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.Derivative
-import Data.Polynomial.RingDivision
+import Algebra.Polynomial.Derivative
+import Algebra.Polynomial.RingDivision
 import RingTheory.EuclideanDomain
 
 #align_import data.polynomial.field_division from "leanprover-community/mathlib"@"cb3ceec8485239a61ed51d944cb9a95b68c6bafc"

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

@@ -49,7 +49,7 @@ theorem derivative_rootMultiplicity_of_root [CharZero R] {p : R[X]} {t : R} (hpt
   set q := p /ₘ (X - C t) ^ (n + 1) with hq
   convert_to root_multiplicity t ((X - C t) ^ n * (derivative q * (X - C t) + q * C ↑(n + 1))) = n
   · congr
-    rw [mul_add, mul_left_comm <| (X - C t) ^ n, ← pow_succ']
+    rw [mul_add, mul_left_comm <| (X - C t) ^ n, ← pow_succ]
     congr 1
     rw [mul_left_comm <| (X - C t) ^ n, mul_comm <| (X - C t) ^ n]
   have h : (derivative q * (X - C t) + q * C ↑(n + 1)).eval t ≠ 0 :=
@@ -496,7 +496,7 @@ theorem exists_root_of_degree_eq_one (h : degree p = 1) : ∃ x, IsRoot p x :=
       rw [← nat_degree_eq_of_degree_eq_some h] <;>
         exact mt leading_coeff_eq_zero.1 fun h0 => by simpa [h0] using h
     conv in p => rw [eq_X_add_C_of_degree_le_one (show degree p ≤ 1 by rw [h] <;> exact le_rfl)] <;>
-      simp [is_root, mul_div_cancel' _ this]⟩
+      simp [is_root, mul_div_cancel₀ _ this]⟩
 #align polynomial.exists_root_of_degree_eq_one Polynomial.exists_root_of_degree_eq_one
 -/
 

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

@@ -137,7 +137,7 @@ variable [DivisionRing R] {p q : R[X]}
 #print Polynomial.degree_pos_of_ne_zero_of_nonunit /-
 theorem degree_pos_of_ne_zero_of_nonunit (hp0 : p ≠ 0) (hp : ¬IsUnit p) : 0 < degree p :=
   lt_of_not_ge fun h => by
-    rw [eq_C_of_degree_le_zero h] at hp0 hp 
+    rw [eq_C_of_degree_le_zero h] at hp0 hp
     exact hp (IsUnit.map C (IsUnit.mk0 (coeff p 0) (mt C_inj.2 (by simpa using hp0))))
 #align polynomial.degree_pos_of_ne_zero_of_nonunit Polynomial.degree_pos_of_ne_zero_of_nonunit
 -/
@@ -182,7 +182,7 @@ theorem isUnit_iff_degree_eq_zero : IsUnit p ↔ degree p = 0 :=
   ⟨degree_eq_zero_of_isUnit, fun h =>
     have : degree p ≤ 0 := by simp [*, le_refl]
     have hc : coeff p 0 ≠ 0 := fun hc => by
-      rw [eq_C_of_degree_le_zero this, hc] at h  <;> simpa using h
+      rw [eq_C_of_degree_le_zero this, hc] at h <;> simpa using h
     isUnit_iff_dvd_one.2
       ⟨C (coeff p 0)⁻¹, by
         conv in p => rw [eq_C_of_degree_le_zero this]
@@ -288,7 +288,7 @@ theorem mod_eq_self_iff (hq0 : q ≠ 0) : p % q = p ↔ degree p < degree q :=
 theorem div_eq_zero_iff (hq0 : q ≠ 0) : p / q = 0 ↔ degree p < degree q :=
   ⟨fun h => by
     have := EuclideanDomain.div_add_mod p q <;>
-      rwa [h, MulZeroClass.mul_zero, zero_add, mod_eq_self_iff hq0] at this ,
+      rwa [h, MulZeroClass.mul_zero, zero_add, mod_eq_self_iff hq0] at this,
     fun h =>
     by
     have hlt : degree p < degree (q * C (leadingCoeff q)⁻¹) := by
@@ -517,7 +517,7 @@ theorem coeff_inv_units (u : R[X]ˣ) (n : ℕ) : ((↑u : R[X]).coeff n)⁻¹ =
 #print Polynomial.monic_normalize /-
 theorem monic_normalize (hp0 : p ≠ 0) : Monic (normalize p) :=
   by
-  rw [Ne.def, ← leading_coeff_eq_zero, ← Ne.def, ← isUnit_iff_ne_zero] at hp0 
+  rw [Ne.def, ← leading_coeff_eq_zero, ← Ne.def, ← isUnit_iff_ne_zero] at hp0
   rw [monic, leading_coeff_normalize, normalize_eq_one]
   apply hp0
 #align polynomial.monic_normalize Polynomial.monic_normalize
@@ -643,9 +643,9 @@ theorem isCoprime_of_is_root_of_eval_derivative_ne_zero {K : Type _} [Field K] (
     exact monic_X_sub_C a
   replace key := congr_arg derivative key
   simp only [derivative_X, derivative_mul, one_mul, sub_zero, derivative_sub,
-    mod_by_monic_X_sub_C_eq_C_eval, derivative_C] at key 
+    mod_by_monic_X_sub_C_eq_C_eval, derivative_C] at key
   have : X - C a ∣ derivative f := key ▸ dvd_add h (dvd_mul_right _ _)
-  rw [← dvd_iff_mod_by_monic_eq_zero (monic_X_sub_C _), mod_by_monic_X_sub_C_eq_C_eval] at this 
+  rw [← dvd_iff_mod_by_monic_eq_zero (monic_X_sub_C _), mod_by_monic_X_sub_C_eq_C_eval] at this
   rw [← C_inj, this, C_0]
 #align polynomial.is_coprime_of_is_root_of_eval_derivative_ne_zero Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zero
 -/

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

@@ -3,9 +3,9 @@ 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.Derivative
-import Mathbin.Data.Polynomial.RingDivision
-import Mathbin.RingTheory.EuclideanDomain
+import Data.Polynomial.Derivative
+import Data.Polynomial.RingDivision
+import RingTheory.EuclideanDomain
 
 #align_import data.polynomial.field_division from "leanprover-community/mathlib"@"cb3ceec8485239a61ed51d944cb9a95b68c6bafc"
 

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

@@ -86,7 +86,7 @@ instance : NormalizationMonoid R[X]
     ⟨C ↑(normUnit p.leadingCoeff), C ↑(normUnit p.leadingCoeff)⁻¹, by
       rw [← RingHom.map_mul, Units.mul_inv, C_1], by rw [← RingHom.map_mul, Units.inv_mul, C_1]⟩
   normUnit_zero := Units.ext (by simp)
-  normUnit_mul p q hp0 hq0 :=
+  normUnit_hMul p q hp0 hq0 :=
     Units.ext
       (by
         dsimp
@@ -268,7 +268,7 @@ instance : EuclideanDomain R[X] :=
     remainder := (· % ·)
     R := _
     r_wellFounded := degree_lt_wf
-    quotient_mul_add_remainder_eq := quotient_mul_add_remainder_eq_aux
+    quotient_mul_add_remainder_eq := quotient_hMul_add_remainder_eq_aux
     remainder_lt := fun p q hq => remainder_lt_aux _ hq
     mul_left_not_lt := fun p q hq => not_lt_of_ge (degree_le_mul_left _ hq) }
 

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

@@ -2,16 +2,13 @@
 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.field_division
-! leanprover-community/mathlib commit cb3ceec8485239a61ed51d944cb9a95b68c6bafc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Polynomial.Derivative
 import Mathbin.Data.Polynomial.RingDivision
 import Mathbin.RingTheory.EuclideanDomain
 
+#align_import data.polynomial.field_division from "leanprover-community/mathlib"@"cb3ceec8485239a61ed51d944cb9a95b68c6bafc"
+
 /-!
 # Theory of univariate polynomials
 

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

@@ -37,6 +37,7 @@ section IsDomain
 
 variable [CommRing R] [IsDomain R]
 
+#print Polynomial.derivative_rootMultiplicity_of_root /-
 theorem derivative_rootMultiplicity_of_root [CharZero R] {p : R[X]} {t : R} (hpt : p.IsRoot t) :
     p.derivative.rootMultiplicity t = p.rootMultiplicity t - 1 :=
   by
@@ -65,7 +66,9 @@ theorem derivative_rootMultiplicity_of_root [CharZero R] {p : R[X]} {t : R} (hpt
   contrapose! h
   rw [h, eval_zero]
 #align polynomial.derivative_root_multiplicity_of_root Polynomial.derivative_rootMultiplicity_of_root
+-/
 
+#print Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicity /-
 theorem rootMultiplicity_sub_one_le_derivative_rootMultiplicity [CharZero R] (p : R[X]) (t : R) :
     p.rootMultiplicity t - 1 ≤ p.derivative.rootMultiplicity t :=
   by
@@ -74,6 +77,7 @@ theorem rootMultiplicity_sub_one_le_derivative_rootMultiplicity [CharZero R] (p
   · rw [root_multiplicity_eq_zero h, zero_tsub]
     exact zero_le _
 #align polynomial.root_multiplicity_sub_one_le_derivative_root_multiplicity Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicity
+-/
 
 section NormalizationMonoid
 
@@ -99,23 +103,31 @@ instance : NormalizationMonoid R[X]
         rcases Polynomial.isUnit_iff.1 ⟨u, rfl⟩ with ⟨_, ⟨w, rfl⟩, h2⟩
         rw [← h2, leading_coeff_C, norm_unit_coe_units, ← C_mul, Units.mul_inv, C_1])
 
+#print Polynomial.coe_normUnit /-
 @[simp]
 theorem coe_normUnit {p : R[X]} : (normUnit p : R[X]) = C ↑(normUnit p.leadingCoeff) := by
   simp [norm_unit]
 #align polynomial.coe_norm_unit Polynomial.coe_normUnit
+-/
 
+#print Polynomial.leadingCoeff_normalize /-
 theorem leadingCoeff_normalize (p : R[X]) :
     leadingCoeff (normalize p) = normalize (leadingCoeff p) := by simp
 #align polynomial.leading_coeff_normalize Polynomial.leadingCoeff_normalize
+-/
 
+#print Polynomial.Monic.normalize_eq_self /-
 theorem Monic.normalize_eq_self {p : R[X]} (hp : p.Monic) : normalize p = p := by
   simp only [Polynomial.coe_normUnit, normalize_apply, hp.leading_coeff, normUnit_one,
     Units.val_one, polynomial.C.map_one, mul_one]
 #align polynomial.monic.normalize_eq_self Polynomial.Monic.normalize_eq_self
+-/
 
+#print Polynomial.roots_normalize /-
 theorem roots_normalize {p : R[X]} : (normalize p).roots = p.roots := by
   rw [normalize_apply, mul_comm, coe_norm_unit, roots_C_mul _ (norm_unit (leading_coeff p)).NeZero]
 #align polynomial.roots_normalize Polynomial.roots_normalize
+-/
 
 end NormalizationMonoid
 
@@ -125,23 +137,29 @@ section DivisionRing
 
 variable [DivisionRing R] {p q : R[X]}
 
+#print Polynomial.degree_pos_of_ne_zero_of_nonunit /-
 theorem degree_pos_of_ne_zero_of_nonunit (hp0 : p ≠ 0) (hp : ¬IsUnit p) : 0 < degree p :=
   lt_of_not_ge fun h => by
     rw [eq_C_of_degree_le_zero h] at hp0 hp 
     exact hp (IsUnit.map C (IsUnit.mk0 (coeff p 0) (mt C_inj.2 (by simpa using hp0))))
 #align polynomial.degree_pos_of_ne_zero_of_nonunit Polynomial.degree_pos_of_ne_zero_of_nonunit
+-/
 
+#print Polynomial.monic_mul_leadingCoeff_inv /-
 theorem monic_mul_leadingCoeff_inv (h : p ≠ 0) : Monic (p * C (leadingCoeff p)⁻¹) := by
   rw [monic, leading_coeff_mul, leading_coeff_C,
     mul_inv_cancel (show leading_coeff p ≠ 0 from mt leading_coeff_eq_zero.1 h)]
 #align polynomial.monic_mul_leading_coeff_inv Polynomial.monic_mul_leadingCoeff_inv
+-/
 
+#print Polynomial.degree_mul_leadingCoeff_inv /-
 theorem degree_mul_leadingCoeff_inv (p : R[X]) (h : q ≠ 0) :
     degree (p * C (leadingCoeff q)⁻¹) = degree p :=
   by
   have h₁ : (leadingCoeff q)⁻¹ ≠ 0 := inv_ne_zero (mt leadingCoeff_eq_zero.1 h)
   rw [degree_mul, degree_C h₁, add_zero]
 #align polynomial.degree_mul_leading_coeff_inv Polynomial.degree_mul_leadingCoeff_inv
+-/
 
 #print Polynomial.map_eq_zero /-
 @[simp]
@@ -162,6 +180,7 @@ section Field
 
 variable [Field R] {p q : R[X]}
 
+#print Polynomial.isUnit_iff_degree_eq_zero /-
 theorem isUnit_iff_degree_eq_zero : IsUnit p ↔ degree p = 0 :=
   ⟨degree_eq_zero_of_isUnit, fun h =>
     have : degree p ≤ 0 := by simp [*, le_refl]
@@ -172,6 +191,7 @@ theorem isUnit_iff_degree_eq_zero : IsUnit p ↔ degree p = 0 :=
         conv in p => rw [eq_C_of_degree_le_zero this]
         rw [← C_mul, _root_.mul_inv_cancel hc, C_1]⟩⟩
 #align polynomial.is_unit_iff_degree_eq_zero Polynomial.isUnit_iff_degree_eq_zero
+-/
 
 #print Polynomial.div /-
 /-- Division of polynomials. See `polynomial.div_by_monic` for more details.-/
@@ -206,13 +226,17 @@ instance : Div R[X] :=
 instance : Mod R[X] :=
   ⟨mod⟩
 
+#print Polynomial.div_def /-
 theorem div_def : p / q = C (leadingCoeff q)⁻¹ * (p /ₘ (q * C (leadingCoeff q)⁻¹)) :=
   rfl
 #align polynomial.div_def Polynomial.div_def
+-/
 
+#print Polynomial.mod_def /-
 theorem mod_def : p % q = p %ₘ (q * C (leadingCoeff q)⁻¹) :=
   rfl
 #align polynomial.mod_def Polynomial.mod_def
+-/
 
 #print Polynomial.modByMonic_eq_mod /-
 theorem modByMonic_eq_mod (p : R[X]) (hq : Monic q) : p %ₘ q = p % q :=
@@ -227,13 +251,17 @@ theorem divByMonic_eq_div (p : R[X]) (hq : Monic q) : p /ₘ q = p / q :=
 #align polynomial.div_by_monic_eq_div Polynomial.divByMonic_eq_div
 -/
 
+#print Polynomial.mod_X_sub_C_eq_C_eval /-
 theorem mod_X_sub_C_eq_C_eval (p : R[X]) (a : R) : p % (X - C a) = C (p.eval a) :=
   modByMonic_eq_mod p (monic_X_sub_C a) ▸ modByMonic_X_sub_C_eq_C_eval _ _
 #align polynomial.mod_X_sub_C_eq_C_eval Polynomial.mod_X_sub_C_eq_C_eval
+-/
 
+#print Polynomial.mul_div_eq_iff_isRoot /-
 theorem mul_div_eq_iff_isRoot : (X - C a) * (p / (X - C a)) = p ↔ IsRoot p a :=
   divByMonic_eq_div p (monic_X_sub_C a) ▸ mul_divByMonic_eq_iff_isRoot
 #align polynomial.mul_div_eq_iff_is_root Polynomial.mul_div_eq_iff_isRoot
+-/
 
 instance : EuclideanDomain R[X] :=
   { Polynomial.commRing,
@@ -319,11 +347,13 @@ theorem natDegree_map [DivisionRing k] (f : R →+* k) : natDegree (p.map f) = n
 #align polynomial.nat_degree_map Polynomial.natDegree_map
 -/
 
+#print Polynomial.leadingCoeff_map /-
 @[simp]
 theorem leadingCoeff_map [DivisionRing k] (f : R →+* k) :
     leadingCoeff (p.map f) = f (leadingCoeff p) := by
   simp only [← coeff_nat_degree, coeff_map f, nat_degree_map]
 #align polynomial.leading_coeff_map Polynomial.leadingCoeff_map
+-/
 
 #print Polynomial.monic_map_iff /-
 theorem monic_map_iff [DivisionRing k] {f : R →+* k} {p : R[X]} : (p.map f).Monic ↔ p.Monic := by
@@ -331,9 +361,11 @@ theorem monic_map_iff [DivisionRing k] {f : R →+* k} {p : R[X]} : (p.map f).Mo
 #align polynomial.monic_map_iff Polynomial.monic_map_iff
 -/
 
+#print Polynomial.isUnit_map /-
 theorem isUnit_map [Field k] (f : R →+* k) : IsUnit (p.map f) ↔ IsUnit p := by
   simp_rw [is_unit_iff_degree_eq_zero, degree_map]
 #align polynomial.is_unit_map Polynomial.isUnit_map
+-/
 
 #print Polynomial.map_div /-
 theorem map_div [Field k] (f : R →+* k) : (p / q).map f = p.map f / q.map f :=
@@ -358,47 +390,61 @@ section
 
 open EuclideanDomain
 
+#print Polynomial.gcd_map /-
 theorem gcd_map [Field k] (f : R →+* k) : gcd (p.map f) (q.map f) = (gcd p q).map f :=
   GCD.induction p q (fun x => by simp_rw [Polynomial.map_zero, EuclideanDomain.gcd_zero_left])
     fun x y hx ih => by rw [gcd_val, ← map_mod, ih, ← gcd_val]
 #align polynomial.gcd_map Polynomial.gcd_map
+-/
 
 end
 
+#print Polynomial.eval₂_gcd_eq_zero /-
 theorem eval₂_gcd_eq_zero [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α : k} (hf : f.eval₂ ϕ α = 0)
     (hg : g.eval₂ ϕ α = 0) : (EuclideanDomain.gcd f g).eval₂ ϕ α = 0 := by
   rw [EuclideanDomain.gcd_eq_gcd_ab f g, Polynomial.eval₂_add, Polynomial.eval₂_mul,
     Polynomial.eval₂_mul, hf, hg, MulZeroClass.zero_mul, MulZeroClass.zero_mul, zero_add]
 #align polynomial.eval₂_gcd_eq_zero Polynomial.eval₂_gcd_eq_zero
+-/
 
+#print Polynomial.eval_gcd_eq_zero /-
 theorem eval_gcd_eq_zero {f g : R[X]} {α : R} (hf : f.eval α = 0) (hg : g.eval α = 0) :
     (EuclideanDomain.gcd f g).eval α = 0 :=
   eval₂_gcd_eq_zero hf hg
 #align polynomial.eval_gcd_eq_zero Polynomial.eval_gcd_eq_zero
+-/
 
+#print Polynomial.root_left_of_root_gcd /-
 theorem root_left_of_root_gcd [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α : k}
     (hα : (EuclideanDomain.gcd f g).eval₂ ϕ α = 0) : f.eval₂ ϕ α = 0 :=
   by
   cases' EuclideanDomain.gcd_dvd_left f g with p hp
   rw [hp, Polynomial.eval₂_mul, hα, MulZeroClass.zero_mul]
 #align polynomial.root_left_of_root_gcd Polynomial.root_left_of_root_gcd
+-/
 
+#print Polynomial.root_right_of_root_gcd /-
 theorem root_right_of_root_gcd [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α : k}
     (hα : (EuclideanDomain.gcd f g).eval₂ ϕ α = 0) : g.eval₂ ϕ α = 0 :=
   by
   cases' EuclideanDomain.gcd_dvd_right f g with p hp
   rw [hp, Polynomial.eval₂_mul, hα, MulZeroClass.zero_mul]
 #align polynomial.root_right_of_root_gcd Polynomial.root_right_of_root_gcd
+-/
 
+#print Polynomial.root_gcd_iff_root_left_right /-
 theorem root_gcd_iff_root_left_right [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α : k} :
     (EuclideanDomain.gcd f g).eval₂ ϕ α = 0 ↔ f.eval₂ ϕ α = 0 ∧ g.eval₂ ϕ α = 0 :=
   ⟨fun h => ⟨root_left_of_root_gcd h, root_right_of_root_gcd h⟩, fun h => eval₂_gcd_eq_zero h.1 h.2⟩
 #align polynomial.root_gcd_iff_root_left_right Polynomial.root_gcd_iff_root_left_right
+-/
 
+#print Polynomial.isRoot_gcd_iff_isRoot_left_right /-
 theorem isRoot_gcd_iff_isRoot_left_right {f g : R[X]} {α : R} :
     (EuclideanDomain.gcd f g).IsRoot α ↔ f.IsRoot α ∧ g.IsRoot α :=
   root_gcd_iff_root_left_right
 #align polynomial.is_root_gcd_iff_is_root_left_right Polynomial.isRoot_gcd_iff_isRoot_left_right
+-/
 
 #print Polynomial.isCoprime_map /-
 theorem isCoprime_map [Field k] (f : R →+* k) : IsCoprime (p.map f) (q.map f) ↔ IsCoprime p q := by
@@ -406,27 +452,36 @@ theorem isCoprime_map [Field k] (f : R →+* k) : IsCoprime (p.map f) (q.map f)
 #align polynomial.is_coprime_map Polynomial.isCoprime_map
 -/
 
+#print Polynomial.mem_roots_map /-
 theorem mem_roots_map [CommRing k] [IsDomain k] {f : R →+* k} {x : k} (hp : p ≠ 0) :
     x ∈ (p.map f).roots ↔ p.eval₂ f x = 0 := by
   rw [mem_roots (map_ne_zero hp), is_root, Polynomial.eval_map] <;> infer_instance
 #align polynomial.mem_roots_map Polynomial.mem_roots_map
+-/
 
+#print Polynomial.rootSet_monomial /-
 theorem rootSet_monomial [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n ≠ 0) {a : R}
     (ha : a ≠ 0) : (monomial n a).rootSet S = {0} := by
   rw [root_set, map_monomial, roots_monomial ((_root_.map_ne_zero (algebraMap R S)).2 ha),
     Multiset.toFinset_nsmul _ _ hn, Multiset.toFinset_singleton, Finset.coe_singleton]
 #align polynomial.root_set_monomial Polynomial.rootSet_monomial
+-/
 
+#print Polynomial.rootSet_C_mul_X_pow /-
 theorem rootSet_C_mul_X_pow [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n ≠ 0) {a : R}
     (ha : a ≠ 0) : (C a * X ^ n).rootSet S = {0} := by
   rw [C_mul_X_pow_eq_monomial, root_set_monomial hn ha]
 #align polynomial.root_set_C_mul_X_pow Polynomial.rootSet_C_mul_X_pow
+-/
 
+#print Polynomial.rootSet_X_pow /-
 theorem rootSet_X_pow [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n ≠ 0) :
     (X ^ n : R[X]).rootSet S = {0} := by
   rw [← one_mul (X ^ n : R[X]), ← C_1, root_set_C_mul_X_pow hn]; exact one_ne_zero
 #align polynomial.root_set_X_pow Polynomial.rootSet_X_pow
+-/
 
+#print Polynomial.rootSet_prod /-
 theorem rootSet_prod [CommRing S] [IsDomain S] [Algebra R S] {ι : Type _} (f : ι → R[X])
     (s : Finset ι) (h : s.Prod f ≠ 0) : (s.Prod f).rootSet S = ⋃ i ∈ s, (f i).rootSet S :=
   by
@@ -434,6 +489,7 @@ theorem rootSet_prod [CommRing S] [IsDomain S] [Algebra R S] {ι : Type _} (f :
   rw [Polynomial.map_prod, roots_prod, Finset.bind_toFinset, s.val_to_finset, Finset.coe_biUnion]
   rwa [← Polynomial.map_prod, Ne, map_eq_zero]
 #align polynomial.root_set_prod Polynomial.rootSet_prod
+-/
 
 #print Polynomial.exists_root_of_degree_eq_one /-
 theorem exists_root_of_degree_eq_one (h : degree p = 1) : ∃ x, IsRoot p x :=
@@ -447,6 +503,7 @@ theorem exists_root_of_degree_eq_one (h : degree p = 1) : ∃ x, IsRoot p x :=
 #align polynomial.exists_root_of_degree_eq_one Polynomial.exists_root_of_degree_eq_one
 -/
 
+#print Polynomial.coeff_inv_units /-
 theorem coeff_inv_units (u : R[X]ˣ) (n : ℕ) : ((↑u : R[X]).coeff n)⁻¹ = (↑u⁻¹ : R[X]).coeff n :=
   by
   rw [eq_C_of_degree_eq_zero (degree_coe_units u), eq_C_of_degree_eq_zero (degree_coe_units u⁻¹),
@@ -458,14 +515,18 @@ theorem coeff_inv_units (u : R[X]ˣ) (n : ℕ) : ((↑u : R[X]).coeff n)⁻¹ =
       simp
   · simp
 #align polynomial.coeff_inv_units Polynomial.coeff_inv_units
+-/
 
+#print Polynomial.monic_normalize /-
 theorem monic_normalize (hp0 : p ≠ 0) : Monic (normalize p) :=
   by
   rw [Ne.def, ← leading_coeff_eq_zero, ← Ne.def, ← isUnit_iff_ne_zero] at hp0 
   rw [monic, leading_coeff_normalize, normalize_eq_one]
   apply hp0
 #align polynomial.monic_normalize Polynomial.monic_normalize
+-/
 
+#print Polynomial.leadingCoeff_div /-
 theorem leadingCoeff_div (hpq : q.degree ≤ p.degree) :
     (p / q).leadingCoeff = p.leadingCoeff / q.leadingCoeff :=
   by
@@ -475,7 +536,9 @@ theorem leadingCoeff_div (hpq : q.degree ≤ p.degree) :
     div_eq_mul_inv]
   rwa [degree_mul_leading_coeff_inv q hq]
 #align polynomial.leading_coeff_div Polynomial.leadingCoeff_div
+-/
 
+#print Polynomial.div_C_mul /-
 theorem div_C_mul : p / (C a * q) = C a⁻¹ * (p / q) :=
   by
   by_cases ha : a = 0
@@ -484,14 +547,18 @@ theorem div_C_mul : p / (C a * q) = C a⁻¹ * (p / q) :=
   congr 3
   rw [mul_left_comm q, ← mul_assoc, ← C.map_mul, mul_inv_cancel ha, C.map_one, one_mul]
 #align polynomial.div_C_mul Polynomial.div_C_mul
+-/
 
+#print Polynomial.C_mul_dvd /-
 theorem C_mul_dvd (ha : a ≠ 0) : C a * p ∣ q ↔ p ∣ q :=
   ⟨fun h => dvd_trans (dvd_mul_left _ _) h, fun ⟨r, hr⟩ =>
     ⟨C a⁻¹ * r, by
       rw [mul_assoc, mul_left_comm p, ← mul_assoc, ← C.map_mul, _root_.mul_inv_cancel ha, C.map_one,
         one_mul, hr]⟩⟩
 #align polynomial.C_mul_dvd Polynomial.C_mul_dvd
+-/
 
+#print Polynomial.dvd_C_mul /-
 theorem dvd_C_mul (ha : a ≠ 0) : p ∣ Polynomial.C a * q ↔ p ∣ q :=
   ⟨fun ⟨r, hr⟩ =>
     ⟨C a⁻¹ * r, by
@@ -499,15 +566,20 @@ theorem dvd_C_mul (ha : a ≠ 0) : p ∣ Polynomial.C a * q ↔ p ∣ q :=
         one_mul]⟩,
     fun h => dvd_trans h (dvd_mul_left _ _)⟩
 #align polynomial.dvd_C_mul Polynomial.dvd_C_mul
+-/
 
+#print Polynomial.coe_normUnit_of_ne_zero /-
 theorem coe_normUnit_of_ne_zero (hp : p ≠ 0) : (normUnit p : R[X]) = C p.leadingCoeff⁻¹ :=
   by
   have : p.leadingCoeff ≠ 0 := mt leadingCoeff_eq_zero.mp hp
   simp [CommGroupWithZero.coe_normUnit _ this]
 #align polynomial.coe_norm_unit_of_ne_zero Polynomial.coe_normUnit_of_ne_zero
+-/
 
