeroClass.{u1, u1} R _inst_1 R (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) r p)) (HSMul.hSMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Polynomial.{u2} S _inst_2) (Polynomial.{u2} S _inst_2) (instHSMul.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Polynomial.{u2} S _inst_2) (SMulZeroClass.toSMul.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2) (Polynomial.smulZeroClass.{u2, u2} S _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (SMulWithZero.toSMulZeroClass.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) S (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (MulZeroClass.toSMulWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2)))))))) (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 r) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_smul Polynomial.map_smulₓ'. -/
 @[simp]
 protected theorem map_smul (r : R) : (r • p).map f = f r • p.map f := by
@@ -1213,7 +1213,7 @@ def mapRingHom (f : R →+* S) : R[X] →+* S[X]
 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)), Eq.{max (succ u1) (succ u2)} ((Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (RingHom.hasCoeToFun.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.mapRingHom.{u1, u2} R S _inst_1 _inst_2 f)) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f)
 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)), Eq.{max (succ u1) (succ u2)} (forall (ᾰ : Polynomial.{u1} R _inst_1), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) ᾰ) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (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)))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) (Polynomial.mapRingHom.{u1, u2} R S _inst_1 _inst_2 f)) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f)
+  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)), Eq.{max (succ u1) (succ u2)} (forall (ᾰ : Polynomial.{u1} R _inst_1), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) ᾰ) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (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)))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) (Polynomial.mapRingHom.{u1, u2} R S _inst_1 _inst_2 f)) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f)
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_map_ring_hom Polynomial.coe_mapRingHomₓ'. -/
 @[simp]
 theorem coe_mapRingHom (f : R →+* S) : ⇑(mapRingHom f) = map f :=
@@ -1253,7 +1253,7 @@ theorem map_dvd (f : R →+* S) {x y : R[X]} : x ∣ y → x.map f ∣ y.map f :
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (n : Nat), Eq.{succ u2} S (Polynomial.coeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) n) (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.coeff.{u1} R _inst_1 p n))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (n : Nat), Eq.{succ u2} S (Polynomial.coeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) n) (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.coeff.{u1} R _inst_1 p n))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (n : Nat), Eq.{succ u2} S (Polynomial.coeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) n) (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.coeff.{u1} R _inst_1 p n))
 Case conversion may be inaccurate. Consider using '#align polynomial.coeff_map Polynomial.coeff_mapₓ'. -/
 @[simp]
 theorem coeff_map (n : ℕ) : coeff (p.map f) n = f (coeff p n) :=
@@ -1305,7 +1305,7 @@ theorem eval₂_eq_eval_map {x : S} : p.eval₂ f x = (p.map f).eval x :=
 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)) -> (Function.Injective.{succ u1, succ u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f))
 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)) -> (Function.Injective.{succ u1, succ u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f))
+  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)) -> (Function.Injective.{succ u1, succ u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_injective Polynomial.map_injectiveₓ'. -/
 theorem map_injective (hf : Function.Injective f) : Function.Injective (map f) := fun p q h =>
   ext fun m => hf <| by rw [← coeff_map f, ← coeff_map f, h]
@@ -1315,7 +1315,7 @@ theorem map_injective (hf : Function.Injective f) : Function.Injective (map f) :
 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.Surjective.{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)) -> (Function.Surjective.{succ u1, succ u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f))
 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.Surjective.{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)) -> (Function.Surjective.{succ u1, succ u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f))
+  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.Surjective.{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)) -> (Function.Surjective.{succ u1, succ u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_surjective Polynomial.map_surjectiveₓ'. -/
 theorem map_surjective (hf : Function.Surjective f) : Function.Surjective (map f) := fun p =>
   Polynomial.induction_on' p
@@ -1349,7 +1349,7 @@ variable {f}
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_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)) -> (Iff (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (OfNat.mk.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.zero.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2))))) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_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)) -> (Iff (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_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)) -> (Iff (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_eq_zero_iff Polynomial.map_eq_zero_iffₓ'. -/
 protected theorem map_eq_zero_iff (hf : Function.Injective f) : p.map f = 0 ↔ p = 0 :=
   map_eq_zero_iff (mapRingHom f) (map_injective f hf)
@@ -1359,7 +1359,7 @@ protected theorem map_eq_zero_iff (hf : Function.Injective f) : p.map f = 0 ↔
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_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)) -> (Iff (Ne.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (OfNat.mk.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.zero.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2))))) (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_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)) -> (Iff (Ne.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))) (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_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)) -> (Iff (Ne.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))) (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_ne_zero_iff Polynomial.map_ne_zero_iffₓ'. -/
 protected theorem map_ne_zero_iff (hf : Function.Injective f) : p.map f ≠ 0 ↔ p ≠ 0 :=
   (Polynomial.map_eq_zero_iff hf).Not
@@ -1369,7 +1369,7 @@ protected theorem map_ne_zero_iff (hf : Function.Injective f) : p.map f ≠ 0 
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Iff (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (OfNat.mk.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.zero.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2))))) (forall (x : R), Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f x) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Iff (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))) (forall (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2))))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Iff (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))) (forall (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_monic_eq_zero_iff Polynomial.map_monic_eq_zero_iffₓ'. -/
 theorem map_monic_eq_zero_iff (hp : p.Monic) : p.map f = 0 ↔ ∀ x, f x = 0 :=
   ⟨fun hfp x =>
@@ -1391,7 +1391,7 @@ theorem map_monic_ne_zero (hp : p.Monic) [Nontrivial S] : p.map f ≠ 0 := fun h
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (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] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 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)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) _inst_2))))) -> (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] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 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)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) _inst_2))))) -> (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_leading_coeff_ne_zero Polynomial.degree_map_eq_of_leadingCoeff_ne_zeroₓ'. -/
 theorem degree_map_eq_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCoeff p) ≠ 0) :
     degree (p.map f) = degree p :=
@@ -1408,7 +1408,7 @@ theorem degree_map_eq_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCo
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (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] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 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)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) _inst_2))))) -> (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] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 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)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) _inst_2))))) -> (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_of_leading_coeff_ne_zero Polynomial.natDegree_map_of_leadingCoeff_ne_zeroₓ'. -/
 theorem natDegree_map_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCoeff p) ≠ 0) :
     natDegree (p.map f) = natDegree p :=
@@ -1419,7 +1419,7 @@ theorem natDegree_map_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCo
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (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] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 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)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) _inst_2))))) -> (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] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 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)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) _inst_2))))) -> (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_of_leading_coeff_ne_zero Polynomial.leadingCoeff_map_of_leadingCoeff_ne_zeroₓ'. -/
 theorem leadingCoeff_map_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCoeff p) ≠ 0) :
     leadingCoeff (p.map f) = f (leadingCoeff p) :=
@@ -1529,7 +1529,7 @@ theorem map_comp (p q : R[X]) : map f (p.comp q) = (map f p).comp (map f q) :=
 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)) (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))))) (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.eval.{u1} R _inst_1 (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))))))) 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)) (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)) (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_zero_map Polynomial.eval_zero_mapₓ'. -/
 @[simp]
 theorem eval_zero_map (f : R →+* S) (p : R[X]) : (p.map f).eval 0 = f (p.eval 0) := by
@@ -1540,7 +1540,7 @@ theorem eval_zero_map (f : R →+* S) (p : R[X]) : (p.map f).eval 0 = f (p.eval
 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)) (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (OfNat.ofNat.{u2} S 1 (OfNat.mk.{u2} S 1 (One.one.{u2} S (AddMonoidWithOne.toOne.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{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.eval.{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))))))) 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)) (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{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)) (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_one_map Polynomial.eval_one_mapₓ'. -/
 @[simp]
 theorem eval_one_map (f : R →+* S) (p : R[X]) : (p.map f).eval 1 = f (p.eval 1) :=
@@ -1556,7 +1556,7 @@ theorem eval_one_map (f : R →+* S) (p : R[X]) : (p.map f).eval 1 = f (p.eval 1
 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)) (p : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u2} Nat S (CoeTCₓ.coe.{1, succ u2} Nat S (Nat.castCoe.{u2} S (AddMonoidWithOne.toNatCast.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))))) n) (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.eval.{u1} R _inst_1 ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) n) 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)) (p : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (Nat.cast.{u2} S (Semiring.toNatCast.{u2} S _inst_2) n) (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.eval.{u1} R _inst_1 (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R _inst_1) n) 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)) (p : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (Nat.cast.{u2} S (Semiring.toNatCast.{u2} S _inst_2) n) (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.eval.{u1} R _inst_1 (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R _inst_1) n) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_nat_cast_map Polynomial.eval_nat_cast_mapₓ'. -/
 @[simp]
 theorem eval_nat_cast_map (f : R →+* S) (p : R[X]) (n : ℕ) : (p.map f).eval n = f (p.eval n) :=
@@ -1572,7 +1572,7 @@ theorem eval_nat_cast_map (f : R →+* S) (p : R[X]) (n : ℕ) : (p.map f).eval
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_3 : Ring.{u1} R] [_inst_4 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (i : Int), Eq.{succ u2} S (Polynomial.eval.{u2} S (Ring.toSemiring.{u2} S _inst_4) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Int S (HasLiftT.mk.{1, succ u2} Int S (CoeTCₓ.coe.{1, succ u2} Int S (Int.castCoe.{u2} S (AddGroupWithOne.toHasIntCast.{u2} S (NonAssocRing.toAddGroupWithOne.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4)))))) i) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u2} S _inst_4) f p)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) f (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_3) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)))))) i) p))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_3 : Ring.{u2} R] [_inst_4 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) (p : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (i : Int), Eq.{succ u1} S (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S _inst_4) (Int.cast.{u1} S (Ring.toIntCast.{u1} S _inst_4) i) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u1} S _inst_4) f p)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4)))))) f (Polynomial.eval.{u2} R (Ring.toSemiring.{u2} R _inst_3) (Int.cast.{u2} R (Ring.toIntCast.{u2} R _inst_3) i) p))
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_3 : Ring.{u2} R] [_inst_4 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) (p : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (i : Int), Eq.{succ u1} S (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S _inst_4) (Int.cast.{u1} S (Ring.toIntCast.{u1} S _inst_4) i) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u1} S _inst_4) f p)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4)))))) f (Polynomial.eval.{u2} R (Ring.toSemiring.{u2} R _inst_3) (Int.cast.{u2} R (Ring.toIntCast.{u2} R _inst_3) i) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_int_cast_map Polynomial.eval_int_cast_mapₓ'. -/
 @[simp]
 theorem eval_int_cast_map {R S : Type _} [Ring R] [Ring S] (f : R →+* S) (p : R[X]) (i : ℤ) :
@@ -1602,7 +1602,7 @@ variable [Semiring S] [Semiring T] (f : R →+* S) (g : S →+* T) (p)
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) [_inst_2 : Semiring.{u2} S] [_inst_3 : Semiring.{u3} T] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (g : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (x : S), Eq.{succ u3} T (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (fun (_x : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) => S -> T) (RingHom.hasCoeToFun.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) g (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p)) (Polynomial.eval₂.{u1, u3} R T _inst_1 _inst_3 (RingHom.comp.{u1, u2, u3} R S T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3) g f) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (fun (_x : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) => S -> T) (RingHom.hasCoeToFun.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) g x) p)
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) [_inst_2 : Semiring.{u2} S] [_inst_3 : Semiring.{u3} T] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (g : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (x : S), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => T) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3))))) g (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p)) (Polynomial.eval₂.{u1, u3} R T _inst_1 _inst_3 (RingHom.comp.{u1, u2, u3} R S T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3) g f) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3))))) g x) p)
+  forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) [_inst_2 : Semiring.{u2} S] [_inst_3 : Semiring.{u3} T] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (g : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (x : S), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => T) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3))))) g (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p)) (Polynomial.eval₂.{u1, u3} R T _inst_1 _inst_3 (RingHom.comp.{u1, u2, u3} R S T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3) g f) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3))))) g x) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.hom_eval₂ Polynomial.hom_eval₂ₓ'. -/
 theorem hom_eval₂ (x : S) : g (p.eval₂ f x) = p.eval₂ (g.comp f) (g x) := by
   rw [← eval₂_map, eval₂_at_apply, eval_map]
@@ -1624,7 +1624,7 @@ variable [Semiring R] {p q : R[X]} {x : R} [Semiring S] (f : R →+* S)
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : R), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f x) 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.eval.{u1} R _inst_1 x p))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : R), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f x) 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.eval.{u1} R _inst_1 x p))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : R), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f x) 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.eval.{u1} R _inst_1 x p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_hom Polynomial.eval₂_homₓ'. -/
 theorem eval₂_hom (x : R) : p.eval₂ f (f x) = f (p.eval x) :=
   RingHom.comp_id f ▸ (hom_eval₂ p (RingHom.id R) f x).symm
@@ -1670,7 +1670,7 @@ def evalRingHom : R → R[X] →+* R :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (r : R), Eq.{succ u1} ((fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> R) (Polynomial.evalRingHom.{u1} R _inst_1 r)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> R) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.evalRingHom.{u1} R _inst_1 r)) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) r)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (r : R), Eq.{succ u1} (forall (a : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => R) a) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Polynomial.evalRingHom.{u1} R _inst_1 r)) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) r)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (r : R), Eq.{succ u1} (forall (a : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => R) a) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Polynomial.evalRingHom.{u1} R _inst_1 r)) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) r)
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_eval_ring_hom Polynomial.coe_evalRingHomₓ'. -/
 @[simp]
 theorem coe_evalRingHom (r : R) : (evalRingHom r : R[X] → R) = eval r :=
@@ -1713,7 +1713,7 @@ def compRingHom : R[X] → R[X] →+* R[X] :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} ((fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.compRingHom.{u1} R _inst_1 q)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.compRingHom.{u1} R _inst_1 q)) (fun (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p q)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} (forall (a : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.compRingHom.{u1} R _inst_1 q)) (fun (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p q)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} (forall (a : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.compRingHom.{u1} R _inst_1 q)) (fun (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p q)
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_comp_ring_hom Polynomial.coe_compRingHomₓ'. -/
 @[simp]
 theorem coe_compRingHom (q : R[X]) : (compRingHom q : R[X] → R[X]) = fun p => comp p q :=
@@ -1724,7 +1724,7 @@ theorem coe_compRingHom (q : R[X]) : (compRingHom q : R[X] → R[X]) = fun p =>
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.compRingHom.{u1} R _inst_1 q) p) (Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p q)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) p) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.compRingHom.{u1} R _inst_1 q) p) (Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p q)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) p) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.compRingHom.{u1} R _inst_1 q) p) (Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p q)
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_comp_ring_hom_apply Polynomial.coe_compRingHom_applyₓ'. -/
 theorem coe_compRingHom_apply (p q : R[X]) : (compRingHom q : R[X] → R[X]) p = comp p q :=
   rfl
@@ -1867,7 +1867,7 @@ theorem support_map_subset [Semiring R] [Semiring S] (f : R →+* S) (p : R[X])
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] (p : Polynomial.{u1} R _inst_1) {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)) -> (Eq.{1} (Finset.{0} Nat) (Polynomial.support.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (Polynomial.support.{u1} R _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] (p : Polynomial.{u1} R _inst_1) {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)) -> (Eq.{1} (Finset.{0} Nat) (Polynomial.support.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (Polynomial.support.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] (p : Polynomial.{u1} R _inst_1) {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)) -> (Eq.{1} (Finset.{0} Nat) (Polynomial.support.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (Polynomial.support.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.support_map_of_injective Polynomial.support_map_of_injectiveₓ'. -/
 theorem support_map_of_injective [Semiring R] [Semiring S] (p : R[X]) {f : R →+* S}
     (hf : Function.Injective f) : (map f p).support = p.support := by
@@ -1898,7 +1898,7 @@ protected theorem map_prod {ι : Type _} (g : ι → R[X]) (s : Finset ι) :
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p x) -> (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) f x))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p x) -> (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{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 (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p x) -> (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{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 (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x))
 Case conversion may be inaccurate. Consider using '#align polynomial.is_root.map Polynomial.IsRoot.mapₓ'. -/
 theorem IsRoot.map {f : R →+* S} {x : R} {p : R[X]} (h : IsRoot p x) : IsRoot (p.map f) (f x) := by
   rw [is_root, eval_map, eval₂_hom, h.eq_zero, f.map_zero]
@@ -1908,7 +1908,7 @@ theorem IsRoot.map {f : R →+* S} {x : R} {p : R[X]} (h : IsRoot p x) : IsRoot
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))} {x : R} {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))}, (Polynomial.IsRoot.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (CommSemiring.toSemiring.{u1} S _inst_2) f p) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) f x)) -> (Function.Injective.{succ u2, succ u1} R S (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) f)) -> (Polynomial.IsRoot.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) p x)
 but is expected to have type
-  forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))}, (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x)) -> (Function.Injective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f)) -> (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p x)
+  forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))}, (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x)) -> (Function.Injective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f)) -> (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p x)
 Case conversion may be inaccurate. Consider using '#align polynomial.is_root.of_map Polynomial.IsRoot.of_mapₓ'. -/
 theorem IsRoot.of_map {R} [CommRing R] {f : R →+* S} {x : R} {p : R[X]} (h : IsRoot (p.map f) (f x))
     (hf : Function.Injective f) : IsRoot p x := by
@@ -1919,7 +1919,7 @@ theorem IsRoot.of_map {R} [CommRing R] {f : R →+* S} {x : R} {p : R[X]} (h : I
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))} {x : R} {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))}, (Function.Injective.{succ u2, succ u1} R S (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) f)) -> (Iff (Polynomial.IsRoot.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (CommSemiring.toSemiring.{u1} S _inst_2) f p) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) f x)) (Polynomial.IsRoot.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) p x))
 but is expected to have type
-  forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))}, (Function.Injective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f)) -> (Iff (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x)) (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p x))
+  forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))}, (Function.Injective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f)) -> (Iff (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x)) (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p x))
 Case conversion may be inaccurate. Consider using '#align polynomial.is_root_map_iff Polynomial.isRoot_map_iffₓ'. -/
 theorem isRoot_map_iff {R : Type _} [CommRing R] {f : R →+* S} {x : R} {p : R[X]}
     (hf : Function.Injective f) : IsRoot (p.map f) (f x) ↔ IsRoot p x :=
@@ -1938,7 +1938,7 @@ variable [Ring R] {p q r : R[X]}
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} (Polynomial.{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)) (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))))) a)) (Neg.neg.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.neg'.{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)) a))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) a)) (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)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) a)) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (Polynomial.neg'.{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)) a))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) a)) (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)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) a)) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (Polynomial.neg'.{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)) a))
 Case conversion may be inaccurate. Consider using '#align polynomial.C_neg Polynomial.C_negₓ'. -/
 theorem C_neg : C (-a) = -C a :=
   RingHom.map_neg C a
@@ -1948,7 +1948,7 @@ theorem C_neg : C (-a) = -C a :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} {b : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} (Polynomial.{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)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) a b)) (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)) (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)) a) (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)) b))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} {b : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) a b)) (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)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) a b)) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) b) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (instHSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (Polynomial.sub.{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)) a) (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)) b))
+  forall {R : Type.{u1}} {a : R} {b : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) a b)) (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)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) a b)) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) b) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (instHSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (Polynomial.sub.{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)) a) (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)) b))
 Case conversion may be inaccurate. Consider using '#align polynomial.C_sub Polynomial.C_subₓ'. -/
 theorem C_sub : C (a - b) = C a - C b :=
   RingHom.map_sub C a b
@@ -2047,7 +2047,7 @@ theorem eval_sub (p q : R[X]) (x : R) : (p - q).eval x = p.eval x - q.eval x :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} {b : R} [_inst_1 : Ring.{u1} R], Iff (Polynomial.IsRoot.{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)) a)) b) (Eq.{succ u1} R a b)
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} {b : R} [_inst_1 : Ring.{u1} R], Iff (Polynomial.IsRoot.{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)) a) (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)) a)) b) (Eq.{succ u1} R a b)
+  forall {R : Type.{u1}} {a : R} {b : R} [_inst_1 : Ring.{u1} R], Iff (Polynomial.IsRoot.{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)) a) (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)) a)) b) (Eq.{succ u1} R a b)
 Case conversion may be inaccurate. Consider using '#align polynomial.root_X_sub_C Polynomial.root_X_sub_Cₓ'. -/
 theorem root_X_sub_C : IsRoot (X - C a) b ↔ a = b := by
   rw [is_root.def, eval_sub, eval_X, eval_C, sub_eq_zero, eq_comm]

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

@@ -78,9 +78,9 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_at_zero Polynomial.eval₂_at_zeroₓ'. -/
 @[simp]
 theorem eval₂_at_zero : p.eval₂ f 0 = f (coeff p 0) := by
-  simp (config := { contextual := true }) only [eval₂_eq_sum, zero_pow_eq, mul_ite, mul_zero,
-    mul_one, Sum, Classical.not_not, mem_support_iff, sum_ite_eq', ite_eq_left_iff,
-    RingHom.map_zero, imp_true_iff, eq_self_iff_true]
+  simp (config := { contextual := true }) only [eval₂_eq_sum, zero_pow_eq, mul_ite,
+    MulZeroClass.mul_zero, mul_one, Sum, Classical.not_not, mem_support_iff, sum_ite_eq',
+    ite_eq_left_iff, RingHom.map_zero, imp_true_iff, eq_self_iff_true]
 #align polynomial.eval₂_at_zero Polynomial.eval₂_at_zero
 
 /- warning: polynomial.eval₂_zero -> Polynomial.eval₂_zero is a dubious translation:
@@ -392,7 +392,7 @@ theorem eval₂_eq_sum_range' (f : R →+* S) {p : R[X]} {n : ℕ} (hn : p.natDe
   by
   rw [eval₂_eq_sum, p.sum_over_range' _ _ hn]
   intro i
-  rw [f.map_zero, zero_mul]
+  rw [f.map_zero, MulZeroClass.zero_mul]
 #align polynomial.eval₂_eq_sum_range' Polynomial.eval₂_eq_sum_range'
 
 end
@@ -715,7 +715,7 @@ theorem eval_monomial_one_add_sub [CommRing S] (d : ℕ) (y : S) :
     skip
     rw [one_pow, mul_one, mul_comm]
   rw [sum_range_succ, mul_add, Nat.choose_self, Nat.cast_one, one_mul, add_sub_cancel, mul_sum,
-    sum_range_succ', Nat.cast_zero, zero_mul, mul_zero, add_zero]
+    sum_range_succ', Nat.cast_zero, MulZeroClass.zero_mul, MulZeroClass.mul_zero, add_zero]
   apply sum_congr rfl fun y hy => _
   rw [← mul_assoc, ← mul_assoc, ← Nat.cast_mul, Nat.succ_mul_choose_eq, Nat.cast_mul,
     Nat.add_sub_cancel]
@@ -1376,7 +1376,7 @@ theorem map_monic_eq_zero_iff (hp : p.Monic) : p.map f = 0 ↔ ∀ x, f x = 0 :=
     calc
       f x = f x * f p.leadingCoeff := by simp only [mul_one, hp.leading_coeff, f.map_one]
       _ = f x * (p.map f).coeff p.natDegree := (congr_arg _ (coeff_map _ _).symm)
-      _ = 0 := by simp only [hfp, mul_zero, coeff_zero]
+      _ = 0 := by simp only [hfp, MulZeroClass.mul_zero, coeff_zero]
       ,
     fun h => ext fun n => by simp only [h, coeff_map, coeff_zero]⟩
 #align polynomial.map_monic_eq_zero_iff Polynomial.map_monic_eq_zero_iff
@@ -1732,13 +1732,13 @@ theorem coe_compRingHom_apply (p q : R[X]) : (compRingHom q : R[X] → R[X]) p =
 
 #print Polynomial.root_mul_left_of_isRoot /-
 theorem root_mul_left_of_isRoot (p : R[X]) {q : R[X]} : IsRoot q a → IsRoot (p * q) a := fun H => by
-  rw [is_root, eval_mul, is_root.def.1 H, mul_zero]
+  rw [is_root, eval_mul, is_root.def.1 H, MulZeroClass.mul_zero]
 #align polynomial.root_mul_left_of_is_root Polynomial.root_mul_left_of_isRoot
 -/
 
 #print Polynomial.root_mul_right_of_isRoot /-
 theorem root_mul_right_of_isRoot {p : R[X]} (q : R[X]) : IsRoot p a → IsRoot (p * q) a := fun H =>
-  by rw [is_root, eval_mul, is_root.def.1 H, zero_mul]
+  by rw [is_root, eval_mul, is_root.def.1 H, MulZeroClass.zero_mul]
 #align polynomial.root_mul_right_of_is_root Polynomial.root_mul_right_of_isRoot
 -/
 

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

@@ -53,7 +53,7 @@ irreducible_def eval₂ (p : R[X]) : S :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {x : S}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Polynomial.sum.{u1, u2} R _inst_1 S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) p (fun (e : Nat) (a : R) => HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (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 a) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x e)))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {x : S}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Polynomial.sum.{u1, u2} R _inst_1 S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) p (fun (e : Nat) (a : R) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2)))) (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.2398 : 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 a) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x e)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {x : S}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Polynomial.sum.{u1, u2} R _inst_1 S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) p (fun (e : Nat) (a : R) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2)))) (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 a) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x e)))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_eq_sum Polynomial.eval₂_eq_sumₓ'. -/
 theorem eval₂_eq_sum {f : R →+* S} {x : S} : p.eval₂ f x = p.Sum fun e a => f a * x ^ e := by
   rw [eval₂]
@@ -74,7 +74,7 @@ theorem eval₂_congr {R S : Type _} [Semiring R] [Semiring S] {f g : R →+* S}
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))))) 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.coeff.{u1} R _inst_1 p (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) 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.2398 : 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.coeff.{u1} R _inst_1 p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) 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.coeff.{u1} R _inst_1 p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_at_zero Polynomial.eval₂_at_zeroₓ'. -/
 @[simp]
 theorem eval₂_at_zero : p.eval₂ f 0 = f (coeff p 0) := by
@@ -97,7 +97,7 @@ theorem eval₂_zero : (0 : R[X]).eval₂ f x = 0 := by simp [eval₂_eq_sum]
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_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)) (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a)) (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 a)
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_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)) (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (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.2398 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) (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.2398 : 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 a)
+  forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_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)) (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) (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 a)
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_C Polynomial.eval₂_Cₓ'. -/
 @[simp]
 theorem eval₂_C : (C a).eval₂ f x = f a := by simp [eval₂_eq_sum]
@@ -113,7 +113,7 @@ theorem eval₂_X : X.eval₂ f x = x := by simp [eval₂_eq_sum]
 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)) (x : S) {n : Nat} {r : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (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 r) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x n))
 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)) (x : S) {n : Nat} {r : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) r) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) r) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) r) _inst_2)))) (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.2398 : 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 r) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x n))
+  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)) (x : S) {n : Nat} {r : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) _inst_2)))) (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 r) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x n))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_monomial Polynomial.eval₂_monomialₓ'. -/
 @[simp]
 theorem eval₂_monomial {n : ℕ} {r : R} : (monomial n r).eval₂ f x = f r * x ^ n := by
@@ -174,7 +174,7 @@ theorem eval₂_bit1 : (bit1 p).eval₂ f x = bit1 (p.eval₂ f x) := by
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (p : Polynomial.{u1} R _inst_1) (x : S) {s : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 g x (SMul.smul.{u1, u1} R (Polynomial.{u1} R _inst_1) (SMulZeroClass.toHasSmul.{u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1) (Polynomial.smulZeroClass.{u1, u1} R _inst_1 R (SMulWithZero.toSmulZeroClass.{u1, u1} R R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) s p)) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (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)) g s) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 g x p))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (p : Polynomial.{u1} R _inst_1) (x : S) {s : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 g x (HSMul.hSMul.{u1, u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1) (Polynomial.smulZeroClass.{u1, u1} R _inst_1 R (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) s p)) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) s) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) s) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) s) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) s) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) s) _inst_2)))) (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.2398 : 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))))) g s) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 g x p))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] (g : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (p : Polynomial.{u1} R _inst_1) (x : S) {s : R}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 g x (HSMul.hSMul.{u1, u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1) (Polynomial.smulZeroClass.{u1, u1} R _inst_1 R (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) s p)) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) s) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) s) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) s) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) s) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) s) _inst_2)))) (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))))) g s) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 g x p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_smul Polynomial.eval₂_smulₓ'. -/
 @[simp]
 theorem eval₂_smul (g : R →+* S) (p : R[X]) (x : S) {s : R} :
@@ -259,7 +259,7 @@ theorem eval₂_finset_sum (s : Finset ι) (g : ι → R[X]) (x : S) :
 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)} {x : S} {p : AddMonoidAlgebra.{u1, 0} R Nat _inst_1}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (Polynomial.ofFinsupp.{u1} R _inst_1 p)) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{0, u1} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (fun (_x : AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{0, u1} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) => (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) -> S) (AddMonoidHom.hasCoeToFun.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{0, u1} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidAlgebra.liftNC.{u1, 0, u2} R Nat S _inst_1 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) ((fun (a : Sort.{max (succ u1) (succ u2)}) (b : Sort.{max (succ u2) (succ u1)}) [self : HasLiftT.{max (succ u1) (succ u2), max (succ u2) (succ u1)} a b] => self.0) (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoidHom.{u1, u2} R S (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (HasLiftT.mk.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoidHom.{u1, u2} R S (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (CoeTCₓ.coe.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoidHom.{u1, u2} R S (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidHom.hasCoeT.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (RingHomClass.toAddMonoidHomClass.{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.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) f) (coeFn.{succ u2, succ u2} (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (fun (_x : MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) => (Multiplicative.{0} Nat) -> S) (MonoidHom.hasCoeToFun.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} S (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) (fun (_x : Equiv.{succ u2, succ u2} S (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) => S -> (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) (Equiv.hasCoeToFun.{succ u2, succ u2} S (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) (powersHom.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) x))) 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)} {x : S} {p : AddMonoidAlgebra.{u1, 0} R Nat _inst_1}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (Polynomial.ofFinsupp.{u1} R _inst_1 p)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (fun (_x : AddMonoidAlgebra.{u1, 0} R Nat _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : AddMonoidAlgebra.{u1, 0} R Nat _inst_1) => S) _x) (AddHomClass.toFunLike.{max u2 u1, u1, u2} (AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddZeroClass.toAdd.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1)))) (AddZeroClass.toAdd.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidHomClass.toAddHomClass.{max u2 u1, u1, u2} (AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (AddMonoidHom.addMonoidHomClass.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) (AddMonoidAlgebra.liftNC.{u1, 0, u2} R Nat S _inst_1 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoidHomClass.toAddMonoidHom.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (RingHomClass.toAddMonoidHomClass.{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) (FunLike.coe.{succ u2, 1, succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x) (Multiplicative.{0} Nat) (fun (_x : Multiplicative.{0} Nat) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Multiplicative.{0} Nat) => S) _x) (MulHomClass.toFunLike.{u2, 0, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x) (Multiplicative.{0} Nat) S (MulOneClass.toMul.{0} (Multiplicative.{0} Nat) (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (MulOneClass.toMul.{u2} S (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (MonoidHomClass.toMulHomClass.{u2, 0, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x) (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (MonoidHom.monoidHomClass.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} S (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} S (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) (powersHom.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) x))) 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)} {x : S} {p : AddMonoidAlgebra.{u1, 0} R Nat _inst_1}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (Polynomial.ofFinsupp.{u1} R _inst_1 p)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (fun (_x : AddMonoidAlgebra.{u1, 0} R Nat _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : AddMonoidAlgebra.{u1, 0} R Nat _inst_1) => S) _x) (AddHomClass.toFunLike.{max u2 u1, u1, u2} (AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddZeroClass.toAdd.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1)))) (AddZeroClass.toAdd.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidHomClass.toAddHomClass.{max u2 u1, u1, u2} (AddMonoidHom.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (AddMonoidHom.addMonoidHomClass.{u1, u2} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) S (AddMonoid.toAddZeroClass.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddCommMonoid.toAddMonoid.{u1} (AddMonoidAlgebra.{u1, 0} R Nat _inst_1) (AddMonoidAlgebra.addCommMonoid.{u1, 0} R Nat _inst_1))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) (AddMonoidAlgebra.liftNC.{u1, 0, u2} R Nat S _inst_1 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoidHomClass.toAddMonoidHom.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (RingHomClass.toAddMonoidHomClass.{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) (FunLike.coe.{succ u2, 1, succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x) (Multiplicative.{0} Nat) (fun (_x : Multiplicative.{0} Nat) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Multiplicative.{0} Nat) => S) _x) (MulHomClass.toFunLike.{u2, 0, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x) (Multiplicative.{0} Nat) S (MulOneClass.toMul.{0} (Multiplicative.{0} Nat) (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (MulOneClass.toMul.{u2} S (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (MonoidHomClass.toMulHomClass.{u2, 0, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x) (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (MonoidHom.monoidHomClass.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} S (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : S) => MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} S (MonoidHom.{0, u2} (Multiplicative.{0} Nat) S (Multiplicative.mulOneClass.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Monoid.toMulOneClass.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))))) (powersHom.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) x))) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_of_finsupp Polynomial.eval₂_ofFinsuppₓ'. -/
 theorem eval₂_ofFinsupp {f : R →+* S} {x : S} {p : AddMonoidAlgebra R ℕ} :
     eval₂ f x (⟨p⟩ : R[X]) = liftNC (↑f) (powersHom S x) p :=
@@ -272,7 +272,7 @@ theorem eval₂_ofFinsupp {f : R →+* S} {x : S} {p : AddMonoidAlgebra R ℕ} :
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), (forall (k : Nat), Commute.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (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.coeff.{u1} R _inst_1 q k)) x) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (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)) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x q)))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), (forall (k : Nat), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) _inst_2))) (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.2398 : 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.coeff.{u1} R _inst_1 q k)) x) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (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)) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x q)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), (forall (k : Nat), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 q k)) _inst_2))) (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.coeff.{u1} R _inst_1 q k)) x) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (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)) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x q)))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_mul_noncomm Polynomial.eval₂_mul_noncommₓ'. -/
 theorem eval₂_mul_noncomm (hf : ∀ k, Commute (f <| q.coeff k) x) :
     eval₂ f x (p * q) = eval₂ f x p * eval₂ f x q :=
@@ -312,7 +312,7 @@ theorem eval₂_X_mul : eval₂ f x (X * p) = eval₂ f x p * x := by rw [X_mul,
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), (Commute.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (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 a) x) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a))) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x 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 a)))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), (Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2))) (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.2398 : 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 a) x) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a))) (HMul.hMul.{u2, u2, u2} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) S (instHMul.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x 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.2398 : 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 a)))
+  forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), (Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2))) (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 a) x) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a))) (HMul.hMul.{u2, u2, u2} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) S (instHMul.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x 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 a)))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_mul_C' Polynomial.eval₂_mul_C'ₓ'. -/
 theorem eval₂_mul_C' (h : Commute (f a) x) : eval₂ f x (p * C a) = eval₂ f x p * f a :=
   by
@@ -327,7 +327,7 @@ theorem eval₂_mul_C' (h : Commute (f a) x) : eval₂ f x (p * C a) = eval₂ f
 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)) (x : S) (ps : List.{u1} (Polynomial.{u1} R _inst_1)), (forall (p : Polynomial.{u1} R _inst_1), (Membership.Mem.{u1, u1} (Polynomial.{u1} R _inst_1) (List.{u1} (Polynomial.{u1} R _inst_1)) (List.hasMem.{u1} (Polynomial.{u1} R _inst_1)) p ps) -> (forall (k : Nat), Commute.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (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.coeff.{u1} R _inst_1 p k)) x)) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (List.prod.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1) (Polynomial.hasOne.{u1} R _inst_1) ps)) (List.prod.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (AddMonoidWithOne.toOne.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (List.map.{u1, u2} (Polynomial.{u1} R _inst_1) S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x) ps)))
 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)) (x : S) (ps : List.{u1} (Polynomial.{u1} R _inst_1)), (forall (p : Polynomial.{u1} R _inst_1), (Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (List.{u1} (Polynomial.{u1} R _inst_1)) (List.instMembershipList.{u1} (Polynomial.{u1} R _inst_1)) p ps) -> (forall (k : Nat), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) _inst_2))) (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.2398 : 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.coeff.{u1} R _inst_1 p k)) x)) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (List.prod.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1) ps)) (List.prod.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toOne.{u2} S _inst_2) (List.map.{u1, u2} (Polynomial.{u1} R _inst_1) S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x) ps)))
+  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)) (x : S) (ps : List.{u1} (Polynomial.{u1} R _inst_1)), (forall (p : Polynomial.{u1} R _inst_1), (Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (List.{u1} (Polynomial.{u1} R _inst_1)) (List.instMembershipList.{u1} (Polynomial.{u1} R _inst_1)) p ps) -> (forall (k : Nat), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p k)) _inst_2))) (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.coeff.{u1} R _inst_1 p k)) x)) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (List.prod.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1) ps)) (List.prod.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toOne.{u2} S _inst_2) (List.map.{u1, u2} (Polynomial.{u1} R _inst_1) S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x) ps)))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_list_prod_noncomm Polynomial.eval₂_list_prod_noncommₓ'. -/
 theorem eval₂_list_prod_noncomm (ps : List R[X])
     (hf : ∀ p ∈ ps, ∀ (k), Commute (f <| coeff p k) x) :
@@ -343,7 +343,7 @@ theorem eval₂_list_prod_noncomm (ps : List R[X])
 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)) (x : S), (forall (a : R), Commute.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (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 a) x) -> (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2))
 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)) (x : S), (forall (a : R), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2))) (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.2398 : 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 a) x) -> (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2))
+  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)) (x : S), (forall (a : R), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2))) (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 a) x) -> (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_ring_hom' Polynomial.eval₂RingHom'ₓ'. -/
 /-- `eval₂` as a `ring_hom` for noncommutative rings -/
 def eval₂RingHom' (f : R →+* S) (x : S) (hf : ∀ a, Commute (f a) x) : R[X] →+* S
@@ -374,7 +374,7 @@ variable [Semiring S] (f : R →+* S) (x : S)
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Finset.sum.{u2, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Polynomial.natDegree.{u1} R _inst_1 p) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (i : Nat) => HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (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.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x i)))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Finset.sum.{u2, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Polynomial.natDegree.{u1} R _inst_1 p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (i : Nat) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) _inst_2)))) (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.2398 : 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.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x i)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Finset.sum.{u2, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Polynomial.natDegree.{u1} R _inst_1 p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (i : Nat) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) _inst_2)))) (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.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x i)))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_eq_sum_range Polynomial.eval₂_eq_sum_rangeₓ'. -/
 theorem eval₂_eq_sum_range :
     p.eval₂ f x = ∑ i in Finset.range (p.natDegree + 1), f (p.coeff i) * x ^ i :=
@@ -385,7 +385,7 @@ theorem eval₂_eq_sum_range :
 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)) {p : Polynomial.{u1} R _inst_1} {n : Nat}, (LT.lt.{0} Nat Nat.hasLt (Polynomial.natDegree.{u1} R _inst_1 p) n) -> (forall (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Finset.sum.{u2, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finset.range n) (fun (i : Nat) => HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (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.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x i))))
 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)) {p : Polynomial.{u1} R _inst_1} {n : Nat}, (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 p) n) -> (forall (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Finset.sum.{u2, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finset.range n) (fun (i : Nat) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) _inst_2)))) (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.2398 : 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.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x i))))
+  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)) {p : Polynomial.{u1} R _inst_1} {n : Nat}, (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 p) n) -> (forall (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p) (Finset.sum.{u2, 0} S Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finset.range n) (fun (i : Nat) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.coeff.{u1} R _inst_1 p i)) _inst_2)))) (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.coeff.{u1} R _inst_1 p i)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) x i))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_eq_sum_range' Polynomial.eval₂_eq_sum_range'ₓ'. -/
 theorem eval₂_eq_sum_range' (f : R →+* S) {p : R[X]} {n : ℕ} (hn : p.natDegree < n) (x : S) :
     eval₂ f x p = ∑ i in Finset.range n, f (p.coeff i) * x ^ i :=
@@ -449,7 +449,7 @@ def eval₂RingHom (f : R →+* S) (x : S) : R[X] →+* S :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (x : S), Eq.{max (succ u1) (succ u2)} ((Polynomial.{u1} R _inst_1) -> S) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => (Polynomial.{u1} R _inst_1) -> S) (RingHom.hasCoeToFun.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.eval₂RingHom.{u1, u2} R S _inst_1 _inst_2 f x)) (Polynomial.eval₂.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) f x)
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (x : S), Eq.{max (succ u1) (succ u2)} (forall (ᾰ : Polynomial.{u1} R _inst_1), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Polynomial.{u1} R _inst_1) => S) ᾰ) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Polynomial.{u1} R _inst_1) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) S (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)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (Polynomial.eval₂RingHom.{u1, u2} R S _inst_1 _inst_2 f x)) (Polynomial.eval₂.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) f x)
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (x : S), Eq.{max (succ u1) (succ u2)} (forall (ᾰ : Polynomial.{u1} R _inst_1), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Polynomial.{u1} R _inst_1) => S) ᾰ) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Polynomial.{u1} R _inst_1) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) S (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)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} (Polynomial.{u1} R _inst_1) S (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (Polynomial.eval₂RingHom.{u1, u2} R S _inst_1 _inst_2 f x)) (Polynomial.eval₂.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) f x)
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_eval₂_ring_hom Polynomial.coe_eval₂RingHomₓ'. -/
 @[simp]
 theorem coe_eval₂RingHom (f : R →+* S) (x) : ⇑(eval₂RingHom f x) = eval₂ f x :=
@@ -542,7 +542,7 @@ theorem eval_eq_sum_range' {p : R[X]} {n : ℕ} (hn : p.natDegree < n) (x : R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (r : R), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (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 r) 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.eval.{u1} R _inst_1 r p))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {p : Polynomial.{u2} R _inst_1} {S : Type.{u1}} [_inst_2 : Semiring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (r : R), Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S _inst_1 _inst_2 f (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f r) p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f (Polynomial.eval.{u2} R _inst_1 r p))
+  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {p : Polynomial.{u2} R _inst_1} {S : Type.{u1}} [_inst_2 : Semiring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (r : R), Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S _inst_1 _inst_2 f (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f r) p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f (Polynomial.eval.{u2} R _inst_1 r p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_at_apply Polynomial.eval₂_at_applyₓ'. -/
 @[simp]
 theorem eval₂_at_apply {S : Type _} [Semiring S] (f : R →+* S) (r : R) :
@@ -556,7 +556,7 @@ theorem eval₂_at_apply {S : Type _} [Semiring S] (f : R →+* S) (r : R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (OfNat.ofNat.{u2} S 1 (OfNat.mk.{u2} S 1 (One.one.{u2} S (AddMonoidWithOne.toOne.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))))) 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.eval.{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))))))) p))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {p : Polynomial.{u2} R _inst_1} {S : Type.{u1}} [_inst_2 : Semiring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)), Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S _inst_1 _inst_2 f (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S _inst_2))) p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f (Polynomial.eval.{u2} R _inst_1 (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R _inst_1))) p))
+  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {p : Polynomial.{u2} R _inst_1} {S : Type.{u1}} [_inst_2 : Semiring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)), Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S _inst_1 _inst_2 f (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S _inst_2))) p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f (Polynomial.eval.{u2} R _inst_1 (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R _inst_1))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_at_one Polynomial.eval₂_at_oneₓ'. -/
 @[simp]
 theorem eval₂_at_one {S : Type _} [Semiring S] (f : R →+* S) : p.eval₂ f 1 = f (p.eval 1) :=
@@ -569,7 +569,7 @@ theorem eval₂_at_one {S : Type _} [Semiring S] (f : R →+* S) : p.eval₂ f 1
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (n : Nat), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u2} Nat S (CoeTCₓ.coe.{1, succ u2} Nat S (Nat.castCoe.{u2} S (AddMonoidWithOne.toNatCast.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))))) n) 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.eval.{u1} R _inst_1 ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) n) p))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {p : Polynomial.{u2} R _inst_1} {S : Type.{u1}} [_inst_2 : Semiring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (n : Nat), Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S _inst_1 _inst_2 f (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S _inst_2) n) p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f (Polynomial.eval.{u2} R _inst_1 (Nat.cast.{u2} R (Semiring.toNatCast.{u2} R _inst_1) n) p))
+  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {p : Polynomial.{u2} R _inst_1} {S : Type.{u1}} [_inst_2 : Semiring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (n : Nat), Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S _inst_1 _inst_2 f (Nat.cast.{u1} S (Semiring.toNatCast.{u1} S _inst_2) n) p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} S _inst_2))))) f (Polynomial.eval.{u2} R _inst_1 (Nat.cast.{u2} R (Semiring.toNatCast.{u2} R _inst_1) n) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_at_nat_cast Polynomial.eval₂_at_nat_castₓ'. -/
 @[simp]
 theorem eval₂_at_nat_cast {S : Type _} [Semiring S] (f : R →+* S) (n : ℕ) :
@@ -582,7 +582,7 @@ theorem eval₂_at_nat_cast {S : Type _} [Semiring S] (f : R →+* S) (n : ℕ)
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a)) a
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (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.2398 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) a
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) a
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_C Polynomial.eval_Cₓ'. -/
 @[simp]
 theorem eval_C : (C a).eval x = a :=
@@ -680,7 +680,7 @@ theorem eval_smul [Monoid S] [DistribMulAction S R] [IsScalarTower S R R] (s : S
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) p)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a (Polynomial.eval.{u1} R _inst_1 x p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (Polynomial.eval.{u1} R _inst_1 x p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (Polynomial.eval.{u1} R _inst_1 x p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_C_mul Polynomial.eval_C_mulₓ'. -/
 @[simp]
 theorem eval_C_mul : (C a * p).eval x = a * p.eval x :=
@@ -856,7 +856,7 @@ theorem IsRoot.dvd {R : Type _} [CommSemiring R] {p q : R[X]} {x : R} (h : p.IsR
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (a : R), (Ne.{succ u1} R 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)))))))) -> (Not (Polynomial.IsRoot.{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) a))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (a : R), (Ne.{succ u1} R r (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Not (Polynomial.IsRoot.{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.2398 : 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) a))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (a : R), (Ne.{succ u1} R r (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Not (Polynomial.IsRoot.{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) a))
 Case conversion may be inaccurate. Consider using '#align polynomial.not_is_root_C Polynomial.not_isRoot_Cₓ'. -/
 theorem not_isRoot_C (r a : R) (hr : r ≠ 0) : ¬IsRoot (C r) a := by simpa using hr
 #align polynomial.not_is_root_C Polynomial.not_isRoot_C
@@ -881,7 +881,7 @@ def comp (p q : R[X]) : R[X] :=
 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}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p q) (Polynomial.sum.{u1, u1} R _inst_1 (Polynomial.{u1} R _inst_1) (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)))) p (fun (e : Nat) (a : R) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) (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))))) q e)))
 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}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p q) (Polynomial.sum.{u1, u1} R _inst_1 (Polynomial.{u1} R _inst_1) (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)))) p (fun (e : Nat) (a : R) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (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))))) q e)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p q) (Polynomial.sum.{u1, u1} R _inst_1 (Polynomial.{u1} R _inst_1) (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)))) p (fun (e : Nat) (a : R) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (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))))) q e)))
 Case conversion may be inaccurate. Consider using '#align polynomial.comp_eq_sum_left Polynomial.comp_eq_sum_leftₓ'. -/
 theorem comp_eq_sum_left : p.comp q = p.Sum fun e a => C a * q ^ e := by rw [comp, eval₂_eq_sum]
 #align polynomial.comp_eq_sum_left Polynomial.comp_eq_sum_left
@@ -906,7 +906,7 @@ theorem X_comp : X.comp p = p :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a)) (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.eval.{u1} R _inst_1 a p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{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.2398 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) (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.2398 : 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.eval.{u1} R _inst_1 a p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) (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.eval.{u1} R _inst_1 a p))
 Case conversion may be inaccurate. Consider using '#align polynomial.comp_C Polynomial.comp_Cₓ'. -/
 @[simp]
 theorem comp_C : p.comp (C a) = C (p.eval a) := by simp [comp, (C : R →+* _).map_sum]
@@ -916,7 +916,7 @@ theorem comp_C : p.comp (C a) = C (p.eval a) := by simp [comp, (C : R →+* _).m
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) p) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a)
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{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.2398 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p) (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.2398 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)
 Case conversion may be inaccurate. Consider using '#align polynomial.C_comp Polynomial.C_compₓ'. -/
 @[simp]
 theorem C_comp : (C a).comp p = C a :=
@@ -933,7 +933,7 @@ theorem nat_cast_comp {n : ℕ} : (n : R[X]).comp p = n := by rw [← C_eq_nat_c
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) (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.eval.{u1} R _inst_1 (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))))))) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) (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.2398 : 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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) p))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) (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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.comp_zero Polynomial.comp_zeroₓ'. -/
 @[simp]
 theorem comp_zero : p.comp (0 : R[X]) = C (p.eval 0) := by rw [← C_0, comp_C]
@@ -949,7 +949,7 @@ theorem zero_comp : comp (0 : R[X]) p = 0 := by rw [← C_0, C_comp]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{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))))) (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.eval.{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))))))) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{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)))) (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.2398 : 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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))) p))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{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)))) (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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.comp_one Polynomial.comp_oneₓ'. -/
 @[simp]
 theorem comp_one : p.comp 1 = C (p.eval 1) := by rw [← C_1, comp_C]
@@ -972,7 +972,7 @@ theorem add_comp : (p + q).comp r = p.comp r + q.comp r :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a) p) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) (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))))) p n))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a) p) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (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))))) p n))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a) p) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (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))))) p n))
 Case conversion may be inaccurate. Consider using '#align polynomial.monomial_comp Polynomial.monomial_compₓ'. -/
 @[simp]
 theorem monomial_comp (n : ℕ) : (monomial n a).comp p = C a * p ^ n :=
@@ -1015,7 +1015,7 @@ theorem mul_X_pow_comp {k : ℕ} : (p * X ^ k).comp r = p.comp r * r ^ k :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {r : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) p) r) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a) (Polynomial.comp.{u1} R _inst_1 p r))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {r : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p) r) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (Polynomial.comp.{u1} R _inst_1 p r))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {r : Polynomial.{u1} R _inst_1}, Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) p) r) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) a) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (Polynomial.comp.{u1} R _inst_1 p r))
 Case conversion may be inaccurate. Consider using '#align polynomial.C_mul_comp Polynomial.C_mul_compₓ'. -/
 @[simp]
 theorem C_mul_comp : (C a * p).comp r = C a * p.comp r :=
@@ -1123,7 +1123,7 @@ def map : R[X] → S[X] :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_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)), Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) a)) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (fun (_x : RingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) => S -> (Polynomial.{u2} S _inst_2)) (RingHom.hasCoeToFun.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.C.{u2} S _inst_2) (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 a))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_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)), Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2)))))) (Polynomial.C.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (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.2398 : 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 a))
+  forall {R : Type.{u1}} {S : Type.{u2}} {a : R} [_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)), Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2)))))) (Polynomial.C.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (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 a))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_C Polynomial.map_Cₓ'. -/
 @[simp]
 theorem map_C : (C a).map f = C (f a) :=
@@ -1141,7 +1141,7 @@ theorem map_X : X.map f = X :=
 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)) {n : Nat} {a : R}, Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) 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 but is expected to have type
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(Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2)))) (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2) (Polynomial.module.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2 (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2)) (RingHom.id.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2))) (Polynomial.monomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) a) _inst_2 n) (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.2398 : 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 a))
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(Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (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)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2 _inst_2 (RingHom.id.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2)))) (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Polynomial.module.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2 (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2)))) (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2) (Polynomial.module.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2 (Semiring.toModule.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2)) (RingHom.id.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2))) (Polynomial.monomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) _inst_2 n) (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 a))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_monomial Polynomial.map_monomialₓ'. -/
 @[simp]
 theorem map_monomial {n a} : (monomial n a).map f = monomial n (f a) :=
@@ -1184,7 +1184,7 @@ protected theorem map_mul : (p * q).map f = p.map f * q.map f :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (r : R), Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (SMul.smul.{u1, u1} R (Polynomial.{u1} R _inst_1) (SMulZeroClass.toHasSmul.{u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1) (Polynomial.smulZeroClass.{u1, u1} R _inst_1 R (SMulWithZero.toSmulZeroClass.{u1, u1} R R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) r p)) (SMul.smul.{u2, u2} S (Polynomial.{u2} S _inst_2) (SMulZeroClass.toHasSmul.{u2, u2} S (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2) (Polynomial.smulZeroClass.{u2, u2} S _inst_2 S (SMulWithZero.toSmulZeroClass.{u2, u2} S S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (MulZeroClass.toSMulWithZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))))) (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 r) (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] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (r : R), Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (HSMul.hSMul.{u1, u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1) (Polynomial.smulZeroClass.{u1, u1} R _inst_1 R (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) r p)) (HSMul.hSMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) r) (Polynomial.{u2} S _inst_2) (Polynomial.{u2} S _inst_2) (instHSMul.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) r) (Polynomial.{u2} S _inst_2) (SMulZeroClass.toSMul.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) r) (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2) (Polynomial.smulZeroClass.{u2, u2} S _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) r) (SMulWithZero.toSMulZeroClass.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) r) S (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) r) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) r) _inst_2)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (MulZeroClass.toSMulWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) r) (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) r) _inst_2)))))))) (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.2398 : 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 r) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (r : R), Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f (HSMul.hSMul.{u1, u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1) (Polynomial.smulZeroClass.{u1, u1} R _inst_1 R (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) r p)) (HSMul.hSMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (Polynomial.{u2} S _inst_2) (Polynomial.{u2} S _inst_2) (instHSMul.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (Polynomial.{u2} S _inst_2) (SMulZeroClass.toSMul.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2) (Polynomial.smulZeroClass.{u2, u2} S _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (SMulWithZero.toSMulZeroClass.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) S (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) _inst_2)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (MulZeroClass.toSMulWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) _inst_2)))))))) (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 r) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_smul Polynomial.map_smulₓ'. -/
 @[simp]
 protected theorem map_smul (r : R) : (r • p).map f = f r • p.map f := by
@@ -1213,7 +1213,7 @@ def mapRingHom (f : R →+* S) : R[X] →+* S[X]
 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)), Eq.{max (succ u1) (succ u2)} ((Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (RingHom.hasCoeToFun.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.mapRingHom.{u1, u2} R S _inst_1 _inst_2 f)) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f)
 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)), Eq.{max (succ u1) (succ u2)} (forall (ᾰ : Polynomial.{u1} R _inst_1), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) ᾰ) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (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)))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) (Polynomial.mapRingHom.{u1, u2} R S _inst_1 _inst_2 f)) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f)
+  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)), Eq.{max (succ u1) (succ u2)} (forall (ᾰ : Polynomial.{u1} R _inst_1), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) ᾰ) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (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)))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) (Polynomial.mapRingHom.{u1, u2} R S _inst_1 _inst_2 f)) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f)
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_map_ring_hom Polynomial.coe_mapRingHomₓ'. -/
 @[simp]
 theorem coe_mapRingHom (f : R →+* S) : ⇑(mapRingHom f) = map f :=
@@ -1253,7 +1253,7 @@ theorem map_dvd (f : R →+* S) {x y : R[X]} : x ∣ y → x.map f ∣ y.map f :
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (n : Nat), Eq.{succ u2} S (Polynomial.coeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) n) (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.coeff.{u1} R _inst_1 p n))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (n : Nat), Eq.{succ u2} S (Polynomial.coeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) n) (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.2398 : 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.coeff.{u1} R _inst_1 p n))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (n : Nat), Eq.{succ u2} S (Polynomial.coeff.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) n) (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.coeff.{u1} R _inst_1 p n))
 Case conversion may be inaccurate. Consider using '#align polynomial.coeff_map Polynomial.coeff_mapₓ'. -/
 @[simp]
 theorem coeff_map (n : ℕ) : coeff (p.map f) n = f (coeff p n) :=
@@ -1305,7 +1305,7 @@ theorem eval₂_eq_eval_map {x : S} : p.eval₂ f x = (p.map f).eval x :=
 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)) -> (Function.Injective.{succ u1, succ u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f))
 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.2398 : 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)) -> (Function.Injective.{succ u1, succ u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f))
+  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)) -> (Function.Injective.{succ u1, succ u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_injective Polynomial.map_injectiveₓ'. -/
 theorem map_injective (hf : Function.Injective f) : Function.Injective (map f) := fun p q h =>
   ext fun m => hf <| by rw [← coeff_map f, ← coeff_map f, h]
@@ -1315,7 +1315,7 @@ theorem map_injective (hf : Function.Injective f) : Function.Injective (map f) :
 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.Surjective.{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)) -> (Function.Surjective.{succ u1, succ u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f))
 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.Surjective.{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.2398 : 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)) -> (Function.Surjective.{succ u1, succ u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f))
+  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.Surjective.{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)) -> (Function.Surjective.{succ u1, succ u2} (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_surjective Polynomial.map_surjectiveₓ'. -/
 theorem map_surjective (hf : Function.Surjective f) : Function.Surjective (map f) := fun p =>
   Polynomial.induction_on' p
@@ -1349,7 +1349,7 @@ variable {f}
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_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)) -> (Iff (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (OfNat.mk.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.zero.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2))))) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_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.2398 : 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)) -> (Iff (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_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)) -> (Iff (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_eq_zero_iff Polynomial.map_eq_zero_iffₓ'. -/
 protected theorem map_eq_zero_iff (hf : Function.Injective f) : p.map f = 0 ↔ p = 0 :=
   map_eq_zero_iff (mapRingHom f) (map_injective f hf)
@@ -1359,7 +1359,7 @@ protected theorem map_eq_zero_iff (hf : Function.Injective f) : p.map f = 0 ↔
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_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)) -> (Iff (Ne.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (OfNat.mk.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.zero.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2))))) (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_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.2398 : 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)) -> (Iff (Ne.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))) (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_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)) -> (Iff (Ne.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))) (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_ne_zero_iff Polynomial.map_ne_zero_iffₓ'. -/
 protected theorem map_ne_zero_iff (hf : Function.Injective f) : p.map f ≠ 0 ↔ p ≠ 0 :=
   (Polynomial.map_eq_zero_iff hf).Not
@@ -1369,7 +1369,7 @@ protected theorem map_ne_zero_iff (hf : Function.Injective f) : p.map f ≠ 0 
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Iff (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (OfNat.mk.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.zero.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2))))) (forall (x : R), Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f x) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Iff (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))) (forall (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) x) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) x) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) x) _inst_2))))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)}, (Polynomial.Monic.{u1} R _inst_1 p) -> (Iff (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))) (forall (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_monic_eq_zero_iff Polynomial.map_monic_eq_zero_iffₓ'. -/
 theorem map_monic_eq_zero_iff (hp : p.Monic) : p.map f = 0 ↔ ∀ x, f x = 0 :=
   ⟨fun hfp x =>
@@ -1391,7 +1391,7 @@ theorem map_monic_ne_zero (hp : p.Monic) [Nontrivial S] : p.map f ≠ 0 := fun h
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (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] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 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.2398 : 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)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) _inst_2))))) -> (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] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 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)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) _inst_2))))) -> (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_leading_coeff_ne_zero Polynomial.degree_map_eq_of_leadingCoeff_ne_zeroₓ'. -/
 theorem degree_map_eq_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCoeff p) ≠ 0) :
     degree (p.map f) = degree p :=
@@ -1408,7 +1408,7 @@ theorem degree_map_eq_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCo
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (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] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 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.2398 : 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)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) _inst_2))))) -> (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] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 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)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) _inst_2))))) -> (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_of_leading_coeff_ne_zero Polynomial.natDegree_map_of_leadingCoeff_ne_zeroₓ'. -/
 theorem natDegree_map_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCoeff p) ≠ 0) :
     natDegree (p.map f) = natDegree p :=
@@ -1419,7 +1419,7 @@ theorem natDegree_map_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCo
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (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] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 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.2398 : 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)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) _inst_2))))) -> (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.2398 : 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] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 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)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Polynomial.leadingCoeff.{u1} R _inst_1 p)) _inst_2))))) -> (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)))
 Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_map_of_leading_coeff_ne_zero Polynomial.leadingCoeff_map_of_leadingCoeff_ne_zeroₓ'. -/
 theorem leadingCoeff_map_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCoeff p) ≠ 0) :
     leadingCoeff (p.map f) = f (leadingCoeff p) :=
@@ -1529,7 +1529,7 @@ theorem map_comp (p q : R[X]) : map f (p.comp q) = (map f p).comp (map f q) :=
 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)) (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))))) (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.eval.{u1} R _inst_1 (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))))))) 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)) (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{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.2398 : 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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)) (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_zero_map Polynomial.eval_zero_mapₓ'. -/
 @[simp]
 theorem eval_zero_map (f : R →+* S) (p : R[X]) : (p.map f).eval 0 = f (p.eval 0) := by
@@ -1540,7 +1540,7 @@ theorem eval_zero_map (f : R →+* S) (p : R[X]) : (p.map f).eval 0 = f (p.eval
 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)) (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (OfNat.ofNat.{u2} S 1 (OfNat.mk.{u2} S 1 (One.one.{u2} S (AddMonoidWithOne.toOne.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{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.eval.{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))))))) 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)) (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{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.2398 : 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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{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)) (p : Polynomial.{u1} R _inst_1), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{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.eval.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_one_map Polynomial.eval_one_mapₓ'. -/
 @[simp]
 theorem eval_one_map (f : R →+* S) (p : R[X]) : (p.map f).eval 1 = f (p.eval 1) :=
@@ -1556,7 +1556,7 @@ theorem eval_one_map (f : R →+* S) (p : R[X]) : (p.map f).eval 1 = f (p.eval 1
 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)) (p : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u2} Nat S (CoeTCₓ.coe.{1, succ u2} Nat S (Nat.castCoe.{u2} S (AddMonoidWithOne.toNatCast.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))))) n) (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.eval.{u1} R _inst_1 ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) n) 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)) (p : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (Nat.cast.{u2} S (Semiring.toNatCast.{u2} S _inst_2) n) (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.2398 : 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.eval.{u1} R _inst_1 (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R _inst_1) n) 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)) (p : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{succ u2} S (Polynomial.eval.{u2} S _inst_2 (Nat.cast.{u2} S (Semiring.toNatCast.{u2} S _inst_2) n) (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.eval.{u1} R _inst_1 (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R _inst_1) n) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_nat_cast_map Polynomial.eval_nat_cast_mapₓ'. -/
 @[simp]
 theorem eval_nat_cast_map (f : R →+* S) (p : R[X]) (n : ℕ) : (p.map f).eval n = f (p.eval n) :=
@@ -1572,7 +1572,7 @@ theorem eval_nat_cast_map (f : R →+* S) (p : R[X]) (n : ℕ) : (p.map f).eval
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_3 : Ring.{u1} R] [_inst_4 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (i : Int), Eq.{succ u2} S (Polynomial.eval.{u2} S (Ring.toSemiring.{u2} S _inst_4) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Int S (HasLiftT.mk.{1, succ u2} Int S (CoeTCₓ.coe.{1, succ u2} Int S (Int.castCoe.{u2} S (AddGroupWithOne.toHasIntCast.{u2} S (NonAssocRing.toAddGroupWithOne.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4)))))) i) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u2} S _inst_4) f p)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_4))) f (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_3) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_3)))))) i) p))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_3 : Ring.{u2} R] [_inst_4 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) (p : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (i : Int), Eq.{succ u1} S (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S _inst_4) (Int.cast.{u1} S (Ring.toIntCast.{u1} S _inst_4) i) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u1} S _inst_4) f p)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4)))))) f (Polynomial.eval.{u2} R (Ring.toSemiring.{u2} R _inst_3) (Int.cast.{u2} R (Ring.toIntCast.{u2} R _inst_3) i) p))
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_3 : Ring.{u2} R] [_inst_4 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) (p : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (i : Int), Eq.{succ u1} S (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S _inst_4) (Int.cast.{u1} S (Ring.toIntCast.{u1} S _inst_4) i) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u1} S _inst_4) f p)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4))) R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_4)))))) f (Polynomial.eval.{u2} R (Ring.toSemiring.{u2} R _inst_3) (Int.cast.{u2} R (Ring.toIntCast.{u2} R _inst_3) i) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_int_cast_map Polynomial.eval_int_cast_mapₓ'. -/
 @[simp]
 theorem eval_int_cast_map {R S : Type _} [Ring R] [Ring S] (f : R →+* S) (p : R[X]) (i : ℤ) :
@@ -1602,7 +1602,7 @@ variable [Semiring S] [Semiring T] (f : R →+* S) (g : S →+* T) (p)
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) [_inst_2 : Semiring.{u2} S] [_inst_3 : Semiring.{u3} T] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (g : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (x : S), Eq.{succ u3} T (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (fun (_x : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) => S -> T) (RingHom.hasCoeToFun.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) g (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p)) (Polynomial.eval₂.{u1, u3} R T _inst_1 _inst_3 (RingHom.comp.{u1, u2, u3} R S T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3) g f) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (fun (_x : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) => S -> T) (RingHom.hasCoeToFun.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) g x) p)
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) [_inst_2 : Semiring.{u2} S] [_inst_3 : Semiring.{u3} T] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (g : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (x : S), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : S) => T) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3))))) g (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p)) (Polynomial.eval₂.{u1, u3} R T _inst_1 _inst_3 (RingHom.comp.{u1, u2, u3} R S T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3) g f) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3))))) g x) p)
+  forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) [_inst_2 : Semiring.{u2} S] [_inst_3 : Semiring.{u3} T] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (g : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (x : S), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => T) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3))))) g (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p)) (Polynomial.eval₂.{u1, u3} R T _inst_1 _inst_3 (RingHom.comp.{u1, u2, u3} R S T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3) g f) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3)) S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u3} T _inst_3))))) g x) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.hom_eval₂ Polynomial.hom_eval₂ₓ'. -/
 theorem hom_eval₂ (x : S) : g (p.eval₂ f x) = p.eval₂ (g.comp f) (g x) := by
   rw [← eval₂_map, eval₂_at_apply, eval_map]
@@ -1624,7 +1624,7 @@ variable [Semiring R] {p q : R[X]} {x : R} [Semiring S] (f : R →+* S)
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : R), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f x) 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.eval.{u1} R _inst_1 x p))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : R), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (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.2398 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f x) 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.2398 : 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.eval.{u1} R _inst_1 x p))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : R), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f x) 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.eval.{u1} R _inst_1 x p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_hom Polynomial.eval₂_homₓ'. -/
 theorem eval₂_hom (x : R) : p.eval₂ f (f x) = f (p.eval x) :=
   RingHom.comp_id f ▸ (hom_eval₂ p (RingHom.id R) f x).symm
@@ -1670,7 +1670,7 @@ def evalRingHom : R → R[X] →+* R :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (r : R), Eq.{succ u1} ((fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> R) (Polynomial.evalRingHom.{u1} R _inst_1 r)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> R) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.evalRingHom.{u1} R _inst_1 r)) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) r)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (r : R), Eq.{succ u1} (forall (a : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => R) a) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Polynomial.evalRingHom.{u1} R _inst_1 r)) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) r)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (r : R), Eq.{succ u1} (forall (a : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => R) a) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Polynomial.evalRingHom.{u1} R _inst_1 r)) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) r)
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_eval_ring_hom Polynomial.coe_evalRingHomₓ'. -/
 @[simp]
 theorem coe_evalRingHom (r : R) : (evalRingHom r : R[X] → R) = eval r :=
@@ -1713,7 +1713,7 @@ def compRingHom : R[X] → R[X] →+* R[X] :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} ((fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.compRingHom.{u1} R _inst_1 q)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.compRingHom.{u1} R _inst_1 q)) (fun (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p q)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} (forall (a : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.compRingHom.{u1} R _inst_1 q)) (fun (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p q)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} (forall (a : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.compRingHom.{u1} R _inst_1 q)) (fun (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p q)
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_comp_ring_hom Polynomial.coe_compRingHomₓ'. -/
 @[simp]
 theorem coe_compRingHom (q : R[X]) : (compRingHom q : R[X] → R[X]) = fun p => comp p q :=
@@ -1724,7 +1724,7 @@ theorem coe_compRingHom (q : R[X]) : (compRingHom q : R[X] → R[X]) = fun p =>
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.compRingHom.{u1} R _inst_1 q) p) (Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p q)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) p) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.compRingHom.{u1} R _inst_1 q) p) (Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p q)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) p) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.compRingHom.{u1} R _inst_1 q) p) (Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p q)
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_comp_ring_hom_apply Polynomial.coe_compRingHom_applyₓ'. -/
 theorem coe_compRingHom_apply (p q : R[X]) : (compRingHom q : R[X] → R[X]) p = comp p q :=
   rfl
@@ -1867,7 +1867,7 @@ theorem support_map_subset [Semiring R] [Semiring S] (f : R →+* S) (p : R[X])
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] (p : Polynomial.{u1} R _inst_1) {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)) -> (Eq.{1} (Finset.{0} Nat) (Polynomial.support.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (Polynomial.support.{u1} R _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] (p : Polynomial.{u1} R _inst_1) {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.2398 : 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)) -> (Eq.{1} (Finset.{0} Nat) (Polynomial.support.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (Polynomial.support.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] (p : Polynomial.{u1} R _inst_1) {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)) -> (Eq.{1} (Finset.{0} Nat) (Polynomial.support.{u2} S _inst_2 (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f p)) (Polynomial.support.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.support_map_of_injective Polynomial.support_map_of_injectiveₓ'. -/
 theorem support_map_of_injective [Semiring R] [Semiring S] (p : R[X]) {f : R →+* S}
     (hf : Function.Injective f) : (map f p).support = p.support := by
@@ -1898,7 +1898,7 @@ protected theorem map_prod {ι : Type _} (g : ι → R[X]) (s : Finset ι) :
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p x) -> (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) f x))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p x) -> (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p x) -> (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{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 (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x))
 Case conversion may be inaccurate. Consider using '#align polynomial.is_root.map Polynomial.IsRoot.mapₓ'. -/
 theorem IsRoot.map {f : R →+* S} {x : R} {p : R[X]} (h : IsRoot p x) : IsRoot (p.map f) (f x) := by
   rw [is_root, eval_map, eval₂_hom, h.eq_zero, f.map_zero]
@@ -1908,7 +1908,7 @@ theorem IsRoot.map {f : R →+* S} {x : R} {p : R[X]} (h : IsRoot p x) : IsRoot
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))} {x : R} {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))}, (Polynomial.IsRoot.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (CommSemiring.toSemiring.{u1} S _inst_2) f p) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) f x)) -> (Function.Injective.{succ u2, succ u1} R S (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) f)) -> (Polynomial.IsRoot.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) p x)
 but is expected to have type
-  forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))}, (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x)) -> (Function.Injective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f)) -> (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p x)
+  forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))}, (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x)) -> (Function.Injective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f)) -> (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p x)
 Case conversion may be inaccurate. Consider using '#align polynomial.is_root.of_map Polynomial.IsRoot.of_mapₓ'. -/
 theorem IsRoot.of_map {R} [CommRing R] {f : R →+* S} {x : R} {p : R[X]} (h : IsRoot (p.map f) (f x))
     (hf : Function.Injective f) : IsRoot p x := by
@@ -1919,7 +1919,7 @@ theorem IsRoot.of_map {R} [CommRing R] {f : R →+* S} {x : R} {p : R[X]} (h : I
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))} {x : R} {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))}, (Function.Injective.{succ u2, succ u1} R S (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) f)) -> (Iff (Polynomial.IsRoot.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (CommSemiring.toSemiring.{u1} S _inst_2) f p) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (fun (_x : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) f x)) (Polynomial.IsRoot.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) p x))
 but is expected to have type
-  forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))}, (Function.Injective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f)) -> (Iff (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x)) (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p x))
+  forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {x : R} {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))}, (Function.Injective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f)) -> (Iff (Polynomial.IsRoot.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) (CommSemiring.toSemiring.{u2} S _inst_2) f p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x)) (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p x))
 Case conversion may be inaccurate. Consider using '#align polynomial.is_root_map_iff Polynomial.isRoot_map_iffₓ'. -/
 theorem isRoot_map_iff {R : Type _} [CommRing R] {f : R →+* S} {x : R} {p : R[X]}
     (hf : Function.Injective f) : IsRoot (p.map f) (f x) ↔ IsRoot p x :=
@@ -1938,7 +1938,7 @@ variable [Ring R] {p q r : R[X]}
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} (Polynomial.{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)) (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))))) a)) (Neg.neg.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.neg'.{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)) a))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) a)) (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.2398 : 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)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) a)) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (Polynomial.neg'.{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.2398 : 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)) a))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) a)) (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)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) a)) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (Polynomial.neg'.{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)) a))
 Case conversion may be inaccurate. Consider using '#align polynomial.C_neg Polynomial.C_negₓ'. -/
 theorem C_neg : C (-a) = -C a :=
   RingHom.map_neg C a
@@ -1948,7 +1948,7 @@ theorem C_neg : C (-a) = -C a :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} {b : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} (Polynomial.{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)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) a b)) (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)) (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)) a) (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)) b))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} {b : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) a b)) (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.2398 : 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)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) a b)) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) b) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (instHSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (Polynomial.sub.{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.2398 : 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)) a) (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.2398 : 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)) b))
+  forall {R : Type.{u1}} {a : R} {b : R} [_inst_1 : Ring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) a b)) (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)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) a b)) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) b) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (instHSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (Polynomial.sub.{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)) a) (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)) b))
 Case conversion may be inaccurate. Consider using '#align polynomial.C_sub Polynomial.C_subₓ'. -/
 theorem C_sub : C (a - b) = C a - C b :=
   RingHom.map_sub C a b
@@ -2047,7 +2047,7 @@ theorem eval_sub (p q : R[X]) (x : R) : (p - q).eval x = p.eval x - q.eval x :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} {b : R} [_inst_1 : Ring.{u1} R], Iff (Polynomial.IsRoot.{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)) a)) b) (Eq.{succ u1} R a b)
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} {b : R} [_inst_1 : Ring.{u1} R], Iff (Polynomial.IsRoot.{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.2398 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (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.2398 : 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)) a)) b) (Eq.{succ u1} R a b)
+  forall {R : Type.{u1}} {a : R} {b : R} [_inst_1 : Ring.{u1} R], Iff (Polynomial.IsRoot.{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)) a) (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)) a)) b) (Eq.{succ u1} R a b)
 Case conversion may be inaccurate. Consider using '#align polynomial.root_X_sub_C Polynomial.root_X_sub_Cₓ'. -/
 theorem root_X_sub_C : IsRoot (X - C a) b ↔ a = b := by
   rw [is_root.def, eval_sub, eval_X, eval_C, sub_eq_zero, eq_comm]