+#print Polynomial.normalize_monic /-
 theorem normalize_monic (h : Monic p) : normalize p = p := by simp [h]
 #align polynomial.normalize_monic Polynomial.normalize_monic
+-/
 
 #print Polynomial.map_dvd_map' /-
 theorem map_dvd_map' [Field k] (f : R →+* k) {x y : R[X]} : x.map f ∣ y.map f ↔ x ∣ y :=
@@ -520,8 +592,10 @@ theorem map_dvd_map' [Field k] (f : R →+* k) {x y : R[X]} : x.map f ∣ y.map
 #align polynomial.map_dvd_map' Polynomial.map_dvd_map'
 -/
 
+#print Polynomial.degree_normalize /-
 theorem degree_normalize : degree (normalize p) = degree p := by simp
 #align polynomial.degree_normalize Polynomial.degree_normalize
+-/
 
 #print Polynomial.prime_of_degree_eq_one /-
 theorem prime_of_degree_eq_one (hp1 : degree p = 1) : Prime p :=
@@ -532,21 +606,28 @@ theorem prime_of_degree_eq_one (hp1 : degree p = 1) : Prime p :=
 #align polynomial.prime_of_degree_eq_one Polynomial.prime_of_degree_eq_one
 -/
 
+#print Polynomial.irreducible_of_degree_eq_one /-
 theorem irreducible_of_degree_eq_one (hp1 : degree p = 1) : Irreducible p :=
   (prime_of_degree_eq_one hp1).Irreducible
 #align polynomial.irreducible_of_degree_eq_one Polynomial.irreducible_of_degree_eq_one
+-/
 
+#print Polynomial.not_irreducible_C /-
 theorem not_irreducible_C (x : R) : ¬Irreducible (C x) :=
   if H : x = 0 then by rw [H, C_0]; exact not_irreducible_zero
   else fun hx => Irreducible.not_unit hx <| isUnit_C.2 <| isUnit_iff_ne_zero.2 H
 #align polynomial.not_irreducible_C Polynomial.not_irreducible_C
+-/
 
+#print Polynomial.degree_pos_of_irreducible /-
 theorem degree_pos_of_irreducible (hp : Irreducible p) : 0 < p.degree :=
   lt_of_not_ge fun hp0 =>
     have := eq_C_of_degree_le_zero hp0
     not_irreducible_C (p.coeff 0) <| this ▸ hp
 #align polynomial.degree_pos_of_irreducible Polynomial.degree_pos_of_irreducible
+-/
 
+#print Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zero /-
 /-- If `f` is a polynomial over a field, and `a : K` satisfies `f' a ≠ 0`,
 then `f / (X - a)` is coprime with `X - a`.
 Note that we do not assume `f a = 0`, because `f / (X - a) = (f - f a) / (X - a)`. -/
@@ -570,6 +651,7 @@ theorem isCoprime_of_is_root_of_eval_derivative_ne_zero {K : Type _} [Field K] (
   rw [← dvd_iff_mod_by_monic_eq_zero (monic_X_sub_C _), mod_by_monic_X_sub_C_eq_C_eval] at this 
   rw [← C_inj, this, C_0]
 #align polynomial.is_coprime_of_is_root_of_eval_derivative_ne_zero Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zero
+-/
 
 end Field
 

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

@@ -281,7 +281,6 @@ theorem degree_add_div (hq0 : q ≠ 0) (hpq : degree q ≤ degree p) :
     calc
       degree (p % q) < degree q := EuclideanDomain.mod_lt _ hq0
       _ ≤ _ := degree_le_mul_left _ (mt (div_eq_zero_iff hq0).1 (not_lt_of_ge hpq))
-      
   conv_rhs =>
     rw [← EuclideanDomain.div_add_mod p q, degree_add_eq_left_of_degree_lt this, degree_mul]
 #align polynomial.degree_add_div Polynomial.degree_add_div

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

@@ -127,7 +127,7 @@ variable [DivisionRing R] {p q : R[X]}
 
 theorem degree_pos_of_ne_zero_of_nonunit (hp0 : p ≠ 0) (hp : ¬IsUnit p) : 0 < degree p :=
   lt_of_not_ge fun h => by
-    rw [eq_C_of_degree_le_zero h] at hp0 hp
+    rw [eq_C_of_degree_le_zero h] at hp0 hp 
     exact hp (IsUnit.map C (IsUnit.mk0 (coeff p 0) (mt C_inj.2 (by simpa using hp0))))
 #align polynomial.degree_pos_of_ne_zero_of_nonunit Polynomial.degree_pos_of_ne_zero_of_nonunit
 
@@ -166,7 +166,7 @@ theorem isUnit_iff_degree_eq_zero : IsUnit p ↔ degree p = 0 :=
   ⟨degree_eq_zero_of_isUnit, fun h =>
     have : degree p ≤ 0 := by simp [*, le_refl]
     have hc : coeff p 0 ≠ 0 := fun hc => by
-      rw [eq_C_of_degree_le_zero this, hc] at h <;> simpa using h
+      rw [eq_C_of_degree_le_zero this, hc] at h  <;> simpa using h
     isUnit_iff_dvd_one.2
       ⟨C (coeff p 0)⁻¹, by
         conv in p => rw [eq_C_of_degree_le_zero this]
@@ -263,7 +263,7 @@ theorem mod_eq_self_iff (hq0 : q ≠ 0) : p % q = p ↔ degree p < degree q :=
 theorem div_eq_zero_iff (hq0 : q ≠ 0) : p / q = 0 ↔ degree p < degree q :=
   ⟨fun h => by
     have := EuclideanDomain.div_add_mod p q <;>
-      rwa [h, MulZeroClass.mul_zero, zero_add, mod_eq_self_iff hq0] at this,
+      rwa [h, MulZeroClass.mul_zero, zero_add, mod_eq_self_iff hq0] at this ,
     fun h =>
     by
     have hlt : degree p < degree (q * C (leadingCoeff q)⁻¹) := by
@@ -462,7 +462,7 @@ theorem coeff_inv_units (u : R[X]ˣ) (n : ℕ) : ((↑u : R[X]).coeff n)⁻¹ =
 
 theorem monic_normalize (hp0 : p ≠ 0) : Monic (normalize p) :=
   by
-  rw [Ne.def, ← leading_coeff_eq_zero, ← Ne.def, ← isUnit_iff_ne_zero] at hp0
+  rw [Ne.def, ← leading_coeff_eq_zero, ← Ne.def, ← isUnit_iff_ne_zero] at hp0 
   rw [monic, leading_coeff_normalize, normalize_eq_one]
   apply hp0
 #align polynomial.monic_normalize Polynomial.monic_normalize
@@ -566,9 +566,9 @@ theorem isCoprime_of_is_root_of_eval_derivative_ne_zero {K : Type _} [Field K] (
     exact monic_X_sub_C a
   replace key := congr_arg derivative key
   simp only [derivative_X, derivative_mul, one_mul, sub_zero, derivative_sub,
-    mod_by_monic_X_sub_C_eq_C_eval, derivative_C] at key
+    mod_by_monic_X_sub_C_eq_C_eval, derivative_C] at key 
   have : X - C a ∣ derivative f := key ▸ dvd_add h (dvd_mul_right _ _)
-  rw [← dvd_iff_mod_by_monic_eq_zero (monic_X_sub_C _), mod_by_monic_X_sub_C_eq_C_eval] at this
+  rw [← dvd_iff_mod_by_monic_eq_zero (monic_X_sub_C _), mod_by_monic_X_sub_C_eq_C_eval] at this 
   rw [← C_inj, this, C_0]
 #align polynomial.is_coprime_of_is_root_of_eval_derivative_ne_zero Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zero
 

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

@@ -25,7 +25,7 @@ This file starts looking like the ring theory of $ R[X] $
 
 noncomputable section
 
-open Classical BigOperators Polynomial
+open scoped Classical BigOperators Polynomial
 
 namespace Polynomial
 
@@ -247,6 +247,7 @@ instance : EuclideanDomain R[X] :=
     remainder_lt := fun p q hq => remainder_lt_aux _ hq
     mul_left_not_lt := fun p q hq => not_lt_of_ge (degree_le_mul_left _ hq) }
 
+#print Polynomial.mod_eq_self_iff /-
 theorem mod_eq_self_iff (hq0 : q ≠ 0) : p % q = p ↔ degree p < degree q :=
   ⟨fun h => h ▸ EuclideanDomain.mod_lt _ hq0, fun h =>
     by
@@ -256,7 +257,9 @@ theorem mod_eq_self_iff (hq0 : q ≠ 0) : p % q = p ↔ degree p < degree q :=
     unfold div_mod_by_monic_aux
     simp only [this, false_and_iff, if_false]⟩
 #align polynomial.mod_eq_self_iff Polynomial.mod_eq_self_iff
+-/
 
+#print Polynomial.div_eq_zero_iff /-
 theorem div_eq_zero_iff (hq0 : q ≠ 0) : p / q = 0 ↔ degree p < degree q :=
   ⟨fun h => by
     have := EuclideanDomain.div_add_mod p q <;>
@@ -268,7 +271,9 @@ theorem div_eq_zero_iff (hq0 : q ≠ 0) : p / q = 0 ↔ degree p < degree q :=
     have hm : Monic (q * C (leadingCoeff q)⁻¹) := monic_mul_leadingCoeff_inv hq0
     rw [div_def, (div_by_monic_eq_zero_iff hm).2 hlt, MulZeroClass.mul_zero]⟩
 #align polynomial.div_eq_zero_iff Polynomial.div_eq_zero_iff
+-/
 
+#print Polynomial.degree_add_div /-
 theorem degree_add_div (hq0 : q ≠ 0) (hpq : degree q ≤ degree p) :
     degree q + degree (p / q) = degree p :=
   by
@@ -280,13 +285,17 @@ theorem degree_add_div (hq0 : q ≠ 0) (hpq : degree q ≤ degree p) :
   conv_rhs =>
     rw [← EuclideanDomain.div_add_mod p q, degree_add_eq_left_of_degree_lt this, degree_mul]
 #align polynomial.degree_add_div Polynomial.degree_add_div
+-/
 
+#print Polynomial.degree_div_le /-
 theorem degree_div_le (p q : R[X]) : degree (p / q) ≤ degree p :=
   if hq : q = 0 then by simp [hq]
   else by
     rw [div_def, mul_comm, degree_mul_leading_coeff_inv _ hq] <;> exact degree_div_by_monic_le _ _
 #align polynomial.degree_div_le Polynomial.degree_div_le
+-/
 
+#print Polynomial.degree_div_lt /-
 theorem degree_div_lt (hp : p ≠ 0) (hq : 0 < degree q) : degree (p / q) < degree p :=
   by
   have hq0 : q ≠ 0 := fun hq0 => by simpa [hq0] using hq
@@ -295,6 +304,7 @@ theorem degree_div_lt (hp : p ≠ 0) (hq : 0 < degree q) : degree (p / q) < degr
       degree_div_by_monic_lt _ (monic_mul_leading_coeff_inv hq0) hp
         (by rw [degree_mul_leading_coeff_inv _ hq0] <;> exact hq)
 #align polynomial.degree_div_lt Polynomial.degree_div_lt
+-/
 
 #print Polynomial.degree_map /-
 @[simp]

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

@@ -37,9 +37,6 @@ section IsDomain
 
 variable [CommRing R] [IsDomain R]
 
-/- warning: polynomial.derivative_root_multiplicity_of_root -> Polynomial.derivative_rootMultiplicity_of_root is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.derivative_root_multiplicity_of_root Polynomial.derivative_rootMultiplicity_of_rootₓ'. -/
 theorem derivative_rootMultiplicity_of_root [CharZero R] {p : R[X]} {t : R} (hpt : p.IsRoot t) :
     p.derivative.rootMultiplicity t = p.rootMultiplicity t - 1 :=
   by
@@ -69,9 +66,6 @@ theorem derivative_rootMultiplicity_of_root [CharZero R] {p : R[X]} {t : R} (hpt
   rw [h, eval_zero]
 #align polynomial.derivative_root_multiplicity_of_root Polynomial.derivative_rootMultiplicity_of_root
 
-/- warning: polynomial.root_multiplicity_sub_one_le_derivative_root_multiplicity -> Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicity is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_sub_one_le_derivative_root_multiplicity Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicityₓ'. -/
 theorem rootMultiplicity_sub_one_le_derivative_rootMultiplicity [CharZero R] (p : R[X]) (t : R) :
     p.rootMultiplicity t - 1 ≤ p.derivative.rootMultiplicity t :=
   by
@@ -105,32 +99,20 @@ instance : NormalizationMonoid R[X]
         rcases Polynomial.isUnit_iff.1 ⟨u, rfl⟩ with ⟨_, ⟨w, rfl⟩, h2⟩
         rw [← h2, leading_coeff_C, norm_unit_coe_units, ← C_mul, Units.mul_inv, C_1])
 
-/- warning: polynomial.coe_norm_unit -> Polynomial.coe_normUnit is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.coe_norm_unit Polynomial.coe_normUnitₓ'. -/
 @[simp]
 theorem coe_normUnit {p : R[X]} : (normUnit p : R[X]) = C ↑(normUnit p.leadingCoeff) := by
   simp [norm_unit]
 #align polynomial.coe_norm_unit Polynomial.coe_normUnit
 
-/- warning: polynomial.leading_coeff_normalize -> Polynomial.leadingCoeff_normalize is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_normalize Polynomial.leadingCoeff_normalizeₓ'. -/
 theorem leadingCoeff_normalize (p : R[X]) :
     leadingCoeff (normalize p) = normalize (leadingCoeff p) := by simp
 #align polynomial.leading_coeff_normalize Polynomial.leadingCoeff_normalize
 
-/- warning: polynomial.monic.normalize_eq_self -> Polynomial.Monic.normalize_eq_self is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.monic.normalize_eq_self Polynomial.Monic.normalize_eq_selfₓ'. -/
 theorem Monic.normalize_eq_self {p : R[X]} (hp : p.Monic) : normalize p = p := by
   simp only [Polynomial.coe_normUnit, normalize_apply, hp.leading_coeff, normUnit_one,
     Units.val_one, polynomial.C.map_one, mul_one]
 #align polynomial.monic.normalize_eq_self Polynomial.Monic.normalize_eq_self
 
-/- warning: polynomial.roots_normalize -> Polynomial.roots_normalize is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.roots_normalize Polynomial.roots_normalizeₓ'. -/
 theorem roots_normalize {p : R[X]} : (normalize p).roots = p.roots := by
   rw [normalize_apply, mul_comm, coe_norm_unit, roots_C_mul _ (norm_unit (leading_coeff p)).NeZero]
 #align polynomial.roots_normalize Polynomial.roots_normalize
@@ -143,32 +125,17 @@ section DivisionRing
 
 variable [DivisionRing R] {p q : R[X]}
 
-/- warning: polynomial.degree_pos_of_ne_zero_of_nonunit -> Polynomial.degree_pos_of_ne_zero_of_nonunit is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))) -> (Not (IsUnit.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) p))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))))) -> (Not (IsUnit.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) p)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)) p))
-Case conversion may be inaccurate. Consider using '#align polynomial.degree_pos_of_ne_zero_of_nonunit Polynomial.degree_pos_of_ne_zero_of_nonunitₓ'. -/
 theorem degree_pos_of_ne_zero_of_nonunit (hp0 : p ≠ 0) (hp : ¬IsUnit p) : 0 < degree p :=
   lt_of_not_ge fun h => by
     rw [eq_C_of_degree_le_zero h] at hp0 hp
     exact hp (IsUnit.map C (IsUnit.mk0 (coeff p 0) (mt C_inj.2 (by simpa using hp0))))
 #align polynomial.degree_pos_of_ne_zero_of_nonunit Polynomial.degree_pos_of_ne_zero_of_nonunit
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.monic_mul_leading_coeff_inv Polynomial.monic_mul_leadingCoeff_invₓ'. -/
 theorem monic_mul_leadingCoeff_inv (h : p ≠ 0) : Monic (p * C (leadingCoeff p)⁻¹) := by
   rw [monic, leading_coeff_mul, leading_coeff_C,
     mul_inv_cancel (show leading_coeff p ≠ 0 from mt leading_coeff_eq_zero.1 h)]
 #align polynomial.monic_mul_leading_coeff_inv Polynomial.monic_mul_leadingCoeff_inv
 
-/- warning: polynomial.degree_mul_leading_coeff_inv -> Polynomial.degree_mul_leadingCoeff_inv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.degree_mul_leading_coeff_inv Polynomial.degree_mul_leadingCoeff_invₓ'. -/
 theorem degree_mul_leadingCoeff_inv (p : R[X]) (h : q ≠ 0) :
     degree (p * C (leadingCoeff q)⁻¹) = degree p :=
   by
@@ -195,12 +162,6 @@ section Field
 
 variable [Field R] {p q : R[X]}
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.is_unit_iff_degree_eq_zero Polynomial.isUnit_iff_degree_eq_zeroₓ'. -/
 theorem isUnit_iff_degree_eq_zero : IsUnit p ↔ degree p = 0 :=
   ⟨degree_eq_zero_of_isUnit, fun h =>
     have : degree p ≤ 0 := by simp [*, le_refl]
@@ -245,16 +206,10 @@ instance : Div R[X] :=
 instance : Mod R[X] :=
   ⟨mod⟩
 
-/- warning: polynomial.div_def -> Polynomial.div_def is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.div_def Polynomial.div_defₓ'. -/
 theorem div_def : p / q = C (leadingCoeff q)⁻¹ * (p /ₘ (q * C (leadingCoeff q)⁻¹)) :=
   rfl
 #align polynomial.div_def Polynomial.div_def
 
-/- warning: polynomial.mod_def -> Polynomial.mod_def is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.mod_def Polynomial.mod_defₓ'. -/
 theorem mod_def : p % q = p %ₘ (q * C (leadingCoeff q)⁻¹) :=
   rfl
 #align polynomial.mod_def Polynomial.mod_def
@@ -272,16 +227,10 @@ theorem divByMonic_eq_div (p : R[X]) (hq : Monic q) : p /ₘ q = p / q :=
 #align polynomial.div_by_monic_eq_div Polynomial.divByMonic_eq_div
 -/
 
-/- warning: polynomial.mod_X_sub_C_eq_C_eval -> Polynomial.mod_X_sub_C_eq_C_eval is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.mod_X_sub_C_eq_C_eval Polynomial.mod_X_sub_C_eq_C_evalₓ'. -/
 theorem mod_X_sub_C_eq_C_eval (p : R[X]) (a : R) : p % (X - C a) = C (p.eval a) :=
   modByMonic_eq_mod p (monic_X_sub_C a) ▸ modByMonic_X_sub_C_eq_C_eval _ _
 #align polynomial.mod_X_sub_C_eq_C_eval Polynomial.mod_X_sub_C_eq_C_eval
 
-/- warning: polynomial.mul_div_eq_iff_is_root -> Polynomial.mul_div_eq_iff_isRoot is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.mul_div_eq_iff_is_root Polynomial.mul_div_eq_iff_isRootₓ'. -/
 theorem mul_div_eq_iff_isRoot : (X - C a) * (p / (X - C a)) = p ↔ IsRoot p a :=
   divByMonic_eq_div p (monic_X_sub_C a) ▸ mul_divByMonic_eq_iff_isRoot
 #align polynomial.mul_div_eq_iff_is_root Polynomial.mul_div_eq_iff_isRoot
@@ -298,12 +247,6 @@ instance : EuclideanDomain R[X] :=
     remainder_lt := fun p q hq => remainder_lt_aux _ hq
     mul_left_not_lt := fun p q hq => not_lt_of_ge (degree_le_mul_left _ hq) }
 
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 theorem mod_eq_self_iff (hq0 : q ≠ 0) : p % q = p ↔ degree p < degree q :=
   ⟨fun h => h ▸ EuclideanDomain.mod_lt _ hq0, fun h =>
     by
@@ -314,12 +257,6 @@ theorem mod_eq_self_iff (hq0 : q ≠ 0) : p % q = p ↔ degree p < degree q :=
     simp only [this, false_and_iff, if_false]⟩
 #align polynomial.mod_eq_self_iff Polynomial.mod_eq_self_iff
 
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 theorem div_eq_zero_iff (hq0 : q ≠ 0) : p / q = 0 ↔ degree p < degree q :=
   ⟨fun h => by
     have := EuclideanDomain.div_add_mod p q <;>
@@ -332,12 +269,6 @@ theorem div_eq_zero_iff (hq0 : q ≠ 0) : p / q = 0 ↔ degree p < degree q :=
     rw [div_def, (div_by_monic_eq_zero_iff hm).2 hlt, MulZeroClass.mul_zero]⟩
 #align polynomial.div_eq_zero_iff Polynomial.div_eq_zero_iff
 
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 theorem degree_add_div (hq0 : q ≠ 0) (hpq : degree q ≤ degree p) :
     degree q + degree (p / q) = degree p :=
   by
@@ -350,24 +281,12 @@ theorem degree_add_div (hq0 : q ≠ 0) (hpq : degree q ≤ degree p) :
     rw [← EuclideanDomain.div_add_mod p q, degree_add_eq_left_of_degree_lt this, degree_mul]
 #align polynomial.degree_add_div Polynomial.degree_add_div
 
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 theorem degree_div_le (p q : R[X]) : degree (p / q) ≤ degree p :=
   if hq : q = 0 then by simp [hq]
   else by
     rw [div_def, mul_comm, degree_mul_leading_coeff_inv _ hq] <;> exact degree_div_by_monic_le _ _
 #align polynomial.degree_div_le Polynomial.degree_div_le
 
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 theorem degree_div_lt (hp : p ≠ 0) (hq : 0 < degree q) : degree (p / q) < degree p :=
   by
   have hq0 : q ≠ 0 := fun hq0 => by simpa [hq0] using hq
@@ -391,12 +310,6 @@ theorem natDegree_map [DivisionRing k] (f : R →+* k) : natDegree (p.map f) = n
 #align polynomial.nat_degree_map Polynomial.natDegree_map
 -/
 
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 @[simp]
 theorem leadingCoeff_map [DivisionRing k] (f : R →+* k) :
     leadingCoeff (p.map f) = f (leadingCoeff p) := by
@@ -409,12 +322,6 @@ theorem monic_map_iff [DivisionRing k] {f : R →+* k} {p : R[X]} : (p.map f).Mo
 #align polynomial.monic_map_iff Polynomial.monic_map_iff
 -/
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.is_unit_map Polynomial.isUnit_mapₓ'. -/
 theorem isUnit_map [Field k] (f : R →+* k) : IsUnit (p.map f) ↔ IsUnit p := by
   simp_rw [is_unit_iff_degree_eq_zero, degree_map]
 #align polynomial.is_unit_map Polynomial.isUnit_map
@@ -442,12 +349,6 @@ section
 
 open EuclideanDomain
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.gcd_map Polynomial.gcd_mapₓ'. -/
 theorem gcd_map [Field k] (f : R →+* k) : gcd (p.map f) (q.map f) = (gcd p q).map f :=
   GCD.induction p q (fun x => by simp_rw [Polynomial.map_zero, EuclideanDomain.gcd_zero_left])
     fun x y hx ih => by rw [gcd_val, ← map_mod, ih, ← gcd_val]
@@ -455,35 +356,17 @@ theorem gcd_map [Field k] (f : R →+* k) : gcd (p.map f) (q.map f) = (gcd p q).
 
 end
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_gcd_eq_zero Polynomial.eval₂_gcd_eq_zeroₓ'. -/
 theorem eval₂_gcd_eq_zero [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α : k} (hf : f.eval₂ ϕ α = 0)
     (hg : g.eval₂ ϕ α = 0) : (EuclideanDomain.gcd f g).eval₂ ϕ α = 0 := by
   rw [EuclideanDomain.gcd_eq_gcd_ab f g, Polynomial.eval₂_add, Polynomial.eval₂_mul,
     Polynomial.eval₂_mul, hf, hg, MulZeroClass.zero_mul, MulZeroClass.zero_mul, zero_add]
 #align polynomial.eval₂_gcd_eq_zero Polynomial.eval₂_gcd_eq_zero
 
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 theorem eval_gcd_eq_zero {f g : R[X]} {α : R} (hf : f.eval α = 0) (hg : g.eval α = 0) :
     (EuclideanDomain.gcd f g).eval α = 0 :=
   eval₂_gcd_eq_zero hf hg
 #align polynomial.eval_gcd_eq_zero Polynomial.eval_gcd_eq_zero
 
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 theorem root_left_of_root_gcd [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α : k}
     (hα : (EuclideanDomain.gcd f g).eval₂ ϕ α = 0) : f.eval₂ ϕ α = 0 :=
   by
@@ -491,12 +374,6 @@ theorem root_left_of_root_gcd [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α
   rw [hp, Polynomial.eval₂_mul, hα, MulZeroClass.zero_mul]
 #align polynomial.root_left_of_root_gcd Polynomial.root_left_of_root_gcd
 
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 theorem root_right_of_root_gcd [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α : k}
     (hα : (EuclideanDomain.gcd f g).eval₂ ϕ α = 0) : g.eval₂ ϕ α = 0 :=
   by
@@ -504,23 +381,11 @@ theorem root_right_of_root_gcd [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {
   rw [hp, Polynomial.eval₂_mul, hα, MulZeroClass.zero_mul]
 #align polynomial.root_right_of_root_gcd Polynomial.root_right_of_root_gcd
 
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 theorem root_gcd_iff_root_left_right [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α : k} :
     (EuclideanDomain.gcd f g).eval₂ ϕ α = 0 ↔ f.eval₂ ϕ α = 0 ∧ g.eval₂ ϕ α = 0 :=
   ⟨fun h => ⟨root_left_of_root_gcd h, root_right_of_root_gcd h⟩, fun h => eval₂_gcd_eq_zero h.1 h.2⟩
 #align polynomial.root_gcd_iff_root_left_right Polynomial.root_gcd_iff_root_left_right
 
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 theorem isRoot_gcd_iff_isRoot_left_right {f g : R[X]} {α : R} :
     (EuclideanDomain.gcd f g).IsRoot α ↔ f.IsRoot α ∧ g.IsRoot α :=
   root_gcd_iff_root_left_right
@@ -532,51 +397,27 @@ theorem isCoprime_map [Field k] (f : R →+* k) : IsCoprime (p.map f) (q.map f)
 #align polynomial.is_coprime_map Polynomial.isCoprime_map
 -/
 
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 theorem mem_roots_map [CommRing k] [IsDomain k] {f : R →+* k} {x : k} (hp : p ≠ 0) :
     x ∈ (p.map f).roots ↔ p.eval₂ f x = 0 := by
   rw [mem_roots (map_ne_zero hp), is_root, Polynomial.eval_map] <;> infer_instance
 #align polynomial.mem_roots_map Polynomial.mem_roots_map
 
-/- warning: polynomial.root_set_monomial -> Polynomial.rootSet_monomial is a dubious translation:
-<too large>
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 theorem rootSet_monomial [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n ≠ 0) {a : R}
     (ha : a ≠ 0) : (monomial n a).rootSet S = {0} := by
   rw [root_set, map_monomial, roots_monomial ((_root_.map_ne_zero (algebraMap R S)).2 ha),
     Multiset.toFinset_nsmul _ _ hn, Multiset.toFinset_singleton, Finset.coe_singleton]
 #align polynomial.root_set_monomial Polynomial.rootSet_monomial
 
-/- warning: polynomial.root_set_C_mul_X_pow -> Polynomial.rootSet_C_mul_X_pow is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.root_set_C_mul_X_pow Polynomial.rootSet_C_mul_X_powₓ'. -/
 theorem rootSet_C_mul_X_pow [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n ≠ 0) {a : R}
     (ha : a ≠ 0) : (C a * X ^ n).rootSet S = {0} := by
   rw [C_mul_X_pow_eq_monomial, root_set_monomial hn ha]
 #align polynomial.root_set_C_mul_X_pow Polynomial.rootSet_C_mul_X_pow
 