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

@@ -41,21 +41,41 @@ variable [Semiring S]
 
 variable (f : R →+* S) (x : S)
 
+#print Polynomial.eval₂ /-
 /-- Evaluate a polynomial `p` given a ring hom `f` from the scalar ring
   to the target and a value `x` for the variable in the target -/
 irreducible_def eval₂ (p : R[X]) : S :=
   p.Sum fun e a => f a * x ^ e
 #align polynomial.eval₂ Polynomial.eval₂
+-/
 
+/- warning: polynomial.eval₂_eq_sum -> Polynomial.eval₂_eq_sum is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_eq_sum Polynomial.eval₂_eq_sumₓ'. -/
 theorem eval₂_eq_sum {f : R →+* S} {x : S} : p.eval₂ f x = p.Sum fun e a => f a * x ^ e := by
   rw [eval₂]
 #align polynomial.eval₂_eq_sum Polynomial.eval₂_eq_sum
 
+/- warning: polynomial.eval₂_congr -> Polynomial.eval₂_congr is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_congr Polynomial.eval₂_congrₓ'. -/
 theorem eval₂_congr {R S : Type _} [Semiring R] [Semiring S] {f g : R →+* S} {s t : S}
     {φ ψ : R[X]} : f = g → s = t → φ = ψ → eval₂ f s φ = eval₂ g t ψ := by
   rintro rfl rfl rfl <;> rfl
 #align polynomial.eval₂_congr Polynomial.eval₂_congr
 
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 @[simp]
 theorem eval₂_at_zero : p.eval₂ f 0 = f (coeff p 0) := by
   simp (config := { contextual := true }) only [eval₂_eq_sum, zero_pow_eq, mul_ite, mul_zero,
@@ -63,31 +83,59 @@ theorem eval₂_at_zero : p.eval₂ f 0 = f (coeff p 0) := by
     RingHom.map_zero, imp_true_iff, eq_self_iff_true]
 #align polynomial.eval₂_at_zero Polynomial.eval₂_at_zero
 
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 @[simp]
 theorem eval₂_zero : (0 : R[X]).eval₂ f x = 0 := by simp [eval₂_eq_sum]
 #align polynomial.eval₂_zero Polynomial.eval₂_zero
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_C Polynomial.eval₂_Cₓ'. -/
 @[simp]
-theorem eval₂_c : (C a).eval₂ f x = f a := by simp [eval₂_eq_sum]
-#align polynomial.eval₂_C Polynomial.eval₂_c
+theorem eval₂_C : (C a).eval₂ f x = f a := by simp [eval₂_eq_sum]
+#align polynomial.eval₂_C Polynomial.eval₂_C
 
+#print Polynomial.eval₂_X /-
 @[simp]
-theorem eval₂_x : X.eval₂ f x = x := by simp [eval₂_eq_sum]
-#align polynomial.eval₂_X Polynomial.eval₂_x
+theorem eval₂_X : X.eval₂ f x = x := by simp [eval₂_eq_sum]
+#align polynomial.eval₂_X Polynomial.eval₂_X
+-/
 
+/- warning: polynomial.eval₂_monomial -> Polynomial.eval₂_monomial is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_monomial Polynomial.eval₂_monomialₓ'. -/
 @[simp]
 theorem eval₂_monomial {n : ℕ} {r : R} : (monomial n r).eval₂ f x = f r * x ^ n := by
   simp [eval₂_eq_sum]
 #align polynomial.eval₂_monomial Polynomial.eval₂_monomial
 
+#print Polynomial.eval₂_X_pow /-
 @[simp]
-theorem eval₂_x_pow {n : ℕ} : (X ^ n).eval₂ f x = x ^ n :=
+theorem eval₂_X_pow {n : ℕ} : (X ^ n).eval₂ f x = x ^ n :=
   by
   rw [X_pow_eq_monomial]
   convert eval₂_monomial f x
   simp
-#align polynomial.eval₂_X_pow Polynomial.eval₂_x_pow
+#align polynomial.eval₂_X_pow Polynomial.eval₂_X_pow
+-/
 
+/- warning: polynomial.eval₂_add -> Polynomial.eval₂_add 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.eval₂_add Polynomial.eval₂_addₓ'. -/
 @[simp]
 theorem eval₂_add : (p + q).eval₂ f x = p.eval₂ f x + q.eval₂ f x :=
   by
@@ -95,19 +143,39 @@ theorem eval₂_add : (p + q).eval₂ f x = p.eval₂ f x + q.eval₂ f x :=
   apply sum_add_index <;> simp [add_mul]
 #align polynomial.eval₂_add Polynomial.eval₂_add
 
+#print Polynomial.eval₂_one /-
 @[simp]
 theorem eval₂_one : (1 : R[X]).eval₂ f x = 1 := by rw [← C_1, eval₂_C, f.map_one]
 #align polynomial.eval₂_one Polynomial.eval₂_one
+-/
 
+/- warning: polynomial.eval₂_bit0 -> Polynomial.eval₂_bit0 is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (bit0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1) p)) (bit0.{u2} S (Distrib.toHasAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_bit0 Polynomial.eval₂_bit0ₓ'. -/
 @[simp]
 theorem eval₂_bit0 : (bit0 p).eval₂ f x = bit0 (p.eval₂ f x) := by rw [bit0, eval₂_add, bit0]
 #align polynomial.eval₂_bit0 Polynomial.eval₂_bit0
 
+/- warning: polynomial.eval₂_bit1 -> Polynomial.eval₂_bit1 is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (x : S), Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x (bit1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.hasOne.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1) p)) (bit1.{u2} S (AddMonoidWithOne.toOne.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Distrib.toHasAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Polynomial.eval₂.{u1, u2} R S _inst_1 _inst_2 f x p))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_bit1 Polynomial.eval₂_bit1ₓ'. -/
 @[simp]
 theorem eval₂_bit1 : (bit1 p).eval₂ f x = bit1 (p.eval₂ f x) := by
   rw [bit1, eval₂_add, eval₂_bit0, eval₂_one, bit1]
 #align polynomial.eval₂_bit1 Polynomial.eval₂_bit1
 
+/- warning: polynomial.eval₂_smul -> Polynomial.eval₂_smul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_smul Polynomial.eval₂_smulₓ'. -/
 @[simp]
 theorem eval₂_smul (g : R →+* S) (p : R[X]) (x : S) {s : R} :
     eval₂ g x (s • p) = g s * eval₂ g x p :=
@@ -118,12 +186,15 @@ theorem eval₂_smul (g : R →+* S) (p : R[X]) (x : S) {s : R} :
     simp [mul_sum, mul_assoc]
 #align polynomial.eval₂_smul Polynomial.eval₂_smul
 
+#print Polynomial.eval₂_C_X /-
 @[simp]
-theorem eval₂_c_x : eval₂ C X p = p :=
+theorem eval₂_C_X : eval₂ C X p = p :=
   Polynomial.induction_on' p (fun p q hp hq => by simp [hp, hq]) fun n x => by
     rw [eval₂_monomial, ← smul_X_eq_monomial, C_mul']
-#align polynomial.eval₂_C_X Polynomial.eval₂_c_x
+#align polynomial.eval₂_C_X Polynomial.eval₂_C_X
+-/
 
+#print Polynomial.eval₂AddMonoidHom /-
 /-- `eval₂_add_monoid_hom (f : R →+* S) (x : S)` is the `add_monoid_hom` from
 `R[X]` to `S` obtained by evaluating the pushforward of `p` along `f` at `x`. -/
 @[simps]
@@ -132,7 +203,9 @@ def eval₂AddMonoidHom : R[X] →+ S where
   map_zero' := eval₂_zero _ _
   map_add' _ _ := eval₂_add _ _
 #align polynomial.eval₂_add_monoid_hom Polynomial.eval₂AddMonoidHom
+-/
 
+#print Polynomial.eval₂_nat_cast /-
 @[simp]
 theorem eval₂_nat_cast (n : ℕ) : (n : R[X]).eval₂ f x = n :=
   by
@@ -140,9 +213,11 @@ theorem eval₂_nat_cast (n : ℕ) : (n : R[X]).eval₂ f x = n :=
   · simp only [eval₂_zero, Nat.cast_zero]
   · rw [n.cast_succ, eval₂_add, ih, eval₂_one, n.cast_succ]
 #align polynomial.eval₂_nat_cast Polynomial.eval₂_nat_cast
+-/
 
 variable [Semiring T]
 
+#print Polynomial.eval₂_sum /-
 theorem eval₂_sum (p : T[X]) (g : ℕ → T → R[X]) (x : S) :
     (p.Sum g).eval₂ f x = p.Sum fun n a => (g n a).eval₂ f x :=
   by
@@ -154,21 +229,38 @@ theorem eval₂_sum (p : T[X]) (g : ℕ → T → R[X]) (x : S) :
   simp only [A]
   rw [Sum, T.map_sum, Sum]
 #align polynomial.eval₂_sum Polynomial.eval₂_sum
+-/
 
+/- warning: polynomial.eval₂_list_sum -> Polynomial.eval₂_list_sum is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_list_sum Polynomial.eval₂_list_sumₓ'. -/
 theorem eval₂_list_sum (l : List R[X]) (x : S) : eval₂ f x l.Sum = (l.map (eval₂ f x)).Sum :=
   map_list_sum (eval₂AddMonoidHom f x) l
 #align polynomial.eval₂_list_sum Polynomial.eval₂_list_sum
 
+#print Polynomial.eval₂_multiset_sum /-
 theorem eval₂_multiset_sum (s : Multiset R[X]) (x : S) :
     eval₂ f x s.Sum = (s.map (eval₂ f x)).Sum :=
   map_multiset_sum (eval₂AddMonoidHom f x) s
 #align polynomial.eval₂_multiset_sum Polynomial.eval₂_multiset_sum
+-/
 
+#print Polynomial.eval₂_finset_sum /-
 theorem eval₂_finset_sum (s : Finset ι) (g : ι → R[X]) (x : S) :
     (∑ i in s, g i).eval₂ f x = ∑ i in s, (g i).eval₂ f x :=
   map_sum (eval₂AddMonoidHom f x) _ _
 #align polynomial.eval₂_finset_sum Polynomial.eval₂_finset_sum
+-/
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_of_finsupp Polynomial.eval₂_ofFinsuppₓ'. -/
 theorem eval₂_ofFinsupp {f : R →+* S} {x : S} {p : AddMonoidAlgebra R ℕ} :
     eval₂ f x (⟨p⟩ : R[X]) = liftNC (↑f) (powersHom S x) p :=
   by
@@ -176,6 +268,12 @@ theorem eval₂_ofFinsupp {f : R →+* S} {x : S} {p : AddMonoidAlgebra R ℕ} :
   rfl
 #align polynomial.eval₂_of_finsupp Polynomial.eval₂_ofFinsupp
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_mul_noncomm Polynomial.eval₂_mul_noncommₓ'. -/
 theorem eval₂_mul_noncomm (hf : ∀ k, Commute (f <| q.coeff k) x) :
     eval₂ f x (p * q) = eval₂ f x p * eval₂ f x q :=
   by
@@ -185,19 +283,37 @@ theorem eval₂_mul_noncomm (hf : ∀ k, Commute (f <| q.coeff k) x) :
   exact lift_nc_mul _ _ p q fun k n hn => (hf k).pow_right n
 #align polynomial.eval₂_mul_noncomm Polynomial.eval₂_mul_noncomm
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_mul_X Polynomial.eval₂_mul_Xₓ'. -/
 @[simp]
-theorem eval₂_mul_x : eval₂ f x (p * X) = eval₂ f x p * x :=
+theorem eval₂_mul_X : eval₂ f x (p * X) = eval₂ f x p * x :=
   by
   refine' trans (eval₂_mul_noncomm _ _ fun k => _) (by rw [eval₂_X])
   rcases em (k = 1) with (rfl | hk)
   · simp
   · simp [coeff_X_of_ne_one hk]
-#align polynomial.eval₂_mul_X Polynomial.eval₂_mul_x
-
-@[simp]
-theorem eval₂_x_mul : eval₂ f x (X * p) = eval₂ f x p * x := by rw [X_mul, eval₂_mul_X]
-#align polynomial.eval₂_X_mul Polynomial.eval₂_x_mul
-
+#align polynomial.eval₂_mul_X Polynomial.eval₂_mul_X
+
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_X_mul Polynomial.eval₂_X_mulₓ'. -/
+@[simp]
+theorem eval₂_X_mul : eval₂ f x (X * p) = eval₂ f x p * x := by rw [X_mul, eval₂_mul_X]
+#align polynomial.eval₂_X_mul Polynomial.eval₂_X_mul
+
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(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 a)))
+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_mul_C' Polynomial.eval₂_mul_C'ₓ'. -/
 theorem eval₂_mul_C' (h : Commute (f a) x) : eval₂ f x (p * C a) = eval₂ f x p * f a :=
   by
   rw [eval₂_mul_noncomm, eval₂_C]
@@ -207,6 +323,12 @@ theorem eval₂_mul_C' (h : Commute (f a) x) : eval₂ f x (p * C a) = eval₂ f
   · simp only [coeff_C_ne_zero hk, RingHom.map_zero, Commute.zero_left]
 #align polynomial.eval₂_mul_C' Polynomial.eval₂_mul_C'
 
+/- warning: polynomial.eval₂_list_prod_noncomm -> Polynomial.eval₂_list_prod_noncomm is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_list_prod_noncomm Polynomial.eval₂_list_prod_noncommₓ'. -/
 theorem eval₂_list_prod_noncomm (ps : List R[X])
     (hf : ∀ p ∈ ps, ∀ (k), Commute (f <| coeff p k) x) :
     eval₂ f x ps.Prod = (ps.map (Polynomial.eval₂ f x)).Prod :=
@@ -217,6 +339,12 @@ theorem eval₂_list_prod_noncomm (ps : List R[X])
     simp [eval₂_mul_noncomm _ _ hf.2, ihp hf.1]
 #align polynomial.eval₂_list_prod_noncomm Polynomial.eval₂_list_prod_noncomm
 
+/- warning: polynomial.eval₂_ring_hom' -> Polynomial.eval₂RingHom' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_ring_hom' Polynomial.eval₂RingHom'ₓ'. -/
 /-- `eval₂` as a `ring_hom` for noncommutative rings -/
 def eval₂RingHom' (f : R →+* S) (x : S) (hf : ∀ a, Commute (f a) x) : R[X] →+* S
     where
@@ -242,11 +370,23 @@ section
 
 variable [Semiring S] (f : R →+* S) (x : S)
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_eq_sum_range Polynomial.eval₂_eq_sum_rangeₓ'. -/
 theorem eval₂_eq_sum_range :
     p.eval₂ f x = ∑ i in Finset.range (p.natDegree + 1), f (p.coeff i) * x ^ i :=
   trans (congr_arg _ p.as_sum_range) (trans (eval₂_finset_sum f _ _ x) (congr_arg _ (by simp)))
 #align polynomial.eval₂_eq_sum_range Polynomial.eval₂_eq_sum_range
 
+/- warning: polynomial.eval₂_eq_sum_range' -> Polynomial.eval₂_eq_sum_range' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_eq_sum_range' Polynomial.eval₂_eq_sum_range'ₓ'. -/
 theorem eval₂_eq_sum_range' (f : R →+* S) {p : R[X]} {n : ℕ} (hn : p.natDegree < n) (x : S) :
     eval₂ f x p = ∑ i in Finset.range n, f (p.coeff i) * x ^ i :=
   by
@@ -261,48 +401,90 @@ section
 
 variable [CommSemiring S] (f : R →+* S) (x : S)
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_mul Polynomial.eval₂_mulₓ'. -/
 @[simp]
 theorem eval₂_mul : (p * q).eval₂ f x = p.eval₂ f x * q.eval₂ f x :=
   eval₂_mul_noncomm _ _ fun k => Commute.all _ _
 #align polynomial.eval₂_mul Polynomial.eval₂_mul
 
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 theorem eval₂_mul_eq_zero_of_left (q : R[X]) (hp : p.eval₂ f x = 0) : (p * q).eval₂ f x = 0 :=
   by
   rw [eval₂_mul f x]
   exact mul_eq_zero_of_left hp (q.eval₂ f x)
 #align polynomial.eval₂_mul_eq_zero_of_left Polynomial.eval₂_mul_eq_zero_of_left
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_mul_eq_zero_of_right Polynomial.eval₂_mul_eq_zero_of_rightₓ'. -/
 theorem eval₂_mul_eq_zero_of_right (p : R[X]) (hq : q.eval₂ f x = 0) : (p * q).eval₂ f x = 0 :=
   by
   rw [eval₂_mul f x]
   exact mul_eq_zero_of_right (p.eval₂ f x) hq
 #align polynomial.eval₂_mul_eq_zero_of_right Polynomial.eval₂_mul_eq_zero_of_right
 
+#print Polynomial.eval₂RingHom /-
 /-- `eval₂` as a `ring_hom` -/
 def eval₂RingHom (f : R →+* S) (x : S) : R[X] →+* S :=
   { eval₂AddMonoidHom f x with
     map_one' := eval₂_one _ _
     map_mul' := fun _ _ => eval₂_mul _ _ }
 #align polynomial.eval₂_ring_hom Polynomial.eval₂RingHom
+-/
 
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 @[simp]
 theorem coe_eval₂RingHom (f : R →+* S) (x) : ⇑(eval₂RingHom f x) = eval₂ f x :=
   rfl
 #align polynomial.coe_eval₂_ring_hom Polynomial.coe_eval₂RingHom
 
+#print Polynomial.eval₂_pow /-
 theorem eval₂_pow (n : ℕ) : (p ^ n).eval₂ f x = p.eval₂ f x ^ n :=
   (eval₂RingHom _ _).map_pow _ _
 #align polynomial.eval₂_pow Polynomial.eval₂_pow
+-/
 
+#print Polynomial.eval₂_dvd /-
 theorem eval₂_dvd : p ∣ q → eval₂ f x p ∣ eval₂ f x q :=
   (eval₂RingHom f x).map_dvd
 #align polynomial.eval₂_dvd Polynomial.eval₂_dvd
+-/
 
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 theorem eval₂_eq_zero_of_dvd_of_eval₂_eq_zero (h : p ∣ q) (h0 : eval₂ f x p = 0) :
     eval₂ f x q = 0 :=
   zero_dvd_iff.mp (h0 ▸ eval₂_dvd f x h)
 #align polynomial.eval₂_eq_zero_of_dvd_of_eval₂_eq_zero Polynomial.eval₂_eq_zero_of_dvd_of_eval₂_eq_zero
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_list_prod Polynomial.eval₂_list_prodₓ'. -/
 theorem eval₂_list_prod (l : List R[X]) (x : S) : eval₂ f x l.Prod = (l.map (eval₂ f x)).Prod :=
   map_list_prod (eval₂RingHom f x) l
 #align polynomial.eval₂_list_prod Polynomial.eval₂_list_prod
@@ -315,27 +497,53 @@ section Eval
 
 variable {x : R}
 
+#print Polynomial.eval /-
 /-- `eval x p` is the evaluation of the polynomial `p` at `x` -/
 def eval : R → R[X] → R :=
   eval₂ (RingHom.id _)
 #align polynomial.eval Polynomial.eval
+-/
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval_eq_sum Polynomial.eval_eq_sumₓ'. -/
 theorem eval_eq_sum : p.eval x = p.Sum fun e a => a * x ^ e :=
   by
   rw [eval, eval₂_eq_sum]
   rfl
 #align polynomial.eval_eq_sum Polynomial.eval_eq_sum
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval_eq_sum_range Polynomial.eval_eq_sum_rangeₓ'. -/
 theorem eval_eq_sum_range {p : R[X]} (x : R) :
     p.eval x = ∑ i in Finset.range (p.natDegree + 1), p.coeff i * x ^ i := by
   rw [eval_eq_sum, sum_over_range] <;> simp
 #align polynomial.eval_eq_sum_range Polynomial.eval_eq_sum_range
 
+/- warning: polynomial.eval_eq_sum_range' -> Polynomial.eval_eq_sum_range' is a dubious translation:
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+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {n : Nat}, (LT.lt.{0} Nat Nat.hasLt (Polynomial.natDegree.{u1} R _inst_1 p) n) -> (forall (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x p) (Finset.sum.{u1, 0} R Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finset.range n) (fun (i : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Polynomial.coeff.{u1} R _inst_1 p i) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x i))))
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval_eq_sum_range' Polynomial.eval_eq_sum_range'ₓ'. -/
 theorem eval_eq_sum_range' {p : R[X]} {n : ℕ} (hn : p.natDegree < n) (x : R) :
     p.eval x = ∑ i in Finset.range n, p.coeff i * x ^ i := by
   rw [eval_eq_sum, p.sum_over_range' _ _ hn] <;> simp
 #align polynomial.eval_eq_sum_range' Polynomial.eval_eq_sum_range'
 
+/- warning: polynomial.eval₂_at_apply -> Polynomial.eval₂_at_apply is a dubious translation:
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 @[simp]
 theorem eval₂_at_apply {S : Type _} [Semiring S] (f : R →+* S) (r : R) :
     p.eval₂ f (f r) = f (p.eval r) :=
@@ -344,6 +552,12 @@ theorem eval₂_at_apply {S : Type _} [Semiring S] (f : R →+* S) (r : R) :
   simp only [f.map_mul, f.map_pow]
 #align polynomial.eval₂_at_apply Polynomial.eval₂_at_apply
 
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 @[simp]
 theorem eval₂_at_one {S : Type _} [Semiring S] (f : R →+* S) : p.eval₂ f 1 = f (p.eval 1) :=
   by
@@ -351,6 +565,12 @@ theorem eval₂_at_one {S : Type _} [Semiring S] (f : R →+* S) : p.eval₂ f 1
   simp
 #align polynomial.eval₂_at_one Polynomial.eval₂_at_one
 
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 @[simp]
 theorem eval₂_at_nat_cast {S : Type _} [Semiring S] (f : R →+* S) (n : ℕ) :
     p.eval₂ f n = f (p.eval n) := by
@@ -358,66 +578,126 @@ theorem eval₂_at_nat_cast {S : Type _} [Semiring S] (f : R →+* S) (n : ℕ)
   simp
 #align polynomial.eval₂_at_nat_cast Polynomial.eval₂_at_nat_cast
 
+/- warning: polynomial.eval_C -> Polynomial.eval_C is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval_C Polynomial.eval_Cₓ'. -/
 @[simp]
-theorem eval_c : (C a).eval x = a :=
-  eval₂_c _ _
-#align polynomial.eval_C Polynomial.eval_c
+theorem eval_C : (C a).eval x = a :=
+  eval₂_C _ _
+#align polynomial.eval_C Polynomial.eval_C
 
+#print Polynomial.eval_nat_cast /-
 @[simp]
 theorem eval_nat_cast {n : ℕ} : (n : R[X]).eval x = n := by simp only [← C_eq_nat_cast, eval_C]
 #align polynomial.eval_nat_cast Polynomial.eval_nat_cast
+-/
 
+#print Polynomial.eval_X /-
 @[simp]
-theorem eval_x : X.eval x = x :=
-  eval₂_x _ _
-#align polynomial.eval_X Polynomial.eval_x
+theorem eval_X : X.eval x = x :=
+  eval₂_X _ _
+#align polynomial.eval_X Polynomial.eval_X
+-/
 
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 @[simp]
 theorem eval_monomial {n a} : (monomial n a).eval x = a * x ^ n :=
   eval₂_monomial _ _
 #align polynomial.eval_monomial Polynomial.eval_monomial
 
+/- warning: polynomial.eval_zero -> Polynomial.eval_zero is a dubious translation:
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 @[simp]
 theorem eval_zero : (0 : R[X]).eval x = 0 :=
   eval₂_zero _ _
 #align polynomial.eval_zero Polynomial.eval_zero
 
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 @[simp]
 theorem eval_add : (p + q).eval x = p.eval x + q.eval x :=
   eval₂_add _ _
 #align polynomial.eval_add Polynomial.eval_add
 
+#print Polynomial.eval_one /-
 @[simp]
 theorem eval_one : (1 : R[X]).eval x = 1 :=
   eval₂_one _ _
 #align polynomial.eval_one Polynomial.eval_one
+-/
 
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 @[simp]
 theorem eval_bit0 : (bit0 p).eval x = bit0 (p.eval x) :=
   eval₂_bit0 _ _
 #align polynomial.eval_bit0 Polynomial.eval_bit0
 
+/- warning: polynomial.eval_bit1 -> Polynomial.eval_bit1 is a dubious translation:
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 @[simp]
 theorem eval_bit1 : (bit1 p).eval x = bit1 (p.eval x) :=
   eval₂_bit1 _ _
 #align polynomial.eval_bit1 Polynomial.eval_bit1
 
+/- warning: polynomial.eval_smul -> Polynomial.eval_smul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_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))))] [_inst_4 : IsScalarTower.{u2, u1, u1} S R 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))) (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (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)))] (s : S) (p : Polynomial.{u1} R _inst_1) (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (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)))) s 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))) s (Polynomial.eval.{u1} R _inst_1 x p))
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_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))))] [_inst_4 : IsScalarTower.{u2, u1, u1} S R R (SMulZeroClass.toSMul.{u2, u1} S R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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))) (SMulZeroClass.toSMul.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u2, u1} S R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))] (s : S) (p : Polynomial.{u1} R _inst_1) (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x (HSMul.hSMul.{u2, u1, u1} S (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHSMul.{u2, u1} S (Polynomial.{u1} R _inst_1) (SMulZeroClass.toSMul.{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))))) s p)) (HSMul.hSMul.{u2, u1, u1} S R R (instHSMul.{u2, u1} S R (SMulZeroClass.toSMul.{u2, u1} S R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))) s (Polynomial.eval.{u1} R _inst_1 x p))
+Case conversion may be inaccurate. Consider using '#align polynomial.eval_smul Polynomial.eval_smulₓ'. -/
 @[simp]
 theorem eval_smul [Monoid S] [DistribMulAction S R] [IsScalarTower S R R] (s : S) (p : R[X])
     (x : R) : (s • p).eval x = s • p.eval x := by
   rw [← smul_one_smul R s p, eval, eval₂_smul, RingHom.id_apply, smul_one_mul]
 #align polynomial.eval_smul Polynomial.eval_smul
 
+/- warning: polynomial.eval_C_mul -> Polynomial.eval_C_mul is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval_C_mul Polynomial.eval_C_mulₓ'. -/
 @[simp]
-theorem eval_c_mul : (C a * p).eval x = a * p.eval x :=
+theorem eval_C_mul : (C a * p).eval x = a * p.eval x :=
   by
   apply Polynomial.induction_on' p
   · intro p q ph qh
     simp only [mul_add, eval_add, ph, qh]
   · intro n b
     simp only [mul_assoc, C_mul_monomial, eval_monomial]
-#align polynomial.eval_C_mul Polynomial.eval_c_mul
-
+#align polynomial.eval_C_mul Polynomial.eval_C_mul
+
+/- warning: polynomial.eval_monomial_one_add_sub -> Polynomial.eval_monomial_one_add_sub is a dubious translation:
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_inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) d) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))))))) (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) y (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) d) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))))))) (Finset.sum.{u1, 0} S Nat (AddCommGroup.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toAddCommGroup.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) d (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (x_1 : Nat) => HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Nat.choose (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) d (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x_1)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat S (HasLiftT.mk.{1, succ u1} Nat S (CoeTCₓ.coe.{1, succ u1} Nat S (Nat.castCoe.{u1} S (AddMonoidWithOne.toNatCast.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (NonAssocRing.toAddGroupWithOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) x_1) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (Ring.toMonoid.{u1} S (CommRing.toRing.{u1} S _inst_2)))) y (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) x_1 (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
+but is expected to have type
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (d : Nat) (y : S), Eq.{succ u1} S (HSub.hSub.{u1, u1, u1} S S S (instHSub.{u1} S (Ring.toSub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.eval.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (NonAssocRing.toOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) y) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.module.{u1, u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.monomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) d) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (Nat.cast.{u1} S 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+Case conversion may be inaccurate. Consider using '#align polynomial.eval_monomial_one_add_sub Polynomial.eval_monomial_one_add_subₓ'. -/
 /-- A reformulation of the expansion of (1 + y)^d:
 $$(d + 1) (1 + y)^d - (d + 1)y^d = \sum_{i = 0}^d {d + 1 \choose i} \cdot i \cdot y^{i - 1}.$$
 -/
@@ -441,6 +721,7 @@ theorem eval_monomial_one_add_sub [CommRing S] (d : ℕ) (y : S) :
     Nat.add_sub_cancel]
 #align polynomial.eval_monomial_one_add_sub Polynomial.eval_monomial_one_add_sub
 
+#print Polynomial.leval /-
 /-- `polynomial.eval` as linear map -/
 @[simps]
 def leval {R : Type _} [Semiring R] (r : R) : R[X] →ₗ[R] R
@@ -449,14 +730,27 @@ def leval {R : Type _} [Semiring R] (r : R) : R[X] →ₗ[R] R
   map_add' f g := eval_add
   map_smul' c f := eval_smul c f r
 #align polynomial.leval Polynomial.leval
+-/
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval_nat_cast_mul Polynomial.eval_nat_cast_mulₓ'. -/
 @[simp]
 theorem eval_nat_cast_mul {n : ℕ} : ((n : R[X]) * p).eval x = n * p.eval x := by
   rw [← C_eq_nat_cast, eval_C_mul]
 #align polynomial.eval_nat_cast_mul Polynomial.eval_nat_cast_mul
 
+/- warning: polynomial.eval_mul_X -> Polynomial.eval_mul_X is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval_mul_X Polynomial.eval_mul_Xₓ'. -/
 @[simp]
-theorem eval_mul_x : (p * X).eval x = p.eval x * x :=
+theorem eval_mul_X : (p * X).eval x = p.eval x * x :=
   by
   apply Polynomial.induction_on' p
   · intro p q ph qh
@@ -464,42 +758,72 @@ theorem eval_mul_x : (p * X).eval x = p.eval x * x :=
   · intro n a
     simp only [← monomial_one_one_eq_X, monomial_mul_monomial, eval_monomial, mul_one, pow_succ',
       mul_assoc]
-#align polynomial.eval_mul_X Polynomial.eval_mul_x
+#align polynomial.eval_mul_X Polynomial.eval_mul_X
 
+/- warning: polynomial.eval_mul_X_pow -> Polynomial.eval_mul_X_pow is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval_mul_X_pow Polynomial.eval_mul_X_powₓ'. -/
 @[simp]
-theorem eval_mul_x_pow {k : ℕ} : (p * X ^ k).eval x = p.eval x * x ^ k :=
+theorem eval_mul_X_pow {k : ℕ} : (p * X ^ k).eval x = p.eval x * x ^ k :=
   by
   induction' k with k ih
   · simp
   · simp [pow_succ', ← mul_assoc, ih]
-#align polynomial.eval_mul_X_pow Polynomial.eval_mul_x_pow
+#align polynomial.eval_mul_X_pow Polynomial.eval_mul_X_pow
 
+#print Polynomial.eval_sum /-
 theorem eval_sum (p : R[X]) (f : ℕ → R → R[X]) (x : R) :
     (p.Sum f).eval x = p.Sum fun n a => (f n a).eval x :=
   eval₂_sum _ _ _ _
 #align polynomial.eval_sum Polynomial.eval_sum
+-/
 
+#print Polynomial.eval_finset_sum /-
 theorem eval_finset_sum (s : Finset ι) (g : ι → R[X]) (x : R) :
     (∑ i in s, g i).eval x = ∑ i in s, (g i).eval x :=
   eval₂_finset_sum _ _ _ _
 #align polynomial.eval_finset_sum Polynomial.eval_finset_sum
+-/
 
+#print Polynomial.IsRoot /-
 /-- `is_root p x` implies `x` is a root of `p`. The evaluation of `p` at `x` is zero -/
 def IsRoot (p : R[X]) (a : R) : Prop :=
   p.eval a = 0
 #align polynomial.is_root Polynomial.IsRoot
+-/
 
 instance [DecidableEq R] : Decidable (IsRoot p a) := by unfold is_root <;> infer_instance
 
+/- warning: polynomial.is_root.def -> Polynomial.IsRoot.def is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.is_root.def Polynomial.IsRoot.defₓ'. -/
 @[simp]
 theorem IsRoot.def : IsRoot p a ↔ p.eval a = 0 :=
   Iff.rfl
 #align polynomial.is_root.def Polynomial.IsRoot.def
 
+/- warning: polynomial.is_root.eq_zero -> Polynomial.IsRoot.eq_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.is_root.eq_zero Polynomial.IsRoot.eq_zeroₓ'. -/
 theorem IsRoot.eq_zero (h : IsRoot p x) : eval x p = 0 :=
   h
 #align polynomial.is_root.eq_zero Polynomial.IsRoot.eq_zero
 
+/- warning: polynomial.coeff_zero_eq_eval_zero -> Polynomial.coeff_zero_eq_eval_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.coeff_zero_eq_eval_zero Polynomial.coeff_zero_eq_eval_zeroₓ'. -/
 theorem coeff_zero_eq_eval_zero (p : R[X]) : coeff p 0 = p.eval 0 :=
   calc
     coeff p 0 = coeff p 0 * 0 ^ 0 := by simp
@@ -511,159 +835,261 @@ theorem coeff_zero_eq_eval_zero (p : R[X]) : coeff p 0 = p.eval 0 :=
     
 #align polynomial.coeff_zero_eq_eval_zero Polynomial.coeff_zero_eq_eval_zero
 
+/- warning: polynomial.zero_is_root_of_coeff_zero_eq_zero -> Polynomial.zero_isRoot_of_coeff_zero_eq_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.zero_is_root_of_coeff_zero_eq_zero Polynomial.zero_isRoot_of_coeff_zero_eq_zeroₓ'. -/
 theorem zero_isRoot_of_coeff_zero_eq_zero {p : R[X]} (hp : p.coeff 0 = 0) : IsRoot p 0 := by
   rwa [coeff_zero_eq_eval_zero] at hp
 #align polynomial.zero_is_root_of_coeff_zero_eq_zero Polynomial.zero_isRoot_of_coeff_zero_eq_zero
 
+#print Polynomial.IsRoot.dvd /-
 theorem IsRoot.dvd {R : Type _} [CommSemiring R] {p q : R[X]} {x : R} (h : p.IsRoot x)
     (hpq : p ∣ q) : q.IsRoot x := by
   rwa [is_root, eval, eval₂_eq_zero_of_dvd_of_eval₂_eq_zero _ _ hpq]
 #align polynomial.is_root.dvd Polynomial.IsRoot.dvd
+-/
 
-theorem not_isRoot_c (r a : R) (hr : r ≠ 0) : ¬IsRoot (C r) a := by simpa using hr
-#align polynomial.not_is_root_C Polynomial.not_isRoot_c
-
-theorem eval_surjective (x : R) : Function.Surjective <| eval x := fun y => ⟨C y, eval_c⟩
+/- warning: polynomial.not_is_root_C -> Polynomial.not_isRoot_C is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.not_is_root_C Polynomial.not_isRoot_Cₓ'. -/
+theorem not_isRoot_C (r a : R) (hr : r ≠ 0) : ¬IsRoot (C r) a := by simpa using hr
+#align polynomial.not_is_root_C Polynomial.not_isRoot_C
+
+#print Polynomial.eval_surjective /-
+theorem eval_surjective (x : R) : Function.Surjective <| eval x := fun y => ⟨C y, eval_C⟩
 #align polynomial.eval_surjective Polynomial.eval_surjective
+-/
 
 end Eval
 
 section Comp
 
+#print Polynomial.comp /-
 /-- The composition of polynomials as a polynomial. -/
 def comp (p q : R[X]) : R[X] :=
   p.eval₂ C q
 #align polynomial.comp Polynomial.comp
+-/
 
+/- warning: polynomial.comp_eq_sum_left -> Polynomial.comp_eq_sum_left is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.comp_eq_sum_left Polynomial.comp_eq_sum_leftₓ'. -/
 theorem comp_eq_sum_left : p.comp q = p.Sum fun e a => C a * q ^ e := by rw [comp, eval₂_eq_sum]
 #align polynomial.comp_eq_sum_left Polynomial.comp_eq_sum_left
 
+#print Polynomial.comp_X /-
 @[simp]
-theorem comp_x : p.comp X = p :=
+theorem comp_X : p.comp X = p :=
   by
   simp only [comp, eval₂, C_mul_X_pow_eq_monomial]
   exact sum_monomial_eq _
-#align polynomial.comp_X Polynomial.comp_x
+#align polynomial.comp_X Polynomial.comp_X
+-/
 
+#print Polynomial.X_comp /-
 @[simp]
-theorem x_comp : X.comp p = p :=
-  eval₂_x _ _
-#align polynomial.X_comp Polynomial.x_comp
+theorem X_comp : X.comp p = p :=
+  eval₂_X _ _
+#align polynomial.X_comp Polynomial.X_comp
+-/
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.comp_C Polynomial.comp_Cₓ'. -/
 @[simp]
-theorem comp_c : p.comp (C a) = C (p.eval a) := by simp [comp, (C : R →+* _).map_sum]
-#align polynomial.comp_C Polynomial.comp_c
+theorem comp_C : p.comp (C a) = C (p.eval a) := by simp [comp, (C : R →+* _).map_sum]
+#align polynomial.comp_C Polynomial.comp_C
 
+/- warning: polynomial.C_comp -> Polynomial.C_comp is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.C_comp Polynomial.C_compₓ'. -/
 @[simp]
-theorem c_comp : (C a).comp p = C a :=
-  eval₂_c _ _
-#align polynomial.C_comp Polynomial.c_comp
+theorem C_comp : (C a).comp p = C a :=
+  eval₂_C _ _
+#align polynomial.C_comp Polynomial.C_comp
 
+#print Polynomial.nat_cast_comp /-
 @[simp]
 theorem nat_cast_comp {n : ℕ} : (n : R[X]).comp p = n := by rw [← C_eq_nat_cast, C_comp]
 #align polynomial.nat_cast_comp Polynomial.nat_cast_comp
+-/
 
+/- warning: polynomial.comp_zero -> Polynomial.comp_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.comp_zero Polynomial.comp_zeroₓ'. -/
 @[simp]
 theorem comp_zero : p.comp (0 : R[X]) = C (p.eval 0) := by rw [← C_0, comp_C]
 #align polynomial.comp_zero Polynomial.comp_zero
 
+#print Polynomial.zero_comp /-
 @[simp]
 theorem zero_comp : comp (0 : R[X]) p = 0 := by rw [← C_0, C_comp]
 #align polynomial.zero_comp Polynomial.zero_comp
+-/
 
+/- warning: polynomial.comp_one -> Polynomial.comp_one is a dubious translation:
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 @[simp]
 theorem comp_one : p.comp 1 = C (p.eval 1) := by rw [← C_1, comp_C]
 #align polynomial.comp_one Polynomial.comp_one
 
+#print Polynomial.one_comp /-
 @[simp]
 theorem one_comp : comp (1 : R[X]) p = 1 := by rw [← C_1, C_comp]
 #align polynomial.one_comp Polynomial.one_comp
+-/
 
+#print Polynomial.add_comp /-
 @[simp]
 theorem add_comp : (p + q).comp r = p.comp r + q.comp r :=
   eval₂_add _ _
 #align polynomial.add_comp Polynomial.add_comp
+-/
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.monomial_comp Polynomial.monomial_compₓ'. -/
 @[simp]
 theorem monomial_comp (n : ℕ) : (monomial n a).comp p = C a * p ^ n :=
   eval₂_monomial _ _
 #align polynomial.monomial_comp Polynomial.monomial_comp
 
+#print Polynomial.mul_X_comp /-
 @[simp]
-theorem mul_x_comp : (p * X).comp r = p.comp r * r :=
+theorem mul_X_comp : (p * X).comp r = p.comp r * r :=
   by
   apply Polynomial.induction_on' p
   · intro p q hp hq
     simp only [hp, hq, add_mul, add_comp]
   · intro n b
     simp only [pow_succ', mul_assoc, monomial_mul_X, monomial_comp]
-#align polynomial.mul_X_comp Polynomial.mul_x_comp
+#align polynomial.mul_X_comp Polynomial.mul_X_comp
+-/
 
+#print Polynomial.X_pow_comp /-
 @[simp]
-theorem x_pow_comp {k : ℕ} : (X ^ k).comp p = p ^ k :=
+theorem X_pow_comp {k : ℕ} : (X ^ k).comp p = p ^ k :=
   by
   induction' k with k ih
   · simp
   · simp [pow_succ', mul_X_comp, ih]
-#align polynomial.X_pow_comp Polynomial.x_pow_comp
+#align polynomial.X_pow_comp Polynomial.X_pow_comp
+-/
 
+#print Polynomial.mul_X_pow_comp /-
 @[simp]
-theorem mul_x_pow_comp {k : ℕ} : (p * X ^ k).comp r = p.comp r * r ^ k :=
+theorem mul_X_pow_comp {k : ℕ} : (p * X ^ k).comp r = p.comp r * r ^ k :=
   by
   induction' k with k ih
   · simp
   · simp [ih, pow_succ', ← mul_assoc, mul_X_comp]
-#align polynomial.mul_X_pow_comp Polynomial.mul_x_pow_comp
+#align polynomial.mul_X_pow_comp Polynomial.mul_X_pow_comp
+-/
 
+/- warning: polynomial.C_mul_comp -> Polynomial.C_mul_comp is a dubious translation:
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_inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) a) (Polynomial.comp.{u1} R _inst_1 p r))
+Case conversion may be inaccurate. Consider using '#align polynomial.C_mul_comp Polynomial.C_mul_compₓ'. -/
 @[simp]
-theorem c_mul_comp : (C a * p).comp r = C a * p.comp r :=
+theorem C_mul_comp : (C a * p).comp r = C a * p.comp r :=
   by
   apply Polynomial.induction_on' p
   · intro p q hp hq
     simp [hp, hq, mul_add]
   · intro n b
     simp [mul_assoc]
-#align polynomial.C_mul_comp Polynomial.c_mul_comp
+#align polynomial.C_mul_comp Polynomial.C_mul_comp
 
+#print Polynomial.nat_cast_mul_comp /-
 @[simp]
 theorem nat_cast_mul_comp {n : ℕ} : ((n : R[X]) * p).comp r = n * p.comp r := by
   rw [← C_eq_nat_cast, C_mul_comp, C_eq_nat_cast]
 #align polynomial.nat_cast_mul_comp Polynomial.nat_cast_mul_comp
+-/
 
+#print Polynomial.mul_comp /-
 @[simp]
 theorem mul_comp {R : Type _} [CommSemiring R] (p q r : R[X]) :
     (p * q).comp r = p.comp r * q.comp r :=
   eval₂_mul _ _
 #align polynomial.mul_comp Polynomial.mul_comp
+-/
 
+#print Polynomial.pow_comp /-
 @[simp]
 theorem pow_comp {R : Type _} [CommSemiring R] (p q : R[X]) (n : ℕ) :
     (p ^ n).comp q = p.comp q ^ n :=
   ((MonoidHom.mk fun r : R[X] => r.comp q) one_comp fun r s => mul_comp r s q).map_pow p n
 #align polynomial.pow_comp Polynomial.pow_comp
+-/
 
+#print Polynomial.bit0_comp /-
 @[simp]
 theorem bit0_comp : comp (bit0 p : R[X]) q = bit0 (p.comp q) := by simp only [bit0, add_comp]
 #align polynomial.bit0_comp Polynomial.bit0_comp
+-/
 
+#print Polynomial.bit1_comp /-
 @[simp]
 theorem bit1_comp : comp (bit1 p : R[X]) q = bit1 (p.comp q) := by
   simp only [bit1, add_comp, bit0_comp, one_comp]
 #align polynomial.bit1_comp Polynomial.bit1_comp
+-/
 
+/- warning: polynomial.smul_comp -> Polynomial.smul_comp is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_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))))] [_inst_4 : IsScalarTower.{u2, u1, u1} S R 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))) (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (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)))] (s : S) (p : Polynomial.{u1} R _inst_1) (q : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{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)))) s p) q) (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)))) s (Polynomial.comp.{u1} R _inst_1 p q))
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_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))))] [_inst_4 : IsScalarTower.{u2, u1, u1} S R R (SMulZeroClass.toSMul.{u2, u1} S R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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))) (SMulZeroClass.toSMul.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u2, u1} S R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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)))] (s : S) (p : Polynomial.{u1} R _inst_1) (q : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.comp.{u1} R _inst_1 (HSMul.hSMul.{u2, u1, u1} S (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHSMul.{u2, u1} S (Polynomial.{u1} R _inst_1) (SMulZeroClass.toSMul.{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))))) s p) q) (HSMul.hSMul.{u2, u1, u1} S (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHSMul.{u2, u1} S (Polynomial.{u1} R _inst_1) (SMulZeroClass.toSMul.{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))))) s (Polynomial.comp.{u1} R _inst_1 p q))
+Case conversion may be inaccurate. Consider using '#align polynomial.smul_comp Polynomial.smul_compₓ'. -/
 @[simp]
 theorem smul_comp [Monoid S] [DistribMulAction S R] [IsScalarTower S R R] (s : S) (p q : R[X]) :
     (s • p).comp q = s • p.comp q := by
   rw [← smul_one_smul R s p, comp, comp, eval₂_smul, ← smul_eq_C_mul, smul_assoc, one_smul]
 #align polynomial.smul_comp Polynomial.smul_comp
 
+#print Polynomial.comp_assoc /-
 theorem comp_assoc {R : Type _} [CommSemiring R] (φ ψ χ : R[X]) :
     (φ.comp ψ).comp χ = φ.comp (ψ.comp χ) := by
   apply Polynomial.induction_on φ <;>
     · intros
       simp_all only [add_comp, mul_comp, C_comp, X_comp, pow_succ', ← mul_assoc]
 #align polynomial.comp_assoc Polynomial.comp_assoc
+-/
 
+/- warning: polynomial.coeff_comp_degree_mul_degree -> Polynomial.coeff_comp_degree_mul_degree 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}, (Ne.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 q) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R _inst_1 (Polynomial.comp.{u1} R _inst_1 p q) (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat Nat.hasMul) (Polynomial.natDegree.{u1} R _inst_1 p) (Polynomial.natDegree.{u1} R _inst_1 q))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Polynomial.leadingCoeff.{u1} R _inst_1 p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (Polynomial.leadingCoeff.{u1} R _inst_1 q) (Polynomial.natDegree.{u1} R _inst_1 p))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Ne.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 q) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R _inst_1 (Polynomial.comp.{u1} R _inst_1 p q) (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat instMulNat) (Polynomial.natDegree.{u1} R _inst_1 p) (Polynomial.natDegree.{u1} R _inst_1 q))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Polynomial.leadingCoeff.{u1} R _inst_1 p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (Polynomial.leadingCoeff.{u1} R _inst_1 q) (Polynomial.natDegree.{u1} R _inst_1 p))))
+Case conversion may be inaccurate. Consider using '#align polynomial.coeff_comp_degree_mul_degree Polynomial.coeff_comp_degree_mul_degreeₓ'. -/
 theorem coeff_comp_degree_mul_degree (hqd0 : natDegree q ≠ 0) :
     coeff (p.comp q) (natDegree p * natDegree q) = leadingCoeff p * leadingCoeff q ^ natDegree p :=
   by
@@ -686,21 +1112,37 @@ variable [Semiring S]
 
 variable (f : R →+* S)
 
+#print Polynomial.map /-
 /-- `map f p` maps a polynomial `p` across a ring hom `f` -/
 def map : R[X] → S[X] :=
   eval₂ (C.comp f) X
 #align polynomial.map Polynomial.map
+-/
 
+/- warning: polynomial.map_C -> Polynomial.map_C is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.map_C Polynomial.map_Cₓ'. -/
 @[simp]
-theorem map_c : (C a).map f = C (f a) :=
-  eval₂_c _ _
-#align polynomial.map_C Polynomial.map_c
+theorem map_C : (C a).map f = C (f a) :=
+  eval₂_C _ _
+#align polynomial.map_C Polynomial.map_C
 
+#print Polynomial.map_X /-
 @[simp]
-theorem map_x : X.map f = X :=
-  eval₂_x _ _
-#align polynomial.map_X Polynomial.map_x
+theorem map_X : X.map f = X :=
+  eval₂_X _ _
+#align polynomial.map_X Polynomial.map_X
+-/
 
+/- warning: polynomial.map_monomial -> Polynomial.map_monomial is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.map_monomial Polynomial.map_monomialₓ'. -/
 @[simp]
 theorem map_monomial {n a} : (monomial n a).map f = monomial n (f a) :=
   by
@@ -708,33 +1150,48 @@ theorem map_monomial {n a} : (monomial n a).map f = monomial n (f a) :=
   rw [eval₂_monomial, ← C_mul_X_pow_eq_monomial]; rfl
 #align polynomial.map_monomial Polynomial.map_monomial
 
+#print Polynomial.map_zero /-
 @[simp]
 protected theorem map_zero : (0 : R[X]).map f = 0 :=
   eval₂_zero _ _
 #align polynomial.map_zero Polynomial.map_zero
+-/
 
+#print Polynomial.map_add /-
 @[simp]
 protected theorem map_add : (p + q).map f = p.map f + q.map f :=
   eval₂_add _ _
 #align polynomial.map_add Polynomial.map_add
+-/
 
+#print Polynomial.map_one /-
 @[simp]
 protected theorem map_one : (1 : R[X]).map f = 1 :=
   eval₂_one _ _
 #align polynomial.map_one Polynomial.map_one
+-/
 
+#print Polynomial.map_mul /-
 @[simp]
 protected theorem map_mul : (p * q).map f = p.map f * q.map f :=
   by
   rw [map, eval₂_mul_noncomm]
   exact fun k => (commute_X _).symm
 #align polynomial.map_mul Polynomial.map_mul
+-/
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.map_smul Polynomial.map_smulₓ'. -/
 @[simp]
 protected theorem map_smul (r : R) : (r • p).map f = f r • p.map f := by
   rw [map, eval₂_smul, RingHom.comp_apply, C_mul']
 #align polynomial.map_smul Polynomial.map_smul
 
+#print Polynomial.mapRingHom /-
 -- `map` is a ring-hom unconditionally, and theoretically the definition could be replaced,
 -- but this turns out not to be easy because `p.map f` does not resolve to `polynomial.map`
 -- if `map` is a `ring_hom` instead of a plain function; the elaborator does not try to coerce
@@ -750,33 +1207,54 @@ def mapRingHom (f : R →+* S) : R[X] →+* S[X]
   map_mul' _ _ := Polynomial.map_mul f
   map_one' := Polynomial.map_one f
 #align polynomial.map_ring_hom Polynomial.mapRingHom
+-/
 
+/- warning: polynomial.coe_map_ring_hom -> Polynomial.coe_mapRingHom is a dubious translation:
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 @[simp]
 theorem coe_mapRingHom (f : R →+* S) : ⇑(mapRingHom f) = map f :=
   rfl
 #align polynomial.coe_map_ring_hom Polynomial.coe_mapRingHom
 
+#print Polynomial.map_nat_cast /-
 -- This is protected to not clash with the global `map_nat_cast`.
 @[simp]
 protected theorem map_nat_cast (n : ℕ) : (n : R[X]).map f = n :=
   map_natCast (mapRingHom f) n
 #align polynomial.map_nat_cast Polynomial.map_nat_cast
+-/
 
+#print Polynomial.map_bit0 /-
 @[simp]
 protected theorem map_bit0 : (bit0 p).map f = bit0 (p.map f) :=
   map_bit0 (mapRingHom f) p
 #align polynomial.map_bit0 Polynomial.map_bit0
+-/
 
+#print Polynomial.map_bit1 /-
 @[simp]
 protected theorem map_bit1 : (bit1 p).map f = bit1 (p.map f) :=
   map_bit1 (mapRingHom f) p
 #align polynomial.map_bit1 Polynomial.map_bit1
+-/
 
+#print Polynomial.map_dvd /-
 --TODO rename to `map_dvd_map`
 theorem map_dvd (f : R →+* S) {x y : R[X]} : x ∣ y → x.map f ∣ y.map f :=
   (mapRingHom f).map_dvd
 #align polynomial.map_dvd Polynomial.map_dvd
+-/
 
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 @[simp]
 theorem coeff_map (n : ℕ) : coeff (p.map f) n = f (coeff p n) :=
   by
@@ -787,6 +1265,12 @@ theorem coeff_map (n : ℕ) : coeff (p.map f) n = f (coeff p n) :=
   split_ifs <;> simp [f.map_zero]
 #align polynomial.coeff_map Polynomial.coeff_map
 
+/- warning: polynomial.map_equiv -> Polynomial.mapEquiv is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.map_equiv Polynomial.mapEquivₓ'. -/
 /-- If `R` and `S` are isomorphic, then so are their polynomial rings. -/
 @[simps]
 def mapEquiv (e : R ≃+* S) : R[X] ≃+* S[X] :=
@@ -794,14 +1278,19 @@ def mapEquiv (e : R ≃+* S) : R[X] ≃+* S[X] :=
     (by ext <;> simp)
 #align polynomial.map_equiv Polynomial.mapEquiv
 
+#print Polynomial.map_map /-
 theorem map_map [Semiring T] (g : S →+* T) (p : R[X]) : (p.map f).map g = p.map (g.comp f) :=
   ext (by simp [coeff_map])
 #align polynomial.map_map Polynomial.map_map
+-/
 
+#print Polynomial.map_id /-
 @[simp]
 theorem map_id : p.map (RingHom.id _) = p := by simp [Polynomial.ext_iff, coeff_map]
 #align polynomial.map_id Polynomial.map_id
+-/
 
+#print Polynomial.eval₂_eq_eval_map /-
 theorem eval₂_eq_eval_map {x : S} : p.eval₂ f x = (p.map f).eval x :=
   by
   apply Polynomial.induction_on' p
@@ -810,11 +1299,24 @@ theorem eval₂_eq_eval_map {x : S} : p.eval₂ f x = (p.map f).eval x :=
   · intro n r
     simp
 #align polynomial.eval₂_eq_eval_map Polynomial.eval₂_eq_eval_map
+-/
 
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 theorem map_injective (hf : Function.Injective f) : Function.Injective (map f) := fun p q h =>
   ext fun m => hf <| by rw [← coeff_map f, ← coeff_map f, h]
 #align polynomial.map_injective Polynomial.map_injective
 
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 theorem map_surjective (hf : Function.Surjective f) : Function.Surjective (map f) := fun p =>
   Polynomial.induction_on' p
     (fun p q hp hq =>
@@ -826,27 +1328,49 @@ theorem map_surjective (hf : Function.Surjective f) : Function.Surjective (map f
     ⟨monomial n r, by rw [map_monomial f, hr]⟩
 #align polynomial.map_surjective Polynomial.map_surjective
 