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 theorem rootSet_X_pow [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n ≠ 0) :
     (X ^ n : R[X]).rootSet S = {0} := by
   rw [← one_mul (X ^ n : R[X]), ← C_1, root_set_C_mul_X_pow hn]; exact one_ne_zero
 #align polynomial.root_set_X_pow Polynomial.rootSet_X_pow
 
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 theorem rootSet_prod [CommRing S] [IsDomain S] [Algebra R S] {ι : Type _} (f : ι → R[X])
     (s : Finset ι) (h : s.Prod f ≠ 0) : (s.Prod f).rootSet S = ⋃ i ∈ s, (f i).rootSet S :=
   by
@@ -597,12 +438,6 @@ theorem exists_root_of_degree_eq_one (h : degree p = 1) : ∃ x, IsRoot p x :=
 #align polynomial.exists_root_of_degree_eq_one Polynomial.exists_root_of_degree_eq_one
 -/
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.coeff_inv_units Polynomial.coeff_inv_unitsₓ'. -/
 theorem coeff_inv_units (u : R[X]ˣ) (n : ℕ) : ((↑u : R[X]).coeff n)⁻¹ = (↑u⁻¹ : R[X]).coeff n :=
   by
   rw [eq_C_of_degree_eq_zero (degree_coe_units u), eq_C_of_degree_eq_zero (degree_coe_units u⁻¹),
@@ -615,9 +450,6 @@ theorem coeff_inv_units (u : R[X]ˣ) (n : ℕ) : ((↑u : R[X]).coeff n)⁻¹ =
   · simp
 #align polynomial.coeff_inv_units Polynomial.coeff_inv_units
 
-/- warning: polynomial.monic_normalize -> Polynomial.monic_normalize is a dubious translation:
-<too large>
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 theorem monic_normalize (hp0 : p ≠ 0) : Monic (normalize p) :=
   by
   rw [Ne.def, ← leading_coeff_eq_zero, ← Ne.def, ← isUnit_iff_ne_zero] at hp0
@@ -625,12 +457,6 @@ theorem monic_normalize (hp0 : p ≠ 0) : Monic (normalize p) :=
   apply hp0
 #align polynomial.monic_normalize Polynomial.monic_normalize
 
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 theorem leadingCoeff_div (hpq : q.degree ≤ p.degree) :
     (p / q).leadingCoeff = p.leadingCoeff / q.leadingCoeff :=
   by
@@ -641,9 +467,6 @@ theorem leadingCoeff_div (hpq : q.degree ≤ p.degree) :
   rwa [degree_mul_leading_coeff_inv q hq]
 #align polynomial.leading_coeff_div Polynomial.leadingCoeff_div
 
-/- warning: polynomial.div_C_mul -> Polynomial.div_C_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.div_C_mul Polynomial.div_C_mulₓ'. -/
 theorem div_C_mul : p / (C a * q) = C a⁻¹ * (p / q) :=
   by
   by_cases ha : a = 0
@@ -653,9 +476,6 @@ theorem div_C_mul : p / (C a * q) = C a⁻¹ * (p / q) :=
   rw [mul_left_comm q, ← mul_assoc, ← C.map_mul, mul_inv_cancel ha, C.map_one, one_mul]
 #align polynomial.div_C_mul Polynomial.div_C_mul
 
-/- warning: polynomial.C_mul_dvd -> Polynomial.C_mul_dvd is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.C_mul_dvd Polynomial.C_mul_dvdₓ'. -/
 theorem C_mul_dvd (ha : a ≠ 0) : C a * p ∣ q ↔ p ∣ q :=
   ⟨fun h => dvd_trans (dvd_mul_left _ _) h, fun ⟨r, hr⟩ =>
     ⟨C a⁻¹ * r, by
@@ -663,9 +483,6 @@ theorem C_mul_dvd (ha : a ≠ 0) : C a * p ∣ q ↔ p ∣ q :=
         one_mul, hr]⟩⟩
 #align polynomial.C_mul_dvd Polynomial.C_mul_dvd
 
-/- warning: polynomial.dvd_C_mul -> Polynomial.dvd_C_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.dvd_C_mul Polynomial.dvd_C_mulₓ'. -/
 theorem dvd_C_mul (ha : a ≠ 0) : p ∣ Polynomial.C a * q ↔ p ∣ q :=
   ⟨fun ⟨r, hr⟩ =>
     ⟨C a⁻¹ * r, by
@@ -674,18 +491,12 @@ theorem dvd_C_mul (ha : a ≠ 0) : p ∣ Polynomial.C a * q ↔ p ∣ q :=
     fun h => dvd_trans h (dvd_mul_left _ _)⟩
 #align polynomial.dvd_C_mul Polynomial.dvd_C_mul
 
-/- warning: polynomial.coe_norm_unit_of_ne_zero -> Polynomial.coe_normUnit_of_ne_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.coe_norm_unit_of_ne_zero Polynomial.coe_normUnit_of_ne_zeroₓ'. -/
 theorem coe_normUnit_of_ne_zero (hp : p ≠ 0) : (normUnit p : R[X]) = C p.leadingCoeff⁻¹ :=
   by
   have : p.leadingCoeff ≠ 0 := mt leadingCoeff_eq_zero.mp hp
   simp [CommGroupWithZero.coe_normUnit _ this]
 #align polynomial.coe_norm_unit_of_ne_zero Polynomial.coe_normUnit_of_ne_zero
 
-/- warning: polynomial.normalize_monic -> Polynomial.normalize_monic is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.normalize_monic Polynomial.normalize_monicₓ'. -/
 theorem normalize_monic (h : Monic p) : normalize p = p := by simp [h]
 #align polynomial.normalize_monic Polynomial.normalize_monic
 
@@ -700,9 +511,6 @@ theorem map_dvd_map' [Field k] (f : R →+* k) {x y : R[X]} : x.map f ∣ y.map
 #align polynomial.map_dvd_map' Polynomial.map_dvd_map'
 -/
 
-/- warning: polynomial.degree_normalize -> Polynomial.degree_normalize is a dubious translation:
-<too large>
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 theorem degree_normalize : degree (normalize p) = degree p := by simp
 #align polynomial.degree_normalize Polynomial.degree_normalize
 
@@ -715,42 +523,21 @@ theorem prime_of_degree_eq_one (hp1 : degree p = 1) : Prime p :=
 #align polynomial.prime_of_degree_eq_one Polynomial.prime_of_degree_eq_one
 -/
 
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 theorem irreducible_of_degree_eq_one (hp1 : degree p = 1) : Irreducible p :=
   (prime_of_degree_eq_one hp1).Irreducible
 #align polynomial.irreducible_of_degree_eq_one Polynomial.irreducible_of_degree_eq_one
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.not_irreducible_C Polynomial.not_irreducible_Cₓ'. -/
 theorem not_irreducible_C (x : R) : ¬Irreducible (C x) :=
   if H : x = 0 then by rw [H, C_0]; exact not_irreducible_zero
   else fun hx => Irreducible.not_unit hx <| isUnit_C.2 <| isUnit_iff_ne_zero.2 H
 #align polynomial.not_irreducible_C Polynomial.not_irreducible_C
 
-/- warning: polynomial.degree_pos_of_irreducible -> Polynomial.degree_pos_of_irreducible is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) p) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) p))
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-Case conversion may be inaccurate. Consider using '#align polynomial.degree_pos_of_irreducible Polynomial.degree_pos_of_irreducibleₓ'. -/
 theorem degree_pos_of_irreducible (hp : Irreducible p) : 0 < p.degree :=
   lt_of_not_ge fun hp0 =>
     have := eq_C_of_degree_le_zero hp0
     not_irreducible_C (p.coeff 0) <| this ▸ hp
 #align polynomial.degree_pos_of_irreducible Polynomial.degree_pos_of_irreducible
 
-/- warning: polynomial.is_coprime_of_is_root_of_eval_derivative_ne_zero -> Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.is_coprime_of_is_root_of_eval_derivative_ne_zero Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zeroₓ'. -/
 /-- If `f` is a polynomial over a field, and `a : K` satisfies `f' a ≠ 0`,
 then `f / (X - a)` is coprime with `X - a`.
 Note that we do not assume `f a = 0`, because `f / (X - a) = (f - f a) / (X - a)`. -/

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

@@ -567,10 +567,8 @@ but is expected to have type
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) Nat (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHPow.{u1, 0} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))))) (Polynomial.X.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) n) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.instSingletonSet.{u2} S) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} S (IsDomain.toCancelCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_X_pow Polynomial.rootSet_X_powₓ'. -/
 theorem rootSet_X_pow [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n ≠ 0) :
-    (X ^ n : R[X]).rootSet S = {0} :=
-  by
-  rw [← one_mul (X ^ n : R[X]), ← C_1, root_set_C_mul_X_pow hn]
-  exact one_ne_zero
+    (X ^ n : R[X]).rootSet S = {0} := by
+  rw [← one_mul (X ^ n : R[X]), ← C_1, root_set_C_mul_X_pow hn]; exact one_ne_zero
 #align polynomial.root_set_X_pow Polynomial.rootSet_X_pow
 
 /- warning: polynomial.root_set_prod -> Polynomial.rootSet_prod is a dubious translation:
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R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R 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 Case conversion may be inaccurate. Consider using '#align polynomial.not_irreducible_C Polynomial.not_irreducible_Cₓ'. -/
 theorem not_irreducible_C (x : R) : ¬Irreducible (C x) :=
-  if H : x = 0 then by
-    rw [H, C_0]
-    exact not_irreducible_zero
+  if H : x = 0 then by rw [H, C_0]; exact not_irreducible_zero
   else fun hx => Irreducible.not_unit hx <| isUnit_C.2 <| isUnit_iff_ne_zero.2 H
 #align polynomial.not_irreducible_C Polynomial.not_irreducible_C
 

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

@@ -38,10 +38,7 @@ section IsDomain
 variable [CommRing R] [IsDomain R]
 
 /- warning: polynomial.derivative_root_multiplicity_of_root -> Polynomial.derivative_rootMultiplicity_of_root is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.derivative_root_multiplicity_of_root Polynomial.derivative_rootMultiplicity_of_rootₓ'. -/
 theorem derivative_rootMultiplicity_of_root [CharZero R] {p : R[X]} {t : R} (hpt : p.IsRoot t) :
     p.derivative.rootMultiplicity t = p.rootMultiplicity t - 1 :=
@@ -73,10 +70,7 @@ theorem derivative_rootMultiplicity_of_root [CharZero R] {p : R[X]} {t : R} (hpt
 #align polynomial.derivative_root_multiplicity_of_root Polynomial.derivative_rootMultiplicity_of_root
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_sub_one_le_derivative_root_multiplicity Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicityₓ'. -/
 theorem rootMultiplicity_sub_one_le_derivative_rootMultiplicity [CharZero R] (p : R[X]) (t : R) :
     p.rootMultiplicity t - 1 ≤ p.derivative.rootMultiplicity t :=
@@ -112,10 +106,7 @@ instance : NormalizationMonoid R[X]
         rw [← h2, leading_coeff_C, norm_unit_coe_units, ← C_mul, Units.mul_inv, C_1])
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_norm_unit Polynomial.coe_normUnitₓ'. -/
 @[simp]
 theorem coe_normUnit {p : R[X]} : (normUnit p : R[X]) = C ↑(normUnit p.leadingCoeff) := by
@@ -123,20 +114,14 @@ theorem coe_normUnit {p : R[X]} : (normUnit p : R[X]) = C ↑(normUnit p.leading
 #align polynomial.coe_norm_unit Polynomial.coe_normUnit
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_normalize Polynomial.leadingCoeff_normalizeₓ'. -/
 theorem leadingCoeff_normalize (p : R[X]) :
     leadingCoeff (normalize p) = normalize (leadingCoeff p) := by simp
 #align polynomial.leading_coeff_normalize Polynomial.leadingCoeff_normalize
 
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(CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R _inst_1 _inst_2 _inst_3)) p) p)
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.monic.normalize_eq_self Polynomial.Monic.normalize_eq_selfₓ'. -/
 theorem Monic.normalize_eq_self {p : R[X]} (hp : p.Monic) : normalize p = p := by
   simp only [Polynomial.coe_normUnit, normalize_apply, hp.leading_coeff, normUnit_one,
@@ -144,10 +129,7 @@ theorem Monic.normalize_eq_self {p : R[X]} (hp : p.Monic) : normalize p = p := b
 #align polynomial.monic.normalize_eq_self Polynomial.Monic.normalize_eq_self
 
 /- warning: polynomial.roots_normalize -> Polynomial.roots_normalize is a dubious translation:
-lean 3 declaration is
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(CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (normalize.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.normalizationMonoid.{u1} R _inst_1 _inst_2 _inst_3)) p)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_normalize Polynomial.roots_normalizeₓ'. -/
 theorem roots_normalize {p : R[X]} : (normalize p).roots = p.roots := by
   rw [normalize_apply, mul_comm, coe_norm_unit, roots_C_mul _ (norm_unit (leading_coeff p)).NeZero]
@@ -185,10 +167,7 @@ theorem monic_mul_leadingCoeff_inv (h : p ≠ 0) : Monic (p * C (leadingCoeff p)
 #align polynomial.monic_mul_leading_coeff_inv Polynomial.monic_mul_leadingCoeff_inv
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_mul_leading_coeff_inv Polynomial.degree_mul_leadingCoeff_invₓ'. -/
 theorem degree_mul_leadingCoeff_inv (p : R[X]) (h : q ≠ 0) :
     degree (p * C (leadingCoeff q)⁻¹) = degree p :=
@@ -255,12 +234,10 @@ private theorem quotient_mul_add_remainder_eq_aux (p q : R[X]) : q * div p q + m
       rhs
       rw [← mod_by_monic_add_div p (monic_mul_leading_coeff_inv h)]
     rw [div, mod, add_comm, mul_assoc]
-#align polynomial.quotient_mul_add_remainder_eq_aux polynomial.quotient_mul_add_remainder_eq_aux
 
 private theorem remainder_lt_aux (p : R[X]) (hq : q ≠ 0) : degree (mod p q) < degree q := by
   rw [← degree_mul_leading_coeff_inv q hq] <;>
     exact degree_mod_by_monic_lt p (monic_mul_leading_coeff_inv hq)
-#align polynomial.remainder_lt_aux polynomial.remainder_lt_aux
 
 instance : Div R[X] :=
   ⟨div⟩
@@ -269,20 +246,14 @@ instance : Mod R[X] :=
   ⟨mod⟩
 
 /- warning: polynomial.div_def -> Polynomial.div_def is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.div_def Polynomial.div_defₓ'. -/
 theorem div_def : p / q = C (leadingCoeff q)⁻¹ * (p /ₘ (q * C (leadingCoeff q)⁻¹)) :=
   rfl
 #align polynomial.div_def Polynomial.div_def
 
 /- warning: polynomial.mod_def -> Polynomial.mod_def is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.mod_def Polynomial.mod_defₓ'. -/
 theorem mod_def : p % q = p %ₘ (q * C (leadingCoeff q)⁻¹) :=
   rfl
@@ -302,20 +273,14 @@ theorem divByMonic_eq_div (p : R[X]) (hq : Monic q) : p /ₘ q = p / q :=
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.mod_X_sub_C_eq_C_eval Polynomial.mod_X_sub_C_eq_C_evalₓ'. -/
 theorem mod_X_sub_C_eq_C_eval (p : R[X]) (a : R) : p % (X - C a) = C (p.eval a) :=
   modByMonic_eq_mod p (monic_X_sub_C a) ▸ modByMonic_X_sub_C_eq_C_eval _ _
 #align polynomial.mod_X_sub_C_eq_C_eval Polynomial.mod_X_sub_C_eq_C_eval
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.mul_div_eq_iff_is_root Polynomial.mul_div_eq_iff_isRootₓ'. -/
 theorem mul_div_eq_iff_isRoot : (X - C a) * (p / (X - C a)) = p ↔ IsRoot p a :=
   divByMonic_eq_div p (monic_X_sub_C a) ▸ mul_divByMonic_eq_iff_isRoot
@@ -579,10 +544,7 @@ theorem mem_roots_map [CommRing k] [IsDomain k] {f : R →+* k} {x : k} (hp : p
 #align polynomial.mem_roots_map Polynomial.mem_roots_map
 
 /- warning: polynomial.root_set_monomial -> Polynomial.rootSet_monomial is a dubious translation:
-lean 3 declaration is
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(LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) (Polynomial.monomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) n) a) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.hasSingleton.{u2} S) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2))))))))))))
-but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (forall {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (Polynomial.monomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) n) a) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.instSingletonSet.{u2} S) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} S (IsDomain.toCancelCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_monomial Polynomial.rootSet_monomialₓ'. -/
 theorem rootSet_monomial [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n ≠ 0) {a : R}
     (ha : a ≠ 0) : (monomial n a).rootSet S = {0} := by
@@ -591,10 +553,7 @@ theorem rootSet_monomial [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn :
 #align polynomial.root_set_monomial Polynomial.rootSet_monomial
 
 /- warning: polynomial.root_set_C_mul_X_pow -> Polynomial.rootSet_C_mul_X_pow is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (forall {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) n)) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.hasSingleton.{u2} S) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2))))))))))))
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_C_mul_X_pow Polynomial.rootSet_C_mul_X_powₓ'. -/
 theorem rootSet_C_mul_X_pow [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n ≠ 0) {a : R}
     (ha : a ≠ 0) : (C a * X ^ n).rootSet S = {0} := by
@@ -659,10 +618,7 @@ theorem coeff_inv_units (u : R[X]ˣ) (n : ℕ) : ((↑u : R[X]).coeff n)⁻¹ =
 #align polynomial.coeff_inv_units Polynomial.coeff_inv_units
 
 /- warning: polynomial.monic_normalize -> Polynomial.monic_normalize is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_normalize Polynomial.monic_normalizeₓ'. -/
 theorem monic_normalize (hp0 : p ≠ 0) : Monic (normalize p) :=
   by
@@ -688,10 +644,7 @@ theorem leadingCoeff_div (hpq : q.degree ≤ p.degree) :
 #align polynomial.leading_coeff_div Polynomial.leadingCoeff_div
 
 /- warning: polynomial.div_C_mul -> Polynomial.div_C_mul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.div_C_mul Polynomial.div_C_mulₓ'. -/
 theorem div_C_mul : p / (C a * q) = C a⁻¹ * (p / q) :=
   by
@@ -703,10 +656,7 @@ theorem div_C_mul : p / (C a * q) = C a⁻¹ * (p / q) :=
 #align polynomial.div_C_mul Polynomial.div_C_mul
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.C_mul_dvd Polynomial.C_mul_dvdₓ'. -/
 theorem C_mul_dvd (ha : a ≠ 0) : C a * p ∣ q ↔ p ∣ q :=
   ⟨fun h => dvd_trans (dvd_mul_left _ _) h, fun ⟨r, hr⟩ =>
@@ -716,10 +666,7 @@ theorem C_mul_dvd (ha : a ≠ 0) : C a * p ∣ q ↔ p ∣ q :=
 #align polynomial.C_mul_dvd Polynomial.C_mul_dvd
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.dvd_C_mul Polynomial.dvd_C_mulₓ'. -/
 theorem dvd_C_mul (ha : a ≠ 0) : p ∣ Polynomial.C a * q ↔ p ∣ q :=
   ⟨fun ⟨r, hr⟩ =>
@@ -730,10 +677,7 @@ theorem dvd_C_mul (ha : a ≠ 0) : p ∣ Polynomial.C a * q ↔ p ∣ q :=
 #align polynomial.dvd_C_mul Polynomial.dvd_C_mul
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_norm_unit_of_ne_zero Polynomial.coe_normUnit_of_ne_zeroₓ'. -/
 theorem coe_normUnit_of_ne_zero (hp : p ≠ 0) : (normUnit p : R[X]) = C p.leadingCoeff⁻¹ :=
   by
@@ -742,10 +686,7 @@ theorem coe_normUnit_of_ne_zero (hp : p ≠ 0) : (normUnit p : R[X]) = C p.leadi
 #align polynomial.coe_norm_unit_of_ne_zero Polynomial.coe_normUnit_of_ne_zero
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.normalize_monic Polynomial.normalize_monicₓ'. -/
 theorem normalize_monic (h : Monic p) : normalize p = p := by simp [h]
 #align polynomial.normalize_monic Polynomial.normalize_monic
@@ -762,10 +703,7 @@ theorem map_dvd_map' [Field k] (f : R →+* k) {x y : R[X]} : x.map f ∣ y.map
 -/
 
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(Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) 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(DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_normalize Polynomial.degree_normalizeₓ'. -/
 theorem degree_normalize : degree (normalize p) = degree p := by simp
 #align polynomial.degree_normalize Polynomial.degree_normalize
@@ -815,10 +753,7 @@ theorem degree_pos_of_irreducible (hp : Irreducible p) : 0 < p.degree :=
 #align polynomial.degree_pos_of_irreducible Polynomial.degree_pos_of_irreducible
 
 /- warning: polynomial.is_coprime_of_is_root_of_eval_derivative_ne_zero -> Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zero is a dubious translation:
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-but is expected to have type
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(Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (Polynomial.derivative.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) f)) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) -> (IsCoprime.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.commSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) 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(Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a)) (Polynomial.divByMonic.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)) f (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.is_coprime_of_is_root_of_eval_derivative_ne_zero Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zeroₓ'. -/
 /-- If `f` is a polynomial over a field, and `a : K` satisfies `f' a ≠ 0`,
 then `f / (X - a)` is coprime with `X - a`.

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

@@ -41,7 +41,7 @@ variable [CommRing R] [IsDomain R]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {t : R}, (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p t) -> (Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 t (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {t : R}, (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p t) -> (Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 t (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {t : R}, (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p t) -> (Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 t (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))
 Case conversion may be inaccurate. Consider using '#align polynomial.derivative_root_multiplicity_of_root Polynomial.derivative_rootMultiplicity_of_rootₓ'. -/
 theorem derivative_rootMultiplicity_of_root [CharZero R] {p : R[X]} {t : R} (hpt : p.IsRoot t) :
     p.derivative.rootMultiplicity t = p.rootMultiplicity t - 1 :=
@@ -76,7 +76,7 @@ theorem derivative_rootMultiplicity_of_root [CharZero R] {p : R[X]} {t : R} (hpt
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (t : R), LE.le.{0} Nat Nat.hasLe (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Polynomial.rootMultiplicity.{u1} R _inst_1 t (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (t : R), LE.le.{0} Nat instLENat (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Polynomial.rootMultiplicity.{u1} R _inst_1 t (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (t : R), LE.le.{0} Nat instLENat (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Polynomial.rootMultiplicity.{u1} R _inst_1 t (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_sub_one_le_derivative_root_multiplicity Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicityₓ'. -/
 theorem rootMultiplicity_sub_one_le_derivative_rootMultiplicity [CharZero R] (p : R[X]) (t : R) :
     p.rootMultiplicity t - 1 ≤ p.derivative.rootMultiplicity t :=
@@ -582,7 +582,7 @@ theorem mem_roots_map [CommRing k] [IsDomain k] {f : R →+* k} {x : k} (hp : p
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (forall {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) (Polynomial.monomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) n) a) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.hasSingleton.{u2} S) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2))))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (forall {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (Polynomial.monomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) n) a) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.instSingletonSet.{u2} S) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} S (IsDomain.toCancelCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3))))))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (forall {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (Polynomial.monomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) n) a) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.instSingletonSet.{u2} S) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} S (IsDomain.toCancelCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_monomial Polynomial.rootSet_monomialₓ'. -/
 theorem rootSet_monomial [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n ≠ 0) {a : R}
     (ha : a ≠ 0) : (monomial n a).rootSet S = {0} := by
@@ -818,7 +818,7 @@ theorem degree_pos_of_irreducible (hp : Irreducible p) : 0 < p.degree :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_2 : Field.{u1} K] (f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (a : K), (Ne.{succ u1} K (Polynomial.eval.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) a (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (fun (_x : LinearMap.{u1, u1, u1, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) => (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} K K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (Polynomial.derivative.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) f)) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))))))))) -> (IsCoprime.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.commSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) a)) (Polynomial.divByMonic.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)) f (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) a))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_2 : Field.{u1} K] (f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (a : K), (Ne.{succ u1} K (Polynomial.eval.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) a (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (fun (_x : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} K K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (Polynomial.derivative.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) f)) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) -> (IsCoprime.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.commSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a)) (Polynomial.divByMonic.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)) f (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a))))
+  forall {K : Type.{u1}} [_inst_2 : Field.{u1} K] (f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (a : K), (Ne.{succ u1} K (Polynomial.eval.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) a (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (fun (_x : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} K K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (Polynomial.derivative.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) f)) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) -> (IsCoprime.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.commSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a)) (Polynomial.divByMonic.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)) f (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a))))
 Case conversion may be inaccurate. Consider using '#align polynomial.is_coprime_of_is_root_of_eval_derivative_ne_zero Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zeroₓ'. -/
 /-- If `f` is a polynomial over a field, and `a : K` satisfies `f' a ≠ 0`,
 then `f / (X - a)` is coprime with `X - a`.