+#print Polynomial.degree_map_le /-
 theorem degree_map_le (p : R[X]) : degree (p.map f) ≤ degree p :=
   by
   apply (degree_le_iff_coeff_zero _ _).2 fun m hm => _
   rw [degree_lt_iff_coeff_zero] at hm
   simp [hm m le_rfl]
 #align polynomial.degree_map_le Polynomial.degree_map_le
+-/
 
+#print Polynomial.natDegree_map_le /-
 theorem natDegree_map_le (p : R[X]) : natDegree (p.map f) ≤ natDegree p :=
   natDegree_le_natDegree (degree_map_le f p)
 #align polynomial.nat_degree_map_le Polynomial.natDegree_map_le
+-/
 
 variable {f}
 
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 protected theorem map_eq_zero_iff (hf : Function.Injective f) : p.map f = 0 ↔ p = 0 :=
   map_eq_zero_iff (mapRingHom f) (map_injective f hf)
 #align polynomial.map_eq_zero_iff Polynomial.map_eq_zero_iff
 
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 protected theorem map_ne_zero_iff (hf : Function.Injective f) : p.map f ≠ 0 ↔ p ≠ 0 :=
   (Polynomial.map_eq_zero_iff hf).Not
 #align polynomial.map_ne_zero_iff Polynomial.map_ne_zero_iff
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.map_monic_eq_zero_iff Polynomial.map_monic_eq_zero_iffₓ'. -/
 theorem map_monic_eq_zero_iff (hp : p.Monic) : p.map f = 0 ↔ ∀ x, f x = 0 :=
   ⟨fun hfp x =>
     calc
@@ -857,10 +1381,18 @@ theorem map_monic_eq_zero_iff (hp : p.Monic) : p.map f = 0 ↔ ∀ x, f x = 0 :=
     fun h => ext fun n => by simp only [h, coeff_map, coeff_zero]⟩
 #align polynomial.map_monic_eq_zero_iff Polynomial.map_monic_eq_zero_iff
 
+#print Polynomial.map_monic_ne_zero /-
 theorem map_monic_ne_zero (hp : p.Monic) [Nontrivial S] : p.map f ≠ 0 := fun h =>
   f.map_one_ne_zero ((map_monic_eq_zero_iff hp).mp h _)
 #align polynomial.map_monic_ne_zero Polynomial.map_monic_ne_zero
+-/
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.degree_map_eq_of_leading_coeff_ne_zero Polynomial.degree_map_eq_of_leadingCoeff_ne_zeroₓ'. -/
 theorem degree_map_eq_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCoeff p) ≠ 0) :
     degree (p.map f) = degree p :=
   le_antisymm (degree_map_le f _) <|
@@ -872,11 +1404,23 @@ theorem degree_map_eq_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCo
     exact hf
 #align polynomial.degree_map_eq_of_leading_coeff_ne_zero Polynomial.degree_map_eq_of_leadingCoeff_ne_zero
 
+/- warning: polynomial.nat_degree_map_of_leading_coeff_ne_zero -> Polynomial.natDegree_map_of_leadingCoeff_ne_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_map_of_leading_coeff_ne_zero Polynomial.natDegree_map_of_leadingCoeff_ne_zeroₓ'. -/
 theorem natDegree_map_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCoeff p) ≠ 0) :
     natDegree (p.map f) = natDegree p :=
   natDegree_eq_of_degree_eq (degree_map_eq_of_leadingCoeff_ne_zero f hf)
 #align polynomial.nat_degree_map_of_leading_coeff_ne_zero Polynomial.natDegree_map_of_leadingCoeff_ne_zero
 
+/- warning: polynomial.leading_coeff_map_of_leading_coeff_ne_zero -> Polynomial.leadingCoeff_map_of_leadingCoeff_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f (Polynomial.leadingCoeff.{u1} R _inst_1 p)) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))))) -> (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
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+Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_map_of_leading_coeff_ne_zero Polynomial.leadingCoeff_map_of_leadingCoeff_ne_zeroₓ'. -/
 theorem leadingCoeff_map_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadingCoeff p) ≠ 0) :
     leadingCoeff (p.map f) = f (leadingCoeff p) :=
   by
@@ -886,26 +1430,40 @@ theorem leadingCoeff_map_of_leadingCoeff_ne_zero (f : R →+* S) (hf : f (leadin
 
 variable (f)
 
+#print Polynomial.mapRingHom_id /-
 @[simp]
 theorem mapRingHom_id : mapRingHom (RingHom.id R) = RingHom.id R[X] :=
   RingHom.ext fun x => map_id
 #align polynomial.map_ring_hom_id Polynomial.mapRingHom_id
+-/
 
+#print Polynomial.mapRingHom_comp /-
 @[simp]
 theorem mapRingHom_comp [Semiring T] (f : S →+* T) (g : R →+* S) :
     (mapRingHom f).comp (mapRingHom g) = mapRingHom (f.comp g) :=
   RingHom.ext <| Polynomial.map_map g f
 #align polynomial.map_ring_hom_comp Polynomial.mapRingHom_comp
+-/
 
+#print Polynomial.map_list_prod /-
 protected theorem map_list_prod (L : List R[X]) : L.Prod.map f = (L.map <| map f).Prod :=
   Eq.symm <| List.prod_hom _ (mapRingHom f).toMonoidHom
 #align polynomial.map_list_prod Polynomial.map_list_prod
+-/
 
+#print Polynomial.map_pow /-
 @[simp]
 protected theorem map_pow (n : ℕ) : (p ^ n).map f = p.map f ^ n :=
   (mapRingHom f).map_pow _ _
 #align polynomial.map_pow Polynomial.map_pow
+-/
 
+/- warning: polynomial.mem_map_srange -> Polynomial.mem_map_rangeS 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.mem_map_srange Polynomial.mem_map_rangeSₓ'. -/
 theorem mem_map_rangeS {p : S[X]} : p ∈ (mapRingHom f).srange ↔ ∀ n, p.coeff n ∈ f.srange :=
   by
   constructor
@@ -921,24 +1479,41 @@ theorem mem_map_rangeS {p : S[X]} : p ∈ (mapRingHom f).srange ↔ ∀ n, p.coe
     rw [coe_map_ring_hom, Polynomial.map_mul, map_C, hc, Polynomial.map_pow, map_X]
 #align polynomial.mem_map_srange Polynomial.mem_map_rangeS
 
+/- warning: polynomial.mem_map_range -> Polynomial.mem_map_range is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.mem_map_range Polynomial.mem_map_rangeₓ'. -/
 theorem mem_map_range {R S : Type _} [Ring R] [Ring S] (f : R →+* S) {p : S[X]} :
     p ∈ (mapRingHom f).range ↔ ∀ n, p.coeff n ∈ f.range :=
   mem_map_rangeS f
 #align polynomial.mem_map_range Polynomial.mem_map_range
 
+#print Polynomial.eval₂_map /-
 theorem eval₂_map [Semiring T] (g : S →+* T) (x : T) : (p.map f).eval₂ g x = p.eval₂ (g.comp f) x :=
   by rw [eval₂_eq_eval_map, eval₂_eq_eval_map, map_map]
 #align polynomial.eval₂_map Polynomial.eval₂_map
+-/
 
+#print Polynomial.eval_map /-
 theorem eval_map (x : S) : (p.map f).eval x = p.eval₂ f x :=
   (eval₂_eq_eval_map f).symm
 #align polynomial.eval_map Polynomial.eval_map
+-/
 
+/- warning: polynomial.map_sum -> Polynomial.map_sum is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.map_sum Polynomial.map_sumₓ'. -/
 protected theorem map_sum {ι : Type _} (g : ι → R[X]) (s : Finset ι) :
     (∑ i in s, g i).map f = ∑ i in s, (g i).map f :=
   (mapRingHom f).map_sum _ _
 #align polynomial.map_sum Polynomial.map_sum
 
+#print Polynomial.map_comp /-
 theorem map_comp (p q : R[X]) : map f (p.comp q) = (map f p).comp (map f q) :=
   Polynomial.induction_on p (by simp only [map_C, forall_const, C_comp, eq_self_iff_true])
     (by
@@ -948,12 +1523,25 @@ theorem map_comp (p q : R[X]) : map f (p.comp q) = (map f p).comp (map f q) :=
       simp (config := { contextual := true }) only [pow_succ', ← mul_assoc, comp, forall_const,
         eval₂_mul_X, imp_true_iff, eq_self_iff_true, map_X, Polynomial.map_mul])
 #align polynomial.map_comp Polynomial.map_comp
+-/
 
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 @[simp]
 theorem eval_zero_map (f : R →+* S) (p : R[X]) : (p.map f).eval 0 = f (p.eval 0) := by
   simp [← coeff_zero_eq_eval_zero]
 #align polynomial.eval_zero_map Polynomial.eval_zero_map
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval_one_map Polynomial.eval_one_mapₓ'. -/
 @[simp]
 theorem eval_one_map (f : R →+* S) (p : R[X]) : (p.map f).eval 1 = f (p.eval 1) :=
   by
@@ -964,6 +1552,12 @@ theorem eval_one_map (f : R →+* S) (p : R[X]) : (p.map f).eval 1 = f (p.eval 1
     simp only [one_pow, mul_one, eval_monomial, map_monomial]
 #align polynomial.eval_one_map Polynomial.eval_one_map
 
+/- warning: polynomial.eval_nat_cast_map -> Polynomial.eval_nat_cast_map is a dubious translation:
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 @[simp]
 theorem eval_nat_cast_map (f : R →+* S) (p : R[X]) (n : ℕ) : (p.map f).eval n = f (p.eval n) :=
   by
@@ -974,6 +1568,12 @@ theorem eval_nat_cast_map (f : R →+* S) (p : R[X]) (n : ℕ) : (p.map f).eval
     simp only [map_natCast f, eval_monomial, map_monomial, f.map_pow, f.map_mul]
 #align polynomial.eval_nat_cast_map Polynomial.eval_nat_cast_map
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval_int_cast_map Polynomial.eval_int_cast_mapₓ'. -/
 @[simp]
 theorem eval_int_cast_map {R S : Type _} [Ring R] [Ring S] (f : R →+* S) (p : R[X]) (i : ℤ) :
     (p.map f).eval i = f (p.eval i) :=
@@ -998,6 +1598,12 @@ section HomEval₂
 
 variable [Semiring S] [Semiring T] (f : R →+* S) (g : S →+* T) (p)
 
+/- warning: polynomial.hom_eval₂ -> Polynomial.hom_eval₂ is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.hom_eval₂ Polynomial.hom_eval₂ₓ'. -/
 theorem hom_eval₂ (x : S) : g (p.eval₂ f x) = p.eval₂ (g.comp f) (g x) := by
   rw [← eval₂_map, eval₂_at_apply, eval_map]
 #align polynomial.hom_eval₂ Polynomial.hom_eval₂
@@ -1014,6 +1620,12 @@ section
 
 variable [Semiring R] {p q : R[X]} {x : R} [Semiring S] (f : R →+* S)
 
+/- warning: polynomial.eval₂_hom -> Polynomial.eval₂_hom 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.eval₂_hom Polynomial.eval₂_homₓ'. -/
 theorem eval₂_hom (x : R) : p.eval₂ f (f x) = f (p.eval x) :=
   RingHom.comp_id f ▸ (hom_eval₂ p (RingHom.id R) f x).symm
 #align polynomial.eval₂_hom Polynomial.eval₂_hom
@@ -1024,9 +1636,11 @@ section
 
 variable [Semiring R] {p q : R[X]} {x : R} [CommSemiring S] (f : R →+* S)
 
+#print Polynomial.eval₂_comp /-
 theorem eval₂_comp {x : S} : eval₂ f x (p.comp q) = eval₂ f (eval₂ f x q) p := by
   rw [comp, p.as_sum_range] <;> simp [eval₂_finset_sum, eval₂_pow]
 #align polynomial.eval₂_comp Polynomial.eval₂_comp
+-/
 
 end
 
@@ -1034,30 +1648,49 @@ section
 
 variable [CommSemiring R] {p q : R[X]} {x : R} [CommSemiring S] (f : R →+* S)
 
+/- warning: polynomial.eval_mul -> Polynomial.eval_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) x (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) p q)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) x p) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) x q))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {x : R}, Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) x (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) p q)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) x p) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) x q))
+Case conversion may be inaccurate. Consider using '#align polynomial.eval_mul Polynomial.eval_mulₓ'. -/
 @[simp]
 theorem eval_mul : (p * q).eval x = p.eval x * q.eval x :=
   eval₂_mul _ _
 #align polynomial.eval_mul Polynomial.eval_mul
 
+#print Polynomial.evalRingHom /-
 /-- `eval r`, regarded as a ring homomorphism from `R[X]` to `R`. -/
 def evalRingHom : R → R[X] →+* R :=
   eval₂RingHom (RingHom.id _)
 #align polynomial.eval_ring_hom Polynomial.evalRingHom
+-/
 
+/- warning: polynomial.coe_eval_ring_hom -> Polynomial.coe_evalRingHom 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.coe_eval_ring_hom Polynomial.coe_evalRingHomₓ'. -/
 @[simp]
 theorem coe_evalRingHom (r : R) : (evalRingHom r : R[X] → R) = eval r :=
   rfl
 #align polynomial.coe_eval_ring_hom Polynomial.coe_evalRingHom
 
+#print Polynomial.evalRingHom_zero /-
 theorem evalRingHom_zero : evalRingHom 0 = constantCoeff :=
   FunLike.ext _ _ fun p => p.coeff_zero_eq_eval_zero.symm
 #align polynomial.eval_ring_hom_zero Polynomial.evalRingHom_zero
+-/
 
+#print Polynomial.eval_pow /-
 @[simp]
 theorem eval_pow (n : ℕ) : (p ^ n).eval x = p.eval x ^ n :=
   eval₂_pow _ _ _
 #align polynomial.eval_pow Polynomial.eval_pow
+-/
 
+#print Polynomial.eval_comp /-
 @[simp]
 theorem eval_comp : (p.comp q).eval x = p.eval (q.eval x) :=
   by
@@ -1067,51 +1700,88 @@ theorem eval_comp : (p.comp q).eval x = p.eval (q.eval x) :=
   · intro n a
     simp
 #align polynomial.eval_comp Polynomial.eval_comp
+-/
 
+#print Polynomial.compRingHom /-
 /-- `comp p`, regarded as a ring homomorphism from `R[X]` to itself. -/
 def compRingHom : R[X] → R[X] →+* R[X] :=
   eval₂RingHom C
 #align polynomial.comp_ring_hom Polynomial.compRingHom
+-/
 
+/- warning: polynomial.coe_comp_ring_hom -> Polynomial.coe_compRingHom is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.coe_comp_ring_hom Polynomial.coe_compRingHomₓ'. -/
 @[simp]
 theorem coe_compRingHom (q : R[X]) : (compRingHom q : R[X] → R[X]) = fun p => comp p q :=
   rfl
 #align polynomial.coe_comp_ring_hom Polynomial.coe_compRingHom
 
+/- warning: polynomial.coe_comp_ring_hom_apply -> Polynomial.coe_compRingHom_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.compRingHom.{u1} R _inst_1 q) p) (Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p q)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) p) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.compRingHom.{u1} R _inst_1 q) p) (Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p q)
+Case conversion may be inaccurate. Consider using '#align polynomial.coe_comp_ring_hom_apply Polynomial.coe_compRingHom_applyₓ'. -/
 theorem coe_compRingHom_apply (p q : R[X]) : (compRingHom q : R[X] → R[X]) p = comp p q :=
   rfl
 #align polynomial.coe_comp_ring_hom_apply Polynomial.coe_compRingHom_apply
 
+#print Polynomial.root_mul_left_of_isRoot /-
 theorem root_mul_left_of_isRoot (p : R[X]) {q : R[X]} : IsRoot q a → IsRoot (p * q) a := fun H => by
   rw [is_root, eval_mul, is_root.def.1 H, mul_zero]
 #align polynomial.root_mul_left_of_is_root Polynomial.root_mul_left_of_isRoot
+-/
 
+#print Polynomial.root_mul_right_of_isRoot /-
 theorem root_mul_right_of_isRoot {p : R[X]} (q : R[X]) : IsRoot p a → IsRoot (p * q) a := fun H =>
   by rw [is_root, eval_mul, is_root.def.1 H, zero_mul]
 #align polynomial.root_mul_right_of_is_root Polynomial.root_mul_right_of_isRoot
+-/
 
+#print Polynomial.eval₂_multiset_prod /-
 theorem eval₂_multiset_prod (s : Multiset R[X]) (x : S) :
     eval₂ f x s.Prod = (s.map (eval₂ f x)).Prod :=
   map_multiset_prod (eval₂RingHom f x) s
 #align polynomial.eval₂_multiset_prod Polynomial.eval₂_multiset_prod
+-/
 
+#print Polynomial.eval₂_finset_prod /-
 theorem eval₂_finset_prod (s : Finset ι) (g : ι → R[X]) (x : S) :
     (∏ i in s, g i).eval₂ f x = ∏ i in s, (g i).eval₂ f x :=
   map_prod (eval₂RingHom f x) _ _
 #align polynomial.eval₂_finset_prod Polynomial.eval₂_finset_prod
+-/
 
+/- warning: polynomial.eval_list_prod -> Polynomial.eval_list_prod is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (l : List.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) x (List.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) l)) (List.prod.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (List.map.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) x) l))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (l : List.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) x (List.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) l)) (List.prod.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (List.map.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) x) l))
+Case conversion may be inaccurate. Consider using '#align polynomial.eval_list_prod Polynomial.eval_list_prodₓ'. -/
 /-- Polynomial evaluation commutes with `list.prod`
 -/
 theorem eval_list_prod (l : List R[X]) (x : R) : eval x l.Prod = (l.map (eval x)).Prod :=
   (evalRingHom x).map_list_prod l
 #align polynomial.eval_list_prod Polynomial.eval_list_prod
 
+#print Polynomial.eval_multiset_prod /-
 /-- Polynomial evaluation commutes with `multiset.prod`
 -/
 theorem eval_multiset_prod (s : Multiset R[X]) (x : R) : eval x s.Prod = (s.map (eval x)).Prod :=
   (evalRingHom x).map_multiset_prod s
 #align polynomial.eval_multiset_prod Polynomial.eval_multiset_prod
+-/
 
+/- warning: polynomial.eval_prod -> Polynomial.eval_prod is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u2}} (s : Finset.{u2} ι) (p : ι -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) x (Finset.prod.{u1, u2} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ι (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) s (fun (j : ι) => p j))) (Finset.prod.{u1, u2} R ι (CommSemiring.toCommMonoid.{u1} R _inst_1) s (fun (j : ι) => Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) x (p j)))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {ι : Type.{u1}} (s : Finset.{u1} ι) (p : ι -> (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (x : R), Eq.{succ u2} R (Polynomial.eval.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1) x (Finset.prod.{u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) ι (CommSemiring.toCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.commSemiring.{u2} R _inst_1)) s (fun (j : ι) => p j))) (Finset.prod.{u2, u1} R ι (CommSemiring.toCommMonoid.{u2} R _inst_1) s (fun (j : ι) => Polynomial.eval.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1) x (p j)))
+Case conversion may be inaccurate. Consider using '#align polynomial.eval_prod Polynomial.eval_prodₓ'. -/
 /-- Polynomial evaluation commutes with `finset.prod`
 -/
 theorem eval_prod {ι : Type _} (s : Finset ι) (p : ι → R[X]) (x : R) :
@@ -1119,38 +1789,64 @@ theorem eval_prod {ι : Type _} (s : Finset ι) (p : ι → R[X]) (x : R) :
   (evalRingHom x).map_prod _ _
 #align polynomial.eval_prod Polynomial.eval_prod
 
+#print Polynomial.list_prod_comp /-
 theorem list_prod_comp (l : List R[X]) (q : R[X]) :
     l.Prod.comp q = (l.map fun p : R[X] => p.comp q).Prod :=
   map_list_prod (compRingHom q) _
 #align polynomial.list_prod_comp Polynomial.list_prod_comp
+-/
 
+#print Polynomial.multiset_prod_comp /-
 theorem multiset_prod_comp (s : Multiset R[X]) (q : R[X]) :
     s.Prod.comp q = (s.map fun p : R[X] => p.comp q).Prod :=
   map_multiset_prod (compRingHom q) _
 #align polynomial.multiset_prod_comp Polynomial.multiset_prod_comp
+-/
 
+/- warning: polynomial.prod_comp -> Polynomial.prod_comp is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u2}} (s : Finset.{u2} ι) (p : ι -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Finset.prod.{u1, u2} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ι (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) s (fun (j : ι) => p j)) q) (Finset.prod.{u1, u2} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ι (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) s (fun (j : ι) => Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (p j) q))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {ι : Type.{u1}} (s : Finset.{u1} ι) (p : ι -> (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (q : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)), Eq.{succ u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.comp.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1) (Finset.prod.{u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) ι (CommSemiring.toCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.commSemiring.{u2} R _inst_1)) s (fun (j : ι) => p j)) q) (Finset.prod.{u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) ι (CommSemiring.toCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.commSemiring.{u2} R _inst_1)) s (fun (j : ι) => Polynomial.comp.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1) (p j) q))
+Case conversion may be inaccurate. Consider using '#align polynomial.prod_comp Polynomial.prod_compₓ'. -/
 theorem prod_comp {ι : Type _} (s : Finset ι) (p : ι → R[X]) (q : R[X]) :
     (∏ j in s, p j).comp q = ∏ j in s, (p j).comp q :=
   map_prod (compRingHom q) _ _
 #align polynomial.prod_comp Polynomial.prod_comp
 
+/- warning: polynomial.is_root_prod -> Polynomial.isRoot_prod is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] [_inst_4 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))] {ι : Type.{u2}} (s : Finset.{u2} ι) (p : ι -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (x : R), Iff (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) (Finset.prod.{u1, u2} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.commRing.{u1} R _inst_3)) s (fun (j : ι) => p j)) x) (Exists.{succ u2} ι (fun (i : ι) => Exists.{0} (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) (fun (H : Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) => Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) (p i) x)))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.is_root_prod Polynomial.isRoot_prodₓ'. -/
 theorem isRoot_prod {R} [CommRing R] [IsDomain R] {ι : Type _} (s : Finset ι) (p : ι → R[X])
     (x : R) : IsRoot (∏ j in s, p j) x ↔ ∃ i ∈ s, IsRoot (p i) x := by
   simp only [is_root, eval_prod, Finset.prod_eq_zero_iff]
 #align polynomial.is_root_prod Polynomial.isRoot_prod
 
+#print Polynomial.eval_dvd /-
 theorem eval_dvd : p ∣ q → eval x p ∣ eval x q :=
   eval₂_dvd _ _
 #align polynomial.eval_dvd Polynomial.eval_dvd
+-/
 
+/- warning: polynomial.eval_eq_zero_of_dvd_of_eval_eq_zero -> Polynomial.eval_eq_zero_of_dvd_of_eval_eq_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval_eq_zero_of_dvd_of_eval_eq_zero Polynomial.eval_eq_zero_of_dvd_of_eval_eq_zeroₓ'. -/
 theorem eval_eq_zero_of_dvd_of_eval_eq_zero : p ∣ q → eval x p = 0 → eval x q = 0 :=
   eval₂_eq_zero_of_dvd_of_eval₂_eq_zero _ _
 #align polynomial.eval_eq_zero_of_dvd_of_eval_eq_zero Polynomial.eval_eq_zero_of_dvd_of_eval_eq_zero
 
+#print Polynomial.eval_geom_sum /-
 @[simp]
 theorem eval_geom_sum {R} [CommSemiring R] {n : ℕ} {x : R} :
     eval x (∑ i in range n, X ^ i) = ∑ i in range n, x ^ i := by simp [eval_finset_sum]
 #align polynomial.eval_geom_sum Polynomial.eval_geom_sum
+-/
 
 end
 
@@ -1158,13 +1854,21 @@ end Eval
 
 section Map
 
+#print Polynomial.support_map_subset /-
 theorem support_map_subset [Semiring R] [Semiring S] (f : R →+* S) (p : R[X]) :
     (map f p).support ⊆ p.support := by
   intro x
   contrapose!
   simp (config := { contextual := true })
 #align polynomial.support_map_subset Polynomial.support_map_subset
+-/
 
+/- warning: polynomial.support_map_of_injective -> Polynomial.support_map_of_injective is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.support_map_of_injective Polynomial.support_map_of_injectiveₓ'. -/
 theorem support_map_of_injective [Semiring R] [Semiring S] (p : R[X]) {f : R →+* S}
     (hf : Function.Injective f) : (map f p).support = p.support := by
   simp_rw [Finset.ext_iff, mem_support_iff, coeff_map, ← map_zero f, hf.ne_iff, iff_self_iff,
@@ -1173,24 +1877,50 @@ theorem support_map_of_injective [Semiring R] [Semiring S] (p : R[X]) {f : R →
 
 variable [CommSemiring R] [CommSemiring S] (f : R →+* S)
 
+#print Polynomial.map_multiset_prod /-
 protected theorem map_multiset_prod (m : Multiset R[X]) : m.Prod.map f = (m.map <| map f).Prod :=
   Eq.symm <| Multiset.prod_hom _ (mapRingHom f).toMonoidHom
 #align polynomial.map_multiset_prod Polynomial.map_multiset_prod
+-/
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.map_prod Polynomial.map_prodₓ'. -/
 protected theorem map_prod {ι : Type _} (g : ι → R[X]) (s : Finset ι) :
     (∏ i in s, g i).map f = ∏ i in s, (g i).map f :=
   (mapRingHom f).map_prod _ _
 #align polynomial.map_prod Polynomial.map_prod
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.is_root.map Polynomial.IsRoot.mapₓ'. -/
 theorem IsRoot.map {f : R →+* S} {x : R} {p : R[X]} (h : IsRoot p x) : IsRoot (p.map f) (f x) := by
   rw [is_root, eval_map, eval₂_hom, h.eq_zero, f.map_zero]
 #align polynomial.is_root.map Polynomial.IsRoot.map
 
+/- warning: polynomial.is_root.of_map -> Polynomial.IsRoot.of_map is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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_inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f)) -> (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p x)
+Case conversion may be inaccurate. Consider using '#align polynomial.is_root.of_map Polynomial.IsRoot.of_mapₓ'. -/
 theorem IsRoot.of_map {R} [CommRing R] {f : R →+* S} {x : R} {p : R[X]} (h : IsRoot (p.map f) (f x))
     (hf : Function.Injective f) : IsRoot p x := by
   rwa [is_root, ← (injective_iff_map_eq_zero' f).mp hf, ← eval₂_hom, ← eval_map]
 #align polynomial.is_root.of_map Polynomial.IsRoot.of_map
 
+/- warning: polynomial.is_root_map_iff -> Polynomial.isRoot_map_iff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.is_root_map_iff Polynomial.isRoot_map_iffₓ'. -/
 theorem isRoot_map_iff {R : Type _} [CommRing R] {f : R →+* S} {x : R} {p : R[X]}
     (hf : Function.Injective f) : IsRoot (p.map f) (f x) ↔ IsRoot p x :=
   ⟨fun h => h.of_map hf, fun h => h.map⟩
@@ -1204,72 +1934,144 @@ section Ring
 
 variable [Ring R] {p q r : R[X]}
 
-theorem c_neg : C (-a) = -C a :=
+/- warning: polynomial.C_neg -> Polynomial.C_neg is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.C_neg Polynomial.C_negₓ'. -/
+theorem C_neg : C (-a) = -C a :=
   RingHom.map_neg C a
-#align polynomial.C_neg Polynomial.c_neg
-
-theorem c_sub : C (a - b) = C a - C b :=
+#align polynomial.C_neg Polynomial.C_neg
+
+/- warning: polynomial.C_sub -> Polynomial.C_sub is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.C_sub Polynomial.C_subₓ'. -/
+theorem C_sub : C (a - b) = C a - C b :=
   RingHom.map_sub C a b
-#align polynomial.C_sub Polynomial.c_sub
+#align polynomial.C_sub Polynomial.C_sub
 
+/- warning: polynomial.map_sub -> Polynomial.map_sub is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.map_sub Polynomial.map_subₓ'. -/
 @[simp]
 protected theorem map_sub {S} [Ring S] (f : R →+* S) : (p - q).map f = p.map f - q.map f :=
   (mapRingHom f).map_sub p q
 #align polynomial.map_sub Polynomial.map_sub
 
+/- warning: polynomial.map_neg -> Polynomial.map_neg is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.map_neg Polynomial.map_negₓ'. -/
 @[simp]
 protected theorem map_neg {S} [Ring S] (f : R →+* S) : (-p).map f = -p.map f :=
   (mapRingHom f).map_neg p
 #align polynomial.map_neg Polynomial.map_neg
 
+/- warning: polynomial.map_int_cast -> Polynomial.map_int_cast 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.map_int_cast Polynomial.map_int_castₓ'. -/
 @[simp]
 theorem map_int_cast {S} [Ring S] (f : R →+* S) (n : ℤ) : map f ↑n = ↑n :=
   map_intCast (mapRingHom f) n
 #align polynomial.map_int_cast Polynomial.map_int_cast
 
+/- warning: polynomial.eval_int_cast -> Polynomial.eval_int_cast is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval_int_cast Polynomial.eval_int_castₓ'. -/
 @[simp]
 theorem eval_int_cast {n : ℤ} {x : R} : (n : R[X]).eval x = n := by
   simp only [← C_eq_int_cast, eval_C]
 #align polynomial.eval_int_cast Polynomial.eval_int_cast
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_neg Polynomial.eval₂_negₓ'. -/
 @[simp]
 theorem eval₂_neg {S} [Ring S] (f : R →+* S) {x : S} : (-p).eval₂ f x = -p.eval₂ f x := by
   rw [eq_neg_iff_add_eq_zero, ← eval₂_add, add_left_neg, eval₂_zero]
 #align polynomial.eval₂_neg Polynomial.eval₂_neg
 
+/- warning: polynomial.eval₂_sub -> Polynomial.eval₂_sub is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_sub Polynomial.eval₂_subₓ'. -/
 @[simp]
 theorem eval₂_sub {S} [Ring S] (f : R →+* S) {x : S} :
     (p - q).eval₂ f x = p.eval₂ f x - q.eval₂ f x := by
   rw [sub_eq_add_neg, eval₂_add, eval₂_neg, sub_eq_add_neg]
 #align polynomial.eval₂_sub Polynomial.eval₂_sub
 
+/- warning: polynomial.eval_neg -> Polynomial.eval_neg 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.eval_neg Polynomial.eval_negₓ'. -/
 @[simp]
 theorem eval_neg (p : R[X]) (x : R) : (-p).eval x = -p.eval x :=
   eval₂_neg _
 #align polynomial.eval_neg Polynomial.eval_neg
 
+/- warning: polynomial.eval_sub -> Polynomial.eval_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)) (q : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x (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)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x p) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x 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)) (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x (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)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x p) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R _inst_1) x q))
+Case conversion may be inaccurate. Consider using '#align polynomial.eval_sub Polynomial.eval_subₓ'. -/
 @[simp]
 theorem eval_sub (p q : R[X]) (x : R) : (p - q).eval x = p.eval x - q.eval x :=
   eval₂_sub _
 #align polynomial.eval_sub Polynomial.eval_sub
 
-theorem root_x_sub_c : IsRoot (X - C a) b ↔ a = b := by
+/- warning: polynomial.root_X_sub_C -> Polynomial.root_X_sub_C is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {a : R} {b : R} [_inst_1 : Ring.{u1} R], Iff (Polynomial.IsRoot.{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)) a)) b) (Eq.{succ u1} R a b)
+but is expected to have type
+  forall {R : Type.{u1}} {a : R} {b : R} [_inst_1 : Ring.{u1} R], Iff (Polynomial.IsRoot.{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.2398 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) a) (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.2398 : 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)) a)) b) (Eq.{succ u1} R a b)
+Case conversion may be inaccurate. Consider using '#align polynomial.root_X_sub_C Polynomial.root_X_sub_Cₓ'. -/
+theorem root_X_sub_C : IsRoot (X - C a) b ↔ a = b := by
   rw [is_root.def, eval_sub, eval_X, eval_C, sub_eq_zero, eq_comm]
-#align polynomial.root_X_sub_C Polynomial.root_x_sub_c
+#align polynomial.root_X_sub_C Polynomial.root_X_sub_C
 
+#print Polynomial.neg_comp /-
 @[simp]
 theorem neg_comp : (-p).comp q = -p.comp q :=
   eval₂_neg _
 #align polynomial.neg_comp Polynomial.neg_comp
+-/
 
+#print Polynomial.sub_comp /-
 @[simp]
 theorem sub_comp : (p - q).comp r = p.comp r - q.comp r :=
   eval₂_sub _
 #align polynomial.sub_comp Polynomial.sub_comp
+-/
 