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

@@ -115,7 +115,7 @@ instance : NormalizationMonoid R[X]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeBase.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Units.hasCoe.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))))) (NormalizationMonoid.normUnit.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.normalizationMonoid.{u1} R _inst_1 _inst_2 _inst_3) p)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) R (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) R (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) R (coeBase.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) R (Units.hasCoe.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))))) (NormalizationMonoid.normUnit.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2) _inst_3 (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Units.val.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (NormalizationMonoid.normUnit.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R _inst_1 _inst_2 _inst_3) p)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (NormalizationMonoid.normUnit.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2) _inst_3 (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Units.val.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (NormalizationMonoid.normUnit.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R _inst_1 _inst_2 _inst_3) p)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (NormalizationMonoid.normUnit.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2) _inst_3 (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p))))
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_norm_unit Polynomial.coe_normUnitₓ'. -/
 @[simp]
 theorem coe_normUnit {p : R[X]} : (normUnit p : R[X]) = C ↑(normUnit p.leadingCoeff) := by
@@ -126,7 +126,7 @@ theorem coe_normUnit {p : R[X]} : (normUnit p : R[X]) = C ↑(normUnit p.leading
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (normalize.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.normalizationMonoid.{u1} R _inst_1 _inst_2 _inst_3)) p)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) (fun (_x : MonoidWithZeroHom.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) => R -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) (normalize.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2) _inst_3) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))))) (normalize.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R _inst_1 _inst_2 _inst_3)) p)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R 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(MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) R R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))))) (normalize.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2) _inst_3) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))))) (normalize.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R _inst_1 _inst_2 _inst_3)) p)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) R R (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) R R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))))) (normalize.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2) _inst_3) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_normalize Polynomial.leadingCoeff_normalizeₓ'. -/
 theorem leadingCoeff_normalize (p : R[X]) :
     leadingCoeff (normalize p) = normalize (leadingCoeff p) := by simp
@@ -136,7 +136,7 @@ theorem leadingCoeff_normalize (p : R[X]) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (normalize.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.normalizationMonoid.{u1} R _inst_1 _inst_2 _inst_3)) p) p)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))))) (normalize.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R _inst_1 _inst_2 _inst_3)) p) p)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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_inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))))) (normalize.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R _inst_1 _inst_2 _inst_3)) p) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.monic.normalize_eq_self Polynomial.Monic.normalize_eq_selfₓ'. -/
 theorem Monic.normalize_eq_self {p : R[X]} (hp : p.Monic) : normalize p = p := by
   simp only [Polynomial.coe_normUnit, normalize_apply, hp.leading_coeff, normUnit_one,
@@ -147,7 +147,7 @@ theorem Monic.normalize_eq_self {p : R[X]} (hp : p.Monic) : normalize p = p := b
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (normalize.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.normalizationMonoid.{u1} R _inst_1 _inst_2 _inst_3)) p)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))))) (normalize.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R _inst_1 _inst_2 _inst_3)) p)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))))) (normalize.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R _inst_1 _inst_2 _inst_3)) p)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_normalize Polynomial.roots_normalizeₓ'. -/
 theorem roots_normalize {p : R[X]} : (normalize p).roots = p.roots := by
   rw [normalize_apply, mul_comm, coe_norm_unit, roots_C_mul _ (norm_unit (leading_coeff p)).NeZero]
@@ -177,7 +177,7 @@ theorem degree_pos_of_ne_zero_of_nonunit (hp0 : p ≠ 0) (hp : ¬IsUnit p) : 0 <
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))) -> (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) p)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))))) -> (Polynomial.Monic.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Inv.inv.{u1} R (DivisionRing.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)) p))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Inv.inv.{u1} R (DivisionRing.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)) p)))))
+  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))))) -> (Polynomial.Monic.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Inv.inv.{u1} R (DivisionRing.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)) p))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Inv.inv.{u1} R (DivisionRing.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)) p)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_mul_leading_coeff_inv Polynomial.monic_mul_leadingCoeff_invₓ'. -/
 theorem monic_mul_leadingCoeff_inv (h : p ≠ 0) : Monic (p * C (leadingCoeff p)⁻¹) := by
   rw [monic, leading_coeff_mul, leading_coeff_C,
@@ -188,7 +188,7 @@ theorem monic_mul_leadingCoeff_inv (h : p ≠ 0) : Monic (p * C (leadingCoeff p)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))} (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))), (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) q (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) q))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))} (p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))), (Ne.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) q (OfNat.ofNat.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Inv.inv.{u1} R (DivisionRing.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)) q))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Inv.inv.{u1} R (DivisionRing.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)) q))))) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)) p))
+  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))} (p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))), (Ne.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) q (OfNat.ofNat.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Inv.inv.{u1} R (DivisionRing.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)) q))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))) p (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Inv.inv.{u1} R (DivisionRing.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)) q))))) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_mul_leading_coeff_inv Polynomial.degree_mul_leadingCoeff_invₓ'. -/
 theorem degree_mul_leadingCoeff_inv (p : R[X]) (h : q ≠ 0) :
     degree (p * C (leadingCoeff q)⁻¹) = degree p :=
@@ -272,7 +272,7 @@ instance : Mod R[X] :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.hasDiv.{u1} R _inst_1)) p q) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) q))) (Polynomial.divByMonic.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) p (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) q (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) q))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1)) p q) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q))) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q))) (Polynomial.divByMonic.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) p (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) q (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q))))))
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1)) p q) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q))) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q))) (Polynomial.divByMonic.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) p (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) q (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.div_def Polynomial.div_defₓ'. -/
 theorem div_def : p / q = C (leadingCoeff q)⁻¹ * (p /ₘ (q * C (leadingCoeff q)⁻¹)) :=
   rfl
@@ -282,7 +282,7 @@ theorem div_def : p / q = C (leadingCoeff q)⁻¹ * (p /ₘ (q * C (leadingCoeff
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (HMod.hMod.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHMod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.hasMod.{u1} R _inst_1)) p q) (Polynomial.modByMonic.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) p (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) q (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) q)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (HMod.hMod.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHMod.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instModPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1)) p q) (Polynomial.modByMonic.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) p (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) q (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q)))))
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (HMod.hMod.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHMod.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instModPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1)) p q) (Polynomial.modByMonic.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) p (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) q (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.mod_def Polynomial.mod_defₓ'. -/
 theorem mod_def : p % q = p %ₘ (q * C (leadingCoeff q)⁻¹) :=
   rfl
@@ -305,7 +305,7 @@ theorem divByMonic_eq_div (p : R[X]) (hq : Monic q) : p /ₘ q = p / q :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (a : R), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (HMod.hMod.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHMod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.hasMod.{u1} R _inst_1)) p (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.sub.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) a p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] (p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (a : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.eval.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) a p)) (HMod.hMod.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.eval.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) a p)) (instHMod.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instModPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1)) p (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHSub.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.sub.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.eval.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) a p))
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] (p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (a : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.eval.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) a p)) (HMod.hMod.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.eval.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) a p)) (instHMod.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instModPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1)) p (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHSub.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.sub.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.eval.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) a p))
 Case conversion may be inaccurate. Consider using '#align polynomial.mod_X_sub_C_eq_C_eval Polynomial.mod_X_sub_C_eq_C_evalₓ'. -/
 theorem mod_X_sub_C_eq_C_eval (p : R[X]) (a : R) : p % (X - C a) = C (p.eval a) :=
   modByMonic_eq_mod p (monic_X_sub_C a) ▸ modByMonic_X_sub_C_eq_C_eval _ _
@@ -315,7 +315,7 @@ theorem mod_X_sub_C_eq_C_eval (p : R[X]) (a : R) : p % (X - C a) = C (p.eval a)
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, Iff (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.sub.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a)) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.hasDiv.{u1} R _inst_1)) p (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.sub.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a)))) p) (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) p a)
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, Iff (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHSub.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.sub.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R 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(DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a)) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1)) p (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHSub.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.sub.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a)))) p) (Polynomial.IsRoot.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p a)
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, Iff (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHSub.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.sub.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a)) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1)) p (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHSub.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.sub.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a)))) p) (Polynomial.IsRoot.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p a)
 Case conversion may be inaccurate. Consider using '#align polynomial.mul_div_eq_iff_is_root Polynomial.mul_div_eq_iff_isRootₓ'. -/
 theorem mul_div_eq_iff_isRoot : (X - C a) * (p / (X - C a)) = p ↔ IsRoot p a :=
   divByMonic_eq_div p (monic_X_sub_C a) ▸ mul_divByMonic_eq_iff_isRoot
@@ -430,7 +430,7 @@ theorem natDegree_map [DivisionRing k] (f : R →+* k) : natDegree (p.map f) = n
 lean 3 declaration is
   forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} [_inst_2 : DivisionRing.{u2} k] (f : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))), Eq.{succ u2} k (Polynomial.leadingCoeff.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_2)) (Polynomial.map.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_2)) f p)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))) (fun (_x : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))) => R -> k) (RingHom.hasCoeToFun.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))) f (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) p))
 but is expected to have type
-  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} [_inst_2 : DivisionRing.{u2} k] (f : RingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)))), Eq.{succ u2} k (Polynomial.leadingCoeff.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)) (Polynomial.map.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)) f p)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => k) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)))) R k (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)))) R k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)))) R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2))))))) f (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p))
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} [_inst_2 : DivisionRing.{u2} k] (f : RingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)))), Eq.{succ u2} k (Polynomial.leadingCoeff.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)) (Polynomial.map.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)) f p)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => k) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)))) R k (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)))) R k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)))) R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2))))))) f (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_map Polynomial.leadingCoeff_mapₓ'. -/
 @[simp]
 theorem leadingCoeff_map [DivisionRing k] (f : R →+* k) :
@@ -594,7 +594,7 @@ theorem rootSet_monomial [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn :
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (forall {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) n)) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.hasSingleton.{u2} S) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2))))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (forall {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) Nat (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHPow.{u1, 0} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))))) (Polynomial.X.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) n)) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.instSingletonSet.{u2} S) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} S (IsDomain.toCancelCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3))))))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (forall {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) Nat (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHPow.{u1, 0} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))))) (Polynomial.X.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) n)) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.instSingletonSet.{u2} S) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} S (IsDomain.toCancelCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_C_mul_X_pow Polynomial.rootSet_C_mul_X_powₓ'. -/
 theorem rootSet_C_mul_X_pow [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n ≠ 0) {a : R}
     (ha : a ≠ 0) : (C a * X ^ n).rootSet S = {0} := by
@@ -662,7 +662,7 @@ theorem coeff_inv_units (u : R[X]ˣ) (n : ℕ) : ((↑u : R[X]).coeff n)⁻¹ =
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) -> (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (normalize.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.normalizationMonoid.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.normalizedGcdMonoid.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Polynomial.Monic.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (fun (_x : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (normalize.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p))
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Polynomial.Monic.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (fun (_x : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (normalize.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_normalize Polynomial.monic_normalizeₓ'. -/
 theorem monic_normalize (hp0 : p ≠ 0) : Monic (normalize p) :=
   by
@@ -691,7 +691,7 @@ theorem leadingCoeff_div (hpq : q.degree ≤ p.degree) :
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.hasDiv.{u1} R _inst_1)) p (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a) q)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) a)) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.hasDiv.{u1} R _inst_1)) p q))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1)) p (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) q)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) a)) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) a)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) a)) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) a)) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1)) p q))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1)) p (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) q)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) a)) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) a)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) a)) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) a)) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1)) p q))
 Case conversion may be inaccurate. Consider using '#align polynomial.div_C_mul Polynomial.div_C_mulₓ'. -/
 theorem div_C_mul : p / (C a * q) = C a⁻¹ * (p / q) :=
   by
@@ -706,7 +706,7 @@ theorem div_C_mul : p / (C a * q) = C a⁻¹ * (p / q) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))))))) -> (Iff (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a) p) q) (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) p q))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Iff (Dvd.dvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (semigroupDvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (SemigroupWithZero.toSemigroup.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (NonUnitalSemiring.toSemigroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (CommRing.toNonUnitalCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) p) q) (Dvd.dvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) p q))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Iff (Dvd.dvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (semigroupDvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (SemigroupWithZero.toSemigroup.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (NonUnitalSemiring.toSemigroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (CommRing.toNonUnitalCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) p) q) (Dvd.dvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) p q))
 Case conversion may be inaccurate. Consider using '#align polynomial.C_mul_dvd Polynomial.C_mul_dvdₓ'. -/
 theorem C_mul_dvd (ha : a ≠ 0) : C a * p ∣ q ↔ p ∣ q :=
   ⟨fun h => dvd_trans (dvd_mul_left _ _) h, fun ⟨r, hr⟩ =>
@@ -719,7 +719,7 @@ theorem C_mul_dvd (ha : a ≠ 0) : C a * p ∣ q ↔ p ∣ q :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))))))) -> (Iff (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) p (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a) q)) (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) p q))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Iff (Dvd.dvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) p (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) q)) (Dvd.dvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) p q))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Iff (Dvd.dvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) p (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R 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(DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) q)) (Dvd.dvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R 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(EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) p q))
 Case conversion may be inaccurate. Consider using '#align polynomial.dvd_C_mul Polynomial.dvd_C_mulₓ'. -/
 theorem dvd_C_mul (ha : a ≠ 0) : p ∣ Polynomial.C a * q ↔ p ∣ q :=
   ⟨fun ⟨r, hr⟩ =>
@@ -733,7 +733,7 @@ theorem dvd_C_mul (ha : a ≠ 0) : p ∣ Polynomial.C a * q ↔ p ∣ q :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, 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R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (coeBase.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 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(Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (NormalizationMonoid.normUnit.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.normalizationMonoid.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.normalizedGcdMonoid.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b))))) p)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) p))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Units.val.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (NormalizationMonoid.normUnit.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b))))) p)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p))))
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Units.val.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (NormalizationMonoid.normUnit.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b))))) p)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p))))
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_norm_unit_of_ne_zero Polynomial.coe_normUnit_of_ne_zeroₓ'. -/
 theorem coe_normUnit_of_ne_zero (hp : p ≠ 0) : (normUnit p : R[X]) = C p.leadingCoeff⁻¹ :=
   by
@@ -745,7 +745,7 @@ theorem coe_normUnit_of_ne_zero (hp : p ≠ 0) : (normUnit p : R[X]) = C p.leadi
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) p) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (normalize.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.normalizationMonoid.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.normalizedGcdMonoid.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p) p)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Polynomial.Monic.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (fun (_x : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (normalize.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p) p)
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Polynomial.Monic.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (fun (_x : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (normalize.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.normalize_monic Polynomial.normalize_monicₓ'. -/
 theorem normalize_monic (h : Monic p) : normalize p = p := by simp [h]
 #align polynomial.normalize_monic Polynomial.normalize_monic
@@ -765,7 +765,7 @@ theorem map_dvd_map' [Field k] (f : R →+* k) {x y : R[X]} : x.map f ∣ y.map
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (normalize.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.normalizationMonoid.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.normalizedGcdMonoid.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p)) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) p)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (fun (_x : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (normalize.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p)) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p)
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (fun (_x : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (normalize.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p)) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_normalize Polynomial.degree_normalizeₓ'. -/
 theorem degree_normalize : degree (normalize p) = degree p := by simp
 #align polynomial.degree_normalize Polynomial.degree_normalize
@@ -793,7 +793,7 @@ theorem irreducible_of_degree_eq_one (hp1 : degree p = 1) : Irreducible p :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] (x : R), Not (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] (x : R), Not (Irreducible.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) x) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) x) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) x))
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] (x : R), Not (Irreducible.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) x) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) x) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) x))
 Case conversion may be inaccurate. Consider using '#align polynomial.not_irreducible_C Polynomial.not_irreducible_Cₓ'. -/
 theorem not_irreducible_C (x : R) : ¬Irreducible (C x) :=
   if H : x = 0 then by
@@ -818,7 +818,7 @@ theorem degree_pos_of_irreducible (hp : Irreducible p) : 0 < p.degree :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_2 : Field.{u1} K] (f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (a : K), (Ne.{succ u1} K (Polynomial.eval.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) a (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (fun (_x : LinearMap.{u1, u1, u1, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) => (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} K K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (Polynomial.derivative.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) f)) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))))))))) -> (IsCoprime.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.commSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) a)) (Polynomial.divByMonic.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)) f (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) a))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_2 : Field.{u1} K] (f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (a : K), (Ne.{succ u1} K (Polynomial.eval.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) a (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (fun (_x : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} K K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (Polynomial.derivative.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) f)) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) -> (IsCoprime.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.commSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a)) (Polynomial.divByMonic.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)) f (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a))))
+  forall {K : Type.{u1}} [_inst_2 : Field.{u1} K] (f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (a : K), (Ne.{succ u1} K (Polynomial.eval.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) a (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (fun (_x : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} K K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (Polynomial.derivative.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) f)) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) -> (IsCoprime.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.commSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a)) (Polynomial.divByMonic.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)) f (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a))))
 Case conversion may be inaccurate. Consider using '#align polynomial.is_coprime_of_is_root_of_eval_derivative_ne_zero Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zeroₓ'. -/
 /-- If `f` is a polynomial over a field, and `a : K` satisfies `f' a ≠ 0`,
 then `f / (X - a)` is coprime with `X - a`.

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

@@ -41,7 +41,7 @@ variable [CommRing R] [IsDomain R]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {t : R}, (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p t) -> (Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 t (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {t : R}, (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p t) -> (Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 t (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {t : R}, (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p t) -> (Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 t (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))
 Case conversion may be inaccurate. Consider using '#align polynomial.derivative_root_multiplicity_of_root Polynomial.derivative_rootMultiplicity_of_rootₓ'. -/
 theorem derivative_rootMultiplicity_of_root [CharZero R] {p : R[X]} {t : R} (hpt : p.IsRoot t) :
     p.derivative.rootMultiplicity t = p.rootMultiplicity t - 1 :=
@@ -76,7 +76,7 @@ theorem derivative_rootMultiplicity_of_root [CharZero R] {p : R[X]} {t : R} (hpt
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (t : R), LE.le.{0} Nat Nat.hasLe (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Polynomial.rootMultiplicity.{u1} R _inst_1 t (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (t : R), LE.le.{0} Nat instLENat (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Polynomial.rootMultiplicity.{u1} R _inst_1 t (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (t : R), LE.le.{0} Nat instLENat (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Polynomial.rootMultiplicity.{u1} R _inst_1 t (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_sub_one_le_derivative_root_multiplicity Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicityₓ'. -/
 theorem rootMultiplicity_sub_one_le_derivative_rootMultiplicity [CharZero R] (p : R[X]) (t : R) :
     p.rootMultiplicity t - 1 ≤ p.derivative.rootMultiplicity t :=
@@ -582,7 +582,7 @@ theorem mem_roots_map [CommRing k] [IsDomain k] {f : R →+* k} {x : k} (hp : p
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (forall {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) (Polynomial.monomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) n) a) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.hasSingleton.{u2} S) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2))))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (forall {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (Polynomial.monomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) n) a) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.instSingletonSet.{u2} S) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} S (IsDomain.toCancelCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3))))))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (forall {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (Polynomial.monomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) n) a) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.instSingletonSet.{u2} S) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} S (IsDomain.toCancelCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_monomial Polynomial.rootSet_monomialₓ'. -/
 theorem rootSet_monomial [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n ≠ 0) {a : R}
     (ha : a ≠ 0) : (monomial n a).rootSet S = {0} := by
@@ -818,7 +818,7 @@ theorem degree_pos_of_irreducible (hp : Irreducible p) : 0 < p.degree :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_2 : Field.{u1} K] (f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (a : K), (Ne.{succ u1} K (Polynomial.eval.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) a (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (fun (_x : LinearMap.{u1, u1, u1, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) => (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} K K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (Polynomial.derivative.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) f)) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))))))))) -> (IsCoprime.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.commSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) a)) (Polynomial.divByMonic.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)) f (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) a))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_2 : Field.{u1} K] (f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (a : K), (Ne.{succ u1} K (Polynomial.eval.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) a (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (fun (_x : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} K K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (Polynomial.derivative.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) f)) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) -> (IsCoprime.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.commSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a)) (Polynomial.divByMonic.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)) f (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a))))
+  forall {K : Type.{u1}} [_inst_2 : Field.{u1} K] (f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (a : K), (Ne.{succ u1} K (Polynomial.eval.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) a (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (fun (_x : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} K K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (Polynomial.derivative.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) f)) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) -> (IsCoprime.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.commSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a)) (Polynomial.divByMonic.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)) f (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a))))
 Case conversion may be inaccurate. Consider using '#align polynomial.is_coprime_of_is_root_of_eval_derivative_ne_zero Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zeroₓ'. -/
 /-- If `f` is a polynomial over a field, and `a : K` satisfies `f' a ≠ 0`,
 then `f / (X - a)` is coprime with `X - a`.

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

@@ -163,7 +163,7 @@ variable [DivisionRing R] {p q : R[X]}
 
 /- warning: polynomial.degree_pos_of_ne_zero_of_nonunit -> Polynomial.degree_pos_of_ne_zero_of_nonunit is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))) -> (Not (IsUnit.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) p))
+  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))) -> (Not (IsUnit.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) p))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))))) -> (Not (IsUnit.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) p)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_pos_of_ne_zero_of_nonunit Polynomial.degree_pos_of_ne_zero_of_nonunitₓ'. -/
@@ -333,7 +333,12 @@ instance : EuclideanDomain R[X] :=
     remainder_lt := fun p q hq => remainder_lt_aux _ hq
     mul_left_not_lt := fun p q hq => not_lt_of_ge (degree_le_mul_left _ hq) }
 
-#print Polynomial.mod_eq_self_iff /-
+/- warning: polynomial.mod_eq_self_iff -> Polynomial.mod_eq_self_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) q (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) -> (Iff (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (HMod.hMod.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHMod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.hasMod.{u1} R _inst_1)) p q) p) (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) p) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) q)))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.mod_eq_self_iff Polynomial.mod_eq_self_iffₓ'. -/
 theorem mod_eq_self_iff (hq0 : q ≠ 0) : p % q = p ↔ degree p < degree q :=
   ⟨fun h => h ▸ EuclideanDomain.mod_lt _ hq0, fun h =>
     by
@@ -343,9 +348,13 @@ theorem mod_eq_self_iff (hq0 : q ≠ 0) : p % q = p ↔ degree p < degree q :=
     unfold div_mod_by_monic_aux
     simp only [this, false_and_iff, if_false]⟩
 #align polynomial.mod_eq_self_iff Polynomial.mod_eq_self_iff
--/
 
-#print Polynomial.div_eq_zero_iff /-
+/- warning: polynomial.div_eq_zero_iff -> Polynomial.div_eq_zero_iff is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.div_eq_zero_iff Polynomial.div_eq_zero_iffₓ'. -/
 theorem div_eq_zero_iff (hq0 : q ≠ 0) : p / q = 0 ↔ degree p < degree q :=
   ⟨fun h => by
     have := EuclideanDomain.div_add_mod p q <;>
@@ -357,9 +366,13 @@ theorem div_eq_zero_iff (hq0 : q ≠ 0) : p / q = 0 ↔ degree p < degree q :=
     have hm : Monic (q * C (leadingCoeff q)⁻¹) := monic_mul_leadingCoeff_inv hq0
     rw [div_def, (div_by_monic_eq_zero_iff hm).2 hlt, MulZeroClass.mul_zero]⟩
 #align polynomial.div_eq_zero_iff Polynomial.div_eq_zero_iff
--/
 
-#print Polynomial.degree_add_div /-
+/- warning: polynomial.degree_add_div -> Polynomial.degree_add_div is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.degree_add_div Polynomial.degree_add_divₓ'. -/
 theorem degree_add_div (hq0 : q ≠ 0) (hpq : degree q ≤ degree p) :
     degree q + degree (p / q) = degree p :=
   by
@@ -371,17 +384,25 @@ theorem degree_add_div (hq0 : q ≠ 0) (hpq : degree q ≤ degree p) :
   conv_rhs =>
     rw [← EuclideanDomain.div_add_mod p q, degree_add_eq_left_of_degree_lt this, degree_mul]
 #align polynomial.degree_add_div Polynomial.degree_add_div
--/
 
-#print Polynomial.degree_div_le /-
+/- warning: polynomial.degree_div_le -> Polynomial.degree_div_le is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.degree_div_le Polynomial.degree_div_leₓ'. -/
 theorem degree_div_le (p q : R[X]) : degree (p / q) ≤ degree p :=
   if hq : q = 0 then by simp [hq]
   else by
     rw [div_def, mul_comm, degree_mul_leading_coeff_inv _ hq] <;> exact degree_div_by_monic_le _ _
 #align polynomial.degree_div_le Polynomial.degree_div_le
--/
 
-#print Polynomial.degree_div_lt /-
+/- warning: polynomial.degree_div_lt -> Polynomial.degree_div_lt is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) q)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.hasDiv.{u1} R _inst_1)) p q)) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) p))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.degree_div_lt Polynomial.degree_div_ltₓ'. -/
 theorem degree_div_lt (hp : p ≠ 0) (hq : 0 < degree q) : degree (p / q) < degree p :=
   by
   have hq0 : q ≠ 0 := fun hq0 => by simpa [hq0] using hq
@@ -390,7 +411,6 @@ theorem degree_div_lt (hp : p ≠ 0) (hq : 0 < degree q) : degree (p / q) < degr
       degree_div_by_monic_lt _ (monic_mul_leading_coeff_inv hq0) hp
         (by rw [degree_mul_leading_coeff_inv _ hq0] <;> exact hq)
 #align polynomial.degree_div_lt Polynomial.degree_div_lt
--/
 
 #print Polynomial.degree_map /-
 @[simp]
@@ -653,7 +673,7 @@ theorem monic_normalize (hp0 : p ≠ 0) : Monic (normalize p) :=
 
 /- warning: polynomial.leading_coeff_div -> Polynomial.leadingCoeff_div is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{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.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) q) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) p)) -> (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.hasDiv.{u1} R _inst_1)) p q)) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) p) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) q)))
 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_div Polynomial.leadingCoeff_divₓ'. -/
@@ -784,7 +804,7 @@ theorem not_irreducible_C (x : R) : ¬Irreducible (C x) :=
 
 /- warning: polynomial.degree_pos_of_irreducible -> Polynomial.degree_pos_of_irreducible is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) p) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) p))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) p) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_pos_of_irreducible Polynomial.degree_pos_of_irreducibleₓ'. -/

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

@@ -686,7 +686,7 @@ theorem div_C_mul : p / (C a * q) = C a⁻¹ * (p / q) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))))))) -> (Iff (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a) p) q) (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) p q))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Iff (Dvd.dvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (semigroupDvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (SemigroupWithZero.toSemigroup.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (NonUnitalSemiring.toSemigroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (CommRing.toNonUnitalCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.commRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) p) q) (Dvd.dvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))))))) p q))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Iff (Dvd.dvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (semigroupDvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (SemigroupWithZero.toSemigroup.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (NonUnitalSemiring.toSemigroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (CommRing.toNonUnitalCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) p) q) (Dvd.dvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) p q))
 Case conversion may be inaccurate. Consider using '#align polynomial.C_mul_dvd Polynomial.C_mul_dvdₓ'. -/
 theorem C_mul_dvd (ha : a ≠ 0) : C a * p ∣ q ↔ p ∣ q :=
   ⟨fun h => dvd_trans (dvd_mul_left _ _) h, fun ⟨r, hr⟩ =>
@@ -699,7 +699,7 @@ theorem C_mul_dvd (ha : a ≠ 0) : C a * p ∣ q ↔ p ∣ q :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))))))) -> (Iff (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) p (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a) q)) (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) p q))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Iff (Dvd.dvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))))))) p (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) q)) (Dvd.dvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))))))) p q))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Iff (Dvd.dvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) p (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) q)) (Dvd.dvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) p q))
 Case conversion may be inaccurate. Consider using '#align polynomial.dvd_C_mul Polynomial.dvd_C_mulₓ'. -/
 theorem dvd_C_mul (ha : a ≠ 0) : p ∣ Polynomial.C a * q ↔ p ∣ q :=
   ⟨fun ⟨r, hr⟩ =>

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -596,15 +596,15 @@ theorem rootSet_X_pow [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n
 
 /- warning: polynomial.root_set_prod -> Polynomial.rootSet_prod is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {ι : Type.{u3}} (f : ι -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (s : Finset.{u3} ι), (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Finset.prod.{u1, u3} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) s f) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Finset.prod.{u1, u3} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) s f) S _inst_2 _inst_3 _inst_4) (Set.unionᵢ.{u2, succ u3} S ι (fun (i : ι) => Set.unionᵢ.{u2, 0} S (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) (fun (H : Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) => Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (f i) S _inst_2 _inst_3 _inst_4))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {ι : Type.{u3}} (f : ι -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (s : Finset.{u3} ι), (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Finset.prod.{u1, u3} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) s f) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Finset.prod.{u1, u3} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) s f) S _inst_2 _inst_3 _inst_4) (Set.iUnion.{u2, succ u3} S ι (fun (i : ι) => Set.iUnion.{u2, 0} S (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) (fun (H : Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) => Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (f i) S _inst_2 _inst_3 _inst_4))))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : Field.{u2} R] [_inst_2 : CommRing.{u3} S] [_inst_3 : IsDomain.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] [_inst_4 : Algebra.{u2, u3} R S (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] {ι : Type.{u1}} (f : ι -> (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1))))) (s : Finset.{u1} ι), (Ne.{succ u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) (Finset.prod.{u2, u1} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) (Polynomial.commRing.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R _inst_1)))) s f) (OfNat.ofNat.{u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) (Polynomial.zero.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1))))))) -> (Eq.{succ u3} (Set.{u3} S) (Polynomial.rootSet.{u2, u3} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R _inst_1)) (Finset.prod.{u2, u1} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) (Polynomial.commRing.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R _inst_1)))) s f) S _inst_2 _inst_3 _inst_4) (Set.unionᵢ.{u3, succ u1} S ι (fun (i : ι) => Set.unionᵢ.{u3, 0} S (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) (fun (H : Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) => Polynomial.rootSet.{u2, u3} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R _inst_1)) (f i) S _inst_2 _inst_3 _inst_4))))
+  forall {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : Field.{u2} R] [_inst_2 : CommRing.{u3} S] [_inst_3 : IsDomain.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] [_inst_4 : Algebra.{u2, u3} R S (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] {ι : Type.{u1}} (f : ι -> (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1))))) (s : Finset.{u1} ι), (Ne.{succ u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) (Finset.prod.{u2, u1} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) (Polynomial.commRing.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R _inst_1)))) s f) (OfNat.ofNat.{u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) (Polynomial.zero.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1))))))) -> (Eq.{succ u3} (Set.{u3} S) (Polynomial.rootSet.{u2, u3} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R _inst_1)) (Finset.prod.{u2, u1} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) (Polynomial.commRing.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R _inst_1)))) s f) S _inst_2 _inst_3 _inst_4) (Set.iUnion.{u3, succ u1} S ι (fun (i : ι) => Set.iUnion.{u3, 0} S (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) (fun (H : Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) => Polynomial.rootSet.{u2, u3} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R _inst_1)) (f i) S _inst_2 _inst_3 _inst_4))))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_prod Polynomial.rootSet_prodₓ'. -/
 theorem rootSet_prod [CommRing S] [IsDomain S] [Algebra R S] {ι : Type _} (f : ι → R[X])
     (s : Finset ι) (h : s.Prod f ≠ 0) : (s.Prod f).rootSet S = ⋃ i ∈ s, (f i).rootSet S :=
   by
   simp only [root_set, ← Finset.mem_coe]
-  rw [Polynomial.map_prod, roots_prod, Finset.bind_toFinset, s.val_to_finset, Finset.coe_bunionᵢ]
+  rw [Polynomial.map_prod, roots_prod, Finset.bind_toFinset, s.val_to_finset, Finset.coe_biUnion]
   rwa [← Polynomial.map_prod, Ne, map_eq_zero]
 #align polynomial.root_set_prod Polynomial.rootSet_prod
 

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

@@ -41,7 +41,7 @@ variable [CommRing R] [IsDomain R]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {t : R}, (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p t) -> (Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 t (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {t : R}, (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p t) -> (Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 t (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {t : R}, (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p t) -> (Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 t (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))
 Case conversion may be inaccurate. Consider using '#align polynomial.derivative_root_multiplicity_of_root Polynomial.derivative_rootMultiplicity_of_rootₓ'. -/
 theorem derivative_rootMultiplicity_of_root [CharZero R] {p : R[X]} {t : R} (hpt : p.IsRoot t) :
     p.derivative.rootMultiplicity t = p.rootMultiplicity t - 1 :=
@@ -76,7 +76,7 @@ theorem derivative_rootMultiplicity_of_root [CharZero R] {p : R[X]} {t : R} (hpt
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (t : R), LE.le.{0} Nat Nat.hasLe (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Polynomial.rootMultiplicity.{u1} R _inst_1 t (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (t : R), LE.le.{0} Nat instLENat (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Polynomial.rootMultiplicity.{u1} R _inst_1 t (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (t : R), LE.le.{0} Nat instLENat (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Polynomial.rootMultiplicity.{u1} R _inst_1 t (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_sub_one_le_derivative_root_multiplicity Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicityₓ'. -/
 theorem rootMultiplicity_sub_one_le_derivative_rootMultiplicity [CharZero R] (p : R[X]) (t : R) :
     p.rootMultiplicity t - 1 ≤ p.derivative.rootMultiplicity t :=
@@ -115,7 +115,7 @@ instance : NormalizationMonoid R[X]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeBase.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Units.hasCoe.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))))) (NormalizationMonoid.normUnit.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.normalizationMonoid.{u1} R _inst_1 _inst_2 _inst_3) p)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) R (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) R (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) R (coeBase.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) R (Units.hasCoe.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))))) (NormalizationMonoid.normUnit.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2) _inst_3 (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Units.val.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (NormalizationMonoid.normUnit.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.instNormalizationMonoidPolynomialToSemiringToRingToCancelCommMonoidWithZeroCommSemiringToCommSemiringInstIsDomainPolynomialToSemiringSemiring.{u1} R _inst_1 _inst_2 _inst_3) p)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (NormalizationMonoid.normUnit.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2) _inst_3 (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Units.val.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (NormalizationMonoid.normUnit.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R _inst_1 _inst_2 _inst_3) p)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (NormalizationMonoid.normUnit.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2) _inst_3 (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p))))
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_norm_unit Polynomial.coe_normUnitₓ'. -/
 @[simp]
 theorem coe_normUnit {p : R[X]} : (normUnit p : R[X]) = C ↑(normUnit p.leadingCoeff) := by
@@ -126,7 +126,7 @@ theorem coe_normUnit {p : R[X]} : (normUnit p : R[X]) = C ↑(normUnit p.leading
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (normalize.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.normalizationMonoid.{u1} R _inst_1 _inst_2 _inst_3)) p)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) (fun (_x : MonoidWithZeroHom.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) => R -> R) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) (normalize.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2) _inst_3) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))))) (normalize.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.instNormalizationMonoidPolynomialToSemiringToRingToCancelCommMonoidWithZeroCommSemiringToCommSemiringInstIsDomainPolynomialToSemiringSemiring.{u1} R _inst_1 _inst_2 _inst_3)) p)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) R R (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) R R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))))) (normalize.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2) _inst_3) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R 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(MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) R R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))) R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} R R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))))) (normalize.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2) _inst_3) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_normalize Polynomial.leadingCoeff_normalizeₓ'. -/
 theorem leadingCoeff_normalize (p : R[X]) :
     leadingCoeff (normalize p) = normalize (leadingCoeff p) := by simp
@@ -136,7 +136,7 @@ theorem leadingCoeff_normalize (p : R[X]) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (normalize.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.normalizationMonoid.{u1} R _inst_1 _inst_2 _inst_3)) p) p)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))))) (normalize.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.instNormalizationMonoidPolynomialToSemiringToRingToCancelCommMonoidWithZeroCommSemiringToCommSemiringInstIsDomainPolynomialToSemiringSemiring.{u1} R _inst_1 _inst_2 _inst_3)) p) p)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))))) (normalize.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R _inst_1 _inst_2 _inst_3)) p) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.monic.normalize_eq_self Polynomial.Monic.normalize_eq_selfₓ'. -/
 theorem Monic.normalize_eq_self {p : R[X]} (hp : p.Monic) : normalize p = p := by
   simp only [Polynomial.coe_normUnit, normalize_apply, hp.leading_coeff, normUnit_one,
@@ -147,7 +147,7 @@ theorem Monic.normalize_eq_self {p : R[X]} (hp : p.Monic) : normalize p = p := b
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (normalize.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.normalizationMonoid.{u1} R _inst_1 _inst_2 _inst_3)) p)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))))) (normalize.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.instNormalizationMonoidPolynomialToSemiringToRingToCancelCommMonoidWithZeroCommSemiringToCommSemiringInstIsDomainPolynomialToSemiringSemiring.{u1} R _inst_1 _inst_2 _inst_3)) p)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))))) (normalize.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R _inst_1 _inst_2 _inst_3)) p)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_normalize Polynomial.roots_normalizeₓ'. -/
 theorem roots_normalize {p : R[X]} : (normalize p).roots = p.roots := by
   rw [normalize_apply, mul_comm, coe_norm_unit, roots_C_mul _ (norm_unit (leading_coeff p)).NeZero]
@@ -410,7 +410,7 @@ theorem natDegree_map [DivisionRing k] (f : R →+* k) : natDegree (p.map f) = n
 lean 3 declaration is
   forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} [_inst_2 : DivisionRing.{u2} k] (f : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))), Eq.{succ u2} k (Polynomial.leadingCoeff.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_2)) (Polynomial.map.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_2)) f p)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))) (fun (_x : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))) => R -> k) (RingHom.hasCoeToFun.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))) f (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) p))
 but is expected to have type
-  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} [_inst_2 : DivisionRing.{u2} k] (f : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))), Eq.{succ u2} k (Polynomial.leadingCoeff.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)) (Polynomial.map.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)) f p)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => k) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))) R k (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))) R k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))) R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2))))))) f (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p))
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} [_inst_2 : DivisionRing.{u2} k] (f : RingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)))), Eq.{succ u2} k (Polynomial.leadingCoeff.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)) (Polynomial.map.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)) f p)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => k) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)))) R k (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)))) R k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)))) R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2))))))) f (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_map Polynomial.leadingCoeff_mapₓ'. -/
 @[simp]
 theorem leadingCoeff_map [DivisionRing k] (f : R →+* k) :
@@ -428,7 +428,7 @@ theorem monic_map_iff [DivisionRing k] {f : R →+* k} {p : R[X]} : (p.map f).Mo
 lean 3 declaration is
   forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} [_inst_2 : Field.{u2} k] (f : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2))))), Iff (IsUnit.{u2} (Polynomial.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2)))) (Ring.toMonoid.{u2} (Polynomial.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2)))) (Polynomial.ring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2)))) (Polynomial.map.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2))) f p)) (IsUnit.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) p)
 but is expected to have type
-  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} [_inst_2 : Field.{u2} k] (f : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2))))), Iff (IsUnit.{u2} (Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) (MonoidWithZero.toMonoid.{u2} (Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) (Semiring.toMonoidWithZero.{u2} (Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) (Polynomial.semiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))))) (Polynomial.map.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2))) f p)) (IsUnit.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) p)
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} [_inst_2 : Field.{u2} k] (f : RingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2))))), Iff (IsUnit.{u2} (Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) (MonoidWithZero.toMonoid.{u2} (Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) (Semiring.toMonoidWithZero.{u2} (Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) (Polynomial.semiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))))) (Polynomial.map.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2))) f p)) (IsUnit.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.is_unit_map Polynomial.isUnit_mapₓ'. -/
 theorem isUnit_map [Field k] (f : R →+* k) : IsUnit (p.map f) ↔ IsUnit p := by
   simp_rw [is_unit_iff_degree_eq_zero, degree_map]
@@ -461,7 +461,7 @@ open EuclideanDomain
 lean 3 declaration is
   forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} [_inst_2 : Field.{u2} k] (f : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2))))), Eq.{succ u2} (Polynomial.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2)))) (EuclideanDomain.gcd.{u2} (Polynomial.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2)))) (Polynomial.euclideanDomain.{u2} k _inst_2) (fun (a : Polynomial.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2)))) (b : Polynomial.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2)))) => Classical.propDecidable (Eq.{succ u2} (Polynomial.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2)))) a b)) (Polynomial.map.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2))) f p) (Polynomial.map.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2))) f q)) (Polynomial.map.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2))) f (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.euclideanDomain.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (b : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a b)) p q))
 but is expected to have type
-  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} [_inst_2 : Field.{u2} k] (f : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2))))), Eq.{succ u2} (Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) (EuclideanDomain.gcd.{u2} (Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} k _inst_2) (fun (a : Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) (b : Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) => Classical.propDecidable (Eq.{succ u2} (Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) a b)) (Polynomial.map.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2))) f p) (Polynomial.map.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2))) f q)) (Polynomial.map.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2))) f (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (b : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a b)) p q))
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} [_inst_2 : Field.{u2} k] (f : RingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2))))), Eq.{succ u2} (Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) (EuclideanDomain.gcd.{u2} (Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} k _inst_2) (fun (a : Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) (b : Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) => Classical.propDecidable (Eq.{succ u2} (Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) a b)) (Polynomial.map.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2))) f p) (Polynomial.map.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2))) f q)) (Polynomial.map.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2))) f (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (b : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a b)) p q))
 Case conversion may be inaccurate. Consider using '#align polynomial.gcd_map Polynomial.gcd_mapₓ'. -/
 theorem gcd_map [Field k] (f : R →+* k) : gcd (p.map f) (q.map f) = (gcd p q).map f :=
   GCD.induction p q (fun x => by simp_rw [Polynomial.map_zero, EuclideanDomain.gcd_zero_left])
@@ -474,7 +474,7 @@ end
 lean 3 declaration is
   forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommSemiring.{u2} k] {ϕ : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))} {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {α : k}, (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α f) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))))))))) -> (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α g) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))))))))) -> (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.euclideanDomain.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (b : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a b)) f g)) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommSemiring.{u2} k] {ϕ : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))} {f : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {g : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {α : k}, (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α f) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2))))) -> (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α g) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2))))) -> (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (b : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a b)) f g)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2)))))
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommSemiring.{u2} k] {ϕ : RingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))} {f : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {g : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {α : k}, (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α f) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2))))) -> (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α g) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2))))) -> (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (b : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a b)) f g)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_gcd_eq_zero Polynomial.eval₂_gcd_eq_zeroₓ'. -/
 theorem eval₂_gcd_eq_zero [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α : k} (hf : f.eval₂ ϕ α = 0)
     (hg : g.eval₂ ϕ α = 0) : (EuclideanDomain.gcd f g).eval₂ ϕ α = 0 := by
@@ -497,7 +497,7 @@ theorem eval_gcd_eq_zero {f g : R[X]} {α : R} (hf : f.eval α = 0) (hg : g.eval
 lean 3 declaration is
   forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommSemiring.{u2} k] {ϕ : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))} {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {α : k}, (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.euclideanDomain.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (b : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a b)) f g)) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))))))))) -> (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α f) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommSemiring.{u2} k] {ϕ : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))} {f : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {g : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {α : k}, (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (b : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a b)) f g)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2))))) -> (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α f) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2)))))
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommSemiring.{u2} k] {ϕ : RingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))} {f : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {g : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {α : k}, (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (b : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a b)) f g)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2))))) -> (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α f) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_left_of_root_gcd Polynomial.root_left_of_root_gcdₓ'. -/
 theorem root_left_of_root_gcd [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α : k}
     (hα : (EuclideanDomain.gcd f g).eval₂ ϕ α = 0) : f.eval₂ ϕ α = 0 :=
@@ -510,7 +510,7 @@ theorem root_left_of_root_gcd [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α
 lean 3 declaration is
   forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommSemiring.{u2} k] {ϕ : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))} {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {α : k}, (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.euclideanDomain.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (b : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a b)) f g)) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))))))))) -> (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α g) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommSemiring.{u2} k] {ϕ : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))} {f : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {g : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {α : k}, (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (b : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a b)) f g)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2))))) -> (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α g) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2)))))
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommSemiring.{u2} k] {ϕ : RingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))} {f : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {g : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {α : k}, (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (b : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a b)) f g)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2))))) -> (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α g) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_right_of_root_gcd Polynomial.root_right_of_root_gcdₓ'. -/
 theorem root_right_of_root_gcd [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α : k}
     (hα : (EuclideanDomain.gcd f g).eval₂ ϕ α = 0) : g.eval₂ ϕ α = 0 :=
@@ -523,7 +523,7 @@ theorem root_right_of_root_gcd [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {
 lean 3 declaration is
   forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommSemiring.{u2} k] {ϕ : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))} {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {α : k}, Iff (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.euclideanDomain.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (b : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a b)) f g)) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))))))))) (And (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α f) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))))))))) (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α g) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommSemiring.{u2} k] {ϕ : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))} {f : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {g : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {α : k}, Iff (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (b : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a b)) f g)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2))))) (And (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α f) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2))))) (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α g) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2))))))
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommSemiring.{u2} k] {ϕ : RingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))} {f : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {g : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {α : k}, Iff (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (b : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a b)) f g)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2))))) (And (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α f) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2))))) (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α g) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_gcd_iff_root_left_right Polynomial.root_gcd_iff_root_left_rightₓ'. -/
 theorem root_gcd_iff_root_left_right [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α : k} :
     (EuclideanDomain.gcd f g).eval₂ ϕ α = 0 ↔ f.eval₂ ϕ α = 0 ∧ g.eval₂ ϕ α = 0 :=
@@ -551,7 +551,7 @@ theorem isCoprime_map [Field k] (f : R →+* k) : IsCoprime (p.map f) (q.map f)
 lean 3 declaration is
   forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} [_inst_2 : CommRing.{u2} k] [_inst_3 : IsDomain.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_2))] {f : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_2)))} {x : k}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) -> (Iff (Membership.Mem.{u2, u2} k (Multiset.{u2} k) (Multiset.hasMem.{u2} k) x (Polynomial.roots.{u2} k _inst_2 _inst_3 (Polynomial.map.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_2)) f p))) (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_2)) f x p) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_2)))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} [_inst_2 : CommRing.{u2} k] [_inst_3 : IsDomain.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_2))] {f : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_2)))} {x : k}, (Ne.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Iff (Membership.mem.{u2, u2} k (Multiset.{u2} k) (Multiset.instMembershipMultiset.{u2} k) x (Polynomial.roots.{u2} k _inst_2 _inst_3 (Polynomial.map.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_2)) f p))) (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_2)) f x p) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} k (IsDomain.toCancelCommMonoidWithZero.{u2} k (CommRing.toCommSemiring.{u2} k _inst_2) _inst_3)))))))
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} [_inst_2 : CommRing.{u2} k] [_inst_3 : IsDomain.{u2} k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_2))] {f : RingHom.{u1, u2} R k (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_2)))} {x : k}, (Ne.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Iff (Membership.mem.{u2, u2} k (Multiset.{u2} k) (Multiset.instMembershipMultiset.{u2} k) x (Polynomial.roots.{u2} k _inst_2 _inst_3 (Polynomial.map.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_2)) f p))) (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_2)) f x p) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} k (IsDomain.toCancelCommMonoidWithZero.{u2} k (CommRing.toCommSemiring.{u2} k _inst_2) _inst_3)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_roots_map Polynomial.mem_roots_mapₓ'. -/
 theorem mem_roots_map [CommRing k] [IsDomain k] {f : R →+* k} {x : k} (hp : p ≠ 0) :
     x ∈ (p.map f).roots ↔ p.eval₂ f x = 0 := by
@@ -562,7 +562,7 @@ theorem mem_roots_map [CommRing k] [IsDomain k] {f : R →+* k} {x : k} (hp : p
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (forall {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))) (Polynomial.monomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) n) a) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.hasSingleton.{u2} S) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2))))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (forall {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (Polynomial.monomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) n) a) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.instSingletonSet.{u2} S) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} S (IsDomain.toCancelCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3))))))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (forall {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (Polynomial.monomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) n) a) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.instSingletonSet.{u2} S) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} S (IsDomain.toCancelCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_monomial Polynomial.rootSet_monomialₓ'. -/
 theorem rootSet_monomial [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n ≠ 0) {a : R}
     (ha : a ≠ 0) : (monomial n a).rootSet S = {0} := by
@@ -574,7 +574,7 @@ theorem rootSet_monomial [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn :
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (forall {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) n)) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.hasSingleton.{u2} S) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2))))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (forall {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) Nat (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHPow.{u1, 0} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))))) (Polynomial.X.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) n)) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.instSingletonSet.{u2} S) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} S (IsDomain.toCancelCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3))))))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (forall {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) Nat (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHPow.{u1, 0} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))))) (Polynomial.X.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) n)) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.instSingletonSet.{u2} S) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} S (IsDomain.toCancelCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_C_mul_X_pow Polynomial.rootSet_C_mul_X_powₓ'. -/
 theorem rootSet_C_mul_X_pow [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n ≠ 0) {a : R}
     (ha : a ≠ 0) : (C a * X ^ n).rootSet S = {0} := by
@@ -585,7 +585,7 @@ theorem rootSet_C_mul_X_pow [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (h
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) n) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.hasSingleton.{u2} S) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) Nat (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHPow.{u1, 0} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))))) (Polynomial.X.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) n) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.instSingletonSet.{u2} S) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} S (IsDomain.toCancelCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3)))))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) Nat (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHPow.{u1, 0} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))))) (Polynomial.X.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) n) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.instSingletonSet.{u2} S) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} S (IsDomain.toCancelCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_X_pow Polynomial.rootSet_X_powₓ'. -/
 theorem rootSet_X_pow [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n ≠ 0) :
     (X ^ n : R[X]).rootSet S = {0} :=
@@ -598,7 +598,7 @@ theorem rootSet_X_pow [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {ι : Type.{u3}} (f : ι -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (s : Finset.{u3} ι), (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Finset.prod.{u1, u3} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) s f) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Finset.prod.{u1, u3} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) s f) S _inst_2 _inst_3 _inst_4) (Set.unionᵢ.{u2, succ u3} S ι (fun (i : ι) => Set.unionᵢ.{u2, 0} S (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) (fun (H : Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) => Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (f i) S _inst_2 _inst_3 _inst_4))))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : Field.{u2} R] [_inst_2 : CommRing.{u3} S] [_inst_3 : IsDomain.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))] [_inst_4 : Algebra.{u2, u3} R S (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))] {ι : Type.{u1}} (f : ι -> (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1))))) (s : Finset.{u1} ι), (Ne.{succ u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) (Finset.prod.{u2, u1} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) (Polynomial.commRing.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R _inst_1)))) s f) (OfNat.ofNat.{u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) (Polynomial.zero.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1))))))) -> (Eq.{succ u3} (Set.{u3} S) (Polynomial.rootSet.{u2, u3} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R _inst_1)) (Finset.prod.{u2, u1} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) (Polynomial.commRing.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R _inst_1)))) s f) S _inst_2 _inst_3 _inst_4) (Set.unionᵢ.{u3, succ u1} S ι (fun (i : ι) => Set.unionᵢ.{u3, 0} S (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) (fun (H : Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) => Polynomial.rootSet.{u2, u3} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R _inst_1)) (f i) S _inst_2 _inst_3 _inst_4))))
+  forall {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : Field.{u2} R] [_inst_2 : CommRing.{u3} S] [_inst_3 : IsDomain.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] [_inst_4 : Algebra.{u2, u3} R S (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] {ι : Type.{u1}} (f : ι -> (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1))))) (s : Finset.{u1} ι), (Ne.{succ u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) (Finset.prod.{u2, u1} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) (Polynomial.commRing.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R _inst_1)))) s f) (OfNat.ofNat.{u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) (Polynomial.zero.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1))))))) -> (Eq.{succ u3} (Set.{u3} S) (Polynomial.rootSet.{u2, u3} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R _inst_1)) (Finset.prod.{u2, u1} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) (Polynomial.commRing.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R _inst_1)))) s f) S _inst_2 _inst_3 _inst_4) (Set.unionᵢ.{u3, succ u1} S ι (fun (i : ι) => Set.unionᵢ.{u3, 0} S (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) (fun (H : Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) => Polynomial.rootSet.{u2, u3} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R _inst_1)) (f i) S _inst_2 _inst_3 _inst_4))))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_prod Polynomial.rootSet_prodₓ'. -/
 theorem rootSet_prod [CommRing S] [IsDomain S] [Algebra R S] {ι : Type _} (f : ι → R[X])
     (s : Finset ι) (h : s.Prod f ≠ 0) : (s.Prod f).rootSet S = ⋃ i ∈ s, (f i).rootSet S :=
@@ -642,7 +642,7 @@ theorem coeff_inv_units (u : R[X]ˣ) (n : ℕ) : ((↑u : R[X]).coeff n)⁻¹ =
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) -> (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (normalize.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.normalizationMonoid.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.normalizedGcdMonoid.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Polynomial.Monic.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (fun (_x : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (normalize.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToRingToCancelCommMonoidWithZeroCommSemiringToCommSemiringInstIsDomainPolynomialToSemiringSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p))
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Polynomial.Monic.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (fun (_x : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (normalize.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_normalize Polynomial.monic_normalizeₓ'. -/
 theorem monic_normalize (hp0 : p ≠ 0) : Monic (normalize p) :=
   by
@@ -686,7 +686,7 @@ theorem div_C_mul : p / (C a * q) = C a⁻¹ * (p / q) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))))))) -> (Iff (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a) p) q) (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) p q))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Iff (Dvd.dvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (semigroupDvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (SemigroupWithZero.toSemigroup.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (NonUnitalSemiring.toSemigroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (NonUnitalRing.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (NonUnitalCommRing.toNonUnitalRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (CommRing.toNonUnitalCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1)))))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) p) q) (Dvd.dvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1)))))))) p q))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Iff (Dvd.dvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (semigroupDvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (SemigroupWithZero.toSemigroup.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (NonUnitalSemiring.toSemigroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (CommRing.toNonUnitalCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.commRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) p) q) (Dvd.dvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))))))) p q))
 Case conversion may be inaccurate. Consider using '#align polynomial.C_mul_dvd Polynomial.C_mul_dvdₓ'. -/
 theorem C_mul_dvd (ha : a ≠ 0) : C a * p ∣ q ↔ p ∣ q :=
   ⟨fun h => dvd_trans (dvd_mul_left _ _) h, fun ⟨r, hr⟩ =>
@@ -699,7 +699,7 @@ theorem C_mul_dvd (ha : a ≠ 0) : C a * p ∣ q ↔ p ∣ q :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))))))) -> (Iff (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) p (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a) q)) (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))))))))) p q))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Iff (Dvd.dvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1)))))))) p (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) q)) (Dvd.dvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1)))))))) p q))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Iff (Dvd.dvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))))))) p (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) q)) (Dvd.dvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))))))) p q))
 Case conversion may be inaccurate. Consider using '#align polynomial.dvd_C_mul Polynomial.dvd_C_mulₓ'. -/
 theorem dvd_C_mul (ha : a ≠ 0) : p ∣ Polynomial.C a * q ↔ p ∣ q :=
   ⟨fun ⟨r, hr⟩ =>
@@ -713,7 +713,7 @@ theorem dvd_C_mul (ha : a ≠ 0) : p ∣ Polynomial.C a * q ↔ p ∣ q :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (coeBase.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Units.hasCoe.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (NormalizationMonoid.normUnit.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.normalizationMonoid.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.normalizedGcdMonoid.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b))))) p)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) p))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Units.val.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (NormalizationMonoid.normUnit.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToRingToCancelCommMonoidWithZeroCommSemiringToCommSemiringInstIsDomainPolynomialToSemiringSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b))))) p)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p))))
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Units.val.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (NormalizationMonoid.normUnit.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b))))) p)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p))))
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_norm_unit_of_ne_zero Polynomial.coe_normUnit_of_ne_zeroₓ'. -/
 theorem coe_normUnit_of_ne_zero (hp : p ≠ 0) : (normUnit p : R[X]) = C p.leadingCoeff⁻¹ :=
   by
@@ -725,7 +725,7 @@ theorem coe_normUnit_of_ne_zero (hp : p ≠ 0) : (normUnit p : R[X]) = C p.leadi
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) p) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (normalize.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.normalizationMonoid.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.normalizedGcdMonoid.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p) p)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Polynomial.Monic.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (fun (_x : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (normalize.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToRingToCancelCommMonoidWithZeroCommSemiringToCommSemiringInstIsDomainPolynomialToSemiringSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p) p)
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Polynomial.Monic.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (fun (_x : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (normalize.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.normalize_monic Polynomial.normalize_monicₓ'. -/
 theorem normalize_monic (h : Monic p) : normalize p = p := by simp [h]
 #align polynomial.normalize_monic Polynomial.normalize_monic
@@ -745,7 +745,7 @@ theorem map_dvd_map' [Field k] (f : R →+* k) {x y : R[X]} : x.map f ∣ y.map
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (normalize.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.normalizationMonoid.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.normalizedGcdMonoid.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p)) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) p)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (fun (_x : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (normalize.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToRingToCancelCommMonoidWithZeroCommSemiringToCommSemiringInstIsDomainPolynomialToSemiringSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p)) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p)
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (fun (_x : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (normalize.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToCommSemiringToCancelCommMonoidWithZeroCommSemiringInstIsDomainPolynomialToSemiringSemiringToRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p)) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_normalize Polynomial.degree_normalizeₓ'. -/
 theorem degree_normalize : degree (normalize p) = degree p := by simp
 #align polynomial.degree_normalize Polynomial.degree_normalize

mathlib commit https://github.com/leanprover-community/mathlib/commit/2651125b48fc5c170ab1111afd0817c903b1fc6c

@@ -624,7 +624,7 @@ theorem exists_root_of_degree_eq_one (h : degree p = 1) : ∃ x, IsRoot p x :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] (u : Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (n : Nat), Eq.{succ u1} R (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (coeBase.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Units.hasCoe.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) u) n)) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (coeBase.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Units.hasCoe.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) (Inv.inv.{u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (Units.hasInv.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) u)) n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] (u : Units.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (n : Nat), Eq.{succ u1} R (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.coeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Units.val.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) u) n)) (Polynomial.coeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Units.val.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (Inv.inv.{u1} (Units.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (Units.instInvUnits.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) u)) n)
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] (u : Units.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (n : Nat), Eq.{succ u1} R (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.coeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Units.val.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) u) n)) (Polynomial.coeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Units.val.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (Inv.inv.{u1} (Units.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (Units.instInv.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) u)) n)
 Case conversion may be inaccurate. Consider using '#align polynomial.coeff_inv_units Polynomial.coeff_inv_unitsₓ'. -/
 theorem coeff_inv_units (u : R[X]ˣ) (n : ℕ) : ((↑u : R[X]).coeff n)⁻¹ = (↑u⁻¹ : R[X]).coeff n :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/c9236f47f5b9df573443aa499c0d3968769628b7