+#print Polynomial.cast_int_comp /-
 @[simp]
 theorem cast_int_comp (i : ℤ) : comp (i : R[X]) p = i := by cases i <;> simp
 #align polynomial.cast_int_comp Polynomial.cast_int_comp
+-/
 
 end Ring
 

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

@@ -68,11 +68,11 @@ theorem eval₂_zero : (0 : R[X]).eval₂ f x = 0 := by simp [eval₂_eq_sum]
 #align polynomial.eval₂_zero Polynomial.eval₂_zero
 
 @[simp]
-theorem eval₂_c : (c a).eval₂ f x = f a := by simp [eval₂_eq_sum]
+theorem eval₂_c : (C a).eval₂ f x = f a := by simp [eval₂_eq_sum]
 #align polynomial.eval₂_C Polynomial.eval₂_c
 
 @[simp]
-theorem eval₂_x : x.eval₂ f x = x := by simp [eval₂_eq_sum]
+theorem eval₂_x : X.eval₂ f x = x := by simp [eval₂_eq_sum]
 #align polynomial.eval₂_X Polynomial.eval₂_x
 
 @[simp]
@@ -81,7 +81,7 @@ theorem eval₂_monomial {n : ℕ} {r : R} : (monomial n r).eval₂ f x = f r *
 #align polynomial.eval₂_monomial Polynomial.eval₂_monomial
 
 @[simp]
-theorem eval₂_x_pow {n : ℕ} : (x ^ n).eval₂ f x = x ^ n :=
+theorem eval₂_x_pow {n : ℕ} : (X ^ n).eval₂ f x = x ^ n :=
   by
   rw [X_pow_eq_monomial]
   convert eval₂_monomial f x
@@ -119,7 +119,7 @@ theorem eval₂_smul (g : R →+* S) (p : R[X]) (x : S) {s : R} :
 #align polynomial.eval₂_smul Polynomial.eval₂_smul
 
 @[simp]
-theorem eval₂_c_x : eval₂ c x p = p :=
+theorem eval₂_c_x : eval₂ C X p = p :=
   Polynomial.induction_on' p (fun p q hp hq => by simp [hp, hq]) fun n x => by
     rw [eval₂_monomial, ← smul_X_eq_monomial, C_mul']
 #align polynomial.eval₂_C_X Polynomial.eval₂_c_x
@@ -169,12 +169,12 @@ theorem eval₂_finset_sum (s : Finset ι) (g : ι → R[X]) (x : S) :
   map_sum (eval₂AddMonoidHom f x) _ _
 #align polynomial.eval₂_finset_sum Polynomial.eval₂_finset_sum
 
-theorem eval₂_of_finsupp {f : R →+* S} {x : S} {p : AddMonoidAlgebra R ℕ} :
+theorem eval₂_ofFinsupp {f : R →+* S} {x : S} {p : AddMonoidAlgebra R ℕ} :
     eval₂ f x (⟨p⟩ : R[X]) = liftNC (↑f) (powersHom S x) p :=
   by
   simp only [eval₂_eq_sum, Sum, to_finsupp_sum, support, coeff]
   rfl
-#align polynomial.eval₂_of_finsupp Polynomial.eval₂_of_finsupp
+#align polynomial.eval₂_of_finsupp Polynomial.eval₂_ofFinsupp
 
 theorem eval₂_mul_noncomm (hf : ∀ k, Commute (f <| q.coeff k) x) :
     eval₂ f x (p * q) = eval₂ f x p * eval₂ f x q :=
@@ -186,7 +186,7 @@ theorem eval₂_mul_noncomm (hf : ∀ k, Commute (f <| q.coeff k) x) :
 #align polynomial.eval₂_mul_noncomm Polynomial.eval₂_mul_noncomm
 
 @[simp]
-theorem eval₂_mul_x : eval₂ f x (p * x) = eval₂ f x p * x :=
+theorem eval₂_mul_x : eval₂ f x (p * X) = eval₂ f x p * x :=
   by
   refine' trans (eval₂_mul_noncomm _ _ fun k => _) (by rw [eval₂_X])
   rcases em (k = 1) with (rfl | hk)
@@ -195,10 +195,10 @@ theorem eval₂_mul_x : eval₂ f x (p * x) = eval₂ f x p * x :=
 #align polynomial.eval₂_mul_X Polynomial.eval₂_mul_x
 
 @[simp]
-theorem eval₂_x_mul : eval₂ f x (x * p) = eval₂ f x p * x := by rw [X_mul, eval₂_mul_X]
+theorem eval₂_x_mul : eval₂ f x (X * p) = eval₂ f x p * x := by rw [X_mul, eval₂_mul_X]
 #align polynomial.eval₂_X_mul Polynomial.eval₂_x_mul
 
-theorem eval₂_mul_C' (h : Commute (f a) x) : eval₂ f x (p * c a) = eval₂ f x p * f a :=
+theorem eval₂_mul_C' (h : Commute (f a) x) : eval₂ f x (p * C a) = eval₂ f x p * f a :=
   by
   rw [eval₂_mul_noncomm, eval₂_C]
   intro k
@@ -359,7 +359,7 @@ theorem eval₂_at_nat_cast {S : Type _} [Semiring S] (f : R →+* S) (n : ℕ)
 #align polynomial.eval₂_at_nat_cast Polynomial.eval₂_at_nat_cast
 
 @[simp]
-theorem eval_c : (c a).eval x = a :=
+theorem eval_c : (C a).eval x = a :=
   eval₂_c _ _
 #align polynomial.eval_C Polynomial.eval_c
 
@@ -368,7 +368,7 @@ theorem eval_nat_cast {n : ℕ} : (n : R[X]).eval x = n := by simp only [← C_e
 #align polynomial.eval_nat_cast Polynomial.eval_nat_cast
 
 @[simp]
-theorem eval_x : x.eval x = x :=
+theorem eval_x : X.eval x = x :=
   eval₂_x _ _
 #align polynomial.eval_X Polynomial.eval_x
 
@@ -409,7 +409,7 @@ theorem eval_smul [Monoid S] [DistribMulAction S R] [IsScalarTower S R R] (s : S
 #align polynomial.eval_smul Polynomial.eval_smul
 
 @[simp]
-theorem eval_c_mul : (c a * p).eval x = a * p.eval x :=
+theorem eval_c_mul : (C a * p).eval x = a * p.eval x :=
   by
   apply Polynomial.induction_on' p
   · intro p q ph qh
@@ -456,7 +456,7 @@ theorem eval_nat_cast_mul {n : ℕ} : ((n : R[X]) * p).eval x = n * p.eval x :=
 #align polynomial.eval_nat_cast_mul Polynomial.eval_nat_cast_mul
 
 @[simp]
-theorem eval_mul_x : (p * x).eval x = p.eval x * x :=
+theorem eval_mul_x : (p * X).eval x = p.eval x * x :=
   by
   apply Polynomial.induction_on' p
   · intro p q ph qh
@@ -467,7 +467,7 @@ theorem eval_mul_x : (p * x).eval x = p.eval x * x :=
 #align polynomial.eval_mul_X Polynomial.eval_mul_x
 
 @[simp]
-theorem eval_mul_x_pow {k : ℕ} : (p * x ^ k).eval x = p.eval x * x ^ k :=
+theorem eval_mul_x_pow {k : ℕ} : (p * X ^ k).eval x = p.eval x * x ^ k :=
   by
   induction' k with k ih
   · simp
@@ -520,10 +520,10 @@ theorem IsRoot.dvd {R : Type _} [CommSemiring R] {p q : R[X]} {x : R} (h : p.IsR
   rwa [is_root, eval, eval₂_eq_zero_of_dvd_of_eval₂_eq_zero _ _ hpq]
 #align polynomial.is_root.dvd Polynomial.IsRoot.dvd
 
-theorem not_isRoot_c (r a : R) (hr : r ≠ 0) : ¬IsRoot (c r) a := by simpa using hr
+theorem not_isRoot_c (r a : R) (hr : r ≠ 0) : ¬IsRoot (C r) a := by simpa using hr
 #align polynomial.not_is_root_C Polynomial.not_isRoot_c
 
-theorem eval_surjective (x : R) : Function.Surjective <| eval x := fun y => ⟨c y, eval_c⟩
+theorem eval_surjective (x : R) : Function.Surjective <| eval x := fun y => ⟨C y, eval_c⟩
 #align polynomial.eval_surjective Polynomial.eval_surjective
 
 end Eval
@@ -532,30 +532,30 @@ section Comp
 
 /-- The composition of polynomials as a polynomial. -/
 def comp (p q : R[X]) : R[X] :=
-  p.eval₂ c q
+  p.eval₂ C q
 #align polynomial.comp Polynomial.comp
 
-theorem comp_eq_sum_left : p.comp q = p.Sum fun e a => c a * q ^ e := by rw [comp, eval₂_eq_sum]
+theorem comp_eq_sum_left : p.comp q = p.Sum fun e a => C a * q ^ e := by rw [comp, eval₂_eq_sum]
 #align polynomial.comp_eq_sum_left Polynomial.comp_eq_sum_left
 
 @[simp]
-theorem comp_x : p.comp x = p :=
+theorem comp_x : p.comp X = p :=
   by
   simp only [comp, eval₂, C_mul_X_pow_eq_monomial]
   exact sum_monomial_eq _
 #align polynomial.comp_X Polynomial.comp_x
 
 @[simp]
-theorem x_comp : x.comp p = p :=
+theorem x_comp : X.comp p = p :=
   eval₂_x _ _
 #align polynomial.X_comp Polynomial.x_comp
 
 @[simp]
-theorem comp_c : p.comp (c a) = c (p.eval a) := by simp [comp, (C : R →+* _).map_sum]
+theorem comp_c : p.comp (C a) = C (p.eval a) := by simp [comp, (C : R →+* _).map_sum]
 #align polynomial.comp_C Polynomial.comp_c
 
 @[simp]
-theorem c_comp : (c a).comp p = c a :=
+theorem c_comp : (C a).comp p = C a :=
   eval₂_c _ _
 #align polynomial.C_comp Polynomial.c_comp
 
@@ -564,7 +564,7 @@ theorem nat_cast_comp {n : ℕ} : (n : R[X]).comp p = n := by rw [← C_eq_nat_c
 #align polynomial.nat_cast_comp Polynomial.nat_cast_comp
 
 @[simp]
-theorem comp_zero : p.comp (0 : R[X]) = c (p.eval 0) := by rw [← C_0, comp_C]
+theorem comp_zero : p.comp (0 : R[X]) = C (p.eval 0) := by rw [← C_0, comp_C]
 #align polynomial.comp_zero Polynomial.comp_zero
 
 @[simp]
@@ -572,7 +572,7 @@ theorem zero_comp : comp (0 : R[X]) p = 0 := by rw [← C_0, C_comp]
 #align polynomial.zero_comp Polynomial.zero_comp
 
 @[simp]
-theorem comp_one : p.comp 1 = c (p.eval 1) := by rw [← C_1, comp_C]
+theorem comp_one : p.comp 1 = C (p.eval 1) := by rw [← C_1, comp_C]
 #align polynomial.comp_one Polynomial.comp_one
 
 @[simp]
@@ -585,12 +585,12 @@ theorem add_comp : (p + q).comp r = p.comp r + q.comp r :=
 #align polynomial.add_comp Polynomial.add_comp
 
 @[simp]
-theorem monomial_comp (n : ℕ) : (monomial n a).comp p = c a * p ^ n :=
+theorem monomial_comp (n : ℕ) : (monomial n a).comp p = C a * p ^ n :=
   eval₂_monomial _ _
 #align polynomial.monomial_comp Polynomial.monomial_comp
 
 @[simp]
-theorem mul_x_comp : (p * x).comp r = p.comp r * r :=
+theorem mul_x_comp : (p * X).comp r = p.comp r * r :=
   by
   apply Polynomial.induction_on' p
   · intro p q hp hq
@@ -600,7 +600,7 @@ theorem mul_x_comp : (p * x).comp r = p.comp r * r :=
 #align polynomial.mul_X_comp Polynomial.mul_x_comp
 
 @[simp]
-theorem x_pow_comp {k : ℕ} : (x ^ k).comp p = p ^ k :=
+theorem x_pow_comp {k : ℕ} : (X ^ k).comp p = p ^ k :=
   by
   induction' k with k ih
   · simp
@@ -608,7 +608,7 @@ theorem x_pow_comp {k : ℕ} : (x ^ k).comp p = p ^ k :=
 #align polynomial.X_pow_comp Polynomial.x_pow_comp
 
 @[simp]
-theorem mul_x_pow_comp {k : ℕ} : (p * x ^ k).comp r = p.comp r * r ^ k :=
+theorem mul_x_pow_comp {k : ℕ} : (p * X ^ k).comp r = p.comp r * r ^ k :=
   by
   induction' k with k ih
   · simp
@@ -616,7 +616,7 @@ theorem mul_x_pow_comp {k : ℕ} : (p * x ^ k).comp r = p.comp r * r ^ k :=
 #align polynomial.mul_X_pow_comp Polynomial.mul_x_pow_comp
 
 @[simp]
-theorem c_mul_comp : (c a * p).comp r = c a * p.comp r :=
+theorem c_mul_comp : (C a * p).comp r = C a * p.comp r :=
   by
   apply Polynomial.induction_on' p
   · intro p q hp hq
@@ -688,16 +688,16 @@ variable (f : R →+* S)
 
 /-- `map f p` maps a polynomial `p` across a ring hom `f` -/
 def map : R[X] → S[X] :=
-  eval₂ (c.comp f) x
+  eval₂ (C.comp f) X
 #align polynomial.map Polynomial.map
 
 @[simp]
-theorem map_c : (c a).map f = c (f a) :=
+theorem map_c : (C a).map f = C (f a) :=
   eval₂_c _ _
 #align polynomial.map_C Polynomial.map_c
 
 @[simp]
-theorem map_x : x.map f = x :=
+theorem map_x : X.map f = X :=
   eval₂_x _ _
 #align polynomial.map_X Polynomial.map_x
 
@@ -1070,7 +1070,7 @@ theorem eval_comp : (p.comp q).eval x = p.eval (q.eval x) :=
 
 /-- `comp p`, regarded as a ring homomorphism from `R[X]` to itself. -/
 def compRingHom : R[X] → R[X] →+* R[X] :=
-  eval₂RingHom c
+  eval₂RingHom C
 #align polynomial.comp_ring_hom Polynomial.compRingHom
 
 @[simp]
@@ -1149,7 +1149,7 @@ theorem eval_eq_zero_of_dvd_of_eval_eq_zero : p ∣ q → eval x p = 0 → eval
 
 @[simp]
 theorem eval_geom_sum {R} [CommSemiring R] {n : ℕ} {x : R} :
-    eval x (∑ i in range n, x ^ i) = ∑ i in range n, x ^ i := by simp [eval_finset_sum]
+    eval x (∑ i in range n, X ^ i) = ∑ i in range n, x ^ i := by simp [eval_finset_sum]
 #align polynomial.eval_geom_sum Polynomial.eval_geom_sum
 
 end
@@ -1204,12 +1204,12 @@ section Ring
 
 variable [Ring R] {p q r : R[X]}
 
-theorem c_neg : c (-a) = -c a :=
-  RingHom.map_neg c a
+theorem c_neg : C (-a) = -C a :=
+  RingHom.map_neg C a
 #align polynomial.C_neg Polynomial.c_neg
 
-theorem c_sub : c (a - b) = c a - c b :=
-  RingHom.map_sub c a b
+theorem c_sub : C (a - b) = C a - C b :=
+  RingHom.map_sub C a b
 #align polynomial.C_sub Polynomial.c_sub
 
 @[simp]
@@ -1253,7 +1253,7 @@ theorem eval_sub (p q : R[X]) (x : R) : (p - q).eval x = p.eval x - q.eval x :=
   eval₂_sub _
 #align polynomial.eval_sub Polynomial.eval_sub
 
-theorem root_x_sub_c : IsRoot (x - c a) b ↔ a = b := by
+theorem root_x_sub_c : IsRoot (X - C a) b ↔ a = b := by
   rw [is_root.def, eval_sub, eval_X, eval_C, sub_eq_zero, eq_comm]
 #align polynomial.root_X_sub_C Polynomial.root_x_sub_c
 

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

@@ -170,7 +170,7 @@ theorem eval₂_finset_sum (s : Finset ι) (g : ι → R[X]) (x : S) :
 #align polynomial.eval₂_finset_sum Polynomial.eval₂_finset_sum
 
 theorem eval₂_of_finsupp {f : R →+* S} {x : S} {p : AddMonoidAlgebra R ℕ} :
-    eval₂ f x (⟨p⟩ : R[X]) = liftNc (↑f) (powersHom S x) p :=
+    eval₂ f x (⟨p⟩ : R[X]) = liftNC (↑f) (powersHom S x) p :=
   by
   simp only [eval₂_eq_sum, Sum, to_finsupp_sum, support, coeff]
   rfl

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

@@ -851,7 +851,7 @@ theorem map_monic_eq_zero_iff (hp : p.Monic) : p.map f = 0 ↔ ∀ x, f x = 0 :=
   ⟨fun hfp x =>
     calc
       f x = f x * f p.leadingCoeff := by simp only [mul_one, hp.leading_coeff, f.map_one]
-      _ = f x * (p.map f).coeff p.natDegree := congr_arg _ (coeff_map _ _).symm
+      _ = f x * (p.map f).coeff p.natDegree := (congr_arg _ (coeff_map _ _).symm)
       _ = 0 := by simp only [hfp, mul_zero, coeff_zero]
       ,
     fun h => ext fun n => by simp only [h, coeff_map, coeff_zero]⟩

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

@@ -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.eval
-! leanprover-community/mathlib commit 565eb991e264d0db702722b4bde52ee5173c9950
+! leanprover-community/mathlib commit e064a7bf82ad94c3c17b5128bbd860d1ec34874e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -523,6 +523,9 @@ theorem IsRoot.dvd {R : Type _} [CommSemiring R] {p q : R[X]} {x : R} (h : p.IsR
 theorem not_isRoot_c (r a : R) (hr : r ≠ 0) : ¬IsRoot (c r) a := by simpa using hr
 #align polynomial.not_is_root_C Polynomial.not_isRoot_c
 
+theorem eval_surjective (x : R) : Function.Surjective <| eval x := fun y => ⟨c y, eval_c⟩
+#align polynomial.eval_surjective Polynomial.eval_surjective
+
 end Eval
 
 section Comp

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

Now that I am defining NNRat.cast, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast/intCast/ratCast over nat_cast/int_cast/rat_cast, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.

@@ -132,12 +132,12 @@ def eval₂AddMonoidHom : R[X] →+ S where
 #align polynomial.eval₂_add_monoid_hom_apply Polynomial.eval₂AddMonoidHom_apply
 
 @[simp]
-theorem eval₂_nat_cast (n : ℕ) : (n : R[X]).eval₂ f x = n := by
+theorem eval₂_natCast (n : ℕ) : (n : R[X]).eval₂ f x = n := by
   induction' n with n ih
   -- Porting note: `Nat.zero_eq` is required.
   · simp only [eval₂_zero, Nat.cast_zero, Nat.zero_eq]
   · rw [n.cast_succ, eval₂_add, ih, eval₂_one, n.cast_succ]
-#align polynomial.eval₂_nat_cast Polynomial.eval₂_nat_cast
+#align polynomial.eval₂_nat_cast Polynomial.eval₂_natCast
 
 -- See note [no_index around OfNat.ofNat]
 @[simp]
@@ -345,11 +345,11 @@ theorem eval₂_at_one {S : Type*} [Semiring S] (f : R →+* S) : p.eval₂ f 1
 #align polynomial.eval₂_at_one Polynomial.eval₂_at_one
 
 @[simp]
-theorem eval₂_at_nat_cast {S : Type*} [Semiring S] (f : R →+* S) (n : ℕ) :
+theorem eval₂_at_natCast {S : Type*} [Semiring S] (f : R →+* S) (n : ℕ) :
     p.eval₂ f n = f (p.eval n) := by
   convert eval₂_at_apply (p := p) f n
   simp
-#align polynomial.eval₂_at_nat_cast Polynomial.eval₂_at_nat_cast
+#align polynomial.eval₂_at_nat_cast Polynomial.eval₂_at_natCast
 
 -- See note [no_index around OfNat.ofNat]
 @[simp]
@@ -363,14 +363,14 @@ theorem eval_C : (C a).eval x = a :=
 #align polynomial.eval_C Polynomial.eval_C
 
 @[simp]
-theorem eval_nat_cast {n : ℕ} : (n : R[X]).eval x = n := by simp only [← C_eq_nat_cast, eval_C]
-#align polynomial.eval_nat_cast Polynomial.eval_nat_cast
+theorem eval_natCast {n : ℕ} : (n : R[X]).eval x = n := by simp only [← C_eq_natCast, eval_C]
+#align polynomial.eval_nat_cast Polynomial.eval_natCast
 
 -- See note [no_index around OfNat.ofNat]
 @[simp]
 lemma eval_ofNat (n : ℕ) [n.AtLeastTwo] (a : R) :
     (no_index (OfNat.ofNat n : R[X])).eval a = OfNat.ofNat n := by
-  simp only [OfNat.ofNat, eval_nat_cast]
+  simp only [OfNat.ofNat, eval_natCast]
 
 @[simp]
 theorem eval_X : X.eval x = x :=
@@ -458,9 +458,9 @@ def leval {R : Type*} [Semiring R] (r : R) : R[X] →ₗ[R] R where
 #align polynomial.leval_apply Polynomial.leval_apply
 
 @[simp]
-theorem eval_nat_cast_mul {n : ℕ} : ((n : R[X]) * p).eval x = n * p.eval x := by
-  rw [← C_eq_nat_cast, eval_C_mul]
-#align polynomial.eval_nat_cast_mul Polynomial.eval_nat_cast_mul
+theorem eval_natCast_mul {n : ℕ} : ((n : R[X]) * p).eval x = n * p.eval x := by
+  rw [← C_eq_natCast, eval_C_mul]
+#align polynomial.eval_nat_cast_mul Polynomial.eval_natCast_mul
 
 @[simp]
 theorem eval_mul_X : (p * X).eval x = p.eval x * x := by
@@ -564,13 +564,13 @@ theorem C_comp : (C a).comp p = C a :=
 #align polynomial.C_comp Polynomial.C_comp
 
 @[simp]
-theorem nat_cast_comp {n : ℕ} : (n : R[X]).comp p = n := by rw [← C_eq_nat_cast, C_comp]
-#align polynomial.nat_cast_comp Polynomial.nat_cast_comp
+theorem natCast_comp {n : ℕ} : (n : R[X]).comp p = n := by rw [← C_eq_natCast, C_comp]
+#align polynomial.nat_cast_comp Polynomial.natCast_comp
 
 -- Porting note (#10756): new theorem
 @[simp]
 theorem ofNat_comp (n : ℕ) [n.AtLeastTwo] : (no_index (OfNat.ofNat n) : R[X]).comp p = n :=
-  nat_cast_comp
+  natCast_comp
 
 @[simp]
 theorem comp_zero : p.comp (0 : R[X]) = C (p.eval 0) := by rw [← C_0, comp_C]
@@ -631,15 +631,15 @@ theorem C_mul_comp : (C a * p).comp r = C a * p.comp r := by
 #align polynomial.C_mul_comp Polynomial.C_mul_comp
 
 @[simp]
-theorem nat_cast_mul_comp {n : ℕ} : ((n : R[X]) * p).comp r = n * p.comp r := by
-  rw [← C_eq_nat_cast, C_mul_comp]
-#align polynomial.nat_cast_mul_comp Polynomial.nat_cast_mul_comp
+theorem natCast_mul_comp {n : ℕ} : ((n : R[X]) * p).comp r = n * p.comp r := by
+  rw [← C_eq_natCast, C_mul_comp]
+#align polynomial.nat_cast_mul_comp Polynomial.natCast_mul_comp
 
-theorem mul_X_add_nat_cast_comp {n : ℕ} :
+theorem mul_X_add_natCast_comp {n : ℕ} :
     (p * (X + (n : R[X]))).comp q = p.comp q * (q + n) := by
-  rw [mul_add, add_comp, mul_X_comp, ← Nat.cast_comm, nat_cast_mul_comp, Nat.cast_comm, mul_add]
+  rw [mul_add, add_comp, mul_X_comp, ← Nat.cast_comm, natCast_mul_comp, Nat.cast_comm, mul_add]
 set_option linter.uppercaseLean3 false in
-#align polynomial.mul_X_add_nat_cast_comp Polynomial.mul_X_add_nat_cast_comp
+#align polynomial.mul_X_add_nat_cast_comp Polynomial.mul_X_add_natCast_comp
 
 @[simp]
 theorem mul_comp {R : Type*} [CommSemiring R] (p q r : R[X]) :
@@ -775,16 +775,16 @@ theorem coe_mapRingHom (f : R →+* S) : ⇑(mapRingHom f) = map f :=
 
 -- This is protected to not clash with the global `map_natCast`.
 @[simp]
-protected theorem map_nat_cast (n : ℕ) : (n : R[X]).map f = n :=
+protected theorem map_natCast (n : ℕ) : (n : R[X]).map f = n :=
   map_natCast (mapRingHom f) n
-#align polynomial.map_nat_cast Polynomial.map_nat_cast
+#align polynomial.map_nat_cast Polynomial.map_natCast
 
 -- Porting note (#10756): new theorem
 -- See note [no_index around OfNat.ofNat]
 @[simp]
 protected theorem map_ofNat (n : ℕ) [n.AtLeastTwo] :
     (no_index (OfNat.ofNat n) : R[X]).map f = OfNat.ofNat n :=
-  show (n : R[X]).map f = n by rw [Polynomial.map_nat_cast]
+  show (n : R[X]).map f = n by rw [Polynomial.map_natCast]
 
 set_option linter.deprecated false in
 @[simp]
@@ -998,24 +998,24 @@ theorem eval_one_map (f : R →+* S) (p : R[X]) : (p.map f).eval 1 = f (p.eval 1
 #align polynomial.eval_one_map Polynomial.eval_one_map
 
 @[simp]
-theorem eval_nat_cast_map (f : R →+* S) (p : R[X]) (n : ℕ) :
+theorem eval_natCast_map (f : R →+* S) (p : R[X]) (n : ℕ) :
     (p.map f).eval (n : S) = f (p.eval n) := by
   induction p using Polynomial.induction_on' with
   | h_add p q hp hq =>
     simp only [hp, hq, Polynomial.map_add, RingHom.map_add, eval_add]
   | h_monomial n r =>
     simp only [map_natCast f, eval_monomial, map_monomial, f.map_pow, f.map_mul]
-#align polynomial.eval_nat_cast_map Polynomial.eval_nat_cast_map
+#align polynomial.eval_nat_cast_map Polynomial.eval_natCast_map
 
 @[simp]
-theorem eval_int_cast_map {R S : Type*} [Ring R] [Ring S] (f : R →+* S) (p : R[X]) (i : ℤ) :
+theorem eval_intCast_map {R S : Type*} [Ring R] [Ring S] (f : R →+* S) (p : R[X]) (i : ℤ) :
     (p.map f).eval (i : S) = f (p.eval i) := by
   induction p using Polynomial.induction_on' with
   | h_add p q hp hq =>
     simp only [hp, hq, Polynomial.map_add, RingHom.map_add, eval_add]
   | h_monomial n r =>
     simp only [map_intCast, eval_monomial, map_monomial, map_pow, map_mul]
-#align polynomial.eval_int_cast_map Polynomial.eval_int_cast_map
+#align polynomial.eval_int_cast_map Polynomial.eval_intCast_map
 
 end Map
 
@@ -1287,15 +1287,14 @@ protected theorem map_neg {S} [Ring S] (f : R →+* S) : (-p).map f = -p.map f :
   (mapRingHom f).map_neg p
 #align polynomial.map_neg Polynomial.map_neg
 
-@[simp]
-theorem map_int_cast {S} [Ring S] (f : R →+* S) (n : ℤ) : map f ↑n = ↑n :=
+@[simp] protected lemma map_intCast {S} [Ring S] (f : R →+* S) (n : ℤ) : map f ↑n = ↑n :=
   map_intCast (mapRingHom f) n
-#align polynomial.map_int_cast Polynomial.map_int_cast
+#align polynomial.map_int_cast Polynomial.map_intCast
 
 @[simp]
-theorem eval_int_cast {n : ℤ} {x : R} : (n : R[X]).eval x = n := by
-  simp only [← C_eq_int_cast, eval_C]
-#align polynomial.eval_int_cast Polynomial.eval_int_cast
+theorem eval_intCast {n : ℤ} {x : R} : (n : R[X]).eval x = n := by
+  simp only [← C_eq_intCast, eval_C]
+#align polynomial.eval_int_cast Polynomial.eval_intCast
 
 @[simp]
 theorem eval₂_neg {S} [Ring S] (f : R →+* S) {x : S} : (-p).eval₂ f x = -p.eval₂ f x := by
@@ -1337,14 +1336,14 @@ theorem cast_int_comp (i : ℤ) : comp (i : R[X]) p = i := by cases i <;> simp
 #align polynomial.cast_int_comp Polynomial.cast_int_comp
 
 @[simp]
-theorem eval₂_at_int_cast {S : Type*} [Ring S] (f : R →+* S) (n : ℤ) :
+theorem eval₂_at_intCast {S : Type*} [Ring S] (f : R →+* S) (n : ℤ) :
     p.eval₂ f n = f (p.eval n) := by
   convert eval₂_at_apply (p := p) f n
   simp
 
-theorem mul_X_sub_int_cast_comp {n : ℕ} :
+theorem mul_X_sub_intCast_comp {n : ℕ} :
     (p * (X - (n : R[X]))).comp q = p.comp q * (q - n) := by
-  rw [mul_sub, sub_comp, mul_X_comp, ← Nat.cast_comm, nat_cast_mul_comp, Nat.cast_comm, mul_sub]
+  rw [mul_sub, sub_comp, mul_X_comp, ← Nat.cast_comm, natCast_mul_comp, Nat.cast_comm, mul_sub]
 
 end Ring
 

These are changes from #11997, the latest adaptation PR for nightly-2024-04-07, which can be made directly on master.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

@@ -808,9 +808,7 @@ theorem coeff_map (n : ℕ) : coeff (p.map f) n = f (coeff p n) := by
   rw [map, eval₂_def, coeff_sum, sum]
   conv_rhs => rw [← sum_C_mul_X_pow_eq p, coeff_sum, sum, map_sum]
   refine' Finset.sum_congr rfl fun x _hx => _
-  -- porting note (#10745): was `simp [Function.comp, coeff_C_mul_X_pow, f.map_mul]`.
-  simp? [Function.comp, coeff_C_mul_X_pow, - map_mul, - coeff_C_mul] says
-    simp only [RingHom.coe_comp, Function.comp_apply, coeff_C_mul_X_pow]
+  simp only [RingHom.coe_comp, Function.comp, coeff_C_mul_X_pow]
   split_ifs <;> simp [f.map_zero]
 #align polynomial.coeff_map Polynomial.coeff_map
 

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

@@ -889,7 +889,7 @@ theorem map_monic_eq_zero_iff (hp : p.Monic) : p.map f = 0 ↔ ∀ x, f x = 0 :=
   ⟨fun hfp x =>
     calc
       f x = f x * f p.leadingCoeff := by simp only [mul_one, hp.leadingCoeff, f.map_one]
-      _ = f x * (p.map f).coeff p.natDegree := (congr_arg _ (coeff_map _ _).symm)
+      _ = f x * (p.map f).coeff p.natDegree := congr_arg _ (coeff_map _ _).symm
       _ = 0 := by simp only [hfp, mul_zero, coeff_zero]
       ,
     fun h => ext fun n => by simp only [h, coeff_map, coeff_zero]⟩

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

@@ -498,12 +498,10 @@ instance IsRoot.decidable [DecidableEq R] : Decidable (IsRoot p a) := by
   unfold IsRoot; infer_instance
 #align polynomial.is_root.decidable Polynomial.IsRoot.decidable
 
--- Adaptation note: 2024-03-15: this was called `def`.
--- Should lean be changed to allow that as a name again?
 @[simp]
-theorem IsRoot.definition : IsRoot p a ↔ p.eval a = 0 :=
+theorem IsRoot.def : IsRoot p a ↔ p.eval a = 0 :=
   Iff.rfl
-#align polynomial.is_root.def Polynomial.IsRoot.definition
+#align polynomial.is_root.def Polynomial.IsRoot.def
 
 theorem IsRoot.eq_zero (h : IsRoot p x) : eval x p = 0 :=
   h
@@ -1160,11 +1158,11 @@ theorem coe_compRingHom_apply (p q : R[X]) : (compRingHom q : R[X] → R[X]) p =
 #align polynomial.coe_comp_ring_hom_apply Polynomial.coe_compRingHom_apply
 
 theorem root_mul_left_of_isRoot (p : R[X]) {q : R[X]} : IsRoot q a → IsRoot (p * q) a := fun H => by
-  rw [IsRoot, eval_mul, IsRoot.definition.1 H, mul_zero]
+  rw [IsRoot, eval_mul, IsRoot.def.1 H, mul_zero]
 #align polynomial.root_mul_left_of_is_root Polynomial.root_mul_left_of_isRoot
 
 theorem root_mul_right_of_isRoot {p : R[X]} (q : R[X]) : IsRoot p a → IsRoot (p * q) a := fun H =>
-  by rw [IsRoot, eval_mul, IsRoot.definition.1 H, zero_mul]
+  by rw [IsRoot, eval_mul, IsRoot.def.1 H, zero_mul]
 #align polynomial.root_mul_right_of_is_root Polynomial.root_mul_right_of_isRoot
 
 theorem eval₂_multiset_prod (s : Multiset R[X]) (x : S) :
@@ -1323,7 +1321,7 @@ theorem eval_sub (p q : R[X]) (x : R) : (p - q).eval x = p.eval x - q.eval x :=
 #align polynomial.eval_sub Polynomial.eval_sub
 
 theorem root_X_sub_C : IsRoot (X - C a) b ↔ a = b := by
-  rw [IsRoot.definition, eval_sub, eval_X, eval_C, sub_eq_zero, eq_comm]
+  rw [IsRoot.def, eval_sub, eval_X, eval_C, sub_eq_zero, eq_comm]
 #align polynomial.root_X_sub_C Polynomial.root_X_sub_C
 
 @[simp]

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

@@ -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 Mathlib.Data.Polynomial.Degree.Definitions
-import Mathlib.Data.Polynomial.Induction
+import Mathlib.Algebra.Polynomial.Degree.Definitions
+import Mathlib.Algebra.Polynomial.Induction
 
 #align_import data.polynomial.eval from "leanprover-community/mathlib"@"728baa2f54e6062c5879a3e397ac6bac323e506f"
 

@@ -1094,8 +1094,8 @@ theorem eval₂_pow' (n : ℕ) :
 theorem eval₂_comp' : eval₂ (algebraMap R S) x (p.comp q) =
     eval₂ (algebraMap R S) (eval₂ (algebraMap R S) x q) p := by
   induction p using Polynomial.induction_on' with
-    | h_add r s hr hs => simp only [add_comp, eval₂_add, hr, hs]
-    | h_monomial n a => simp only [monomial_comp, eval₂_mul', eval₂_C, eval₂_monomial, eval₂_pow']
+  | h_add r s hr hs => simp only [add_comp, eval₂_add, hr, hs]
+  | h_monomial n a => simp only [monomial_comp, eval₂_mul', eval₂_C, eval₂_monomial, eval₂_pow']
 
 end Algebra
 

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.