@@ -642,7 +642,7 @@ theorem coeff_inv_units (u : R[X]ˣ) (n : ℕ) : ((↑u : R[X]).coeff n)⁻¹ =
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) -> (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (normalize.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.normalizationMonoid.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.normalizedGcdMonoid.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Polynomial.Monic.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (fun (_x : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (normalize.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToRingToCancelCommMonoidWithZeroCommSemiringToCommSemiringInstIsDomainPolynomialToSemiringSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p))
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Polynomial.Monic.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (fun (_x : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (normalize.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToRingToCancelCommMonoidWithZeroCommSemiringToCommSemiringInstIsDomainPolynomialToSemiringSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_normalize Polynomial.monic_normalizeₓ'. -/
 theorem monic_normalize (hp0 : p ≠ 0) : Monic (normalize p) :=
   by
@@ -713,7 +713,7 @@ theorem dvd_C_mul (ha : a ≠ 0) : p ∣ Polynomial.C a * q ↔ p ∣ q :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (coeBase.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Units.hasCoe.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (NormalizationMonoid.normUnit.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.normalizationMonoid.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.normalizedGcdMonoid.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b))))) p)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) p))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Units.val.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (NormalizationMonoid.normUnit.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToRingToCancelCommMonoidWithZeroCommSemiringToCommSemiringInstIsDomainPolynomialToSemiringSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b))))) p)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p))))
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Units.val.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (NormalizationMonoid.normUnit.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToRingToCancelCommMonoidWithZeroCommSemiringToCommSemiringInstIsDomainPolynomialToSemiringSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b))))) p)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p))))
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_norm_unit_of_ne_zero Polynomial.coe_normUnit_of_ne_zeroₓ'. -/
 theorem coe_normUnit_of_ne_zero (hp : p ≠ 0) : (normUnit p : R[X]) = C p.leadingCoeff⁻¹ :=
   by
@@ -725,7 +725,7 @@ theorem coe_normUnit_of_ne_zero (hp : p ≠ 0) : (normUnit p : R[X]) = C p.leadi
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) p) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (normalize.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.normalizationMonoid.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.normalizedGcdMonoid.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p) p)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Polynomial.Monic.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (fun (_x : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (normalize.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToRingToCancelCommMonoidWithZeroCommSemiringToCommSemiringInstIsDomainPolynomialToSemiringSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p) p)
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Polynomial.Monic.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (fun (_x : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (normalize.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToRingToCancelCommMonoidWithZeroCommSemiringToCommSemiringInstIsDomainPolynomialToSemiringSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.normalize_monic Polynomial.normalize_monicₓ'. -/
 theorem normalize_monic (h : Monic p) : normalize p = p := by simp [h]
 #align polynomial.normalize_monic Polynomial.normalize_monic
@@ -745,7 +745,7 @@ theorem map_dvd_map' [Field k] (f : R →+* k) {x y : R[X]} : x.map f ∣ y.map
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (fun (_x : MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (normalize.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.normalizationMonoid.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.normalizedGcdMonoid.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p)) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) p)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (fun (_x : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (normalize.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToRingToCancelCommMonoidWithZeroCommSemiringToCommSemiringInstIsDomainPolynomialToSemiringSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p)) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p)
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (fun (_x : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (normalize.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R 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(CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p)) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_normalize Polynomial.degree_normalizeₓ'. -/
 theorem degree_normalize : degree (normalize p) = degree p := by simp
 #align polynomial.degree_normalize Polynomial.degree_normalize

mathlib commit https://github.com/leanprover-community/mathlib/commit/d95bef0d215ea58c0fd7bbc4b151bf3fe952c095

@@ -301,15 +301,15 @@ theorem divByMonic_eq_div (p : R[X]) (hq : Monic q) : p /ₘ q = p / q :=
 #align polynomial.div_by_monic_eq_div Polynomial.divByMonic_eq_div
 -/
 
-/- warning: polynomial.mod_X_sub_C_eq_C_eval -> Polynomial.mod_x_sub_c_eq_c_eval is a dubious translation:
+/- warning: polynomial.mod_X_sub_C_eq_C_eval -> Polynomial.mod_X_sub_C_eq_C_eval is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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(Polynomial.eval.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) a p)) (instHMod.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instModPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1)) p (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHSub.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) 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(Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.eval.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) a p))
-Case conversion may be inaccurate. Consider using '#align polynomial.mod_X_sub_C_eq_C_eval Polynomial.mod_x_sub_c_eq_c_evalₓ'. -/
-theorem mod_x_sub_c_eq_c_eval (p : R[X]) (a : R) : p % (X - C a) = C (p.eval a) :=
+Case conversion may be inaccurate. Consider using '#align polynomial.mod_X_sub_C_eq_C_eval Polynomial.mod_X_sub_C_eq_C_evalₓ'. -/
+theorem mod_X_sub_C_eq_C_eval (p : R[X]) (a : R) : p % (X - C a) = C (p.eval a) :=
   modByMonic_eq_mod p (monic_X_sub_C a) ▸ modByMonic_X_sub_C_eq_C_eval _ _
-#align polynomial.mod_X_sub_C_eq_C_eval Polynomial.mod_x_sub_c_eq_c_eval
+#align polynomial.mod_X_sub_C_eq_C_eval Polynomial.mod_X_sub_C_eq_C_eval
 
 /- warning: polynomial.mul_div_eq_iff_is_root -> Polynomial.mul_div_eq_iff_isRoot is a dubious translation:
 lean 3 declaration is
@@ -769,18 +769,18 @@ theorem irreducible_of_degree_eq_one (hp1 : degree p = 1) : Irreducible p :=
   (prime_of_degree_eq_one hp1).Irreducible
 #align polynomial.irreducible_of_degree_eq_one Polynomial.irreducible_of_degree_eq_one
 
-/- warning: polynomial.not_irreducible_C -> Polynomial.not_irreducible_c is a dubious translation:
+/- warning: polynomial.not_irreducible_C -> Polynomial.not_irreducible_C is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] (x : R), Not (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) x))
 but is expected to have type
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(Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) x))
-Case conversion may be inaccurate. Consider using '#align polynomial.not_irreducible_C Polynomial.not_irreducible_cₓ'. -/
-theorem not_irreducible_c (x : R) : ¬Irreducible (C x) :=
+Case conversion may be inaccurate. Consider using '#align polynomial.not_irreducible_C Polynomial.not_irreducible_Cₓ'. -/
+theorem not_irreducible_C (x : R) : ¬Irreducible (C x) :=
   if H : x = 0 then by
     rw [H, C_0]
     exact not_irreducible_zero
   else fun hx => Irreducible.not_unit hx <| isUnit_C.2 <| isUnit_iff_ne_zero.2 H
-#align polynomial.not_irreducible_C Polynomial.not_irreducible_c
+#align polynomial.not_irreducible_C Polynomial.not_irreducible_C
 
 /- warning: polynomial.degree_pos_of_irreducible -> Polynomial.degree_pos_of_irreducible is a dubious translation:
 lean 3 declaration is
@@ -791,7 +791,7 @@ Case conversion may be inaccurate. Consider using '#align polynomial.degree_pos_
 theorem degree_pos_of_irreducible (hp : Irreducible p) : 0 < p.degree :=
   lt_of_not_ge fun hp0 =>
     have := eq_C_of_degree_le_zero hp0
-    not_irreducible_c (p.coeff 0) <| this ▸ hp
+    not_irreducible_C (p.coeff 0) <| this ▸ hp
 #align polynomial.degree_pos_of_irreducible Polynomial.degree_pos_of_irreducible
 
 /- warning: polynomial.is_coprime_of_is_root_of_eval_derivative_ne_zero -> Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zero is a dubious translation:

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

@@ -39,7 +39,7 @@ variable [CommRing R] [IsDomain R]
 
 /- warning: polynomial.derivative_root_multiplicity_of_root -> Polynomial.derivative_rootMultiplicity_of_root is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {t : R}, (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p t) -> (Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 t (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} 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(CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {t : R}, (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p t) -> (Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 t (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))
 Case conversion may be inaccurate. Consider using '#align polynomial.derivative_root_multiplicity_of_root Polynomial.derivative_rootMultiplicity_of_rootₓ'. -/
@@ -74,7 +74,7 @@ theorem derivative_rootMultiplicity_of_root [CharZero R] {p : R[X]} {t : R} (hpt
 
 /- warning: polynomial.root_multiplicity_sub_one_le_derivative_root_multiplicity -> Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicity is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (t : R), LE.le.{0} Nat Nat.hasLe (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Polynomial.rootMultiplicity.{u1} R _inst_1 t (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (t : R), LE.le.{0} Nat Nat.hasLe (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Polynomial.rootMultiplicity.{u1} R _inst_1 t (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (t : R), LE.le.{0} Nat instLENat (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Polynomial.rootMultiplicity.{u1} R _inst_1 t (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_sub_one_le_derivative_root_multiplicity Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicityₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/55d771df074d0dd020139ee1cd4b95521422df9f

@@ -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.field_division
-! leanprover-community/mathlib commit bbeb185db4ccee8ed07dc48449414ebfa39cb821
+! leanprover-community/mathlib commit cb3ceec8485239a61ed51d944cb9a95b68c6bafc
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.RingTheory.EuclideanDomain
 /-!
 # Theory of univariate polynomials
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file starts looking like the ring theory of $ R[X] $
 
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/b19481deb571022990f1baa9cbf9172e6757a479

@@ -34,6 +34,12 @@ section IsDomain
 
 variable [CommRing R] [IsDomain R]
 
+/- warning: polynomial.derivative_root_multiplicity_of_root -> Polynomial.derivative_rootMultiplicity_of_root is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {t : R}, (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p t) -> (Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 t (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R 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+Case conversion may be inaccurate. Consider using '#align polynomial.derivative_root_multiplicity_of_root Polynomial.derivative_rootMultiplicity_of_rootₓ'. -/
 theorem derivative_rootMultiplicity_of_root [CharZero R] {p : R[X]} {t : R} (hpt : p.IsRoot t) :
     p.derivative.rootMultiplicity t = p.rootMultiplicity t - 1 :=
   by
@@ -63,6 +69,12 @@ theorem derivative_rootMultiplicity_of_root [CharZero R] {p : R[X]} {t : R} (hpt
   rw [h, eval_zero]
 #align polynomial.derivative_root_multiplicity_of_root Polynomial.derivative_rootMultiplicity_of_root
 
+/- warning: polynomial.root_multiplicity_sub_one_le_derivative_root_multiplicity -> Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicity is a dubious translation:
+lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (t : R), LE.le.{0} Nat instLENat (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.rootMultiplicity.{u1} R _inst_1 t p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Polynomial.rootMultiplicity.{u1} R _inst_1 t (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p))
+Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_sub_one_le_derivative_root_multiplicity Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicityₓ'. -/
 theorem rootMultiplicity_sub_one_le_derivative_rootMultiplicity [CharZero R] (p : R[X]) (t : R) :
     p.rootMultiplicity t - 1 ≤ p.derivative.rootMultiplicity t :=
   by
@@ -96,20 +108,44 @@ instance : NormalizationMonoid R[X]
         rcases Polynomial.isUnit_iff.1 ⟨u, rfl⟩ with ⟨_, ⟨w, rfl⟩, h2⟩
         rw [← h2, leading_coeff_C, norm_unit_coe_units, ← C_mul, Units.mul_inv, C_1])
 
+/- warning: polynomial.coe_norm_unit -> Polynomial.coe_normUnit is a dubious translation:
+lean 3 declaration is
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(MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))) (NormalizationMonoid.normUnit.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2) _inst_3 (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p))))
+Case conversion may be inaccurate. Consider using '#align polynomial.coe_norm_unit Polynomial.coe_normUnitₓ'. -/
 @[simp]
 theorem coe_normUnit {p : R[X]} : (normUnit p : R[X]) = C ↑(normUnit p.leadingCoeff) := by
   simp [norm_unit]
 #align polynomial.coe_norm_unit Polynomial.coe_normUnit
 
+/- warning: polynomial.leading_coeff_normalize -> Polynomial.leadingCoeff_normalize is a dubious translation:
+lean 3 declaration is
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_inst_2)))))))) (normalize.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2) _inst_3) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p))
+Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_normalize Polynomial.leadingCoeff_normalizeₓ'. -/
 theorem leadingCoeff_normalize (p : R[X]) :
     leadingCoeff (normalize p) = normalize (leadingCoeff p) := by simp
 #align polynomial.leading_coeff_normalize Polynomial.leadingCoeff_normalize
 
+/- warning: polynomial.monic.normalize_eq_self -> Polynomial.Monic.normalize_eq_self is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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_inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)))))) (normalize.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.isDomain.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.normalizationMonoid.{u1} R _inst_1 _inst_2 _inst_3)) p) p)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R 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(Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2))))))))) (normalize.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1) _inst_2)) (Polynomial.instNormalizationMonoidPolynomialToSemiringToRingToCancelCommMonoidWithZeroCommSemiringToCommSemiringInstIsDomainPolynomialToSemiringSemiring.{u1} R _inst_1 _inst_2 _inst_3)) p) p)
+Case conversion may be inaccurate. Consider using '#align polynomial.monic.normalize_eq_self Polynomial.Monic.normalize_eq_selfₓ'. -/
 theorem Monic.normalize_eq_self {p : R[X]} (hp : p.Monic) : normalize p = p := by
   simp only [Polynomial.coe_normUnit, normalize_apply, hp.leading_coeff, normUnit_one,
     Units.val_one, polynomial.C.map_one, mul_one]
 #align polynomial.monic.normalize_eq_self Polynomial.Monic.normalize_eq_self
 
+/- warning: polynomial.roots_normalize -> Polynomial.roots_normalize is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : NormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R 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+Case conversion may be inaccurate. Consider using '#align polynomial.roots_normalize Polynomial.roots_normalizeₓ'. -/
 theorem roots_normalize {p : R[X]} : (normalize p).roots = p.roots := by
   rw [normalize_apply, mul_comm, coe_norm_unit, roots_C_mul _ (norm_unit (leading_coeff p)).NeZero]
 #align polynomial.roots_normalize Polynomial.roots_normalize
@@ -122,17 +158,35 @@ section DivisionRing
 
 variable [DivisionRing R] {p q : R[X]}
 
+/- warning: polynomial.degree_pos_of_ne_zero_of_nonunit -> Polynomial.degree_pos_of_ne_zero_of_nonunit is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))) -> (Not (IsUnit.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) p))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.degree_pos_of_ne_zero_of_nonunit Polynomial.degree_pos_of_ne_zero_of_nonunitₓ'. -/
 theorem degree_pos_of_ne_zero_of_nonunit (hp0 : p ≠ 0) (hp : ¬IsUnit p) : 0 < degree p :=
   lt_of_not_ge fun h => by
     rw [eq_C_of_degree_le_zero h] at hp0 hp
     exact hp (IsUnit.map C (IsUnit.mk0 (coeff p 0) (mt C_inj.2 (by simpa using hp0))))
 #align polynomial.degree_pos_of_ne_zero_of_nonunit Polynomial.degree_pos_of_ne_zero_of_nonunit
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.monic_mul_leading_coeff_inv Polynomial.monic_mul_leadingCoeff_invₓ'. -/
 theorem monic_mul_leadingCoeff_inv (h : p ≠ 0) : Monic (p * C (leadingCoeff p)⁻¹) := by
   rw [monic, leading_coeff_mul, leading_coeff_C,
     mul_inv_cancel (show leading_coeff p ≠ 0 from mt leading_coeff_eq_zero.1 h)]
 #align polynomial.monic_mul_leading_coeff_inv Polynomial.monic_mul_leadingCoeff_inv
 
+/- warning: polynomial.degree_mul_leading_coeff_inv -> Polynomial.degree_mul_leadingCoeff_inv is a dubious translation:
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(DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) 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(DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)) q))))) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)) p))
+Case conversion may be inaccurate. Consider using '#align polynomial.degree_mul_leading_coeff_inv Polynomial.degree_mul_leadingCoeff_invₓ'. -/
 theorem degree_mul_leadingCoeff_inv (p : R[X]) (h : q ≠ 0) :
     degree (p * C (leadingCoeff q)⁻¹) = degree p :=
   by
@@ -140,14 +194,18 @@ theorem degree_mul_leadingCoeff_inv (p : R[X]) (h : q ≠ 0) :
   rw [degree_mul, degree_C h₁, add_zero]
 #align polynomial.degree_mul_leading_coeff_inv Polynomial.degree_mul_leadingCoeff_inv
 
+#print Polynomial.map_eq_zero /-
 @[simp]
 theorem map_eq_zero [Semiring S] [Nontrivial S] (f : R →+* S) : p.map f = 0 ↔ p = 0 := by
   simp only [Polynomial.ext_iff, map_eq_zero, coeff_map, coeff_zero]
 #align polynomial.map_eq_zero Polynomial.map_eq_zero
+-/
 
+#print Polynomial.map_ne_zero /-
 theorem map_ne_zero [Semiring S] [Nontrivial S] {f : R →+* S} (hp : p ≠ 0) : p.map f ≠ 0 :=
   mt (map_eq_zero f).1 hp
 #align polynomial.map_ne_zero Polynomial.map_ne_zero
+-/
 
 end DivisionRing
 
@@ -155,6 +213,12 @@ section Field
 
 variable [Field R] {p q : R[X]}
 
+/- warning: polynomial.is_unit_iff_degree_eq_zero -> Polynomial.isUnit_iff_degree_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, Iff (IsUnit.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) p) (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) p) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, Iff (IsUnit.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) p) (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))))
+Case conversion may be inaccurate. Consider using '#align polynomial.is_unit_iff_degree_eq_zero Polynomial.isUnit_iff_degree_eq_zeroₓ'. -/
 theorem isUnit_iff_degree_eq_zero : IsUnit p ↔ degree p = 0 :=
   ⟨degree_eq_zero_of_isUnit, fun h =>
     have : degree p ≤ 0 := by simp [*, le_refl]
@@ -166,15 +230,19 @@ theorem isUnit_iff_degree_eq_zero : IsUnit p ↔ degree p = 0 :=
         rw [← C_mul, _root_.mul_inv_cancel hc, C_1]⟩⟩
 #align polynomial.is_unit_iff_degree_eq_zero Polynomial.isUnit_iff_degree_eq_zero
 
+#print Polynomial.div /-
 /-- Division of polynomials. See `polynomial.div_by_monic` for more details.-/
 def div (p q : R[X]) :=
   C (leadingCoeff q)⁻¹ * (p /ₘ (q * C (leadingCoeff q)⁻¹))
 #align polynomial.div Polynomial.div
+-/
 
+#print Polynomial.mod /-
 /-- Remainder of polynomial division. See `polynomial.mod_by_monic` for more details. -/
 def mod (p q : R[X]) :=
   p %ₘ (q * C (leadingCoeff q)⁻¹)
 #align polynomial.mod Polynomial.mod
+-/
 
 private theorem quotient_mul_add_remainder_eq_aux (p q : R[X]) : q * div p q + mod p q = p :=
   if h : q = 0 then by simp only [h, MulZeroClass.zero_mul, mod, mod_by_monic_zero, zero_add]
@@ -197,27 +265,55 @@ instance : Div R[X] :=
 instance : Mod R[X] :=
   ⟨mod⟩
 
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1)) p q) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q))) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q))) (Polynomial.divByMonic.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) p (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) q (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.div_def Polynomial.div_defₓ'. -/
 theorem div_def : p / q = C (leadingCoeff q)⁻¹ * (p /ₘ (q * C (leadingCoeff q)⁻¹)) :=
   rfl
 #align polynomial.div_def Polynomial.div_def
 
+/- warning: polynomial.mod_def -> Polynomial.mod_def is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (HMod.hMod.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHMod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.hasMod.{u1} R _inst_1)) p q) (Polynomial.modByMonic.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) p (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) q (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) q)))))
+but is expected to have type
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R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) q)))))
+Case conversion may be inaccurate. Consider using '#align polynomial.mod_def Polynomial.mod_defₓ'. -/
 theorem mod_def : p % q = p %ₘ (q * C (leadingCoeff q)⁻¹) :=
   rfl
 #align polynomial.mod_def Polynomial.mod_def
 
+#print Polynomial.modByMonic_eq_mod /-
 theorem modByMonic_eq_mod (p : R[X]) (hq : Monic q) : p %ₘ q = p % q :=
   show p %ₘ q = p %ₘ (q * C (leadingCoeff q)⁻¹) by simp only [monic.def.1 hq, inv_one, mul_one, C_1]
 #align polynomial.mod_by_monic_eq_mod Polynomial.modByMonic_eq_mod
+-/
 
+#print Polynomial.divByMonic_eq_div /-
 theorem divByMonic_eq_div (p : R[X]) (hq : Monic q) : p /ₘ q = p / q :=
   show p /ₘ q = C (leadingCoeff q)⁻¹ * (p /ₘ (q * C (leadingCoeff q)⁻¹)) by
     simp only [monic.def.1 hq, inv_one, C_1, one_mul, mul_one]
 #align polynomial.div_by_monic_eq_div Polynomial.divByMonic_eq_div
+-/
 
+/- warning: polynomial.mod_X_sub_C_eq_C_eval -> Polynomial.mod_x_sub_c_eq_c_eval is a dubious translation:
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RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) a p))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] (p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (a : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.eval.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) a p)) (HMod.hMod.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.eval.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) a p)) (instHMod.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instModPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1)) p (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHSub.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.sub.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R 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_inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R 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R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) R 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(Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (Polynomial.C.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.eval.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) a p))
+Case conversion may be inaccurate. Consider using '#align polynomial.mod_X_sub_C_eq_C_eval Polynomial.mod_x_sub_c_eq_c_evalₓ'. -/
 theorem mod_x_sub_c_eq_c_eval (p : R[X]) (a : R) : p % (X - C a) = C (p.eval a) :=
   modByMonic_eq_mod p (monic_X_sub_C a) ▸ modByMonic_X_sub_C_eq_C_eval _ _
 #align polynomial.mod_X_sub_C_eq_C_eval Polynomial.mod_x_sub_c_eq_c_eval
 
+/- warning: polynomial.mul_div_eq_iff_is_root -> Polynomial.mul_div_eq_iff_isRoot is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.mul_div_eq_iff_is_root Polynomial.mul_div_eq_iff_isRootₓ'. -/
 theorem mul_div_eq_iff_isRoot : (X - C a) * (p / (X - C a)) = p ↔ IsRoot p a :=
   divByMonic_eq_div p (monic_X_sub_C a) ▸ mul_divByMonic_eq_iff_isRoot
 #align polynomial.mul_div_eq_iff_is_root Polynomial.mul_div_eq_iff_isRoot
@@ -234,6 +330,7 @@ instance : EuclideanDomain R[X] :=
     remainder_lt := fun p q hq => remainder_lt_aux _ hq
     mul_left_not_lt := fun p q hq => not_lt_of_ge (degree_le_mul_left _ hq) }
 
+#print Polynomial.mod_eq_self_iff /-
 theorem mod_eq_self_iff (hq0 : q ≠ 0) : p % q = p ↔ degree p < degree q :=
   ⟨fun h => h ▸ EuclideanDomain.mod_lt _ hq0, fun h =>
     by
@@ -243,7 +340,9 @@ theorem mod_eq_self_iff (hq0 : q ≠ 0) : p % q = p ↔ degree p < degree q :=
     unfold div_mod_by_monic_aux
     simp only [this, false_and_iff, if_false]⟩
 #align polynomial.mod_eq_self_iff Polynomial.mod_eq_self_iff
+-/
 
+#print Polynomial.div_eq_zero_iff /-
 theorem div_eq_zero_iff (hq0 : q ≠ 0) : p / q = 0 ↔ degree p < degree q :=
   ⟨fun h => by
     have := EuclideanDomain.div_add_mod p q <;>
@@ -255,7 +354,9 @@ theorem div_eq_zero_iff (hq0 : q ≠ 0) : p / q = 0 ↔ degree p < degree q :=
     have hm : Monic (q * C (leadingCoeff q)⁻¹) := monic_mul_leadingCoeff_inv hq0
     rw [div_def, (div_by_monic_eq_zero_iff hm).2 hlt, MulZeroClass.mul_zero]⟩
 #align polynomial.div_eq_zero_iff Polynomial.div_eq_zero_iff
+-/
 
+#print Polynomial.degree_add_div /-
 theorem degree_add_div (hq0 : q ≠ 0) (hpq : degree q ≤ degree p) :
     degree q + degree (p / q) = degree p :=
   by
@@ -267,13 +368,17 @@ theorem degree_add_div (hq0 : q ≠ 0) (hpq : degree q ≤ degree p) :
   conv_rhs =>
     rw [← EuclideanDomain.div_add_mod p q, degree_add_eq_left_of_degree_lt this, degree_mul]
 #align polynomial.degree_add_div Polynomial.degree_add_div
+-/
 
+#print Polynomial.degree_div_le /-
 theorem degree_div_le (p q : R[X]) : degree (p / q) ≤ degree p :=
   if hq : q = 0 then by simp [hq]
   else by
     rw [div_def, mul_comm, degree_mul_leading_coeff_inv _ hq] <;> exact degree_div_by_monic_le _ _
 #align polynomial.degree_div_le Polynomial.degree_div_le
+-/
 
+#print Polynomial.degree_div_lt /-
 theorem degree_div_lt (hp : p ≠ 0) (hq : 0 < degree q) : degree (p / q) < degree p :=
   by
   have hq0 : q ≠ 0 := fun hq0 => by simpa [hq0] using hq
@@ -282,31 +387,51 @@ theorem degree_div_lt (hp : p ≠ 0) (hq : 0 < degree q) : degree (p / q) < degr
       degree_div_by_monic_lt _ (monic_mul_leading_coeff_inv hq0) hp
         (by rw [degree_mul_leading_coeff_inv _ hq0] <;> exact hq)
 #align polynomial.degree_div_lt Polynomial.degree_div_lt
+-/
 
+#print Polynomial.degree_map /-
 @[simp]
 theorem degree_map [DivisionRing k] (p : R[X]) (f : R →+* k) : degree (p.map f) = degree p :=
   p.degree_map_eq_of_injective f.Injective
 #align polynomial.degree_map Polynomial.degree_map
+-/
 
+#print Polynomial.natDegree_map /-
 @[simp]
 theorem natDegree_map [DivisionRing k] (f : R →+* k) : natDegree (p.map f) = natDegree p :=
   natDegree_eq_of_degree_eq (degree_map _ f)
 #align polynomial.nat_degree_map Polynomial.natDegree_map
+-/
 
+/- warning: polynomial.leading_coeff_map -> Polynomial.leadingCoeff_map is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} [_inst_2 : DivisionRing.{u2} k] (f : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))), Eq.{succ u2} k (Polynomial.leadingCoeff.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_2)) (Polynomial.map.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_2)) f p)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))) (fun (_x : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))) => R -> k) (RingHom.hasCoeToFun.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))) f (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) p))
+but is expected to have type
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} [_inst_2 : DivisionRing.{u2} k] (f : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))), Eq.{succ u2} k (Polynomial.leadingCoeff.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)) (Polynomial.map.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_2)) f p)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => k) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))) R k (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))) R k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2)))) R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_2))))))) f (Polynomial.leadingCoeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p))
+Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_map Polynomial.leadingCoeff_mapₓ'. -/
 @[simp]
 theorem leadingCoeff_map [DivisionRing k] (f : R →+* k) :
     leadingCoeff (p.map f) = f (leadingCoeff p) := by
   simp only [← coeff_nat_degree, coeff_map f, nat_degree_map]
 #align polynomial.leading_coeff_map Polynomial.leadingCoeff_map
 
+#print Polynomial.monic_map_iff /-
 theorem monic_map_iff [DivisionRing k] {f : R →+* k} {p : R[X]} : (p.map f).Monic ↔ p.Monic := by
   rw [monic, leading_coeff_map, ← f.map_one, Function.Injective.eq_iff f.injective, monic]
 #align polynomial.monic_map_iff Polynomial.monic_map_iff
+-/
 
+/- warning: polynomial.is_unit_map -> Polynomial.isUnit_map is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} [_inst_2 : Field.{u2} k] (f : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2))))), Iff (IsUnit.{u2} (Polynomial.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2)))) (Ring.toMonoid.{u2} (Polynomial.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2)))) (Polynomial.ring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2)))) (Polynomial.map.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2))) f p)) (IsUnit.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) p)
+but is expected to have type
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} [_inst_2 : Field.{u2} k] (f : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2))))), Iff (IsUnit.{u2} (Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) (MonoidWithZero.toMonoid.{u2} (Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) (Semiring.toMonoidWithZero.{u2} (Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) (Polynomial.semiring.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))))) (Polynomial.map.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2))) f p)) (IsUnit.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) p)
+Case conversion may be inaccurate. Consider using '#align polynomial.is_unit_map Polynomial.isUnit_mapₓ'. -/
 theorem isUnit_map [Field k] (f : R →+* k) : IsUnit (p.map f) ↔ IsUnit p := by
   simp_rw [is_unit_iff_degree_eq_zero, degree_map]
 #align polynomial.is_unit_map Polynomial.isUnit_map
 
+#print Polynomial.map_div /-
 theorem map_div [Field k] (f : R →+* k) : (p / q).map f = p.map f / q.map f :=
   if hq0 : q = 0 then by simp [hq0]
   else by
@@ -314,18 +439,27 @@ theorem map_div [Field k] (f : R →+* k) : (p / q).map f = p.map f / q.map f :=
         map_div_by_monic f (monic_mul_leading_coeff_inv hq0)] <;>
       simp [coeff_map f]
 #align polynomial.map_div Polynomial.map_div
+-/
 
+#print Polynomial.map_mod /-
 theorem map_mod [Field k] (f : R →+* k) : (p % q).map f = p.map f % q.map f :=
   if hq0 : q = 0 then by simp [hq0]
   else by
     rw [mod_def, mod_def, leading_coeff_map f, ← map_inv₀ f, ← map_C f, ← Polynomial.map_mul f,
       map_mod_by_monic f (monic_mul_leading_coeff_inv hq0)]
 #align polynomial.map_mod Polynomial.map_mod
+-/
 
 section
 
 open EuclideanDomain
 
+/- warning: polynomial.gcd_map -> Polynomial.gcd_map is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} [_inst_2 : Field.{u2} k] (f : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2))))), Eq.{succ u2} (Polynomial.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2)))) (EuclideanDomain.gcd.{u2} (Polynomial.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2)))) (Polynomial.euclideanDomain.{u2} k _inst_2) (fun (a : Polynomial.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2)))) (b : Polynomial.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2)))) => Classical.propDecidable (Eq.{succ u2} (Polynomial.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2)))) a b)) (Polynomial.map.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2))) f p) (Polynomial.map.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2))) f q)) (Polynomial.map.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2))) f (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.euclideanDomain.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (b : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a b)) p q))
+but is expected to have type
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} [_inst_2 : Field.{u2} k] (f : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k _inst_2))))), Eq.{succ u2} (Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) (EuclideanDomain.gcd.{u2} (Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} k _inst_2) (fun (a : Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) (b : Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) => Classical.propDecidable (Eq.{succ u2} (Polynomial.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2)))) a b)) (Polynomial.map.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2))) f p) (Polynomial.map.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2))) f q)) (Polynomial.map.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (Field.toSemifield.{u2} k _inst_2))) f (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (b : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a b)) p q))
+Case conversion may be inaccurate. Consider using '#align polynomial.gcd_map Polynomial.gcd_mapₓ'. -/
 theorem gcd_map [Field k] (f : R →+* k) : gcd (p.map f) (q.map f) = (gcd p q).map f :=
   GCD.induction p q (fun x => by simp_rw [Polynomial.map_zero, EuclideanDomain.gcd_zero_left])
     fun x y hx ih => by rw [gcd_val, ← map_mod, ih, ← gcd_val]
@@ -333,17 +467,35 @@ theorem gcd_map [Field k] (f : R →+* k) : gcd (p.map f) (q.map f) = (gcd p q).
 
 end
 
+/- warning: polynomial.eval₂_gcd_eq_zero -> Polynomial.eval₂_gcd_eq_zero is a dubious translation:
+lean 3 declaration is
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+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommSemiring.{u2} k] {ϕ : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))} {f : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {g : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {α : k}, (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α f) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2))))) -> (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α g) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2))))) -> (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (b : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a b)) f g)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2)))))
+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_gcd_eq_zero Polynomial.eval₂_gcd_eq_zeroₓ'. -/
 theorem eval₂_gcd_eq_zero [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α : k} (hf : f.eval₂ ϕ α = 0)
     (hg : g.eval₂ ϕ α = 0) : (EuclideanDomain.gcd f g).eval₂ ϕ α = 0 := by
   rw [EuclideanDomain.gcd_eq_gcd_ab f g, Polynomial.eval₂_add, Polynomial.eval₂_mul,
     Polynomial.eval₂_mul, hf, hg, MulZeroClass.zero_mul, MulZeroClass.zero_mul, zero_add]
 #align polynomial.eval₂_gcd_eq_zero Polynomial.eval₂_gcd_eq_zero
 
+/- warning: polynomial.eval_gcd_eq_zero -> Polynomial.eval_gcd_eq_zero is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {f : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {g : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {α : R}, (Eq.{succ u1} R (Polynomial.eval.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) α f) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) α g) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) α (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (b : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a b)) f g)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.eval_gcd_eq_zero Polynomial.eval_gcd_eq_zeroₓ'. -/
 theorem eval_gcd_eq_zero {f g : R[X]} {α : R} (hf : f.eval α = 0) (hg : g.eval α = 0) :
     (EuclideanDomain.gcd f g).eval α = 0 :=
   eval₂_gcd_eq_zero hf hg
 #align polynomial.eval_gcd_eq_zero Polynomial.eval_gcd_eq_zero
 
+/- warning: polynomial.root_left_of_root_gcd -> Polynomial.root_left_of_root_gcd is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommSemiring.{u2} k] {ϕ : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))} {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {α : k}, (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.euclideanDomain.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (b : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a b)) f g)) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))))))))) -> (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α f) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2)))))))))
+but is expected to have type
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommSemiring.{u2} k] {ϕ : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))} {f : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {g : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {α : k}, (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (b : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a b)) f g)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2))))) -> (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α f) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2)))))
+Case conversion may be inaccurate. Consider using '#align polynomial.root_left_of_root_gcd Polynomial.root_left_of_root_gcdₓ'. -/
 theorem root_left_of_root_gcd [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α : k}
     (hα : (EuclideanDomain.gcd f g).eval₂ ϕ α = 0) : f.eval₂ ϕ α = 0 :=
   by
@@ -351,6 +503,12 @@ theorem root_left_of_root_gcd [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α
   rw [hp, Polynomial.eval₂_mul, hα, MulZeroClass.zero_mul]
 #align polynomial.root_left_of_root_gcd Polynomial.root_left_of_root_gcd
 
+/- warning: polynomial.root_right_of_root_gcd -> Polynomial.root_right_of_root_gcd is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommSemiring.{u2} k] {ϕ : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))} {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {α : k}, (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.euclideanDomain.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (b : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a b)) f g)) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))))))))) -> (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α g) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2)))))))))
+but is expected to have type
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommSemiring.{u2} k] {ϕ : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))} {f : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {g : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {α : k}, (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (b : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a b)) f g)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2))))) -> (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α g) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2)))))
+Case conversion may be inaccurate. Consider using '#align polynomial.root_right_of_root_gcd Polynomial.root_right_of_root_gcdₓ'. -/
 theorem root_right_of_root_gcd [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α : k}
     (hα : (EuclideanDomain.gcd f g).eval₂ ϕ α = 0) : g.eval₂ ϕ α = 0 :=
   by
@@ -358,43 +516,87 @@ theorem root_right_of_root_gcd [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {
   rw [hp, Polynomial.eval₂_mul, hα, MulZeroClass.zero_mul]
 #align polynomial.root_right_of_root_gcd Polynomial.root_right_of_root_gcd
 
+/- warning: polynomial.root_gcd_iff_root_left_right -> Polynomial.root_gcd_iff_root_left_right is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommSemiring.{u2} k] {ϕ : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))} {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {α : k}, Iff (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.euclideanDomain.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (b : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a b)) f g)) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))))))))) (And (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α f) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))))))))) (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α g) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommSemiring.{u2} k] {ϕ : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k _inst_2))} {f : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {g : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {α : k}, Iff (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (b : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a b)) f g)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2))))) (And (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α f) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2))))) (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} k _inst_2) ϕ α g) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommSemiring.toCommMonoidWithZero.{u2} k _inst_2))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.root_gcd_iff_root_left_right Polynomial.root_gcd_iff_root_left_rightₓ'. -/
 theorem root_gcd_iff_root_left_right [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α : k} :
     (EuclideanDomain.gcd f g).eval₂ ϕ α = 0 ↔ f.eval₂ ϕ α = 0 ∧ g.eval₂ ϕ α = 0 :=
   ⟨fun h => ⟨root_left_of_root_gcd h, root_right_of_root_gcd h⟩, fun h => eval₂_gcd_eq_zero h.1 h.2⟩
 #align polynomial.root_gcd_iff_root_left_right Polynomial.root_gcd_iff_root_left_right
 
+/- warning: polynomial.is_root_gcd_iff_is_root_left_right -> Polynomial.isRoot_gcd_iff_isRoot_left_right is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} {α : R}, Iff (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.euclideanDomain.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (b : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a b)) f g) α) (And (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) f α) (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) g α))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {f : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {g : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {α : R}, Iff (Polynomial.IsRoot.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (EuclideanDomain.gcd.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1) (fun (a : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (b : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a b)) f g) α) (And (Polynomial.IsRoot.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) f α) (Polynomial.IsRoot.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) g α))
+Case conversion may be inaccurate. Consider using '#align polynomial.is_root_gcd_iff_is_root_left_right Polynomial.isRoot_gcd_iff_isRoot_left_rightₓ'. -/
 theorem isRoot_gcd_iff_isRoot_left_right {f g : R[X]} {α : R} :
     (EuclideanDomain.gcd f g).IsRoot α ↔ f.IsRoot α ∧ g.IsRoot α :=
   root_gcd_iff_root_left_right
 #align polynomial.is_root_gcd_iff_is_root_left_right Polynomial.isRoot_gcd_iff_isRoot_left_right
 
+#print Polynomial.isCoprime_map /-
 theorem isCoprime_map [Field k] (f : R →+* k) : IsCoprime (p.map f) (q.map f) ↔ IsCoprime p q := by
   rw [← EuclideanDomain.gcd_isUnit_iff, ← EuclideanDomain.gcd_isUnit_iff, gcd_map, is_unit_map]
 #align polynomial.is_coprime_map Polynomial.isCoprime_map
+-/
 
+/- warning: polynomial.mem_roots_map -> Polynomial.mem_roots_map is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))} [_inst_2 : CommRing.{u2} k] [_inst_3 : IsDomain.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_2))] {f : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_2)))} {x : k}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) -> (Iff (Membership.Mem.{u2, u2} k (Multiset.{u2} k) (Multiset.hasMem.{u2} k) x (Polynomial.roots.{u2} k _inst_2 _inst_3 (Polynomial.map.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_2)) f p))) (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_2)) f x p) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_2)))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} {k : Type.{u2}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} [_inst_2 : CommRing.{u2} k] [_inst_3 : IsDomain.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_2))] {f : RingHom.{u1, u2} R k (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_2)))} {x : k}, (Ne.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Iff (Membership.mem.{u2, u2} k (Multiset.{u2} k) (Multiset.instMembershipMultiset.{u2} k) x (Polynomial.roots.{u2} k _inst_2 _inst_3 (Polynomial.map.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_2)) f p))) (Eq.{succ u2} k (Polynomial.eval₂.{u1, u2} R k (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_2)) f x p) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} k (IsDomain.toCancelCommMonoidWithZero.{u2} k (CommRing.toCommSemiring.{u2} k _inst_2) _inst_3)))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.mem_roots_map Polynomial.mem_roots_mapₓ'. -/
 theorem mem_roots_map [CommRing k] [IsDomain k] {f : R →+* k} {x : k} (hp : p ≠ 0) :
     x ∈ (p.map f).roots ↔ p.eval₂ f x = 0 := by
   rw [mem_roots (map_ne_zero hp), is_root, Polynomial.eval_map] <;> infer_instance
 #align polynomial.mem_roots_map Polynomial.mem_roots_map
 
+/- warning: polynomial.root_set_monomial -> Polynomial.rootSet_monomial is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (forall {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} 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(Field.toEuclideanDomain.{u1} R _inst_1)))) n) a) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.hasSingleton.{u2} S) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2))))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (forall {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) 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+Case conversion may be inaccurate. Consider using '#align polynomial.root_set_monomial Polynomial.rootSet_monomialₓ'. -/
 theorem rootSet_monomial [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n ≠ 0) {a : R}
     (ha : a ≠ 0) : (monomial n a).rootSet S = {0} := by
   rw [root_set, map_monomial, roots_monomial ((_root_.map_ne_zero (algebraMap R S)).2 ha),
     Multiset.toFinset_nsmul _ _ hn, Multiset.toFinset_singleton, Finset.coe_singleton]
 #align polynomial.root_set_monomial Polynomial.rootSet_monomial
 
-theorem rootSet_c_mul_x_pow [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n ≠ 0) {a : R}
+/- warning: polynomial.root_set_C_mul_X_pow -> Polynomial.rootSet_C_mul_X_pow is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (forall {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) n)) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.hasSingleton.{u2} S) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2))))))))))))
+but is expected to have type
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(DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))))) (Polynomial.X.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) n)) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.instSingletonSet.{u2} S) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} S (IsDomain.toCancelCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3))))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.root_set_C_mul_X_pow Polynomial.rootSet_C_mul_X_powₓ'. -/
+theorem rootSet_C_mul_X_pow [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n ≠ 0) {a : R}
     (ha : a ≠ 0) : (C a * X ^ n).rootSet S = {0} := by
   rw [C_mul_X_pow_eq_monomial, root_set_monomial hn ha]
-#align polynomial.root_set_C_mul_X_pow Polynomial.rootSet_c_mul_x_pow
-
-theorem rootSet_x_pow [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n ≠ 0) :
+#align polynomial.root_set_C_mul_X_pow Polynomial.rootSet_C_mul_X_pow
+
+/- warning: polynomial.root_set_X_pow -> Polynomial.rootSet_X_pow is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) n) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.hasSingleton.{u2} S) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) Nat (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHPow.{u1, 0} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))))) (Polynomial.X.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) n) S _inst_2 _inst_3 _inst_4) (Singleton.singleton.{u2, u2} S (Set.{u2} S) (Set.instSingletonSet.{u2} S) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} S (IsDomain.toCancelCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3)))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.root_set_X_pow Polynomial.rootSet_X_powₓ'. -/
+theorem rootSet_X_pow [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n ≠ 0) :
     (X ^ n : R[X]).rootSet S = {0} :=
   by
   rw [← one_mul (X ^ n : R[X]), ← C_1, root_set_C_mul_X_pow hn]
   exact one_ne_zero
-#align polynomial.root_set_X_pow Polynomial.rootSet_x_pow
-
+#align polynomial.root_set_X_pow Polynomial.rootSet_X_pow
+
+/- warning: polynomial.root_set_prod -> Polynomial.rootSet_prod is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Field.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} R S (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {ι : Type.{u3}} (f : ι -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (s : Finset.{u3} ι), (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Finset.prod.{u1, u3} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) s f) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) -> (Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Finset.prod.{u1, u3} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)))) s f) S _inst_2 _inst_3 _inst_4) (Set.unionᵢ.{u2, succ u3} S ι (fun (i : ι) => Set.unionᵢ.{u2, 0} S (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) (fun (H : Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) => Polynomial.rootSet.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (f i) S _inst_2 _inst_3 _inst_4))))
+but is expected to have type
+  forall {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : Field.{u2} R] [_inst_2 : CommRing.{u3} S] [_inst_3 : IsDomain.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))] [_inst_4 : Algebra.{u2, u3} R S (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))] {ι : Type.{u1}} (f : ι -> (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1))))) (s : Finset.{u1} ι), (Ne.{succ u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) (Finset.prod.{u2, u1} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) (Polynomial.commRing.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R _inst_1)))) s f) (OfNat.ofNat.{u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) (Polynomial.zero.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1))))))) -> (Eq.{succ u3} (Set.{u3} S) (Polynomial.rootSet.{u2, u3} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R _inst_1)) (Finset.prod.{u2, u1} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R _inst_1)))) (Polynomial.commRing.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R _inst_1)))) s f) S _inst_2 _inst_3 _inst_4) (Set.unionᵢ.{u3, succ u1} S ι (fun (i : ι) => Set.unionᵢ.{u3, 0} S (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) (fun (H : Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) => Polynomial.rootSet.{u2, u3} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R _inst_1)) (f i) S _inst_2 _inst_3 _inst_4))))
+Case conversion may be inaccurate. Consider using '#align polynomial.root_set_prod Polynomial.rootSet_prodₓ'. -/
 theorem rootSet_prod [CommRing S] [IsDomain S] [Algebra R S] {ι : Type _} (f : ι → R[X])
     (s : Finset ι) (h : s.Prod f ≠ 0) : (s.Prod f).rootSet S = ⋃ i ∈ s, (f i).rootSet S :=
   by
@@ -403,6 +605,7 @@ theorem rootSet_prod [CommRing S] [IsDomain S] [Algebra R S] {ι : Type _} (f :
   rwa [← Polynomial.map_prod, Ne, map_eq_zero]
 #align polynomial.root_set_prod Polynomial.rootSet_prod
 
+#print Polynomial.exists_root_of_degree_eq_one /-
 theorem exists_root_of_degree_eq_one (h : degree p = 1) : ∃ x, IsRoot p x :=
   ⟨-(p.coeff 0 / p.coeff 1),
     by
@@ -412,7 +615,14 @@ theorem exists_root_of_degree_eq_one (h : degree p = 1) : ∃ x, IsRoot p x :=
     conv in p => rw [eq_X_add_C_of_degree_le_one (show degree p ≤ 1 by rw [h] <;> exact le_rfl)] <;>
       simp [is_root, mul_div_cancel' _ this]⟩
 #align polynomial.exists_root_of_degree_eq_one Polynomial.exists_root_of_degree_eq_one
+-/
 
+/- warning: polynomial.coeff_inv_units -> Polynomial.coeff_inv_units is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] (u : Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (n : Nat), Eq.{succ u1} R (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (coeBase.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Units.hasCoe.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) u) n)) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (coeBase.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Units.hasCoe.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) (Inv.inv.{u1} (Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (Units.hasInv.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) u)) n)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] (u : Units.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (n : Nat), Eq.{succ u1} R (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Polynomial.coeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Units.val.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) u) n)) (Polynomial.coeff.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Units.val.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (Inv.inv.{u1} (Units.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (Units.instInvUnits.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) u)) n)
+Case conversion may be inaccurate. Consider using '#align polynomial.coeff_inv_units Polynomial.coeff_inv_unitsₓ'. -/
 theorem coeff_inv_units (u : R[X]ˣ) (n : ℕ) : ((↑u : R[X]).coeff n)⁻¹ = (↑u⁻¹ : R[X]).coeff n :=
   by
   rw [eq_C_of_degree_eq_zero (degree_coe_units u), eq_C_of_degree_eq_zero (degree_coe_units u⁻¹),
@@ -425,6 +635,12 @@ theorem coeff_inv_units (u : R[X]ˣ) (n : ℕ) : ((↑u : R[X]).coeff n)⁻¹ =
   · simp
 #align polynomial.coeff_inv_units Polynomial.coeff_inv_units
 
+/- warning: polynomial.monic_normalize -> Polynomial.monic_normalize is a dubious translation:
+lean 3 declaration is
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(DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (normalize.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.normalizationMonoid.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.normalizedGcdMonoid.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.zero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) -> (Polynomial.Monic.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (fun (_x : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R 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(Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToRingToCancelCommMonoidWithZeroCommSemiringToCommSemiringInstIsDomainPolynomialToSemiringSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p))
+Case conversion may be inaccurate. Consider using '#align polynomial.monic_normalize Polynomial.monic_normalizeₓ'. -/
 theorem monic_normalize (hp0 : p ≠ 0) : Monic (normalize p) :=
   by
   rw [Ne.def, ← leading_coeff_eq_zero, ← Ne.def, ← isUnit_iff_ne_zero] at hp0
@@ -432,6 +648,12 @@ theorem monic_normalize (hp0 : p ≠ 0) : Monic (normalize p) :=
   apply hp0
 #align polynomial.monic_normalize Polynomial.monic_normalize
 
+/- warning: polynomial.leading_coeff_div -> Polynomial.leadingCoeff_div is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_div Polynomial.leadingCoeff_divₓ'. -/
 theorem leadingCoeff_div (hpq : q.degree ≤ p.degree) :
     (p / q).leadingCoeff = p.leadingCoeff / q.leadingCoeff :=
   by
@@ -442,39 +664,70 @@ theorem leadingCoeff_div (hpq : q.degree ≤ p.degree) :
   rwa [degree_mul_leading_coeff_inv q hq]
 #align polynomial.leading_coeff_div Polynomial.leadingCoeff_div
 
-theorem div_c_mul : p / (C a * q) = C a⁻¹ * (p / q) :=
+/- warning: polynomial.div_C_mul -> Polynomial.div_C_mul is a dubious translation:
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(DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) a)) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.hasDiv.{u1} R _inst_1)) p q))
+but is expected to have type
+  forall {R : Type.{u1}} {a : R} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))} {q : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, Eq.{succ u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) a) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} R 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+Case conversion may be inaccurate. Consider using '#align polynomial.div_C_mul Polynomial.div_C_mulₓ'. -/
+theorem div_C_mul : p / (C a * q) = C a⁻¹ * (p / q) :=
   by
   by_cases ha : a = 0
   · simp [ha]
   simp only [div_def, leading_coeff_mul, mul_inv, leading_coeff_C, C.map_mul, mul_assoc]
   congr 3
   rw [mul_left_comm q, ← mul_assoc, ← C.map_mul, mul_inv_cancel ha, C.map_one, one_mul]
-#align polynomial.div_C_mul Polynomial.div_c_mul
-
-theorem c_mul_dvd (ha : a ≠ 0) : C a * p ∣ q ↔ p ∣ q :=
+#align polynomial.div_C_mul Polynomial.div_C_mul
+
+/- warning: polynomial.C_mul_dvd -> Polynomial.C_mul_dvd is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.C_mul_dvd Polynomial.C_mul_dvdₓ'. -/
+theorem C_mul_dvd (ha : a ≠ 0) : C a * p ∣ q ↔ p ∣ q :=
   ⟨fun h => dvd_trans (dvd_mul_left _ _) h, fun ⟨r, hr⟩ =>
     ⟨C a⁻¹ * r, by
       rw [mul_assoc, mul_left_comm p, ← mul_assoc, ← C.map_mul, _root_.mul_inv_cancel ha, C.map_one,
         one_mul, hr]⟩⟩
-#align polynomial.C_mul_dvd Polynomial.c_mul_dvd
-
-theorem dvd_c_mul (ha : a ≠ 0) : p ∣ Polynomial.C a * q ↔ p ∣ q :=
+#align polynomial.C_mul_dvd Polynomial.C_mul_dvd
+
+/- warning: polynomial.dvd_C_mul -> Polynomial.dvd_C_mul is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} R _inst_1)))))))) p q))
+Case conversion may be inaccurate. Consider using '#align polynomial.dvd_C_mul Polynomial.dvd_C_mulₓ'. -/
+theorem dvd_C_mul (ha : a ≠ 0) : p ∣ Polynomial.C a * q ↔ p ∣ q :=
   ⟨fun ⟨r, hr⟩ =>
     ⟨C a⁻¹ * r, by
       rw [mul_left_comm p, ← hr, ← mul_assoc, ← C.map_mul, _root_.inv_mul_cancel ha, C.map_one,
         one_mul]⟩,
     fun h => dvd_trans h (dvd_mul_left _ _)⟩
-#align polynomial.dvd_C_mul Polynomial.dvd_c_mul
-
+#align polynomial.dvd_C_mul Polynomial.dvd_C_mul
+
+/- warning: polynomial.coe_norm_unit_of_ne_zero -> Polynomial.coe_normUnit_of_ne_zero 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.coe_norm_unit_of_ne_zero Polynomial.coe_normUnit_of_ne_zeroₓ'. -/
 theorem coe_normUnit_of_ne_zero (hp : p ≠ 0) : (normUnit p : R[X]) = C p.leadingCoeff⁻¹ :=
   by
   have : p.leadingCoeff ≠ 0 := mt leadingCoeff_eq_zero.mp hp
   simp [CommGroupWithZero.coe_normUnit _ this]
 #align polynomial.coe_norm_unit_of_ne_zero Polynomial.coe_normUnit_of_ne_zero
 
+/- warning: polynomial.normalize_monic -> Polynomial.normalize_monic is a dubious translation:
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(Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.isDomain.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.normalizationMonoid.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.normalizedGcdMonoid.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p) p)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Polynomial.Monic.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) p) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (fun (_x : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) 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(Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (normalize.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToRingToCancelCommMonoidWithZeroCommSemiringToCommSemiringInstIsDomainPolynomialToSemiringSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p) p)
+Case conversion may be inaccurate. Consider using '#align polynomial.normalize_monic Polynomial.normalize_monicₓ'. -/
 theorem normalize_monic (h : Monic p) : normalize p = p := by simp [h]
 #align polynomial.normalize_monic Polynomial.normalize_monic
 
+#print Polynomial.map_dvd_map' /-
 theorem map_dvd_map' [Field k] (f : R →+* k) {x y : R[X]} : x.map f ∣ y.map f ↔ x ∣ y :=
   if H : x = 0 then by rw [H, Polynomial.map_zero, zero_dvd_iff, zero_dvd_iff, map_eq_zero]
   else by
@@ -483,21 +736,42 @@ theorem map_dvd_map' [Field k] (f : R →+* k) {x y : R[X]} : x.map f ∣ y.map
       leading_coeff_map, ← map_inv₀ f, ← map_C, ← Polynomial.map_mul,
       map_dvd_map _ f.injective (monic_mul_leading_coeff_inv H)]
 #align polynomial.map_dvd_map' Polynomial.map_dvd_map'
+-/
 
+/- warning: polynomial.degree_normalize -> Polynomial.degree_normalize is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R 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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (fun (_x : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) => Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MulOneClass.toMul.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MulZeroOneClass.toMulOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))))))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Polynomial.{u1} R 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(Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1)))))))))) (normalize.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (IsDomain.toCancelCommMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.commSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Polynomial.instIsDomainPolynomialToSemiringSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1))) (Polynomial.instNormalizationMonoidPolynomialToSemiringToRingToCancelCommMonoidWithZeroCommSemiringToCommSemiringInstIsDomainPolynomialToSemiringSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1)) (Field.isDomain.{u1} R _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_1))) (Field.isDomain.{u1} R _inst_1)) (CommGroupWithZero.instNormalizedGCDMonoidCancelCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)) (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)))))) p)) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p)
+Case conversion may be inaccurate. Consider using '#align polynomial.degree_normalize Polynomial.degree_normalizeₓ'. -/
 theorem degree_normalize : degree (normalize p) = degree p := by simp
 #align polynomial.degree_normalize Polynomial.degree_normalize
 
+#print Polynomial.prime_of_degree_eq_one /-
 theorem prime_of_degree_eq_one (hp1 : degree p = 1) : Prime p :=
   have : Prime (normalize p) :=
     Monic.prime_of_degree_eq_one (hp1 ▸ degree_normalize)
       (monic_normalize fun hp0 => absurd hp1 (hp0.symm ▸ by simp <;> exact by decide))
   (normalize_associated _).Prime this
 #align polynomial.prime_of_degree_eq_one Polynomial.prime_of_degree_eq_one
+-/
 
+/- warning: polynomial.irreducible_of_degree_eq_one -> Polynomial.irreducible_of_degree_eq_one is a dubious translation:
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+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) p) (OfNat.ofNat.{0} (WithBot.{0} Nat) 1 (OfNat.mk.{0} (WithBot.{0} Nat) 1 (One.one.{0} (WithBot.{0} Nat) (WithBot.hasOne.{0} Nat Nat.hasOne))))) -> (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) p)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.irreducible_of_degree_eq_one Polynomial.irreducible_of_degree_eq_oneₓ'. -/
 theorem irreducible_of_degree_eq_one (hp1 : degree p = 1) : Irreducible p :=
   (prime_of_degree_eq_one hp1).Irreducible
 #align polynomial.irreducible_of_degree_eq_one Polynomial.irreducible_of_degree_eq_one
 