@@ -468,7 +468,7 @@ theorem eval_mul_X : (p * X).eval x = p.eval x * x := by
   | h_add p q ph qh =>
     simp only [add_mul, eval_add, ph, qh]
   | h_monomial n a =>
-    simp only [← monomial_one_one_eq_X, monomial_mul_monomial, eval_monomial, mul_one, pow_succ',
+    simp only [← monomial_one_one_eq_X, monomial_mul_monomial, eval_monomial, mul_one, pow_succ,
       mul_assoc]
 #align polynomial.eval_mul_X Polynomial.eval_mul_X
 
@@ -476,7 +476,7 @@ theorem eval_mul_X : (p * X).eval x = p.eval x * x := by
 theorem eval_mul_X_pow {k : ℕ} : (p * X ^ k).eval x = p.eval x * x ^ k := by
   induction' k with k ih
   · simp
-  · simp [pow_succ', ← mul_assoc, ih]
+  · simp [pow_succ, ← mul_assoc, ih]
 #align polynomial.eval_mul_X_pow Polynomial.eval_mul_X_pow
 
 theorem eval_sum (p : R[X]) (f : ℕ → R → R[X]) (x : R) :
@@ -606,21 +606,21 @@ theorem mul_X_comp : (p * X).comp r = p.comp r * r := by
   | h_add p q hp hq =>
     simp only [hp, hq, add_mul, add_comp]
   | h_monomial n b =>
-    simp only [pow_succ', mul_assoc, monomial_mul_X, monomial_comp]
+    simp only [pow_succ, mul_assoc, monomial_mul_X, monomial_comp]
 #align polynomial.mul_X_comp Polynomial.mul_X_comp
 
 @[simp]
 theorem X_pow_comp {k : ℕ} : (X ^ k).comp p = p ^ k := by
   induction' k with k ih
   · simp
-  · simp [pow_succ', mul_X_comp, ih]
+  · simp [pow_succ, mul_X_comp, ih]
 #align polynomial.X_pow_comp Polynomial.X_pow_comp
 
 @[simp]
 theorem mul_X_pow_comp {k : ℕ} : (p * X ^ k).comp r = p.comp r * r ^ k := by
   induction' k with k ih
   · simp
-  · simp [ih, pow_succ', ← mul_assoc, mul_X_comp]
+  · simp [ih, pow_succ, ← mul_assoc, mul_X_comp]
 #align polynomial.mul_X_pow_comp Polynomial.mul_X_pow_comp
 
 @[simp]
@@ -677,7 +677,7 @@ theorem comp_assoc {R : Type*} [CommSemiring R] (φ ψ χ : R[X]) :
     (φ.comp ψ).comp χ = φ.comp (ψ.comp χ) := by
   refine Polynomial.induction_on φ ?_ ?_ ?_ <;>
     · intros
-      simp_all only [add_comp, mul_comp, C_comp, X_comp, pow_succ', ← mul_assoc]
+      simp_all only [add_comp, mul_comp, C_comp, X_comp, pow_succ, ← mul_assoc]
 #align polynomial.comp_assoc Polynomial.comp_assoc
 
 theorem coeff_comp_degree_mul_degree (hqd0 : natDegree q ≠ 0) :
@@ -983,7 +983,7 @@ theorem map_comp (p q : R[X]) : map f (p.comp q) = (map f p).comp (map f q) :=
       simp (config := { contextual := true }) only [Polynomial.map_add, add_comp, forall_const,
         imp_true_iff, eq_self_iff_true])
     (by
-      simp (config := { contextual := true }) only [pow_succ', ← mul_assoc, comp, forall_const,
+      simp (config := { contextual := true }) only [pow_succ, ← mul_assoc, comp, forall_const,
         eval₂_mul_X, imp_true_iff, eq_self_iff_true, map_X, Polynomial.map_mul])
 #align polynomial.map_comp Polynomial.map_comp
 

Cherry-picked from #9607 Co-authored-by: @semorrison

@@ -334,7 +334,7 @@ theorem eval_eq_sum_range' {p : R[X]} {n : ℕ} (hn : p.natDegree < n) (x : R) :
 @[simp]
 theorem eval₂_at_apply {S : Type*} [Semiring S] (f : R →+* S) (r : R) :
     p.eval₂ f (f r) = f (p.eval r) := by
-  rw [eval₂_eq_sum, eval_eq_sum, sum, sum, f.map_sum]
+  rw [eval₂_eq_sum, eval_eq_sum, sum, sum, map_sum f]
   simp only [f.map_mul, f.map_pow]
 #align polynomial.eval₂_at_apply Polynomial.eval₂_at_apply
 
@@ -557,7 +557,7 @@ theorem X_comp : X.comp p = p :=
 #align polynomial.X_comp Polynomial.X_comp
 
 @[simp]
-theorem comp_C : p.comp (C a) = C (p.eval a) := by simp [comp, (C : R →+* _).map_sum]
+theorem comp_C : p.comp (C a) = C (p.eval a) := by simp [comp, map_sum (C : R →+* _)]
 #align polynomial.comp_C Polynomial.comp_C
 
 @[simp]
@@ -974,7 +974,7 @@ theorem eval_map (x : S) : (p.map f).eval x = p.eval₂ f x :=
 
 protected theorem map_sum {ι : Type*} (g : ι → R[X]) (s : Finset ι) :
     (∑ i in s, g i).map f = ∑ i in s, (g i).map f :=
-  (mapRingHom f).map_sum _ _
+  map_sum (mapRingHom f) _ _
 #align polynomial.map_sum Polynomial.map_sum
 
 theorem map_comp (p q : R[X]) : map f (p.comp q) = (map f p).comp (map f q) :=
@@ -1193,7 +1193,7 @@ theorem eval_multiset_prod (s : Multiset R[X]) (x : R) : eval x s.prod = (s.map
 -/
 theorem eval_prod {ι : Type*} (s : Finset ι) (p : ι → R[X]) (x : R) :
     eval x (∏ j in s, p j) = ∏ j in s, eval x (p j) :=
-  (evalRingHom x).map_prod _ _
+  map_prod (evalRingHom x) _ _
 #align polynomial.eval_prod Polynomial.eval_prod
 
 theorem list_prod_comp (l : List R[X]) (q : R[X]) :
@@ -1256,7 +1256,7 @@ protected theorem map_multiset_prod (m : Multiset R[X]) : m.prod.map f = (m.map
 
 protected theorem map_prod {ι : Type*} (g : ι → R[X]) (s : Finset ι) :
     (∏ i in s, g i).map f = ∏ i in s, (g i).map f :=
-  (mapRingHom f).map_prod _ _
+  map_prod (mapRingHom f) _ _
 #align polynomial.map_prod Polynomial.map_prod
 
 theorem IsRoot.map {f : R →+* S} {x : R} {p : R[X]} (h : IsRoot p x) : IsRoot (p.map f) (f x) := by

Lemma names around cancellation of multiplication and division are a mess.

This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero lemma name, the Group lemma, the AddGroup lemma name).

| Statement | New name | Old name | |

@@ -441,8 +441,8 @@ theorem eval_monomial_one_add_sub [CommRing S] (d : ℕ) (y : S) :
         · skip
         · ext
           rw [one_pow, mul_one, mul_comm]
-  rw [sum_range_succ, mul_add, Nat.choose_self, Nat.cast_one, one_mul, add_sub_cancel, mul_sum,
-    sum_range_succ', Nat.cast_zero, zero_mul, mul_zero, add_zero]
+  rw [sum_range_succ, mul_add, Nat.choose_self, Nat.cast_one, one_mul, add_sub_cancel_right,
+    mul_sum, sum_range_succ', Nat.cast_zero, zero_mul, mul_zero, add_zero]
   refine sum_congr rfl fun y _hy => ?_
   rw [← mul_assoc, ← mul_assoc, ← Nat.cast_mul, Nat.succ_mul_choose_eq, Nat.cast_mul,
     Nat.add_sub_cancel]

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

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

@@ -498,10 +498,12 @@ instance IsRoot.decidable [DecidableEq R] : Decidable (IsRoot p a) := by
   unfold IsRoot; infer_instance
 #align polynomial.is_root.decidable Polynomial.IsRoot.decidable
 
+-- Adaptation note: 2024-03-15: this was called `def`.
+-- Should lean be changed to allow that as a name again?
 @[simp]
-theorem IsRoot.def : IsRoot p a ↔ p.eval a = 0 :=
+theorem IsRoot.definition : IsRoot p a ↔ p.eval a = 0 :=
   Iff.rfl
-#align polynomial.is_root.def Polynomial.IsRoot.def
+#align polynomial.is_root.def Polynomial.IsRoot.definition
 
 theorem IsRoot.eq_zero (h : IsRoot p x) : eval x p = 0 :=
   h
@@ -1158,11 +1160,11 @@ theorem coe_compRingHom_apply (p q : R[X]) : (compRingHom q : R[X] → R[X]) p =
 #align polynomial.coe_comp_ring_hom_apply Polynomial.coe_compRingHom_apply
 
 theorem root_mul_left_of_isRoot (p : R[X]) {q : R[X]} : IsRoot q a → IsRoot (p * q) a := fun H => by
-  rw [IsRoot, eval_mul, IsRoot.def.1 H, mul_zero]
+  rw [IsRoot, eval_mul, IsRoot.definition.1 H, mul_zero]
 #align polynomial.root_mul_left_of_is_root Polynomial.root_mul_left_of_isRoot
 
 theorem root_mul_right_of_isRoot {p : R[X]} (q : R[X]) : IsRoot p a → IsRoot (p * q) a := fun H =>
-  by rw [IsRoot, eval_mul, IsRoot.def.1 H, zero_mul]
+  by rw [IsRoot, eval_mul, IsRoot.definition.1 H, zero_mul]
 #align polynomial.root_mul_right_of_is_root Polynomial.root_mul_right_of_isRoot
 
 theorem eval₂_multiset_prod (s : Multiset R[X]) (x : S) :
@@ -1321,7 +1323,7 @@ theorem eval_sub (p q : R[X]) (x : R) : (p - q).eval x = p.eval x - q.eval x :=
 #align polynomial.eval_sub Polynomial.eval_sub
 
 theorem root_X_sub_C : IsRoot (X - C a) b ↔ a = b := by
-  rw [IsRoot.def, eval_sub, eval_X, eval_C, sub_eq_zero, eq_comm]
+  rw [IsRoot.definition, eval_sub, eval_X, eval_C, sub_eq_zero, eq_comm]
 #align polynomial.root_X_sub_C Polynomial.root_X_sub_C
 
 @[simp]

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -37,7 +37,6 @@ variable [Semiring R] {p q r : R[X]}
 section
 
 variable [Semiring S]
-
 variable (f : R →+* S) (x : S)
 
 /-- Evaluate a polynomial `p` given a ring hom `f` from the scalar ring
@@ -705,7 +704,6 @@ end Comp
 section Map
 
 variable [Semiring S]
-
 variable (f : R →+* S)
 
 /-- `map f p` maps a polynomial `p` across a ring hom `f` -/

Classifies by adding issue number #10756 to porting notes claiming anything equivalent to:

• "added theorem"
• "added theorems"
• "new theorem"
• "new theorems"
• "added lemma"
• "new lemma"
• "new lemmas"

@@ -568,7 +568,7 @@ theorem C_comp : (C a).comp p = C a :=
 theorem nat_cast_comp {n : ℕ} : (n : R[X]).comp p = n := by rw [← C_eq_nat_cast, C_comp]
 #align polynomial.nat_cast_comp Polynomial.nat_cast_comp
 
--- Porting note: new theorem
+-- Porting note (#10756): new theorem
 @[simp]
 theorem ofNat_comp (n : ℕ) [n.AtLeastTwo] : (no_index (OfNat.ofNat n) : R[X]).comp p = n :=
   nat_cast_comp
@@ -781,7 +781,7 @@ protected theorem map_nat_cast (n : ℕ) : (n : R[X]).map f = n :=
   map_natCast (mapRingHom f) n
 #align polynomial.map_nat_cast Polynomial.map_nat_cast
 
--- Porting note: new theorem
+-- Porting note (#10756): new theorem
 -- See note [no_index around OfNat.ofNat]
 @[simp]
 protected theorem map_ofNat (n : ℕ) [n.AtLeastTwo] :

Resolves porting notes claiming "apply → induction" since the new induction is more idiomatic than apply.

@@ -418,7 +418,6 @@ theorem eval_smul [Monoid S] [DistribMulAction S R] [IsScalarTower S R R] (s : S
 
 @[simp]
 theorem eval_C_mul : (C a * p).eval x = a * p.eval x := by
-  -- Porting note: `apply` → `induction`
   induction p using Polynomial.induction_on' with
   | h_add p q ph qh =>
     simp only [mul_add, eval_add, ph, qh]
@@ -466,7 +465,6 @@ theorem eval_nat_cast_mul {n : ℕ} : ((n : R[X]) * p).eval x = n * p.eval x :=
 
 @[simp]
 theorem eval_mul_X : (p * X).eval x = p.eval x * x := by
-  -- Porting note: `apply` → `induction`
   induction p using Polynomial.induction_on' with
   | h_add p q ph qh =>
     simp only [add_mul, eval_add, ph, qh]
@@ -603,7 +601,6 @@ theorem monomial_comp (n : ℕ) : (monomial n a).comp p = C a * p ^ n :=
 
 @[simp]
 theorem mul_X_comp : (p * X).comp r = p.comp r * r := by
-  -- Porting note: `apply` → `induction`
   induction p using Polynomial.induction_on' with
   | h_add p q hp hq =>
     simp only [hp, hq, add_mul, add_comp]
@@ -627,7 +624,6 @@ theorem mul_X_pow_comp {k : ℕ} : (p * X ^ k).comp r = p.comp r * r ^ k := by
 
 @[simp]
 theorem C_mul_comp : (C a * p).comp r = C a * p.comp r := by
-  -- Porting note: `apply` → `induction`
   induction p using Polynomial.induction_on' with
   | h_add p q hp hq =>
     simp [hp, hq, mul_add]
@@ -849,7 +845,6 @@ def piEquiv {ι} [Finite ι] (R : ι → Type*) [∀ i, Semiring (R i)] :
           contrapose! hn; exact funext hn), by ext i n; exact coeff_map _ _⟩⟩
 
 theorem eval₂_eq_eval_map {x : S} : p.eval₂ f x = (p.map f).eval x := by
-  -- Porting note: `apply` → `induction`
   induction p using Polynomial.induction_on' with
   | h_add p q hp hq =>
     simp [hp, hq]
@@ -999,7 +994,6 @@ theorem eval_zero_map (f : R →+* S) (p : R[X]) : (p.map f).eval 0 = f (p.eval
 
 @[simp]
 theorem eval_one_map (f : R →+* S) (p : R[X]) : (p.map f).eval 1 = f (p.eval 1) := by
-  -- Porting note: `apply` → `induction`
   induction p using Polynomial.induction_on' with
   | h_add p q hp hq =>
     simp only [hp, hq, Polynomial.map_add, RingHom.map_add, eval_add]
@@ -1010,7 +1004,6 @@ theorem eval_one_map (f : R →+* S) (p : R[X]) : (p.map f).eval 1 = f (p.eval 1
 @[simp]
 theorem eval_nat_cast_map (f : R →+* S) (p : R[X]) (n : ℕ) :
     (p.map f).eval (n : S) = f (p.eval n) := by
-  -- Porting note: `apply` → `induction`
   induction p using Polynomial.induction_on' with
   | h_add p q hp hq =>
     simp only [hp, hq, Polynomial.map_add, RingHom.map_add, eval_add]
@@ -1021,7 +1014,6 @@ theorem eval_nat_cast_map (f : R →+* S) (p : R[X]) (n : ℕ) :
 @[simp]
 theorem eval_int_cast_map {R S : Type*} [Ring R] [Ring S] (f : R →+* S) (p : R[X]) (i : ℤ) :
     (p.map f).eval (i : S) = f (p.eval i) := by
-  -- Porting note: `apply` → `induction`
   induction p using Polynomial.induction_on' with
   | h_add p q hp hq =>
     simp only [hp, hq, Polynomial.map_add, RingHom.map_add, eval_add]
@@ -1137,7 +1129,6 @@ theorem eval_pow (n : ℕ) : (p ^ n).eval x = p.eval x ^ n :=
 
 @[simp]
 theorem eval_comp : (p.comp q).eval x = p.eval (q.eval x) := by
-  -- Porting note: `apply` → `induction`
   induction p using Polynomial.induction_on' with
   | h_add r s hr hs =>
     simp [add_comp, hr, hs]

• Prove isSemisimple_of_mem_adjoin: if two commuting endomorphisms of a finite-dimensional vector space over a perfect field are both semisimple, then every endomorphism in the algebra generated by them (in particular their product and sum) is semisimple.

• In the same file LinearAlgebra/Semisimple.lean, eq_zero_of_isNilpotent_isSemisimple and isSemisimple_of_squarefree_aeval_eq_zero are golfed, and IsSemisimple.minpoly_squarefree is proved

RingTheory/SimpleModule.lean:

• Define IsSemisimpleRing R to mean that R is a semisimple R-module. add properties of simple modules and a characterization (they are exactly the quotients of the ring by maximal left ideals).

• The annihilator of a semisimple module is a radical ideal.

• Any module over a semisimple ring is semisimple.

• A finite product of semisimple rings is semisimple.

• Any quotient of a semisimple ring is semisimple.

• Add Artin--Wedderburn as a TODO (proof_wanted).

• Order/Atoms.lean: add the instance from IsSimpleOrder to ComplementedLattice, so that IsSimpleModule → IsSemisimpleModule is automatically inferred.

Prerequisites for showing a product of semisimple rings is semisimple:

• Algebra/Module/Submodule/Map.lean: generalize orderIsoMapComap so that it only requires RingHomSurjective rather than RingHomInvPair

• Algebra/Ring/CompTypeclasses.lean, Mathlib/Algebra/Ring/Pi.lean, Algebra/Ring/Prod.lean: add RingHomSurjective instances

RingTheory/Artinian.lean:

• quotNilradicalEquivPi: the quotient of a commutative Artinian ring R by its nilradical is isomorphic to the (finite) product of its quotients by maximal ideals (therefore a product of fields). equivPi: if the ring is moreover reduced, then the ring itself is a product of fields. Deduce that R is a semisimple ring and both R and R[X] are decomposition monoids. Requires RingEquiv.quotientBot in RingTheory/Ideal/QuotientOperations.lean.

• Data/Polynomial/Eval.lean: the polynomial ring over a finite product of rings is isomorphic to the product of polynomial rings over individual rings. (Used to show R[X] is a decomposition monoid.)

Other necessary results:

• FieldTheory/Minpoly/Field.lean: the minimal polynomial of an element in a reduced algebra over a field is radical.

• RingTheory/PowerBasis.lean: generalize PowerBasis.finiteDimensional and rename it to .finite.

Annihilator stuff, some of which do not end up being used:

• RingTheory/Ideal/Operations.lean: define Module.annihilator and redefine Submodule.annihilator in terms of it; add lemmas, including one that says an arbitrary intersection of radical ideals is radical. The new lemma Ideal.isRadical_iff_pow_one_lt depends on pow_imp_self_of_one_lt in Mathlib/Data/Nat/Interval.lean, which is also used to golf the proof of isRadical_iff_pow_one_lt.

• Algebra/Module/Torsion.lean: add a lemma and an instance (unused)

• Data/Polynomial/Module/Basic.lean: add a def (unused) and a lemma

• LinearAlgebra/AnnihilatingPolynomial.lean: add lemma span_minpoly_eq_annihilator

Some results about idempotent linear maps (projections) and idempotent elements, used to show that any (left) ideal in a semisimple ring is spanned by an idempotent element (unused):

• LinearAlgebra/Projection.lean: add def isIdempotentElemEquiv

• LinearAlgebra/Span.lean: add two lemmas

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

@@ -837,6 +837,17 @@ theorem map_map [Semiring T] (g : S →+* T) (p : R[X]) : (p.map f).map g = p.ma
 theorem map_id : p.map (RingHom.id _) = p := by simp [Polynomial.ext_iff, coeff_map]
 #align polynomial.map_id Polynomial.map_id
 
+/-- The polynomial ring over a finite product of rings is isomorphic to
+the product of polynomial rings over individual rings. -/
+def piEquiv {ι} [Finite ι] (R : ι → Type*) [∀ i, Semiring (R i)] :
+    (∀ i, R i)[X] ≃+* ∀ i, (R i)[X] :=
+  .ofBijective (Pi.ringHom fun i ↦ mapRingHom (Pi.evalRingHom R i))
+    ⟨fun p q h ↦ by ext n i; simpa using congr_arg (fun p ↦ coeff (p i) n) h,
+      fun p ↦ ⟨.ofFinsupp (.ofSupportFinite (fun n i ↦ coeff (p i) n) <|
+        (Set.finite_iUnion fun i ↦ (p i).support.finite_toSet).subset fun n hn ↦ by
+          simp only [Set.mem_iUnion, Finset.mem_coe, mem_support_iff, Function.mem_support] at hn ⊢
+          contrapose! hn; exact funext hn), by ext i n; exact coeff_map _ _⟩⟩
+
 theorem eval₂_eq_eval_map {x : S} : p.eval₂ f x = (p.map f).eval x := by
   -- Porting note: `apply` → `induction`
   induction p using Polynomial.induction_on' with

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -570,7 +570,7 @@ theorem C_comp : (C a).comp p = C a :=
 theorem nat_cast_comp {n : ℕ} : (n : R[X]).comp p = n := by rw [← C_eq_nat_cast, C_comp]
 #align polynomial.nat_cast_comp Polynomial.nat_cast_comp
 
---Porting note: new theorem
+-- Porting note: new theorem
 @[simp]
 theorem ofNat_comp (n : ℕ) [n.AtLeastTwo] : (no_index (OfNat.ofNat n) : R[X]).comp p = n :=
   nat_cast_comp
@@ -785,7 +785,7 @@ protected theorem map_nat_cast (n : ℕ) : (n : R[X]).map f = n :=
   map_natCast (mapRingHom f) n
 #align polynomial.map_nat_cast Polynomial.map_nat_cast
 
---Porting note: new theorem
+-- Porting note: new theorem
 -- See note [no_index around OfNat.ofNat]
 @[simp]
 protected theorem map_ofNat (n : ℕ) [n.AtLeastTwo] :

Classifies by adding issue number (#10745) to porting notes claiming was simp.

@@ -814,7 +814,7 @@ theorem coeff_map (n : ℕ) : coeff (p.map f) n = f (coeff p n) := by
   rw [map, eval₂_def, coeff_sum, sum]
   conv_rhs => rw [← sum_C_mul_X_pow_eq p, coeff_sum, sum, map_sum]
   refine' Finset.sum_congr rfl fun x _hx => _
-  -- Porting note: Was `simp [Function.comp, coeff_C_mul_X_pow, f.map_mul]`.
+  -- porting note (#10745): was `simp [Function.comp, coeff_C_mul_X_pow, f.map_mul]`.
   simp? [Function.comp, coeff_C_mul_X_pow, - map_mul, - coeff_C_mul] says
     simp only [RingHom.coe_comp, Function.comp_apply, coeff_C_mul_X_pow]
   split_ifs <;> simp [f.map_zero]

Remove unnecessary "rw"s.

@@ -637,7 +637,7 @@ theorem C_mul_comp : (C a * p).comp r = C a * p.comp r := by
 
 @[simp]
 theorem nat_cast_mul_comp {n : ℕ} : ((n : R[X]) * p).comp r = n * p.comp r := by
-  rw [← C_eq_nat_cast, C_mul_comp, C_eq_nat_cast]
+  rw [← C_eq_nat_cast, C_mul_comp]
 #align polynomial.nat_cast_mul_comp Polynomial.nat_cast_mul_comp
 
 theorem mul_X_add_nat_cast_comp {n : ℕ} :

We define generalized binomial coefficients, and prove a couple basic properties. In particular, we show that multiplication by a suitable factorial yields a descending Pochhammer evaluation. We also show that casting Nat.choose is the same as taking Ring.choose of a natural number cast. To prove these, we add some results about polynomial evaluation.

@@ -1071,6 +1071,31 @@ theorem iterate_comp_eval₂ (k : ℕ) (t : S) :
 
 end
 
+section Algebra
+
+variable [CommSemiring R] [Semiring S] [Algebra R S] (x : S) (p q : R[X])
+
+@[simp]
+theorem eval₂_mul' :
+    (p * q).eval₂ (algebraMap R S) x = p.eval₂ (algebraMap R S) x * q.eval₂ (algebraMap R S) x := by
+  exact eval₂_mul_noncomm _ _ fun k => Algebra.commute_algebraMap_left (coeff q k) x
+
+@[simp]
+theorem eval₂_pow' (n : ℕ) :
+    (p ^ n).eval₂ (algebraMap R S) x = (p.eval₂ (algebraMap R S) x) ^ n := by
+  induction n with
+  | zero => simp only [Nat.zero_eq, pow_zero, eval₂_one]
+  | succ n ih => rw [pow_succ, pow_succ, eval₂_mul', ih]
+
+@[simp]
+theorem eval₂_comp' : eval₂ (algebraMap R S) x (p.comp q) =
+    eval₂ (algebraMap R S) (eval₂ (algebraMap R S) x q) p := by
+  induction p using Polynomial.induction_on' with
+    | h_add r s hr hs => simp only [add_comp, eval₂_add, hr, hs]
+    | h_monomial n a => simp only [monomial_comp, eval₂_mul', eval₂_C, eval₂_monomial, eval₂_pow']
+
+end Algebra
+
 section
 
 variable [CommSemiring R] {p q : R[X]} {x : R} [CommSemiring S] (f : R →+* S)

Inspired by #9271

Prove the main theorem rootMultiplicity_expand and derive corollaries about Polynomial.roots. Refactor rootsExpand(Pow)EquivRoots using the new lemmas.

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

@@ -1115,6 +1115,9 @@ theorem iterate_comp_eval :
   iterate_comp_eval₂ _
 #align polynomial.iterate_comp_eval Polynomial.iterate_comp_eval
 
+lemma isRoot_comp {R} [CommSemiring R] {p q : R[X]} {r : R} :
+    (p.comp q).IsRoot r ↔ p.IsRoot (q.eval r) := by simp_rw [IsRoot, eval_comp]
+
 /-- `comp p`, regarded as a ring homomorphism from `R[X]` to itself. -/
 def compRingHom : R[X] → R[X] →+* R[X] :=
   eval₂RingHom C

This involves moving lemmas from Algebra.GroupPower.Ring to Algebra.GroupWithZero.Basic and changing some 0 < n assumptions to n ≠ 0.

From LeanAPAP

@@ -516,8 +516,7 @@ theorem coeff_zero_eq_eval_zero (p : R[X]) : coeff p 0 = p.eval 0 :=
     _ = p.eval 0 := by
       symm
       rw [eval_eq_sum]
-      exact
-        Finset.sum_eq_single _ (fun b _ hb => by simp [zero_pow (Nat.pos_of_ne_zero hb)]) (by simp)
+      exact Finset.sum_eq_single _ (fun b _ hb => by simp [zero_pow hb]) (by simp)
 #align polynomial.coeff_zero_eq_eval_zero Polynomial.coeff_zero_eq_eval_zero
 
 theorem zero_isRoot_of_coeff_zero_eq_zero {p : R[X]} (hp : p.coeff 0 = 0) : IsRoot p 0 := by

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

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

@@ -1092,7 +1092,7 @@ theorem coe_evalRingHom (r : R) : (evalRingHom r : R[X] → R) = eval r :=
 #align polynomial.coe_eval_ring_hom Polynomial.coe_evalRingHom
 
 theorem evalRingHom_zero : evalRingHom 0 = constantCoeff :=
-  FunLike.ext _ _ fun p => p.coeff_zero_eq_eval_zero.symm
+  DFunLike.ext _ _ fun p => p.coeff_zero_eq_eval_zero.symm
 #align polynomial.eval_ring_hom_zero Polynomial.evalRingHom_zero
 
 @[simp]

Removes nonterminal uses of simp at. Replaces most of these with instances of simp? ... says.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -816,7 +816,8 @@ theorem coeff_map (n : ℕ) : coeff (p.map f) n = f (coeff p n) := by
   conv_rhs => rw [← sum_C_mul_X_pow_eq p, coeff_sum, sum, map_sum]
   refine' Finset.sum_congr rfl fun x _hx => _
   -- Porting note: Was `simp [Function.comp, coeff_C_mul_X_pow, f.map_mul]`.
-  simp [Function.comp, coeff_C_mul_X_pow, - map_mul, - coeff_C_mul]
+  simp? [Function.comp, coeff_C_mul_X_pow, - map_mul, - coeff_C_mul] says
+    simp only [RingHom.coe_comp, Function.comp_apply, coeff_C_mul_X_pow]
   split_ifs <;> simp [f.map_zero]
 #align polynomial.coeff_map Polynomial.coeff_map
 

@@ -156,7 +156,7 @@ theorem eval₂_sum (p : T[X]) (g : ℕ → T → R[X]) (x : S) :
       map_add' := fun p q => eval₂_add _ _ }
   have A : ∀ y, eval₂ f x y = T y := fun y => rfl
   simp only [A]
-  rw [sum, T.map_sum, sum]
+  rw [sum, map_sum, sum]
 #align polynomial.eval₂_sum Polynomial.eval₂_sum
 
 theorem eval₂_list_sum (l : List R[X]) (x : S) : eval₂ f x l.sum = (l.map (eval₂ f x)).sum :=

Co-authored-by: timotree3 <timorcb@gmail.com>

@@ -140,6 +140,7 @@ theorem eval₂_nat_cast (n : ℕ) : (n : R[X]).eval₂ f x = n := by
   · rw [n.cast_succ, eval₂_add, ih, eval₂_one, n.cast_succ]
 #align polynomial.eval₂_nat_cast Polynomial.eval₂_nat_cast
 
+-- See note [no_index around OfNat.ofNat]
 @[simp]
 lemma eval₂_ofNat {S : Type*} [Semiring S] (n : ℕ) [n.AtLeastTwo] (f : R →+* S) (a : S) :
     (no_index (OfNat.ofNat n : R[X])).eval₂ f a = OfNat.ofNat n := by
@@ -351,6 +352,7 @@ theorem eval₂_at_nat_cast {S : Type*} [Semiring S] (f : R →+* S) (n : ℕ) :
   simp
 #align polynomial.eval₂_at_nat_cast Polynomial.eval₂_at_nat_cast
 
+-- See note [no_index around OfNat.ofNat]
 @[simp]
 theorem eval₂_at_ofNat {S : Type*} [Semiring S] (f : R →+* S) (n : ℕ) [n.AtLeastTwo] :
     p.eval₂ f (no_index (OfNat.ofNat n)) = f (p.eval (OfNat.ofNat n)) := by
@@ -365,6 +367,7 @@ theorem eval_C : (C a).eval x = a :=
 theorem eval_nat_cast {n : ℕ} : (n : R[X]).eval x = n := by simp only [← C_eq_nat_cast, eval_C]
 #align polynomial.eval_nat_cast Polynomial.eval_nat_cast
 
+-- See note [no_index around OfNat.ofNat]
 @[simp]
 lemma eval_ofNat (n : ℕ) [n.AtLeastTwo] (a : R) :
     (no_index (OfNat.ofNat n : R[X])).eval a = OfNat.ofNat n := by
@@ -784,6 +787,7 @@ protected theorem map_nat_cast (n : ℕ) : (n : R[X]).map f = n :=
 #align polynomial.map_nat_cast Polynomial.map_nat_cast
 
 --Porting note: new theorem
+-- See note [no_index around OfNat.ofNat]
 @[simp]
 protected theorem map_ofNat (n : ℕ) [n.AtLeastTwo] :
     (no_index (OfNat.ofNat n) : R[X]).map f = OfNat.ofNat n :=

This adds an AlgHom version of eval₂RingHom', and a stronger ext lemma for noncommutative algebras. This is a follow-up to leanprover-community/mathlib#9250

This better ext lemma golfs away most of a nasty proof.