+/- warning: polynomial.not_irreducible_C -> Polynomial.not_irreducible_c is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.not_irreducible_C Polynomial.not_irreducible_cₓ'. -/
 theorem not_irreducible_c (x : R) : ¬Irreducible (C x) :=
   if H : x = 0 then by
     rw [H, C_0]
@@ -505,12 +779,24 @@ theorem not_irreducible_c (x : R) : ¬Irreducible (C x) :=
   else fun hx => Irreducible.not_unit hx <| isUnit_C.2 <| isUnit_iff_ne_zero.2 H
 #align polynomial.not_irreducible_C Polynomial.not_irreducible_c
 
+/- warning: polynomial.degree_pos_of_irreducible -> Polynomial.degree_pos_of_irreducible is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Polynomial.ring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) p) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) p))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] {p : Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Polynomial.semiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) p) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) p))
+Case conversion may be inaccurate. Consider using '#align polynomial.degree_pos_of_irreducible Polynomial.degree_pos_of_irreducibleₓ'. -/
 theorem degree_pos_of_irreducible (hp : Irreducible p) : 0 < p.degree :=
   lt_of_not_ge fun hp0 =>
     have := eq_C_of_degree_le_zero hp0
     not_irreducible_c (p.coeff 0) <| this ▸ hp
 #align polynomial.degree_pos_of_irreducible Polynomial.degree_pos_of_irreducible
 
+/- warning: polynomial.is_coprime_of_is_root_of_eval_derivative_ne_zero -> Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zero is a dubious translation:
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(Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) a))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_2 : Field.{u1} K] (f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (a : K), (Ne.{succ u1} K (Polynomial.eval.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) a (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (fun (_x : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} K K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (Polynomial.module.{u1, u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (Polynomial.derivative.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) f)) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) -> (IsCoprime.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.commSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a)) (Polynomial.divByMonic.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)) f (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) a))))
+Case conversion may be inaccurate. Consider using '#align polynomial.is_coprime_of_is_root_of_eval_derivative_ne_zero Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zeroₓ'. -/
 /-- If `f` is a polynomial over a field, and `a : K` satisfies `f' a ≠ 0`,
 then `f / (X - a)` is coprime with `X - a`.
 Note that we do not assume `f a = 0`, because `f / (X - a) = (f - f a) / (X - a)`. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/1f4705ccdfe1e557fc54a0ce081a05e33d2e6240

@@ -215,7 +215,7 @@ theorem divByMonic_eq_div (p : R[X]) (hq : Monic q) : p /ₘ q = p / q :=
 #align polynomial.div_by_monic_eq_div Polynomial.divByMonic_eq_div
 
 theorem mod_x_sub_c_eq_c_eval (p : R[X]) (a : R) : p % (X - C a) = C (p.eval a) :=
-  modByMonic_eq_mod p (monic_X_sub_C a) ▸ modByMonic_x_sub_c_eq_c_eval _ _
+  modByMonic_eq_mod p (monic_X_sub_C a) ▸ modByMonic_X_sub_C_eq_C_eval _ _
 #align polynomial.mod_X_sub_C_eq_C_eval Polynomial.mod_x_sub_c_eq_c_eval
 
 theorem mul_div_eq_iff_isRoot : (X - C a) * (p / (X - C a)) = p ↔ IsRoot p a :=

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

@@ -177,7 +177,7 @@ def mod (p q : R[X]) :=
 #align polynomial.mod Polynomial.mod
 
 private theorem quotient_mul_add_remainder_eq_aux (p q : R[X]) : q * div p q + mod p q = p :=
-  if h : q = 0 then by simp only [h, zero_mul, mod, mod_by_monic_zero, zero_add]
+  if h : q = 0 then by simp only [h, MulZeroClass.zero_mul, mod, mod_by_monic_zero, zero_add]
   else
     by
     conv =>
@@ -247,13 +247,13 @@ theorem mod_eq_self_iff (hq0 : q ≠ 0) : p % q = p ↔ degree p < degree q :=
 theorem div_eq_zero_iff (hq0 : q ≠ 0) : p / q = 0 ↔ degree p < degree q :=
   ⟨fun h => by
     have := EuclideanDomain.div_add_mod p q <;>
-      rwa [h, mul_zero, zero_add, mod_eq_self_iff hq0] at this,
+      rwa [h, MulZeroClass.mul_zero, zero_add, mod_eq_self_iff hq0] at this,
     fun h =>
     by
     have hlt : degree p < degree (q * C (leadingCoeff q)⁻¹) := by
       rwa [degree_mul_leading_coeff_inv q hq0]
     have hm : Monic (q * C (leadingCoeff q)⁻¹) := monic_mul_leadingCoeff_inv hq0
-    rw [div_def, (div_by_monic_eq_zero_iff hm).2 hlt, mul_zero]⟩
+    rw [div_def, (div_by_monic_eq_zero_iff hm).2 hlt, MulZeroClass.mul_zero]⟩
 #align polynomial.div_eq_zero_iff Polynomial.div_eq_zero_iff
 
 theorem degree_add_div (hq0 : q ≠ 0) (hpq : degree q ≤ degree p) :
@@ -336,7 +336,7 @@ end
 theorem eval₂_gcd_eq_zero [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α : k} (hf : f.eval₂ ϕ α = 0)
     (hg : g.eval₂ ϕ α = 0) : (EuclideanDomain.gcd f g).eval₂ ϕ α = 0 := by
   rw [EuclideanDomain.gcd_eq_gcd_ab f g, Polynomial.eval₂_add, Polynomial.eval₂_mul,
-    Polynomial.eval₂_mul, hf, hg, zero_mul, zero_mul, zero_add]
+    Polynomial.eval₂_mul, hf, hg, MulZeroClass.zero_mul, MulZeroClass.zero_mul, zero_add]
 #align polynomial.eval₂_gcd_eq_zero Polynomial.eval₂_gcd_eq_zero
 
 theorem eval_gcd_eq_zero {f g : R[X]} {α : R} (hf : f.eval α = 0) (hg : g.eval α = 0) :
@@ -348,14 +348,14 @@ theorem root_left_of_root_gcd [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α
     (hα : (EuclideanDomain.gcd f g).eval₂ ϕ α = 0) : f.eval₂ ϕ α = 0 :=
   by
   cases' EuclideanDomain.gcd_dvd_left f g with p hp
-  rw [hp, Polynomial.eval₂_mul, hα, zero_mul]
+  rw [hp, Polynomial.eval₂_mul, hα, MulZeroClass.zero_mul]
 #align polynomial.root_left_of_root_gcd Polynomial.root_left_of_root_gcd
 
 theorem root_right_of_root_gcd [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α : k}
     (hα : (EuclideanDomain.gcd f g).eval₂ ϕ α = 0) : g.eval₂ ϕ α = 0 :=
   by
   cases' EuclideanDomain.gcd_dvd_right f g with p hp
-  rw [hp, Polynomial.eval₂_mul, hα, zero_mul]
+  rw [hp, Polynomial.eval₂_mul, hα, MulZeroClass.zero_mul]
 #align polynomial.root_right_of_root_gcd Polynomial.root_right_of_root_gcd
 
 theorem root_gcd_iff_root_left_right [CommSemiring k] {ϕ : R →+* k} {f g : R[X]} {α : k} :

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

@@ -215,11 +215,11 @@ theorem divByMonic_eq_div (p : R[X]) (hq : Monic q) : p /ₘ q = p / q :=
 #align polynomial.div_by_monic_eq_div Polynomial.divByMonic_eq_div
 
 theorem mod_x_sub_c_eq_c_eval (p : R[X]) (a : R) : p % (X - C a) = C (p.eval a) :=
-  modByMonic_eq_mod p (monic_x_sub_c a) ▸ modByMonic_x_sub_c_eq_c_eval _ _
+  modByMonic_eq_mod p (monic_X_sub_C a) ▸ modByMonic_x_sub_c_eq_c_eval _ _
 #align polynomial.mod_X_sub_C_eq_C_eval Polynomial.mod_x_sub_c_eq_c_eval
 
 theorem mul_div_eq_iff_isRoot : (X - C a) * (p / (X - C a)) = p ↔ IsRoot p a :=
-  divByMonic_eq_div p (monic_x_sub_c a) ▸ mul_divByMonic_eq_iff_isRoot
+  divByMonic_eq_div p (monic_X_sub_C a) ▸ mul_divByMonic_eq_iff_isRoot
 #align polynomial.mul_div_eq_iff_is_root Polynomial.mul_div_eq_iff_isRoot
 
 instance : EuclideanDomain R[X] :=

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

@@ -507,7 +507,7 @@ theorem not_irreducible_c (x : R) : ¬Irreducible (C x) :=
 
 theorem degree_pos_of_irreducible (hp : Irreducible p) : 0 < p.degree :=
   lt_of_not_ge fun hp0 =>
-    have := eq_c_of_degree_le_zero hp0
+    have := eq_C_of_degree_le_zero hp0
     not_irreducible_c (p.coeff 0) <| this ▸ hp
 #align polynomial.degree_pos_of_irreducible Polynomial.degree_pos_of_irreducible
 
@@ -520,7 +520,7 @@ theorem isCoprime_of_is_root_of_eval_derivative_ne_zero {K : Type _} [Field K] (
   refine'
     Or.resolve_left
       (EuclideanDomain.dvd_or_coprime (X - C a) (f /ₘ (X - C a))
-        (irreducible_of_degree_eq_one (Polynomial.degree_x_sub_c a)))
+        (irreducible_of_degree_eq_one (Polynomial.degree_X_sub_C a)))
       _
   contrapose! hf' with h
   have key : (X - C a) * (f /ₘ (X - C a)) = f - f %ₘ (X - C a) :=

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

@@ -79,7 +79,7 @@ variable [NormalizationMonoid R]
 instance : NormalizationMonoid R[X]
     where
   normUnit p :=
-    ⟨c ↑(normUnit p.leadingCoeff), c ↑(normUnit p.leadingCoeff)⁻¹, by
+    ⟨C ↑(normUnit p.leadingCoeff), C ↑(normUnit p.leadingCoeff)⁻¹, by
       rw [← RingHom.map_mul, Units.mul_inv, C_1], by rw [← RingHom.map_mul, Units.inv_mul, C_1]⟩
   normUnit_zero := Units.ext (by simp)
   normUnit_mul p q hp0 hq0 :=
@@ -97,7 +97,7 @@ instance : NormalizationMonoid R[X]
         rw [← h2, leading_coeff_C, norm_unit_coe_units, ← C_mul, Units.mul_inv, C_1])
 
 @[simp]
-theorem coe_normUnit {p : R[X]} : (normUnit p : R[X]) = c ↑(normUnit p.leadingCoeff) := by
+theorem coe_normUnit {p : R[X]} : (normUnit p : R[X]) = C ↑(normUnit p.leadingCoeff) := by
   simp [norm_unit]
 #align polynomial.coe_norm_unit Polynomial.coe_normUnit
 
@@ -128,13 +128,13 @@ theorem degree_pos_of_ne_zero_of_nonunit (hp0 : p ≠ 0) (hp : ¬IsUnit p) : 0 <
     exact hp (IsUnit.map C (IsUnit.mk0 (coeff p 0) (mt C_inj.2 (by simpa using hp0))))
 #align polynomial.degree_pos_of_ne_zero_of_nonunit Polynomial.degree_pos_of_ne_zero_of_nonunit
 
-theorem monic_mul_leadingCoeff_inv (h : p ≠ 0) : Monic (p * c (leadingCoeff p)⁻¹) := by
+theorem monic_mul_leadingCoeff_inv (h : p ≠ 0) : Monic (p * C (leadingCoeff p)⁻¹) := by
   rw [monic, leading_coeff_mul, leading_coeff_C,
     mul_inv_cancel (show leading_coeff p ≠ 0 from mt leading_coeff_eq_zero.1 h)]
 #align polynomial.monic_mul_leading_coeff_inv Polynomial.monic_mul_leadingCoeff_inv
 
 theorem degree_mul_leadingCoeff_inv (p : R[X]) (h : q ≠ 0) :
-    degree (p * c (leadingCoeff q)⁻¹) = degree p :=
+    degree (p * C (leadingCoeff q)⁻¹) = degree p :=
   by
   have h₁ : (leadingCoeff q)⁻¹ ≠ 0 := inv_ne_zero (mt leadingCoeff_eq_zero.1 h)
   rw [degree_mul, degree_C h₁, add_zero]
@@ -161,19 +161,19 @@ theorem isUnit_iff_degree_eq_zero : IsUnit p ↔ degree p = 0 :=
     have hc : coeff p 0 ≠ 0 := fun hc => by
       rw [eq_C_of_degree_le_zero this, hc] at h <;> simpa using h
     isUnit_iff_dvd_one.2
-      ⟨c (coeff p 0)⁻¹, by
+      ⟨C (coeff p 0)⁻¹, by
         conv in p => rw [eq_C_of_degree_le_zero this]
         rw [← C_mul, _root_.mul_inv_cancel hc, C_1]⟩⟩
 #align polynomial.is_unit_iff_degree_eq_zero Polynomial.isUnit_iff_degree_eq_zero
 
 /-- Division of polynomials. See `polynomial.div_by_monic` for more details.-/
 def div (p q : R[X]) :=
-  c (leadingCoeff q)⁻¹ * (p /ₘ (q * c (leadingCoeff q)⁻¹))
+  C (leadingCoeff q)⁻¹ * (p /ₘ (q * C (leadingCoeff q)⁻¹))
 #align polynomial.div Polynomial.div
 
 /-- Remainder of polynomial division. See `polynomial.mod_by_monic` for more details. -/
 def mod (p q : R[X]) :=
-  p %ₘ (q * c (leadingCoeff q)⁻¹)
+  p %ₘ (q * C (leadingCoeff q)⁻¹)
 #align polynomial.mod Polynomial.mod
 
 private theorem quotient_mul_add_remainder_eq_aux (p q : R[X]) : q * div p q + mod p q = p :=
@@ -197,28 +197,28 @@ instance : Div R[X] :=
 instance : Mod R[X] :=
   ⟨mod⟩
 
-theorem div_def : p / q = c (leadingCoeff q)⁻¹ * (p /ₘ (q * c (leadingCoeff q)⁻¹)) :=
+theorem div_def : p / q = C (leadingCoeff q)⁻¹ * (p /ₘ (q * C (leadingCoeff q)⁻¹)) :=
   rfl
 #align polynomial.div_def Polynomial.div_def
 
-theorem mod_def : p % q = p %ₘ (q * c (leadingCoeff q)⁻¹) :=
+theorem mod_def : p % q = p %ₘ (q * C (leadingCoeff q)⁻¹) :=
   rfl
 #align polynomial.mod_def Polynomial.mod_def
 
 theorem modByMonic_eq_mod (p : R[X]) (hq : Monic q) : p %ₘ q = p % q :=
-  show p %ₘ q = p %ₘ (q * c (leadingCoeff q)⁻¹) by simp only [monic.def.1 hq, inv_one, mul_one, C_1]
+  show p %ₘ q = p %ₘ (q * C (leadingCoeff q)⁻¹) by simp only [monic.def.1 hq, inv_one, mul_one, C_1]
 #align polynomial.mod_by_monic_eq_mod Polynomial.modByMonic_eq_mod
 
 theorem divByMonic_eq_div (p : R[X]) (hq : Monic q) : p /ₘ q = p / q :=
-  show p /ₘ q = c (leadingCoeff q)⁻¹ * (p /ₘ (q * c (leadingCoeff q)⁻¹)) by
+  show p /ₘ q = C (leadingCoeff q)⁻¹ * (p /ₘ (q * C (leadingCoeff q)⁻¹)) by
     simp only [monic.def.1 hq, inv_one, C_1, one_mul, mul_one]
 #align polynomial.div_by_monic_eq_div Polynomial.divByMonic_eq_div
 
-theorem mod_x_sub_c_eq_c_eval (p : R[X]) (a : R) : p % (x - c a) = c (p.eval a) :=
+theorem mod_x_sub_c_eq_c_eval (p : R[X]) (a : R) : p % (X - C a) = C (p.eval a) :=
   modByMonic_eq_mod p (monic_x_sub_c a) ▸ modByMonic_x_sub_c_eq_c_eval _ _
 #align polynomial.mod_X_sub_C_eq_C_eval Polynomial.mod_x_sub_c_eq_c_eval
 
-theorem mul_div_eq_iff_isRoot : (x - c a) * (p / (x - c a)) = p ↔ IsRoot p a :=
+theorem mul_div_eq_iff_isRoot : (X - C a) * (p / (X - C a)) = p ↔ IsRoot p a :=
   divByMonic_eq_div p (monic_x_sub_c a) ▸ mul_divByMonic_eq_iff_isRoot
 #align polynomial.mul_div_eq_iff_is_root Polynomial.mul_div_eq_iff_isRoot
 
@@ -237,7 +237,7 @@ instance : EuclideanDomain R[X] :=
 theorem mod_eq_self_iff (hq0 : q ≠ 0) : p % q = p ↔ degree p < degree q :=
   ⟨fun h => h ▸ EuclideanDomain.mod_lt _ hq0, fun h =>
     by
-    have : ¬degree (q * c (leadingCoeff q)⁻¹) ≤ degree p :=
+    have : ¬degree (q * C (leadingCoeff q)⁻¹) ≤ degree p :=
       not_le_of_gt <| by rwa [degree_mul_leading_coeff_inv q hq0]
     rw [mod_def, mod_by_monic, dif_pos (monic_mul_leading_coeff_inv hq0)]
     unfold div_mod_by_monic_aux
@@ -250,9 +250,9 @@ theorem div_eq_zero_iff (hq0 : q ≠ 0) : p / q = 0 ↔ degree p < degree q :=
       rwa [h, mul_zero, zero_add, mod_eq_self_iff hq0] at this,
     fun h =>
     by
-    have hlt : degree p < degree (q * c (leadingCoeff q)⁻¹) := by
+    have hlt : degree p < degree (q * C (leadingCoeff q)⁻¹) := by
       rwa [degree_mul_leading_coeff_inv q hq0]
-    have hm : Monic (q * c (leadingCoeff q)⁻¹) := monic_mul_leadingCoeff_inv hq0
+    have hm : Monic (q * C (leadingCoeff q)⁻¹) := monic_mul_leadingCoeff_inv hq0
     rw [div_def, (div_by_monic_eq_zero_iff hm).2 hlt, mul_zero]⟩
 #align polynomial.div_eq_zero_iff Polynomial.div_eq_zero_iff
 
@@ -384,12 +384,12 @@ theorem rootSet_monomial [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn :
 #align polynomial.root_set_monomial Polynomial.rootSet_monomial
 
 theorem rootSet_c_mul_x_pow [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n ≠ 0) {a : R}
-    (ha : a ≠ 0) : (c a * x ^ n).rootSet S = {0} := by
+    (ha : a ≠ 0) : (C a * X ^ n).rootSet S = {0} := by
   rw [C_mul_X_pow_eq_monomial, root_set_monomial hn ha]
 #align polynomial.root_set_C_mul_X_pow Polynomial.rootSet_c_mul_x_pow
 
 theorem rootSet_x_pow [CommRing S] [IsDomain S] [Algebra R S] {n : ℕ} (hn : n ≠ 0) :
-    (x ^ n : R[X]).rootSet S = {0} :=
+    (X ^ n : R[X]).rootSet S = {0} :=
   by
   rw [← one_mul (X ^ n : R[X]), ← C_1, root_set_C_mul_X_pow hn]
   exact one_ne_zero
@@ -442,7 +442,7 @@ theorem leadingCoeff_div (hpq : q.degree ≤ p.degree) :
   rwa [degree_mul_leading_coeff_inv q hq]
 #align polynomial.leading_coeff_div Polynomial.leadingCoeff_div
 
-theorem div_c_mul : p / (c a * q) = c a⁻¹ * (p / q) :=
+theorem div_c_mul : p / (C a * q) = C a⁻¹ * (p / q) :=
   by
   by_cases ha : a = 0
   · simp [ha]
@@ -451,22 +451,22 @@ theorem div_c_mul : p / (c a * q) = c a⁻¹ * (p / q) :=
   rw [mul_left_comm q, ← mul_assoc, ← C.map_mul, mul_inv_cancel ha, C.map_one, one_mul]
 #align polynomial.div_C_mul Polynomial.div_c_mul
 
-theorem c_mul_dvd (ha : a ≠ 0) : c a * p ∣ q ↔ p ∣ q :=
+theorem c_mul_dvd (ha : a ≠ 0) : C a * p ∣ q ↔ p ∣ q :=
   ⟨fun h => dvd_trans (dvd_mul_left _ _) h, fun ⟨r, hr⟩ =>
-    ⟨c a⁻¹ * r, by
+    ⟨C a⁻¹ * r, by
       rw [mul_assoc, mul_left_comm p, ← mul_assoc, ← C.map_mul, _root_.mul_inv_cancel ha, C.map_one,
         one_mul, hr]⟩⟩
 #align polynomial.C_mul_dvd Polynomial.c_mul_dvd
 
-theorem dvd_c_mul (ha : a ≠ 0) : p ∣ Polynomial.c a * q ↔ p ∣ q :=
+theorem dvd_c_mul (ha : a ≠ 0) : p ∣ Polynomial.C a * q ↔ p ∣ q :=
   ⟨fun ⟨r, hr⟩ =>
-    ⟨c a⁻¹ * r, by
+    ⟨C a⁻¹ * r, by
       rw [mul_left_comm p, ← hr, ← mul_assoc, ← C.map_mul, _root_.inv_mul_cancel ha, C.map_one,
         one_mul]⟩,
     fun h => dvd_trans h (dvd_mul_left _ _)⟩
 #align polynomial.dvd_C_mul Polynomial.dvd_c_mul
 
-theorem coe_normUnit_of_ne_zero (hp : p ≠ 0) : (normUnit p : R[X]) = c p.leadingCoeff⁻¹ :=
+theorem coe_normUnit_of_ne_zero (hp : p ≠ 0) : (normUnit p : R[X]) = C p.leadingCoeff⁻¹ :=
   by
   have : p.leadingCoeff ≠ 0 := mt leadingCoeff_eq_zero.mp hp
   simp [CommGroupWithZero.coe_normUnit _ this]
@@ -498,11 +498,11 @@ theorem irreducible_of_degree_eq_one (hp1 : degree p = 1) : Irreducible p :=
   (prime_of_degree_eq_one hp1).Irreducible
 #align polynomial.irreducible_of_degree_eq_one Polynomial.irreducible_of_degree_eq_one
 
-theorem not_irreducible_c (x : R) : ¬Irreducible (c x) :=
+theorem not_irreducible_c (x : R) : ¬Irreducible (C x) :=
   if H : x = 0 then by
     rw [H, C_0]
     exact not_irreducible_zero
-  else fun hx => Irreducible.not_unit hx <| isUnit_c.2 <| isUnit_iff_ne_zero.2 H
+  else fun hx => Irreducible.not_unit hx <| isUnit_C.2 <| isUnit_iff_ne_zero.2 H
 #align polynomial.not_irreducible_C Polynomial.not_irreducible_c
 
 theorem degree_pos_of_irreducible (hp : Irreducible p) : 0 < p.degree :=
@@ -515,7 +515,7 @@ theorem degree_pos_of_irreducible (hp : Irreducible p) : 0 < p.degree :=
 then `f / (X - a)` is coprime with `X - a`.
 Note that we do not assume `f a = 0`, because `f / (X - a) = (f - f a) / (X - a)`. -/
 theorem isCoprime_of_is_root_of_eval_derivative_ne_zero {K : Type _} [Field K] (f : K[X]) (a : K)
-    (hf' : f.derivative.eval a ≠ 0) : IsCoprime (x - c a : K[X]) (f /ₘ (x - c a)) :=
+    (hf' : f.derivative.eval a ≠ 0) : IsCoprime (X - C a : K[X]) (f /ₘ (X - C a)) :=
   by
   refine'
     Or.resolve_left

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

@@ -337,7 +337,7 @@ theorem mul_div_eq_iff_isRoot : (X - C a) * (p / (X - C a)) = p ↔ IsRoot p a :
   divByMonic_eq_div p (monic_X_sub_C a) ▸ mul_divByMonic_eq_iff_isRoot
 #align polynomial.mul_div_eq_iff_is_root Polynomial.mul_div_eq_iff_isRoot
 
-instance : EuclideanDomain R[X] :=
+instance instEuclideanDomain : EuclideanDomain R[X] :=
   { Polynomial.commRing,
     Polynomial.nontrivial with
     quotient := (· / ·)

A PR analogous to #12338 and #12361: reformatting proofs following the multiple goals linter of #12339.

@@ -661,7 +661,7 @@ theorem irreducible_iff_degree_lt (p : R[X]) (hp0 : p ≠ 0) (hpu : ¬ IsUnit p)
     Irreducible p ↔ ∀ q, q.degree ≤ ↑(natDegree p / 2) → q ∣ p → IsUnit q := by
   rw [← irreducible_mul_leadingCoeff_inv,
       (monic_mul_leadingCoeff_inv hp0).irreducible_iff_degree_lt]
-  simp [hp0, natDegree_mul_leadingCoeff_inv]
+  · simp [hp0, natDegree_mul_leadingCoeff_inv]
   · contrapose! hpu
     exact isUnit_of_mul_eq_one _ _ hpu
 

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.

@@ -69,7 +69,7 @@ theorem eval_iterate_derivative_rootMultiplicity {p : R[X]} {t : R} :
   conv_lhs => rw [← p.pow_mul_divByMonic_rootMultiplicity_eq t, ← hm]
   rw [iterate_derivative_mul, eval_finset_sum, sum_eq_single_of_mem _ (mem_range.mpr m.succ_pos)]
   · rw [m.choose_zero_right, one_smul, eval_mul, m.sub_zero, iterate_derivative_X_sub_pow_self,
-      eval_nat_cast, nsmul_eq_mul]; rfl
+      eval_natCast, nsmul_eq_mul]; rfl
   · intro b hb hb0
     rw [iterate_derivative_X_sub_pow, eval_smul, eval_mul, eval_smul, eval_pow,
       Nat.sub_sub_self (mem_range_succ_iff.mp hb), eval_sub, eval_X, eval_C, sub_self,

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

@@ -320,12 +320,12 @@ theorem mod_def : p % q = p %ₘ (q * C (leadingCoeff q)⁻¹) := rfl
 
 theorem modByMonic_eq_mod (p : R[X]) (hq : Monic q) : p %ₘ q = p % q :=
   show p %ₘ q = p %ₘ (q * C (leadingCoeff q)⁻¹) by
-    simp only [Monic.def'.1 hq, inv_one, mul_one, C_1]
+    simp only [Monic.def.1 hq, inv_one, mul_one, C_1]
 #align polynomial.mod_by_monic_eq_mod Polynomial.modByMonic_eq_mod
 
 theorem divByMonic_eq_div (p : R[X]) (hq : Monic q) : p /ₘ q = p / q :=
   show p /ₘ q = C (leadingCoeff q)⁻¹ * (p /ₘ (q * C (leadingCoeff q)⁻¹)) by
-    simp only [Monic.def'.1 hq, inv_one, C_1, one_mul, mul_one]
+    simp only [Monic.def.1 hq, inv_one, C_1, one_mul, mul_one]
 #align polynomial.div_by_monic_eq_div Polynomial.divByMonic_eq_div
 
 theorem mod_X_sub_C_eq_C_eval (p : R[X]) (a : R) : p % (X - C a) = C (p.eval a) :=

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -283,7 +283,7 @@ theorem isUnit_iff_degree_eq_zero : IsUnit p ↔ degree p = 0 :=
         rw [← C_mul, _root_.mul_inv_cancel hc, C_1]⟩⟩
 #align polynomial.is_unit_iff_degree_eq_zero Polynomial.isUnit_iff_degree_eq_zero
 
-/-- Division of polynomials. See `Polynomial.divByMonic` for more details.-/
+/-- Division of polynomials. See `Polynomial.divByMonic` for more details. -/
 def div (p q : R[X]) :=
   C (leadingCoeff q)⁻¹ * (p /ₘ (q * C (leadingCoeff q)⁻¹))
 #align polynomial.div Polynomial.div