@@ -216,6 +216,7 @@ theorem eval₂_list_prod_noncomm (ps : List R[X])
 #align polynomial.eval₂_list_prod_noncomm Polynomial.eval₂_list_prod_noncomm
 
 /-- `eval₂` as a `RingHom` for noncommutative rings -/
+@[simps]
 def eval₂RingHom' (f : R →+* S) (x : S) (hf : ∀ a, Commute (f a) x) : R[X] →+* S where
   toFun := eval₂ f x
   map_add' _ _ := eval₂_add _ _

Adds degree_sub_C, natDegree_sub_C, analogous to ..._add_C.

Also relocates C_neg and C_sub to Basic.lean (where C_add is) so that the new lemmas can be in the same file as their add counterparts.

@@ -1246,14 +1246,6 @@ section Ring
 
 variable [Ring R] {p q r : R[X]}
 
-theorem C_neg : C (-a) = -C a :=
-  RingHom.map_neg C a
-#align polynomial.C_neg Polynomial.C_neg
-
-theorem C_sub : C (a - b) = C a - C b :=
-  RingHom.map_sub C a b
-#align polynomial.C_sub Polynomial.C_sub
-
 @[simp]
 protected theorem map_sub {S} [Ring S] (f : R →+* S) : (p - q).map f = p.map f - q.map f :=
   (mapRingHom f).map_sub p q

@@ -698,6 +698,9 @@ theorem coeff_comp_degree_mul_degree (hqd0 : natDegree q ≠ 0) :
     simp (config := { contextual := true })
 #align polynomial.coeff_comp_degree_mul_degree Polynomial.coeff_comp_degree_mul_degree
 
+@[simp] lemma sum_comp (s : Finset ι) (p : ι → R[X]) (q : R[X]) :
+    (∑ i in s, p i).comp q = ∑ i in s, (p i).comp q := Polynomial.eval₂_finset_sum _ _ _ _
+
 end Comp
 
 section Map

@@ -140,6 +140,11 @@ theorem eval₂_nat_cast (n : ℕ) : (n : R[X]).eval₂ f x = n := by
   · rw [n.cast_succ, eval₂_add, ih, eval₂_one, n.cast_succ]
 #align polynomial.eval₂_nat_cast Polynomial.eval₂_nat_cast
 
+@[simp]
+lemma eval₂_ofNat {S : Type*} [Semiring S] (n : ℕ) [n.AtLeastTwo] (f : R →+* S) (a : S) :
+    (no_index (OfNat.ofNat n : R[X])).eval₂ f a = OfNat.ofNat n := by
+  simp [OfNat.ofNat]
+
 variable [Semiring T]
 
 theorem eval₂_sum (p : T[X]) (g : ℕ → T → R[X]) (x : S) :
@@ -345,6 +350,11 @@ theorem eval₂_at_nat_cast {S : Type*} [Semiring S] (f : R →+* S) (n : ℕ) :
   simp
 #align polynomial.eval₂_at_nat_cast Polynomial.eval₂_at_nat_cast
 
+@[simp]
+theorem eval₂_at_ofNat {S : Type*} [Semiring S] (f : R →+* S) (n : ℕ) [n.AtLeastTwo] :
+    p.eval₂ f (no_index (OfNat.ofNat n)) = f (p.eval (OfNat.ofNat n)) := by
+  simp [OfNat.ofNat]
+
 @[simp]
 theorem eval_C : (C a).eval x = a :=
   eval₂_C _ _
@@ -354,6 +364,11 @@ theorem eval_C : (C a).eval x = a :=
 theorem eval_nat_cast {n : ℕ} : (n : R[X]).eval x = n := by simp only [← C_eq_nat_cast, eval_C]
 #align polynomial.eval_nat_cast Polynomial.eval_nat_cast
 
+@[simp]
+lemma eval_ofNat (n : ℕ) [n.AtLeastTwo] (a : R) :
+    (no_index (OfNat.ofNat n : R[X])).eval a = OfNat.ofNat n := by
+  simp only [OfNat.ofNat, eval_nat_cast]
+
 @[simp]
 theorem eval_X : X.eval x = x :=
   eval₂_X _ _

Introduce the notation R[A] for AddMonoidAlgebra R A. This is to align Mathlibs notation with the standard notation for group ring.

The notation is scoped in AddMonoidAlgebra and there is no analogous notation for MonoidAlgebra.

I only used the notation for single-character R and As and only in the range [a-zA-Z].

The extra lines are all in Mathlib/Algebra/MonoidAlgebra/Basic.lean. They are accounted for by extra text in the doc-module and the actual notation.

Affected files:

Counterexamples/ZeroDivisorsInAddMonoidAlgebras
Algebra/AlgebraicCard
Algebra/MonoidAlgebra/Basic
Algebra/MonoidAlgebra/Degree
Algebra/MonoidAlgebra/Division
Algebra/MonoidAlgebra/Grading
Algebra/MonoidAlgebra/NoZeroDivisors
Algebra/MonoidAlgebra/Support
Data/Polynomial/AlgebraMap
Data/Polynomial/Basic
Data/Polynomial/Eval
Data/Polynomial/Laurent
RingTheory/FiniteType

@@ -167,7 +167,7 @@ theorem eval₂_finset_sum (s : Finset ι) (g : ι → R[X]) (x : S) :
   map_sum (eval₂AddMonoidHom f x) _ _
 #align polynomial.eval₂_finset_sum Polynomial.eval₂_finset_sum
 
-theorem eval₂_ofFinsupp {f : R →+* S} {x : S} {p : AddMonoidAlgebra R ℕ} :
+theorem eval₂_ofFinsupp {f : R →+* S} {x : S} {p : R[ℕ]} :
     eval₂ f x (⟨p⟩ : R[X]) = liftNC (↑f) (powersHom S x) p := by
   simp only [eval₂_eq_sum, sum, toFinsupp_sum, support, coeff]
   rfl

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

@@ -622,6 +622,12 @@ theorem nat_cast_mul_comp {n : ℕ} : ((n : R[X]) * p).comp r = n * p.comp r :=
   rw [← C_eq_nat_cast, C_mul_comp, C_eq_nat_cast]
 #align polynomial.nat_cast_mul_comp Polynomial.nat_cast_mul_comp
 
+theorem mul_X_add_nat_cast_comp {n : ℕ} :
+    (p * (X + (n : R[X]))).comp q = p.comp q * (q + n) := by
+  rw [mul_add, add_comp, mul_X_comp, ← Nat.cast_comm, nat_cast_mul_comp, Nat.cast_comm, mul_add]
+set_option linter.uppercaseLean3 false in
+#align polynomial.mul_X_add_nat_cast_comp Polynomial.mul_X_add_nat_cast_comp
+
 @[simp]
 theorem mul_comp {R : Type*} [CommSemiring R] (p q r : R[X]) :
     (p * q).comp r = p.comp r * q.comp r :=
@@ -1295,6 +1301,10 @@ theorem eval₂_at_int_cast {S : Type*} [Ring S] (f : R →+* S) (n : ℤ) :
   convert eval₂_at_apply (p := p) f n
   simp
 
+theorem mul_X_sub_int_cast_comp {n : ℕ} :
+    (p * (X - (n : R[X]))).comp q = p.comp q * (q - n) := by
+  rw [mul_sub, sub_comp, mul_X_comp, ← Nat.cast_comm, nat_cast_mul_comp, Nat.cast_comm, mul_sub]
+
 end Ring
 
 end Polynomial

• depends on: #6917

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

@@ -1289,6 +1289,12 @@ theorem sub_comp : (p - q).comp r = p.comp r - q.comp r :=
 theorem cast_int_comp (i : ℤ) : comp (i : R[X]) p = i := by cases i <;> simp
 #align polynomial.cast_int_comp Polynomial.cast_int_comp
 
+@[simp]
+theorem eval₂_at_int_cast {S : Type*} [Ring S] (f : R →+* S) (n : ℤ) :
+    p.eval₂ f n = f (p.eval n) := by
+  convert eval₂_at_apply (p := p) f n
+  simp
+
 end Ring
 
 end Polynomial

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

This has nice performance benefits.

@@ -50,7 +50,7 @@ theorem eval₂_eq_sum {f : R →+* S} {x : S} : p.eval₂ f x = p.sum fun e a =
   rw [eval₂_def]
 #align polynomial.eval₂_eq_sum Polynomial.eval₂_eq_sum
 
-theorem eval₂_congr {R S : Type _} [Semiring R] [Semiring S] {f g : R →+* S} {s t : S}
+theorem eval₂_congr {R S : Type*} [Semiring R] [Semiring S] {f g : R →+* S} {s t : S}
     {φ ψ : R[X]} : f = g → s = t → φ = ψ → eval₂ f s φ = eval₂ g t ψ := by
   rintro rfl rfl rfl; rfl
 #align polynomial.eval₂_congr Polynomial.eval₂_congr
@@ -326,20 +326,20 @@ theorem eval_eq_sum_range' {p : R[X]} {n : ℕ} (hn : p.natDegree < n) (x : R) :
 #align polynomial.eval_eq_sum_range' Polynomial.eval_eq_sum_range'
 
 @[simp]
-theorem eval₂_at_apply {S : Type _} [Semiring S] (f : R →+* S) (r : R) :
+theorem eval₂_at_apply {S : Type*} [Semiring S] (f : R →+* S) (r : R) :
     p.eval₂ f (f r) = f (p.eval r) := by
   rw [eval₂_eq_sum, eval_eq_sum, sum, sum, f.map_sum]
   simp only [f.map_mul, f.map_pow]
 #align polynomial.eval₂_at_apply Polynomial.eval₂_at_apply
 
 @[simp]
-theorem eval₂_at_one {S : Type _} [Semiring S] (f : R →+* S) : p.eval₂ f 1 = f (p.eval 1) := by
+theorem eval₂_at_one {S : Type*} [Semiring S] (f : R →+* S) : p.eval₂ f 1 = f (p.eval 1) := by
   convert eval₂_at_apply (p := p) f 1
   simp
 #align polynomial.eval₂_at_one Polynomial.eval₂_at_one
 
 @[simp]
-theorem eval₂_at_nat_cast {S : Type _} [Semiring S] (f : R →+* S) (n : ℕ) :
+theorem eval₂_at_nat_cast {S : Type*} [Semiring S] (f : R →+* S) (n : ℕ) :
     p.eval₂ f n = f (p.eval n) := by
   convert eval₂_at_apply (p := p) f n
   simp
@@ -433,7 +433,7 @@ theorem eval_monomial_one_add_sub [CommRing S] (d : ℕ) (y : S) :
 
 /-- `Polynomial.eval` as linear map -/
 @[simps]
-def leval {R : Type _} [Semiring R] (r : R) : R[X] →ₗ[R] R where
+def leval {R : Type*} [Semiring R] (r : R) : R[X] →ₗ[R] R where
   toFun f := f.eval r
   map_add' _f _g := eval_add
   map_smul' c f := eval_smul c f r
@@ -505,7 +505,7 @@ theorem zero_isRoot_of_coeff_zero_eq_zero {p : R[X]} (hp : p.coeff 0 = 0) : IsRo
   rwa [coeff_zero_eq_eval_zero] at hp
 #align polynomial.zero_is_root_of_coeff_zero_eq_zero Polynomial.zero_isRoot_of_coeff_zero_eq_zero
 
-theorem IsRoot.dvd {R : Type _} [CommSemiring R] {p q : R[X]} {x : R} (h : p.IsRoot x)
+theorem IsRoot.dvd {R : Type*} [CommSemiring R] {p q : R[X]} {x : R} (h : p.IsRoot x)
     (hpq : p ∣ q) : q.IsRoot x := by
   rwa [IsRoot, eval, eval₂_eq_zero_of_dvd_of_eval₂_eq_zero _ _ hpq]
 #align polynomial.is_root.dvd Polynomial.IsRoot.dvd
@@ -623,13 +623,13 @@ theorem nat_cast_mul_comp {n : ℕ} : ((n : R[X]) * p).comp r = n * p.comp r :=
 #align polynomial.nat_cast_mul_comp Polynomial.nat_cast_mul_comp
 
 @[simp]
-theorem mul_comp {R : Type _} [CommSemiring R] (p q r : R[X]) :
+theorem mul_comp {R : Type*} [CommSemiring R] (p q r : R[X]) :
     (p * q).comp r = p.comp r * q.comp r :=
   eval₂_mul _ _
 #align polynomial.mul_comp Polynomial.mul_comp
 
 @[simp]
-theorem pow_comp {R : Type _} [CommSemiring R] (p q : R[X]) (n : ℕ) :
+theorem pow_comp {R : Type*} [CommSemiring R] (p q : R[X]) (n : ℕ) :
     (p ^ n).comp q = p.comp q ^ n :=
   (MonoidHom.mk (OneHom.mk (fun r : R[X] => r.comp q) one_comp) fun r s => mul_comp r s q).map_pow
     p n
@@ -652,7 +652,7 @@ theorem smul_comp [Monoid S] [DistribMulAction S R] [IsScalarTower S R R] (s : S
   rw [← smul_one_smul R s p, comp, comp, eval₂_smul, ← smul_eq_C_mul, smul_assoc, one_smul]
 #align polynomial.smul_comp Polynomial.smul_comp
 
-theorem comp_assoc {R : Type _} [CommSemiring R] (φ ψ χ : R[X]) :
+theorem comp_assoc {R : Type*} [CommSemiring R] (φ ψ χ : R[X]) :
     (φ.comp ψ).comp χ = φ.comp (ψ.comp χ) := by
   refine Polynomial.induction_on φ ?_ ?_ ?_ <;>
     · intros
@@ -924,7 +924,7 @@ theorem mem_map_rangeS {p : S[X]} : p ∈ (mapRingHom f).rangeS ↔ ∀ n, p.coe
     rw [coe_mapRingHom, Polynomial.map_mul, map_C, hc, Polynomial.map_pow, map_X]
 #align polynomial.mem_map_srange Polynomial.mem_map_rangeS
 
-theorem mem_map_range {R S : Type _} [Ring R] [Ring S] (f : R →+* S) {p : S[X]} :
+theorem mem_map_range {R S : Type*} [Ring R] [Ring S] (f : R →+* S) {p : S[X]} :
     p ∈ (mapRingHom f).range ↔ ∀ n, p.coeff n ∈ f.range :=
   mem_map_rangeS f
 #align polynomial.mem_map_range Polynomial.mem_map_range
@@ -937,7 +937,7 @@ theorem eval_map (x : S) : (p.map f).eval x = p.eval₂ f x :=
   (eval₂_eq_eval_map f).symm
 #align polynomial.eval_map Polynomial.eval_map
 
-protected theorem map_sum {ι : Type _} (g : ι → R[X]) (s : Finset ι) :
+protected theorem map_sum {ι : Type*} (g : ι → R[X]) (s : Finset ι) :
     (∑ i in s, g i).map f = ∑ i in s, (g i).map f :=
   (mapRingHom f).map_sum _ _
 #align polynomial.map_sum Polynomial.map_sum
@@ -979,7 +979,7 @@ theorem eval_nat_cast_map (f : R →+* S) (p : R[X]) (n : ℕ) :
 #align polynomial.eval_nat_cast_map Polynomial.eval_nat_cast_map
 
 @[simp]
-theorem eval_int_cast_map {R S : Type _} [Ring R] [Ring S] (f : R →+* S) (p : R[X]) (i : ℤ) :
+theorem eval_int_cast_map {R S : Type*} [Ring R] [Ring S] (f : R →+* S) (p : R[X]) (i : ℤ) :
     (p.map f).eval (i : S) = f (p.eval i) := by
   -- Porting note: `apply` → `induction`
   induction p using Polynomial.induction_on' with
@@ -1132,7 +1132,7 @@ theorem eval_multiset_prod (s : Multiset R[X]) (x : R) : eval x s.prod = (s.map
 
 /-- Polynomial evaluation commutes with `Finset.prod`
 -/
-theorem eval_prod {ι : Type _} (s : Finset ι) (p : ι → R[X]) (x : R) :
+theorem eval_prod {ι : Type*} (s : Finset ι) (p : ι → R[X]) (x : R) :
     eval x (∏ j in s, p j) = ∏ j in s, eval x (p j) :=
   (evalRingHom x).map_prod _ _
 #align polynomial.eval_prod Polynomial.eval_prod
@@ -1147,12 +1147,12 @@ theorem multiset_prod_comp (s : Multiset R[X]) (q : R[X]) :
   map_multiset_prod (compRingHom q) _
 #align polynomial.multiset_prod_comp Polynomial.multiset_prod_comp
 
-theorem prod_comp {ι : Type _} (s : Finset ι) (p : ι → R[X]) (q : R[X]) :
+theorem prod_comp {ι : Type*} (s : Finset ι) (p : ι → R[X]) (q : R[X]) :
     (∏ j in s, p j).comp q = ∏ j in s, (p j).comp q :=
   map_prod (compRingHom q) _ _
 #align polynomial.prod_comp Polynomial.prod_comp
 
-theorem isRoot_prod {R} [CommRing R] [IsDomain R] {ι : Type _} (s : Finset ι) (p : ι → R[X])
+theorem isRoot_prod {R} [CommRing R] [IsDomain R] {ι : Type*} (s : Finset ι) (p : ι → R[X])
     (x : R) : IsRoot (∏ j in s, p j) x ↔ ∃ i ∈ s, IsRoot (p i) x := by
   simp only [IsRoot, eval_prod, Finset.prod_eq_zero_iff]
 #align polynomial.is_root_prod Polynomial.isRoot_prod
@@ -1195,7 +1195,7 @@ protected theorem map_multiset_prod (m : Multiset R[X]) : m.prod.map f = (m.map
   Eq.symm <| Multiset.prod_hom _ (mapRingHom f).toMonoidHom
 #align polynomial.map_multiset_prod Polynomial.map_multiset_prod
 
-protected theorem map_prod {ι : Type _} (g : ι → R[X]) (s : Finset ι) :
+protected theorem map_prod {ι : Type*} (g : ι → R[X]) (s : Finset ι) :
     (∏ i in s, g i).map f = ∏ i in s, (g i).map f :=
   (mapRingHom f).map_prod _ _
 #align polynomial.map_prod Polynomial.map_prod
@@ -1209,7 +1209,7 @@ theorem IsRoot.of_map {R} [CommRing R] {f : R →+* S} {x : R} {p : R[X]} (h : I
   rwa [IsRoot, ← (injective_iff_map_eq_zero' f).mp hf, ← eval₂_hom, ← eval_map]
 #align polynomial.is_root.of_map Polynomial.IsRoot.of_map
 
-theorem isRoot_map_iff {R : Type _} [CommRing R] {f : R →+* S} {x : R} {p : R[X]}
+theorem isRoot_map_iff {R : Type*} [CommRing R] {f : R →+* S} {x : R} {p : R[X]}
     (hf : Function.Injective f) : IsRoot (p.map f) (f x) ↔ IsRoot p x :=
   ⟨fun h => h.of_map hf, fun h => h.map⟩
 #align polynomial.is_root_map_iff Polynomial.isRoot_map_iff

• 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.eval
-! leanprover-community/mathlib commit 728baa2f54e6062c5879a3e397ac6bac323e506f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Polynomial.Degree.Definitions
 import Mathlib.Data.Polynomial.Induction
 
+#align_import data.polynomial.eval from "leanprover-community/mathlib"@"728baa2f54e6062c5879a3e397ac6bac323e506f"
+
 /-!
 # Theory of univariate polynomials
 

• depends on: https://github.com/leanprover/std4/pull/163
• depends on: #5584
• depends on: #5715
• depends on: #5729
• depends on: https://github.com/leanprover/std4/pull/173

Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -557,7 +557,7 @@ theorem nat_cast_comp {n : ℕ} : (n : R[X]).comp p = n := by rw [← C_eq_nat_c
 
 --Porting note: new theorem
 @[simp]
-theorem ofNat_comp (n : ℕ) [n.AtLeastTwo] : (OfNat.ofNat n : R[X]).comp p = n :=
+theorem ofNat_comp (n : ℕ) [n.AtLeastTwo] : (no_index (OfNat.ofNat n) : R[X]).comp p = n :=
   nat_cast_comp
 
 @[simp]
@@ -763,7 +763,8 @@ protected theorem map_nat_cast (n : ℕ) : (n : R[X]).map f = n :=
 
 --Porting note: new theorem
 @[simp]
-protected theorem map_ofNat (n : ℕ) [n.AtLeastTwo] : (OfNat.ofNat n : R[X]).map f = OfNat.ofNat n :=
+protected theorem map_ofNat (n : ℕ) [n.AtLeastTwo] :
+    (no_index (OfNat.ofNat n) : R[X]).map f = OfNat.ofNat n :=
   show (n : R[X]).map f = n by rw [Polynomial.map_nat_cast]
 
 set_option linter.deprecated false in

@@ -1036,7 +1036,7 @@ theorem eval₂_comp {x : S} : eval₂ f x (p.comp q) = eval₂ f (eval₂ f x q
 
 @[simp]
 theorem iterate_comp_eval₂ (k : ℕ) (t : S) :
-    eval₂ f t ((p.comp^[k]) q) = ((fun x => eval₂ f x p)^[k]) (eval₂ f t q) := by
+    eval₂ f t (p.comp^[k] q) = (fun x => eval₂ f x p)^[k] (eval₂ f t q) := by
   induction' k with k IH
   · simp
   · rw [Function.iterate_succ_apply', Function.iterate_succ_apply', eval₂_comp, IH]
@@ -1084,7 +1084,7 @@ theorem eval_comp : (p.comp q).eval x = p.eval (q.eval x) := by
 
 @[simp]
 theorem iterate_comp_eval :
-    ∀ (k : ℕ) (t : R), ((p.comp^[k]) q).eval t = ((fun x => p.eval x)^[k]) (q.eval t) :=
+    ∀ (k : ℕ) (t : R), (p.comp^[k] q).eval t = (fun x => p.eval x)^[k] (q.eval t) :=
   iterate_comp_eval₂ _
 #align polynomial.iterate_comp_eval Polynomial.iterate_comp_eval
 

@@ -1082,6 +1082,12 @@ theorem eval_comp : (p.comp q).eval x = p.eval (q.eval x) := by
     simp
 #align polynomial.eval_comp Polynomial.eval_comp
 
+@[simp]
+theorem iterate_comp_eval :
+    ∀ (k : ℕ) (t : R), ((p.comp^[k]) q).eval t = ((fun x => p.eval x)^[k]) (q.eval t) :=
+  iterate_comp_eval₂ _
+#align polynomial.iterate_comp_eval Polynomial.iterate_comp_eval
+
 /-- `comp p`, regarded as a ring homomorphism from `R[X]` to itself. -/
 def compRingHom : R[X] → R[X] →+* R[X] :=
   eval₂RingHom C

• Run a non-interactive version of fix-comments.py on all files.
• Go through the diff and manually add/discard/edit chunks.

@@ -755,7 +755,7 @@ theorem coe_mapRingHom (f : R →+* S) : ⇑(mapRingHom f) = map f :=
   rfl
 #align polynomial.coe_map_ring_hom Polynomial.coe_mapRingHom
 
--- This is protected to not clash with the global `map_nat_cast`.
+-- This is protected to not clash with the global `map_natCast`.
 @[simp]
 protected theorem map_nat_cast (n : ℕ) : (n : R[X]).map f = n :=
   map_natCast (mapRingHom f) n

Now that leanprover/lean4#2210 has been merged, this PR:

• removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
• removes many but not quite all set_option maxHeartbeats commands
• makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -980,7 +980,6 @@ theorem eval_nat_cast_map (f : R →+* S) (p : R[X]) (n : ℕ) :
     simp only [map_natCast f, eval_monomial, map_monomial, f.map_pow, f.map_mul]
 #align polynomial.eval_nat_cast_map Polynomial.eval_nat_cast_map
 
-set_option synthInstance.etaExperiment true in
 @[simp]
 theorem eval_int_cast_map {R S : Type _} [Ring R] [Ring S] (f : R →+* S) (p : R[X]) (i : ℤ) :
     (p.map f).eval (i : S) = f (p.eval i) := by

We make sure that the canonical path from NonAssocSemiring to Ring passes through Semiring, as this is a path which is followed all the time in linear algebra where the defining semilinear map σ : R →+* S depends on the NonAssocSemiring structure of R and S while the module definition depends on the Semiring structure.

Tt is not currently possible to adjust priorities by hand (see lean4#2115). Instead, the last declared instance is used, so we make sure that Semiring is declared after NonAssocRing, so that Semiring -> NonAssocSemiring is tried before NonAssocRing -> NonAssocSemiring.

@@ -980,6 +980,7 @@ theorem eval_nat_cast_map (f : R →+* S) (p : R[X]) (n : ℕ) :
     simp only [map_natCast f, eval_monomial, map_monomial, f.map_pow, f.map_mul]
 #align polynomial.eval_nat_cast_map Polynomial.eval_nat_cast_map
 
+set_option synthInstance.etaExperiment true in
 @[simp]
 theorem eval_int_cast_map {R S : Type _} [Ring R] [Ring S] (f : R →+* S) (p : R[X]) (i : ℤ) :
     (p.map f).eval (i : S) = f (p.eval i) := by

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".

@@ -663,8 +663,8 @@ theorem comp_assoc {R : Type _} [CommSemiring R] (φ ψ χ : R[X]) :
 #align polynomial.comp_assoc Polynomial.comp_assoc
 
 theorem coeff_comp_degree_mul_degree (hqd0 : natDegree q ≠ 0) :
-    coeff (p.comp q) (natDegree p * natDegree q) = leadingCoeff p * leadingCoeff q ^ natDegree p :=
-  by
+    coeff (p.comp q) (natDegree p * natDegree q) =
+    leadingCoeff p * leadingCoeff q ^ natDegree p := by
   rw [comp, eval₂_def, coeff_sum]
   -- Porting note: `convert` → `refine`
   refine Eq.trans (Finset.sum_eq_single p.natDegree ?h₀ ?h₁) ?h₂

closes #3680, see https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Stepping.20through.20simp_rw/near/326712986

@@ -1181,7 +1181,7 @@ theorem support_map_subset [Semiring R] [Semiring S] (f : R →+* S) (p : R[X])
 
 theorem support_map_of_injective [Semiring R] [Semiring S] (p : R[X]) {f : R →+* S}
     (hf : Function.Injective f) : (map f p).support = p.support := by
-  simp_rw [Finset.ext_iff, mem_support_iff, coeff_map, ← map_zero f, hf.ne_iff, iff_self_iff,
+  simp_rw [Finset.ext_iff, mem_support_iff, coeff_map, ← map_zero f, hf.ne_iff,
     forall_const]
 #align polynomial.support_map_of_injective Polynomial.support_map_of_injective
 

This PR fixes two things:

• Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
• All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

@@ -502,7 +502,6 @@ theorem coeff_zero_eq_eval_zero (p : R[X]) : coeff p 0 = p.eval 0 :=
       rw [eval_eq_sum]
       exact
         Finset.sum_eq_single _ (fun b _ hb => by simp [zero_pow (Nat.pos_of_ne_zero hb)]) (by simp)
-
 #align polynomial.coeff_zero_eq_eval_zero Polynomial.coeff_zero_eq_eval_zero
 
 theorem zero_isRoot_of_coeff_zero_eq_zero {p : R[X]} (hp : p.coeff 0 = 0) : IsRoot p 0 := by

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

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

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

@@ -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.eval
-! leanprover-community/mathlib commit e064a7bf82ad94c3c17b5128bbd860d1ec34874e
+! leanprover-community/mathlib commit 728baa2f54e6062c5879a3e397ac6bac323e506f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1035,6 +1035,14 @@ theorem eval₂_comp {x : S} : eval₂ f x (p.comp q) = eval₂ f (eval₂ f x q
   rw [comp, p.as_sum_range]; simp [eval₂_finset_sum, eval₂_pow]
 #align polynomial.eval₂_comp Polynomial.eval₂_comp
 
+@[simp]
+theorem iterate_comp_eval₂ (k : ℕ) (t : S) :
+    eval₂ f t ((p.comp^[k]) q) = ((fun x => eval₂ f x p)^[k]) (eval₂ f t q) := by
+  induction' k with k IH
+  · simp
+  · rw [Function.iterate_succ_apply', Function.iterate_succ_apply', eval₂_comp, IH]
+#align polynomial.iterate_comp_eval₂ Polynomial.iterate_comp_eval₂
+
 end
 
 section

Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: int-y1 <jason_yuen2007@hotmail.com> Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -556,6 +556,11 @@ theorem C_comp : (C a).comp p = C a :=
 theorem nat_cast_comp {n : ℕ} : (n : R[X]).comp p = n := by rw [← C_eq_nat_cast, C_comp]
 #align polynomial.nat_cast_comp Polynomial.nat_cast_comp
 
+--Porting note: new theorem
+@[simp]
+theorem ofNat_comp (n : ℕ) [n.AtLeastTwo] : (OfNat.ofNat n : R[X]).comp p = n :=
+  nat_cast_comp
+
 @[simp]
 theorem comp_zero : p.comp (0 : R[X]) = C (p.eval 0) := by rw [← C_0, comp_C]
 #align polynomial.comp_zero Polynomial.comp_zero
@@ -757,6 +762,11 @@ protected theorem map_nat_cast (n : ℕ) : (n : R[X]).map f = n :=
   map_natCast (mapRingHom f) n
 #align polynomial.map_nat_cast Polynomial.map_nat_cast
 
+--Porting note: new theorem
+@[simp]
+protected theorem map_ofNat (n : ℕ) [n.AtLeastTwo] : (OfNat.ofNat n : R[X]).map f = OfNat.ofNat n :=
+  show (n : R[X]).map f = n by rw [Polynomial.map_nat_cast]
+
 set_option linter.deprecated false in
 @[simp]
 protected theorem map_bit0 : (bit0 p).map f = bit0 (p.map f) :=